# SAFETY PHARMACOLOGY – RISK ASSESSMENT QT INTERVAL PROLONGATION AND BEYOND

EDITED BY : Eleonora Grandi, Stefano Morotti, Esther Pueyo and Blanca Rodriguez PUBLISHED IN : Frontiers in Physiology and Frontiers in Pharmacology

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# SAFETY PHARMACOLOGY – RISK ASSESSMENT QT INTERVAL PROLONGATION AND BEYOND

Topic Editors:

Eleonora Grandi, University of California Davis, United States Stefano Morotti, University of California Davis, United States Esther Pueyo, University of Zaragoza, Spain Blanca Rodriguez, University of Oxford, United Kingdom

Getting to the heart of Safety Pharmacology. Image: Stefano Morotti.

Current regulatory guidelines for cardiac safety utilize hERG block and QT interval prolongation as risk markers. This strategy has been successful at preventing harmful drugs from being marketed, but criticized for leading to early withdrawal of potentially safe drugs. Here we collected a series of articles presenting new technological and conceptual advances, including refinement of ex vivo and in vitro assays, screens and models, and in silico approaches reflecting the increasing effort that has been put forward by regulatory agencies, industry, and academia to try and address the need of a more accurate, mechanistically-based paradigm of proarrhythmic potential of drugs.

#### *This Research Topic is dedicated to the memory of Dr. J. Jeremy Rice, our wonderful friend and colleague.*

Citation: Grandi, E., Morotti, S., Pueyo, E., Rodriguez, B., eds. (2018). Safety Pharmacology – Risk Assessment QT Interval Prolongation and Beyond. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-539-3

# Table of Contents

*06 Editorial: Safety Pharmacology – Risk Assessment QT Interval Prolongation and Beyond*

Eleonora Grandi, Stefano Morotti, Esther Pueyo and Blanca Rodriguez

#### MULTISCALE MODELING FOR SAFETY PHARMACOLOGY


William Lee, Monique J. Windley, Jamie I. Vandenberg and Adam P. Hill


Sara Dutta, Kelly C. Chang, Kylie A. Beattie, Jiansong Sheng, Phu N. Tran, Wendy W. Wu, Min Wu, David G. Strauss, Thomas Colatsky and Zhihua Li

*101 Corrigendum: Optimization of an* In Silico *Cardiac Cell Model for Proarrhythmia Risk Assessment*

Sara Dutta, Kelly C. Chang, Kylie A. Beattie, Jiansong Sheng, Phu N. Tran, Wendy W. Wu, Min Wu, David G. Strauss, Thomas Colatsky and Zhihua Li

*103 Uncertainty Quantification Reveals the Importance of Data Variability and Experimental Design Considerations for* In Silico *Proarrhythmia Risk Assessment*

Kelly C. Chang, Sara Dutta, Gary R. Mirams, Kylie A. Beattie, Jiansong Sheng, Phu N. Tran, Min Wu, Wendy W. Wu, Thomas Colatsky, David G. Strauss and Zhihua Li

*120 Composite Biomarkers Derived From Micro-Electrode Array Measurements and Computer Simulations Improve the Classification of Drug-Induced Channel Block*

Eliott Tixier, Fabien Raphel, Damiano Lombardi and Jean-Frédéric Gerbeau

*137 Novel Two-Step Classifier for Torsades de Pointes Risk Stratification From Direct Features*

Jaimit Parikh, Viatcheslav Gurev and John J. Rice

*155 Synergistic Anti-Arrhythmic Effects in Human Atria With Combined Use of Sodium Blockers and Acacetin*

Haibo Ni, Dominic G. Whittaker, Wei Wang, Wayne R. Giles, Sanjiv M. Narayan and Henggui Zhang


Ilija Uzelac, Yanyan C. Ji, Daniel Hornung, Johannes Schröder-Scheteling, Stefan Luther, Richard A. Gray, Elizabeth M. Cherry and Flavio H. Fenton

*208 Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics* Jaehee V. Shim, Bryan Chun, Johan G. C. van Hasselt, Marc R. Birtwistle, Jeffrey J. Saucerman and Eric A. Sobie

#### ACCOUNTING FOR PATIENTS' CONDITION AND INTER-SUBJECT VARIABILITY

*219 Proton Pump Inhibitors and Serum Magnesium Levels in Patients With Torsades de Pointes*

Pietro E. Lazzerini, Iacopo Bertolozzi, Francesco Finizola, Maurizio Acampa, Mariarita Natale, Francesca Vanni, Rosella Fulceri, Alessandra Gamberucci, Marco Rossi, Beatrice Giabbani, Michele Caselli, Ilaria Lamberti, Gabriele Cevenini, Franco Laghi-Pasini and Pier L. Capecchi


Jem D. Lane and Andrew Tinker


#### USE OF HUMAN ADULT AND IPSC-CMS FOR SAFETY PHARMACOLOGY

*293 Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology*

Chon Lok Lei, Ken Wang, Michael Clerx, Ross H. Johnstone, Maria P. Hortigon-Vinagre, Victor Zamora, Andrew Allan, Godfrey L. Smith, David J. Gavaghan, Gary R. Mirams and Liudmila Polonchuk


Susann Björk, Elina A. Ojala, Tommy Nordström, Antti Ahola, Mikko Liljeström, Jari Hyttinen, Esko Kankuri and Eero Mervaala


Yusheng Qu, Guy Page, Najah Abi-Gerges, Paul E. Miller, Andre Ghetti and Hugo M. Vargas

# Editorial: Safety Pharmacology – Risk Assessment QT Interval Prolongation and Beyond

#### Eleonora Grandi <sup>1</sup> \*, Stefano Morotti <sup>1</sup> , Esther Pueyo<sup>2</sup> and Blanca Rodriguez <sup>3</sup>

<sup>1</sup> Department of Pharmacology, University of California, Davis, Davis, CA, United States, <sup>2</sup> Biomedical Signal Interpretation and Computational Simulation Group, Aragón Institute of Engineering Research, IIS Aragón, University of Zaragoza, Zaragoza, Spain, <sup>3</sup> Department of Computer Science, University of Oxford, Oxford, United Kingdom

#### Edited by:

Geoffrey A. Head, Baker Heart and Diabetes Institute, Australia

#### Reviewed by:

Arun V. Holden, University of Leeds, United Kingdom Osmar Antonio Centurion, Universidad Nacional de Asunción, Paraguay

> \*Correspondence: Eleonora Grandi

ele.grandi@gmail.com

#### In Memoriam:

This Research Topic is dedicated to the memory of Dr. J. Jeremy Rice, our wonderful friend and colleague.

#### Specialty section:

This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology

Received: 19 April 2018 Accepted: 15 May 2018 Published: 08 June 2018

#### Citation:

Grandi E, Morotti S, Pueyo E and Rodriguez B (2018) Editorial: Safety Pharmacology – Risk Assessment QT Interval Prolongation and Beyond. Front. Physiol. 9:678. doi: 10.3389/fphys.2018.00678 Keywords: cardiotoxicity, QT interval prolongation, drug-induced arrhythmia, multi-scale modeling, cardiac electrophysiology

**Editorial on the Research Topic**

**Safety Pharmacology – Risk Assessment QT Interval Prolongation and Beyond**

#### THE NEED OF NEW PARADIGMS FOR CARDIAC SAFETY

The scope of safety pharmacology is to predict whether a drug is likely to cause potentially lethal adverse effects if administered to humans. While safety pharmacology has broadened its interests in recent years to the whole cardiovascular, respiratory, and central nervous systems (and is now extending to other body functions), a major focus since its inception has been assessing drug-induced prolongation in the QT interval—a surrogate biomarker for torsades de pointes (TdP) liability. Because the vast majority of drugs that can cause QT prolongation inhibit hERG channels, current regulatory guidelines concerning cardiac safety recommend that all compounds are evaluated in vitro for their hERG inhibitory potency (Redfern et al., 2003) and in vivo for their ability to cause QT/QTc interval prolongation (Food and Drug Administration, 2005) in an appropriate animal model and in humans. However, it has now become apparent that QT/QTc prolongation and hERG block are an insufficient proxy for TdP risk. While the current approach based on these markers has been successful in terms of preventing TdP risk, this regulatory paradigm might lead to withdrawal from the drug development pipeline and clinical use of potentially safe drugs. There is therefore a crucial need to develop a more accurate assessment of proarrhythmic potential of drugs. Notably, in 2014 the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative was proposed as a new strategy by expert working groups sponsored by the US Food and Drug Administration (FDA), the Cardiac Safety Research Consortium (CSRC), and the Health and Environmental Science Institute (HESI), and has quickly become a global effort, also involving many industry and academia partners (Sager et al., 2014). CiPA aims at developing and validating a new paradigm for cardiac safety evaluation of new drugs that provides a more accurate and comprehensive mechanisticbased assessment of proarrhythmic (rather than QT prolonging) potential of drugs (Gintant et al., 2016). This involves assessment of (i) high-throughput in vitro screening of drug effects on multiple human ion channels, (ii) coupled with in silico modeling of human cardiac myocytes to assess integrated electrophysiological responses, and (iii) verification of predicted responses in human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CMs). Safety pharmacology has evolved in recent years to identify and incorporate new technologies for clinical and non-clinical applications, including refinement of ex vivo and in vitro assays and screens, in vivo models, noninvasive clinical modalities, and in silico approaches. Here we collected a series of review, perspective, and original research articles that summarize the state of our knowledge and the latest advances in these technologies, and how these might contribute to shaping new and improved cardiac safety guidelines.

#### MULTISCALE MODELING FOR SAFETY PHARMACOLOGY

There is a wide range of length and time scales covered in this Research Topic, from the atom and ns to the whole organism and month/year (**Figure 1** top left to bottom right), all of which are relevant to safety pharmacology. Structural studies, including modeling of ion channel gating (Perissinotti et al.) and interactions with drugs, and drug partitioning, are critical for drug discovery efforts, and perhaps also a necessary approach for safety considerations. For example, the study by DeMarco et al. utilized all-atom molecular dynamics simulations to show that ionization of drug molecules (specifically Sotalol) can significantly affect their membrane permeability and partitioning kinetics, and should therefore be a consideration in ongoing in silico safety pharmacology efforts. Given the complexity of the interaction between drugs and ion channels, the drug binding kinetics, state dependent binding, and temperature dependence could significantly alter drugs' impact on the action potential (AP), even when drugs display similar steady-state block. Lee et al. highlighted some of the challenges involved in modeling of the hERG channel and also discussed limitations and need for improved voltage-clamp protocols to characterize drug-channel interaction in in vitro experiments. Ellinwood et al. looked at the consequences of drug binding kinetics and state dependence of KV1.5 targeting drugs on atrial electrophysiology, and revealed that ionic remodeling also affects the degree of efficacy and safety of state-specific IKur inhibitors, by modifying the AP trajectory. These studies highlight the potential need for extraordinary detail in the in vitro characterization for accurate in silico prediction of (cardiac-region specific, Morotti et al., 2016; Ellinwood et al., 2017; Ellinwood et al.) drug effects on channels and cardiac electrophysiology.

While the ion channel gating and drug-interaction models might require further refinement and increased complexity, significant efforts have been put forward to improve existing cardiomyocyte models and to take advantage of the existence (and convergence) of competing mathematical models to narrow hypotheses or explore alternative hypotheses (Sarkar and Sobie, 2011; Sánchez et al., 2012; Gemmell et al., 2014; Mann et al., 2016; Pueyo et al., 2016a,b; Gong et al., 2017; Muszkiewicz et al., 2017). For example, recent work has shown that, when forced to reproduce the same data, three competing models of human ventricular myocytes (Ten Tusscher and Panfilov, 2006; Grandi et al., 2010; O'Hara et al., 2011) became substantially more similar than they were originally (Mann et al., 2016). Notably, the work by Krogh-Madsen et al. used clinical congenital LQT data (as done by Mann et al., 2016) and physiological constraints on intracellular ionic concentrations to optimize parameters in the O'Hara-Rudy (ORd) human model (O'Hara et al., 2011). This in turn improved the accuracy and robustness of TdP risk prediction (Lancaster and Sobie, 2016), which the authors attributed to the importance of Ca2<sup>+</sup> dynamics in repolarization and to an improved balance of IKs vs. IKr in the new model. A different parameterization of the ORd model by Dutta et al. and Dutta et al. also yielded a better correspondence with drug response data and improved the identification of proarrhythmic drugs. The authors developed a new metric qNet, which quantifies the net electronic charge carried by major inward and outward ionic currents during the steady state AP, to separate low-, intermediate-, and high-risk hERG blockers. A follow up study appraised the robustness of qNet as a biomarker for TdP by considering how uncertainty in the model parameters propagates to the phenotype level (Chang et al.). The authors were thus able to identify the conditions under which decisions on risk can be made reliably and objectively. Yet, questions remain regarding the physiological meaning of this new metric, and whether multiple metrics should be utilized that account for a broader range of behaviors and mechanisms. Tixier et al. used an in silico model of multi-electrode array electrophysiology and machine learning to identify predictive biomarkers that should be measured to improve classifications of drugs. These investigations add to several previous efforts to build computational frameworks for assessment of TdP risk (Mirams et al., 2011; Kramer et al., 2013; Lancaster and Sobie, 2016). On the other hand, Parikh et al. showed that a simpler classification method based on direct features (ion channel block information) performed with comparable or higher accuracy than existing methods based on simulated metrics. One potential limitation of this approach is that direct feature classifiers might fail identifying the proarrhythmic risk of drugs affecting channels that are not included in the training set, whereas predictive modeling is more likely to yield an accurate classification.

Biophysical modeling can not only provide means for drug classification, but also understanding of the mechanistic underpinning of drug responses, as in the multiscale simulations by Ni et al. and Colman et al. These studies are important reminders that AP duration changes are rarely homogenous (e.g., there exist gradients—transmurally, or from base to apex) and can increase the tissue-level substrates for arrhythmias (Antzelevitch, 2005; Glukhov et al., 2010). Indeed, multiscale in silico models can be very powerful tools to investigate the response of candidate antiarrhythmic compounds at the level of the electrocardiogram (ECG). The simulated data may also serve to identify novel ECG-derived biomarkers detecting block of inward and/or outward currents based on ECG features (Vicente et al., 2016). Using Langendorff perfused ex vivo rabbit hearts the Fenton group measured and analyzed the complex dynamics of spatially discordant alternans, which provide the substrate

for reentrant arrhythmia (Uzelac et al.) The authors noted that current AP models fail to reproduce some key dynamics such as voltage amplitude alternans, smooth development of Ca2<sup>+</sup> alternans in time, and conduction. Experimental characterization of these dynamics can inform refining of existing models to analyze mechanisms.

# ACCOUNTING FOR PATIENTS' CONDITION AND INTER-SUBJECT VARIABILITY

Clinical risk assessment and trial suggest that patient conditions, i.e., sex (Yang et al., 2017; Vorobyov and Clancy, 2018), age, disease, electrolyte imbalance (Lazzerini et al.), interaction with other drugs (Lv et al.) should all be taken into account in risk assessment (Lane and Tinker)—which is not yet addressed by CiPA efforts. Along the same lines, Wisniowska et al. reviewed the different sources of variability (both intrinsic and extrinsic) that exist in the human population in response to drug action, and emphasized the need of accounting for these aspects in modeling approaches for safety pharmacology. Two studies by the Rodriguez group establish the potential of populationbased approaches as very powerful in silico tools for safety pharmacology investigations. Passini et al. showed that human in silico drug trials using repolarization abnormality quantification as the main metric do better than animal models in detecting drugs with TdP risk. They also show agreement of in silico predictions and two established experimental models (rabbit wedge ECGs and hiPSC-CMs). Other statistical methods, e.g., logistic regression, have been previously employed to assess the proarrhythmic risk in a population of computational model variants (Lee et al., 2013; Morotti and Grandi, 2017). Calibrated populations of models of heart cells could generally reproduce experimental drug effects on human tissue for dofetilide, whereas lack of agreement between experiments and simulations for quinidine and verapamil suggest further work is needed to understand the more complex electrophysiological effects of these multichannel blocking drugs (Britton et al.).

#### USE OF IPSC-CMS FOR SAFETY PHARMACOLOGY

Because iPSC-CMs are a readily-obtainable and renewable source of human cardiac myocytes, they are gaining popularity as a platform to screen drugs for toxicity testing. However, given the iPSC immature phenotype, and phenotypic differences across iPSC-CM cell lines (Lei et al.), it remains unclear how well drug tests performed in iPSC-CMs will recapitulate the effects observed in adult human cardiomyocytes and hearts. Koivumaki et al. developed a computational model of the iPSC-CMs that recapitulates the cells' immature phenotype, and explore differences in ionic behavior underlying the AP in paced vs. spontaneous modes, phenotypic variability in iPSC-CMs, and iPSC-CM model's ability to recapitulate physiological properties of adult cells. Recently, statistical methods have also been established to provide accurate predictions of adult myocyte drug responses from iPSC-CM simulations (Gong and Sobie, 2018). iPSC-CM utilization in drug discovery and safety investigations is reviewed by Ortega et al. An important advancement in the technological approach of improving the utility of iPSC-CMs for safety pharmacology is the augmentation of IK1 using dynamic clamp. Plagued by low-throughput, Goversen et al. have moved toward demonstrating that such dynamic clamp can be performed in a high throughput manner. Bjork et al. reported that the expression of optogenetic tools in iPSC-CMs did not significantly affect the baseline electrophysiological properties of these cells, thus allowing electrophysiological assessments comparable to conventional patch clamp studies. Nevertheless, adult human ventricular cardiomyocytes (Nguyen et al.) and trabeculae (Qu et al.) might still be a more reliable model to test the cardiotoxic risk associated with novel drugs, with some advantages over animal and iPSC models.

#### REFERENCES


# CONCLUSIONS AND FUTURE DIRECTIONS

There is a growing body of work supporting the integration of new and established computational and experimental approaches to understanding and predicting the risk of TdP. While mechanistic systems modeling is mature in the cardiac arrhythmia field, use of similar approaches can improve understanding and prediction of cardiotoxicity caused by other drugs, e.g., cancer therapeutics (Shim et al.). Given the focus on TdP and QT interval, however, the deleterious effects of drugs on cardiac function are evaluated only in terms of changes in electrophysiological properties. Future work should therefore extend the current paradigm to include other major cellular functions (such as contraction, energetics, and cell death, i.e., via apoptosis), which dysregulation can severely impact cardiac performance. In addition to cardiotoxicity, safety pharmacology aims to determine the potential undesirable pharmacodynamic effects of a drug on the central nervous, vascular and respiratory systems (Pugsley et al., 2008). Thus, extension of the described approaches to these systems seems desirable, and might contribute to further advancement of these key areas of biomedical research.

#### AUTHOR CONTRIBUTIONS

EG and SM wrote the editorial. EP and BR provided comments and edits.

#### FUNDING

Sources of support are the American Heart Association grant 15SDG24910015, the National Institutes of Health Stimulating Peripheral Activity to Relieve Conditions (SPARC) grant 1OT2OD023848-01, the National Heart, Lung, And Blood Institute (NHLBI) grants R01HL131517 and R01HL41214 (to EG); the NHLBI K99HL138160 award and the Heart Rhythm Society post-doctoral fellowship 16OA9HRS (to SM); projects DPI2016-75458-R (MINECO), ERC-2014-StG 638284 (European Research Council) and T39-17R (Aragón Government and European Regional Development Fund) (to EP); a Wellcome Trust Senior Research Fellowship in Basic Biomedical Sciences 100246/Z/12/Z and a NC3Rs Infrastructure for Impact Award (NC/P001076/1) (to BR).


to-beat variability in ventricular repolarization and its response to ionic current inhibition. PLoS ONE 11:e0151461. doi: 10.1371/journal.pone.0151461


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Grandi, Morotti, Pueyo and Rodriguez. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Determinants of Isoform-Specific Gating Kinetics of hERG1 Channel: Combined Experimental and Simulation Study

Laura L. Perissinotti <sup>1</sup> \* † , Pablo M. De Biase1†, Jiqing Guo2†, Pei-Chi Yang3† , Miranda C. Lee<sup>1</sup> , Colleen E. Clancy <sup>3</sup> \*, Henry J. Duff <sup>2</sup> \* and Sergei Y. Noskov <sup>1</sup> \*

*<sup>1</sup> Centre for Molecular Simulations, Department of Biological Sciences, Faculty of Science, University of Calgary, Calgary, AB, Canada, <sup>2</sup> Libin Cardiovascular Institute of Alberta, Faculty of Medicine, University of Calgary, Calgary, AB, Canada, <sup>3</sup> Department of Physiology and Membrane Biology, University of California, Davis, Davis, CA, United States*

#### *Edited by:*

*Esther Pueyo, University of Zaragoza, Spain*

*Reviewed by: Henggui Zhang, University of Manchester, United Kingdom Jamie Vandenberg, Victor Chang Cardiac Research Institute, Australia*

#### *\*Correspondence:*

*Laura L. Perissinotti laura.perissinotti@ucalgary.ca Colleen E. Clancy ceclancy@ucdavis.edu Henry J. Duff hduff@ucalgary.ca Sergei Y. Noskov snoskov@ucalgary.ca*

*† These authors have contributed equally to this work.*

#### *Specialty section:*

*This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology*

*Received: 30 August 2017 Accepted: 23 February 2018 Published: 12 April 2018*

#### *Citation:*

*Perissinotti LL, De Biase PM, Guo J, Yang P-C, Lee MC, Clancy CE, Duff HJ and Noskov SY (2018) Determinants of Isoform-Specific Gating Kinetics of hERG1 Channel: Combined Experimental and Simulation Study. Front. Physiol. 9:207. doi: 10.3389/fphys.2018.00207* IKr is the rapidly activating component of the delayed rectifier potassium current, the ion current largely responsible for the repolarization of the cardiac action potential. Inherited forms of long QT syndrome (LQTS) (Lees-Miller et al., 1997) in humans are linked to functional modifications in the Kv11.1 (hERG) ion channel and potentially life threatening arrhythmias. There is little doubt now that hERG-related component of IKr in the heart depends on the tetrameric (homo- or hetero-) channels formed by two alternatively processed isoforms of hERG, termed hERG1a and hERG1b. Isoform composition (hERG1a- vs. the b-isoform) has recently been reported to alter pharmacologic responses to some hERG blockers and was proposed to be an essential factor pre-disposing patients for drug-induced QT prolongation. Very little is known about the gating and pharmacological properties of two isoforms in heart membranes. For example, how gating mechanisms of the hERG1a channels differ from that of hERG1b is still unknown. The mechanisms by which hERG 1a/1b hetero-tetramers contribute to function in the heart, or what role hERG1b might play in disease are all questions to be answered. Structurally, the two isoforms differ only in the N-terminal region located in the cytoplasm: hERG1b is 340 residues shorter than hERG1a and the initial 36 residues of hERG1b are unique to this isoform. In this study, we combined electrophysiological measurements for HEK cells, kinetics and structural modeling to tease out the individual contributions of each isoform to Action Potential formation and then make predictions about the effects of having various mixture ratios of the two isoforms. By coupling electrophysiological data with computational kinetic modeling, two proposed mechanisms of hERG gating in two homo-tetramers were examined. Sets of data from various experimental stimulation protocols (HEK cells) were analyzed simultaneously and fitted to Markov-chain models (M-models). The minimization procedure presented here, allowed assessment of suitability of different Markov model topologies and the corresponding parameters that describe the channel kinetics. The kinetics modeling pointed to key differences in the gating kinetics that were linked to the full channel structure. Interactions between soluble domains and the transmembrane part of the channel appeared to be critical determinants of the gating kinetics. The structures of the full channel in the open and closed states were compared for the first time using the recent Cryo-EM resolved structure for full open hERG channel and an homology model for the closed state, based on the highly homolog EAG1 channel. Key potential interactions which emphasize the importance of electrostatic interactions between N-PAS cap, S4-S5, and C-linker are suggested based on the structural analysis. The derived kinetic parameters were later used in higher order models of cells and tissue to track down the effect of varying the ratios of hERG1a and hERG1b on cardiac action potentials and computed electrocardiograms. Simulations suggest that the recovery from inactivation of hERG1b may contribute to its physiologic role of this isoform in the action potential. Finally, the results presented here contribute to the growing body of evidence that hERG1b significantly affects the generation of the cardiac Ikr and plays an important role in cardiac electrophysiology. We highlight the importance of carefully revisiting the Markov models previously proposed in order to properly account for the relative abundance of the hERG1 a- and b- isoforms.

Keywords: long-QT, hERG Isoforms, gating kinetics, arrhythmias, computational models, Markov process

# INTRODUCTION

The IKr current is a primary contributor to the repolarization of the human cardiac muscle, a delayed rectifier potassium current conducted by the Kv11.1 ion channel (more commonly referred to as human ether-a-go-go-related gene, or hERG1) (Sanguinetti et al., 1995; Li et al., 1996). The Kv11.1 channel is homologous in structure to other voltage-gated potassium channels (**Figure 1**) and is assembled as a tetramer to become a fully functioning ion channel, but has very different kinetics compared to other potassium channels. Inactivation is much faster than activation, and consequently, current is suppressed at positive potentials but rebounds on repolarization as channels quickly recover from inactivation and slowly close. During an action potential, this gating behavior produces a resurgent current that peaks during the repolarization phase. Mutations, channels block by drugs and/or impaired trafficking of Kv11.1 channels to the cell membrane lead to prolongation of the QT interval on the surface electrocardiogram (LQTS), leading to a potentially life threatening ventricular arrhythmia (Behere et al., 2014). Since the physiological role of IKr is to repolarize the late phase of cardiac action potentials, hERG1 has a clear link to these arrhythmias (Robertson et al., 2008; Gustina and Trudeau, 2009; Robertson, 2012; Vandenberg et al., 2012). That is, if IKr is reduced, due to loss-of-function mutations or action of small molecules (drugs), patients are more likely to develop severe arrhythmias initiated by premature beats.

Up to date, our understanding of how IKr contributes to the ventricular repolarization is based primarily on studies utilizing heterologous expression of the originally identified hERG1 a-isoform (Sanguinetti et al., 1995; Trudeau et al., 1995; Smith et al., 1996; Wang et al., 1997). More recent studies showed that native IKr result from hetero-tetramers formed by the co-assembly of two hERG isoforms termed hERG1a and hERG1b. Two splice variants—hERG1a and hERG1b are co-expressed not only in cardiac tissue, but also in neurons and smooth muscles (Chiesa et al., 1997; Ohya et al., 2002). Importantly, isoforms display very different gating kinetics (Lees-Miller et al., 2003). The hERG gating is modulated by the cytoplasmic domains (N-terminal or PAS domain, CNBD and C-linker) in a way that still remains largely unknown but of a critical importance for unraveling structural mechanisms responsible for QT prolongation. In particular, a mutation in the N-terminal of hERG1b was discovered in a patient with long QT Syndrome (LQTS), highlighting the importance of this isoform in cardiac repolarization (Robertson et al., 2008; Robertson, 2012).

Many drugs are known to block ion current across Kv11.1 channels, resulting in an acquired form of LQTS (Larsen et al., 2010). Many blockers exhibit state-dependent activity and hence their propensity to later hERG currents is related to the channel's gating kinetics. It has recently been shown that EA4031, a selective blocker of hERG1 currents, differs in effectiveness on homo-tetrameric vs. hetero-tetrameric channels formed of different isoforms (Sale et al., 2008). Similar findings were also reported for hERG1 activators. Larsen et al. (2010) showed that activators such as NS1643 display differential effects on the homo-tetrameric channels formed by two hERG1 isoforms (Holzem et al., 2016). Due to the therapeutic risks hidden in hERG1 blockers and potential of hERG1 activators, establishing differences in gating mechanisms of two isoforms is critically important. Structurally, the two isoforms differ only in the Nterminal region located in the cytoplasm: hERG1b is 340 residues shorter than hERG1a and the initial 36 residues of hERG1b are unique to this isoform (Lees-Miller et al., 1997; Splawski et al., 1998) (**Figure 1**). As mentioned above, the channel gating is modulated by the cytoplasmic domains (PAS, CNBD, and Clinker) in a way that still remains unknown (Trudeau et al., 2011; Ng et al., 2014; Morais-Cabral and Robertson, 2015; Perry et al., 2015). Consequently, as hERG1b is lacking the entire PAS/Pascap domains, it has a different gating behavior compared to hERG1a.

The isoform originally discovered was hERG1a which is considered the full length transcript of the associated gene, and is often referred to simply as hERG1 when not being compared to other isoforms. Additionally, these isoforms are present in relatively fixed ratios, which depend on the cellular environment (Larsen et al., 2007, 2008). Deviations from these ratios, leading to abnormal abundance of a particular Kv11.1 isoform, may result in heart beat anomalies (Larsen et al., 2008; Kannankeril et al., 2010; Robertson, 2012).

Recently, hERG1b was found to be critical for human cardiac repolarization and a 1b-specific mutation associated with intrauterine fetal death was discovered (Jones et al., 2014, 2015, 2016). Additionally, the relative levels of expression appear to be greater in the young compared with the adult heart (Wang et al., 2008; Crotti et al., 2013). Evidence supports that when hERG1a and hERG1b are present in heterologous expression systems, they co-assemble to form hetero-tetrameric channels, although it is unknown if there is a preferred stoichiometry of these channels (London et al., 1997).

As previously mentioned, the two isoforms gating properties differ substantially. The hERG1 b- isoform is characterized by faster kinetics of activation, recovery from inactivation, and most prominently, deactivation (Larsen et al., 2008, 2010). These differences in gating kinetics are due mainly to the differences in the N-terminal regions of the two isoforms. More specifically, steady state activation is affected by the absence of the proximal N-terminal region in hERG1b, and the activation rate is suggested to be dependent on a short sequence of residues in the proximal portion of the hERG1a N-terminus (Saenen et al., 2006; Trudeau et al., 2011). Consequently, activation rates are much faster in hERG1b channels where these residues are missing (Larsen et al., 2008). Regarding deactivation, it has been suggested that the slow deactivation of hERG1a channels might be facilitated by the first 16 residues of the N-terminus, among other factors (Wang et al., 2008). According to that, faster deactivation rates in hERG1b can be explained by the presence of a unique N-terminal. The inactivation rate was shown to be similar between the two isoforms (Larsen et al., 2008). This finding is expected, as the mechanism by which fast inactivation occurs has been proposed to rely mainly on voltage induced changes in the structure of the outer mouth of the pore (Schönherr and Heinemann, 1996; Perry et al., 2013a,b; Thomson et al., 2014) and the sequence spanning this region is identical in both isoforms. Lastly, recovery from inactivation is significantly faster in hERG1b compared

to hERG1a, potentially implying that by some means, the Nterminus contributes to this process with already proposed stabilizing interactions (Saenen et al., 2006; Gustina and Trudeau, 2011).

Despite the evidence that heterometric hERG 1a/1b channels underlie cardiac Ikr, little is known about the gating and pharmacological properties of these channels, how hERG1a channels differ from hERG1b homomers, 1a/1b heteromers, or which role hERG1b might play in disease. Two broadly accepted gating mechanisms were established on the basis of kinetic modeling driven by the experimental data from electrophysiology studies of Kv11.1a channel. The first gating mechanism that successfully describes gating kinetics was proposed by Rasmusson, and later refined by Fink et al. and Romero et al. (termed M-model 1, **Figure 2**) (Wang et al., 1997; Fink et al., 2008; Romero et al., 2015). The modified M-model 1 (Fink et al., 2008) for hERG1 channel has been combined with the cardiac cell model (Ten-Tusscher Model; Ten Tusscher and Panfilov, 2006) in order to reproduce, and explain in terms of kinetics, measurements in oocytes, and HEK cells and showed overall good performance. The second hERG1 current scheme with different connectivity between gating states was developed by both Clancy et al. (Clancy and Rudy, 2001; Clancy et al., 2007) and Mazhari et al. (2001) (termed M-model2, **Figure 2**) on the basis of M-model originally proposed by Kiehn et al. (1999).

There are only a limited number of studies that employ kinetic modeling to understanding of gating kinetics in hERG1 isoforms. Sale et al. (2008) previously attempted to study the hetero channels formed by hERG1a/1b in HEK cells in presence and absence of E-4031 blocker. The M-model 2 was used to describe gating process in a-isoform and a-,b- heteromer. To explain apparent challenges in fitting experimental currents, Sale et al. proposed that the presence of the extended N termini in all 4 subunits in hERG 1a may alter gating process; hence an alternative gating mode ("N-mode") was considered. Another previous work modified the M-model 1 parameters proposed by Fink et al. (2008) and implemented them in the cardiac cell model (Ten Tusscher and Panfilov, 2006) in order to reproduce, and explain measurements in oocytes and HEK cells. However, none of the previous works (Robertson et al., 2008; Sale et al., 2008; Larsen et al., 2010; Holzem et al., 2016) tested the quality of the proposed kinetic models in fitting the hERG1b homo-tetramer experimental data, nor attempted to derive the set of model parameters for this isoform or suggest structural mechanisms explaining differences in isoform gating kinetics (Wacker et al., 2017).

The rapid progress in the structural biology finally resulted in the Cryo-EM high-resolution structure of hERG1 channel. The structure of the full hERG1 channel in its open state together with other highly homologous channels EAG1 and other closely-related channels from CNG and HCN families were published in 2016-2017 (Whicher and Mackinnon, 2016; Lee and Mackinnon, 2017; Li et al., 2017; Wang and Mackinnon, 2017). The availability of this new structural data provides a unique opportunity to connect well-established kinetic models of hERG1 channel to its structural determinant.

This work is striving to achieve several goals. First goal is the methodological one, where we developed and compared optimal gating schemes for hERG a- and b- isoforms. The second goal is to provide a perspective view on the potential structural mechanisms responsible for apparent kinetic differences between two isoforms and then to explore and discuss its implications at the tissue level. To achieve our methodological goal we systematically compared two gating schemes using available and novel electrophysiological recordings performed in HEK cell lines. The kinetic schemes illuminated profound differences in deactivation kinetics between two isoforms. To understand underlying reasons for different deactivation process, we employed structural modeling of hERG1 channel in open and closed-states using recently published structures of EAG1 and hERG1 channels from Cryo-EM (Whicher and Mackinnon, 2016; Wang and Mackinnon, 2017). We found that the available structures allowed identification of potential mutants with altered kinetics in good agreement with developed kinetic models. Finally, to provide a perspective on the potential role of isoforms in cellular dynamics, we undertook the cardiac cell simulations to reveal the conditions (i.e., isoform composition of hERG channels) leading to QT alterations. To provide initial glimpses into cellular roles of different isoform expression, a selected kinetic model, together with the optimized parameters, was incorporated into a higher dimensional model of the cardiac cell (O'hara et al., 2011) to simulate cellular and tissue dynamics effects as function of hERG isoform ratio.

#### MATERIALS AND METHODS

#### Expression of hERG1a and hERG1b in HEK Cells

Lees-Miller et al. first reported the electrophysiology of the hERG1 b-isoform (Lees-Miller et al., 1997). The hERG1 b-isoform was cloned from human atrium. hERG1 isoforms were cloned into the pIRES-hr green fluorescent protein-1a vector (Agilent Technologies, Santa Clara, CA) for co-expression

with humanized Renilla reniformis GPF. Human embryonic kidney (HEK) 293 cells were transfected by using calcium phosphate and cultured in Dulbecco's modified Eagle's medium supplemented with 10% horse serum (Invitrogen, Carlsbad, CA). Transfection was monitored by green fluorescence. HEK cells were chosen because their background potassium currents are small. More importantly, no dofetilide-sensitive tail current has been observed by using the voltage-clamp protocol in untransfected HEK cells.

#### General Setup for Electrophysiological Recordings

Transfected HEK cells on glass coverslips were placed in a chamber mounted on a modified stage of an inverted microscope. The chamber was superfused at a rate of 2 ml/min with a normal external solution. Micropipettes were pulled from borosilicate glass capillary tubes on a programmable horizontal puller (Sutter Instrument Company, Novato, CA). Standard patch-clamp methods were used to measure the whole-cell currents of hERG1 mutants expressed in HEK 293 cells by using the Axopatch 200B amplifier (Molecular Devices, Sunnyvale, CA) (Lees-Miller et al., 2009). The pipette solution contained the following: 10 mM KCl, 110 mM K-aspartate, 5 mM MgCl2, 5 mM Na2ATP, 10 mM ethylene glycol-bis(β-aminoethyl ether)- N,N,N′ ,N′ tetraacetic acid, 5 mM HEPES, and 1 mM CaCl2. The solution was adjusted to pH 7.2 with KOH. The EC solution contained the following: 140 mM NaCl, 5.4 mM KCl, 1 mM CaCl2, 1 mM MgCl2, 5 mM HEPES, and 5.5 mM glucose. The solution was adjusted to pH 7.4 with NaOH. In patch clamp experiments, serious resistance and capacitance during the whole cell patch clamp recording were compensated to 90% through Axopatch 200B patch clamp amplifier. Whole cell patch clamp experiments were performed when access resistance was <10 MOme. No leak subtraction was performed. The junction potential of −10 mV was adjusted on all the membrane potentials recorded. All experiments were conducted at room temperature.

#### Voltage Protocols

#### **Voltage-dependence of activation**

From a holding potential of −80 mV cells were depolarized for 1 s to a range of voltages from −100 to +40 mV followed by a step to −100 mV (1 s) to record the tail currents (**Figure 3**). The isochronal tail current-voltage plots were fit to a single Boltzmann function (1):

$$\frac{I}{I\_{\text{max}}} = \frac{1}{\langle 1 + \exp[\frac{(V\_{\frac{1}{2}} - V\_m)}{k}] \rangle} \tag{1}$$

Where I / Imax is the normalized current, V1/<sup>2</sup> is voltage of the half-maximal activation, k is the slope factor and V<sup>m</sup> is the membrane potential.

#### **Envelope of tails**

The activation of hERG1a and hERG1b channels was examined at +40 mV in HEK cells. The protocol is shown in **Figure 4**. The measurements were carried out by activating the channels at +40 mV for various durations of time (from 5 to 500 ms) and then measuring the tail current at −100 mV (3 s). The peak amplitude of the tail current was used as a measure of the relative amount of activated channels at a given time point. The peak amplitudes were normalized to the maximum amplitude and plotted as a function of the duration of the activating step.

#### **Deactivation**

Deactivation of hERG1a/1b tail current was measured by activating channels al +40, followed with a short (5 ms) repolarization step to −120 mV and deactivating step at −120, −100, −60, −40 mV. Currents at different voltages were normalized and averaged (n = 10) time course data was plotted for each isoform at the different voltages (**Figure 5**).

#### **Statistical analysis**

Statsview (Abacus Concepts, Berkeley, CA) or QTIplot (Vasilef, 2013), Grace (http://plasma-gate.weizmann.ac.il/Grace/) were used to analyze the data. Data are presented as mean ± SEM.

#### Computational Methods

#### Kinetic Modeling: Vgckimo Program Package<sup>1</sup>

The dominant paradigm for ion transport over the past 60 years has been based on the seminal experiments of Hodgkin and Huxley (Hodgkin and Huxley, 1952; Hodgkin et al., 1952). However, a much more detailed picture of the mechanisms underlying membrane excitation can be described in terms of Markov models (M-models) (Rudy and Silva, 2006; Moreno et al., 2011), where the conducting and non-conducting states are

properties at +40 mV. (A) Representative current traces elicited by the protocol shown at the top corresponding to 5–500 ms of activation are shown. (B)The data were normalized to the maximum amplitude of the tail current and plotted against time. hERG1a (*n* = 10); hERG1b (*n* = 10). All data are shown as mean ± SEM.

interconnected by rate constants dependent on the membrane potential. The essence of M-models is that, for any single step in the gating mechanism, the transition probability (i.e., the microscopic equivalent of the rate constant) is time independent. In an M-model of ion channels, transition rates define the interstate dynamics. These rates may depend on environmental variables such us membrane potential or ligand concentration.

The state probabilities in the model are calculated by solving the following differential equation (Equation. 2):

$$\frac{d\overrightarrow{\overline{p}}}{dt} = Q\overrightarrow{\overline{p}}\tag{2}$$

where −→<sup>p</sup> is the vector of state probabilities and <sup>Q</sup> is the system matrix of the transition rate constants. Each transition rate constant is assumed to have the following expression:

$$k\_i = \alpha\_i e^{\beta\_i V} \tag{3}$$

where α<sup>i</sup> = kBT h • e 1Si <sup>R</sup> <sup>−</sup> 1Hi RT (ms−<sup>1</sup> ), β<sup>i</sup> = ziF RT (mV −1 ); V is the external electric potential in mV; z<sup>i</sup> is the effective valence of moving charges; T(K) is the temperature; 1H<sup>i</sup> (J/M) the change in enthalpy; 1Si(J/M/K) the change in entropy. k<sup>B</sup> =

<sup>1</sup>Voltage-Gated Ion Channels Kinetic Modeling from whole-cell voltage-clamp data (VGC-KiMo) is a standalone tool written in C++ language, working on Linux machines and parallelized with OpenMP (see the Supporting Material for the scalability benchmarks). VGC-KiMo code is distributed under GNU General Public License thus freely available for download from https://github.com/ vgckimo/vgckimo, together with documentation and tutorial files. See Supporting Material for a complete description of the code.

1.381 10−<sup>23</sup> J K −1 (Boltzmann constant); h = 6.626 10−<sup>34</sup> J s−<sup>1</sup> (Planck constant); R = 8.315 Jmol−<sup>1</sup> K −1 (ideal gas constant); F = 96785 C M−<sup>1</sup> (Faraday constant).

Once Equation (2) is solved, the probability of being in the open state (pO: conducting state) is found and the current is calculated using the following equations:

$$I\_{Kr} = \text{g}\_{Kr} \rho\_O \left( V - E\_k \right) \tag{4}$$

$$\mathbf{g}\_{\mathbf{K}r} = \mathbf{g}\_{Kr}^{0} \left( aT + b \right) \left( \frac{[K+]\_{O}}{5.4 \text{ } mM} \right)^{\frac{1}{2}} \tag{5}$$

Where g 0 Kr =0.024 pA/pF/mV, a = 1/35, and b = −55/7, O is the open probability (see SM and (Fink et al., 2008) for more details).

Through the Global-Fitting procedure described in Balser et al. (1990) and implemented in VGC-KiMo<sup>1</sup> , the rate constants of a given M-model can be estimated from macroscopic ion channel currents in voltage-clamped membranes. The use of comprehensive and extensive data sets of experimental information from a broad range of ion current responses to multiple voltage stimulations conditions (voltage protocols, membrane potentials, temperature, etc.), shrinks the universe of possible solutions to the model system mechanism ensuring the robustness of the parameter set. Although several methods exist for analyzing voltage dependent currents (Wang et al., 1997; Mazhari et al., 2001; Fink et al., 2008; Bett et al., 2011; Moreno et al., 2011; Ben-Shalom et al., 2012) most of them are published only as a set of equations without the simulation tools. Others, from the neurophysiology field, are designed to use the full current traces, data that are neither commonly available nor easy to extract from published literature (Gurkiewicz and Korngreen, 2007; Ben-Shalom et al., 2012).

In the current form, VGC-KiMo<sup>1</sup> source code includes two Markov formulations for the Kv11.1, best known as the hERG K<sup>+</sup> channel. Any other channel can be added to the source code in addition to the current one, as well as different Markov models and other voltage protocols. The experimental data chosen for the model validation was not used for the development of the model's parameters and belongs to a different cell line than the one used to originally derive the parameters for the M-model (HEK cells), see SM (Section 2: Validation). The performance of the original parameters is fairly good but corrections were needed to reproduce the data from CHO cell line, suggesting that the published set of parameters is robust and reliable. A preliminary version of VGC-KiMo has also been used recently to simulate WT hERG and a variant using experimental data from HEK cell line (Guo et al., 2015; Perissinotti et al., 2015).

#### Cell Simulations

An IKr Markov model (Romero et al., 2015) was incorporated into the O'Hara-Rudy human ventricular action potential model(O'hara et al., 2011) and its maximum conductance (gKr = 0.0422) was scaled to elicit a close value of the peak Ikr as the original O'Hara model at 1 Hz. Physiological action potential simulations were subsequently performed at 37◦C. b-Isoform and a-Isoform transition rate constants together with the corresponding temperature correction are shown in Table S12.

Simulated action potentials (APs) were recorded in endocardial cells at the 1000th paced beat (BCL = 1000 ms). The numerical method used for updating the voltage was forward Euler. All the Simulations were encoded in C/C++ and run on Mac Pro 3.06 GHz 12-Core computers. The time step was set to 0.00005 ms during AP upstroke, otherwise the time step was 0.005 ms. Numerical results were visualized using MATLAB R2014a by The Math Works, Inc.

#### **Transmural fiber simulations**

We simulated a transmural fiber composed of 165 ventricular cells (1x = 1y = 100µm) connected by resistances to simulate gap junctions (Faber and Rudy, 2000). The fiber contains an endocardial (cells 1 to 60), M-cell (cells 61 to 105), and epicardial (cells 106 to 165) regions, as described by O'Hara et al. The fiber was paced at BCL = 1,000 ms for 2,000 beats. The stimulus was applied to the first cell. Current flow is described by the following equation:

$$\frac{\partial V(\mathbf{x},t)}{\partial t} = D \frac{\partial^2 V(\mathbf{x},t)}{\partial \mathbf{x}^2} - \frac{I\_{ion\\_I} I\_{stim}}{C\_m} \tag{6}$$

Where V is the membrane potential, t is time, D is the tissue diffusion coefficient [0.00092 cm<sup>2</sup> /ms, calculated from Shaw and Rudy (Shaw and Rudy, 1997)], Iion is the sum of transmembrane ionic currents, Istim is the stimulus current (300 µA/cm<sup>2</sup> for 0.5 ms), and C<sup>m</sup> is the membrane capacitance (1 µF/cm<sup>2</sup> ).

#### **ECG computation**

Extracellular unipolar potentials (8e) generated by the fiber in an extensive medium of conductivity σe, were computed from the transmembrane potential V<sup>m</sup> using the integral expression as in Gima and Rudy (Gima and Rudy, 2002):

$$\Phi\_{\varepsilon}(\mathbf{x}', \mathbf{y}', \mathbf{z}') = \frac{a^2 \sigma\_{\bar{t}}}{4\sigma\_{\varepsilon}} \int \left(-\nabla V\_m\right) \bullet \left[\nabla \frac{1}{r}\right] d\mathbf{x} \tag{7}$$

$$r = \left[\left(x - x'\right)^2 + \left(y - y'\right)^2 + \left(z - z'\right)^2\right]^{1/2} \tag{8}$$

where ∇V is the spatial gradient of Vm, a is the radius of the fiber, σ<sup>i</sup> is the intracellular conductivity, σ<sup>e</sup> is the extracellular conductivity, and r is the distance from a source point (x, y, z) to a field point (x', y', z'). Φ<sup>e</sup> was computed at an "electrode" site 2.0 cm away from the distal end along the fiber axis.

#### Structural Modeling

Recently published full hERG (hERGT) open channel solved by Cryo-EM at 3.8 angstrom resolution (PDB ID 5VA2) was used for the structural analysis. The construct used for structural studies has functional properties very similar to WT but is lacking residues between 141 and 350, that correspond to the structure between PAS and S1; and 871-1005 (C-terminal). The structure was cut right after CNBD ends and missing residues at the outer pore mouth were added and modeled as extracellular loops that were minimized using NAMD2.10 (Phillips et al., 2005). The 3D structure of the closed-state hERG channel used in this study is based on the homology modeling to EAG1 Cryo-EM structure (PDB ID 5K7L) determined at 3.78 angstrom resolution (Yang et al., 2017). This structure represents the closed pore while the voltage sensing domain (VSD) displays an open conformation (Whicher and Mackinnon, 2016). The SWISS-MODEL homology modeling program (Arnold et al., 2006) was used for the development of the hERG closed model from TABLE 1 | Experimental data for HEK cells at room temperature.


*Each value is an average of n experiments. Equation (1) was used to obtain V1/2 and k, data are presented as mean* ± *SEM.*

the available EAG1 channel structure as described previously (Yang et al., 2017). Sequence alignment was performed using the CLUSTALW algorithm (Larkin et al., 2007; Goujon et al., 2010). Protein models were generated from the alignment in a stepwise manner. The generated model was later minimized using NAMD2.10 (Phillips et al., 2005).

#### RESULTS AND DISCUSSIONS

#### Experimental Measurements

The whole-cell patch clamp configuration at room temperature was used to study the voltage-dependent activation by applying a standard step protocol described in the methodology. The normalized tail currents measured at −100 mV were plotted against the membrane potential of the previous step and fitted to a Boltzmann function. The V1/<sup>2</sup> of activation is shifted around 10 mV in the negative direction for hERG1b compared to hERG1a (**Figure 3**, **Table 1**). The mean current levels measured at the end of the 1-s depolarizing pulse to +40 mV were used to construct the current-voltage (I-V) relationship (**Figure 3C**). Similar to what is observed for hERG1a, the b-isoform shows a strong inward rectification, resulting in the characteristic bellshaped curve. Kinetics of activation was studied by applying an envelope of tails protocol, as described in the methodology section. The b-isoform shows a similar sigmoid shape of activation, but a much faster rate compared to the a-isoform (**Figure 4**).

Deactivation kinetics was characterized by recording tail currents at potentials ranging from −40 to −120 mV after an activating step to +40 mV (see methods). Current traces for selected voltages are shown in **Figure 5**. The deactivating currents were best fitted to a double exponential function and time constants corresponding to the fast and slow deactivation processes are shown in Table S13. Both deactivating components are significantly reduced for hERG1b. The observed reduction depends on the voltage, at −60 mV, the slow and fast components are around 10 to 14 times faster for hERG1b while the difference is around 4 to 7 times for −40 and −100 mV, respectively. As it was found before for CHO cells by Larsen et al. (2008), the relative contribution of the fast component of deactivation depends on the voltage and is much more pronounced for hERG1b compared to hERG1a, in fact at −120 mV there is no slow component according to the experimental fit. Regarding TABLE 2 | M-model 1 rate constants for transitions within hERG gating for a-isoform and b-isoform.


α *(1/ms) indicates voltage independent rate, and* β *(1/mV) indicates voltage dependent rate as follows: k* = α\**exp(*β\**V) The transitions between O and I states are also dependent on extracellular potassium concentration [K*+*]* 0 . *That dependence is accounted for in the model by modifying the transition rate for inactivation (O* → *I, bi) as: kbi([K*+*] 0 )*=*k'bi(5.4mM/[K*+*] 0 ) 0.4. Bold values indicate moderate change of the corresponding transitions calculated as a ratio. Transitions that are strongly affected are shown in bold red. Transitions that are affected the most are shown as underlined red bold values. For details of the optimizations, original model parameters and optimization from CHO data see Tables S1–S4.*

the inactivation process, there was not significant difference and was not further investigated here (Larsen et al., 2008) (data not shown). Time constants for recovery from inactivation for a-isoform and b-isoform display a significant difference and are collected in **Table 1**.

#### Markov Kinetic Models to Describe hERG a- and b-Isoforms

The most pronounced difference evident from the experimental raw current traces is the markedly faster deactivation rate and the faster activation rate of hERG1b compared to hERG1a. This is in agreement to what was also found for CHO cells (Larsen et al., 2008). The experimental measurements in the HEK cell line focus in these events and the M-models were fitted to the data presented in the above section. All transition rates were defined using Equation (3). The previously derived values for α<sup>i</sup> and β<sup>i</sup> were used for initial guess (see Table S1 in Supplemental Materials). For M-model 1, the initial guess values were derived using the comprehensive experimental data-set from Berecki et al. at room temperature and 37◦C respectively (Berecki et al., 2005). Two correction terms, a and b were introduced to α and β parameters for quality monitoring during optimization routine TABLE 3 | M-model 2 rate constants for transitions within hERG gating for a-isoform and b-isoform.


α *(1/ms) indicates voltage independent rate, and* β *(1/mV) indicates voltage dependent rate as follows: k*= α\**exp(*β\**V).* \**Constraint by microscopic reversibility. Bold values indicate moderate change of the corresponding transitions calculated as a ratio. Transitions that are strongly affected are shown in bold red. Transitions that are affected the most are shown as underlined red bold values. For additional details on the optimizations and original model parameters see Tables S1–S4.*

(Equation 9). α and β were set to the constant values, while **a** and **b** parameters were introduced as free variables for optimization routine.

$$k\_i = a\_i \alpha\_i e^{b\_i \beta\_i V} \tag{9}$$

Correction to individual parameters (**a**i , **b**i : Equation 5) from Fink et al. and Mazhari et al. has been done to reproduce available data from HEK-cell measurements at room temperature (23). All fitted parameters for the kinetic mechanism considered, can be found in **Tables 2**, **3** and Tables S4, S5. Note that β was set to zero for transitions ain and bin (**Figure 2**) and thus, these transitions are modeled as voltage independent. Maximum single channel conductance was assumed to be the same for hERG1a and hERG1b, so all differences are attributed to channel kinetics.

Three and/or four different voltage protocols were included simultaneously in the optimization protocol (see Supplementary Materials for a complete description of the voltage protocols). Different optimization routines were performed and the correction factors were defined for each of the parameters. All parameters required corrections to the initial guesses. The best fits are shown in **Tables 2**, **3** for two isoforms and each model, respectively. Further improvement of the optimizations was achieved by using the random initial guess generator around the already fitted values and assigning different weight to the partial cost function. In all the cases, the stability analysis showed that all values were well-converged. The simulated voltage protocols and computed currents are in reasonable agreement with the measured ones, meaning that voltage dependence and curve shapes are qualitatively well-reproduced. Overall, both gating mechanisms from the literature were able to reproduce the gating kinetics for both isoforms. However, the optimized parameters showed some interesting differences and limitations in quantitatively reproducing the time course of the deactivation kinetics at different voltages.

#### Performance of M-Model 1

The M-model 1 implies linear connectivity between different gating states. The channel has to go through the open state to fully inactivate. The experimental basis for this scheme was extensively discussed in the literature (Bett et al., 2011). Assuming that both isoforms follow same kinetic scheme (Sale et al., 2008), the key differences between the a-isoform and bisoform kinetics lie essentially in the highlighted steps shown in **Table 2**. According to the results collected in **Table 2**, the best fit within M-model 1 indicates that the main difference between two hERG isoforms is in the late deactivation step. The late deactivation is about eight times faster for the b-isoform. These parameters also show an increase in the activation rate steps, together with an increase in the recovery from inactivation rate in agreement with the experimental data (**Table 1**). Simulated data from CHO cell line (SM) also display a good agreement with the optimal fit (Tables S3, S4, S9). **Figure 6** shows the simulated data together with the experiments. An excellent agreement is obtained for the activation and Steady State Activation curves for both isoforms (**Figure 9**). However, the main challenges are in the modeling of the deactivation kinetics for different voltage protocols (−40, −60, −100, −120 mV). For b-isoform in particular, the quality of the optimization is limited, although it qualitatively reproduces the behavior at the different voltages.

#### Performance of M-Model 2

This model, in contrast to the M-model 1, is not linear, but instead, includes a direct transition to the inactivated state from the closed state immediately preceding the open state. In one of the previous formulations (Mazhari et al., 2001), this transition is negligible compared to the transition to the open state and so, numerically, this model is almost linear. In our work, Mmodel 2 was tested assuming a range of different values for this transition and in all the cases a very small rate was obtained for both isoforms. Although the obtained value was small and almost negligible, it is almost 1000 times faster for the b-isoform. The M-model 2 shows a similar performance compared to the M-model 1 although the fit quality is consistently lower than that of M-model 1. The differences between a-isoform and bisoform are distributed over the activation steps but mainly in the late deactivation and the new extra step considered in this scheme (**Table 3**). Simulated current traces elicited by the voltage protocols and the activation curves are well-reproduced by this model (**Figure 7**). Similar to what was observed for M-model 1, the quality of the optimization is poor, although it qualitatively reproduces the behavior at the different voltages.

Taking together the results from M-model 1 and 2, we conclude that both models capture the main kinetic difference between the isoforms. The pivotal feature of isoform kinetics is a considerable increase in the late deactivation step. Both models point to a moderate increase in the activation and recovery from inactivation steps, the changes and their magnitudes depend on the model. The current traces simulated by each model and elicited by the SSA voltage protocol are shown in **Figure 8**. It can be seen that they qualitatively reproduce the experimental behavior shown in **Figure 3**. The b-isoform displays larger currents, an increased activation rate, faster recovery from inactivation and clearly shows a much faster deactivation rate under the repolarizing pulse. The simulated I-V relationships show the typical curve shape and qualitatively reproduce the experimental differences characteristic of each isoform, although they show significant deviations for voltages above 10 mV. At these voltages background currents are relatively high, while hERG current is relatively small. The combination of these two factors presents a natural challenge and led to the discussed discrepancy between simulated and experimental data.

The best optimization for M-model 1 which also shows fair agreement with the fit to CHO data (Table S9), suggests that although the main difference is in the late deactivation step, being eight times faster for the b-isoform when compared to a-isoform, early and late activation are also increased by a factor of ∼2 and 4, respectively. According to this fit, the voltage independent rates are increased in forward and backward directions by a factor of 2 and the recovery from inactivation rate by a factor of 4. M-model 2 suggests similar changes and fair agreement with CHO data (Table S10); late deactivation is 15 times faster for the b- compared to the a-isoform, but also early and late activation, being 3 and 2 times faster respectively. It also shows a threefold increase for the recovery from inactivation and an increase for both voltage insensitive rates, being 2.5 times faster in the deactivating direction.

#### Limitations of the Kinetic Modeling

It is important to mention that the time course of deactivation was not well-fitted by the M-models used in this work for both HEK and CHO cell lines. We observed that the quality of the fit is different for different voltages. To improve modeling of the deactivation kinetics, a number of different conditions were tested for both models, i.e., randomization of initial values, constraints, boundaries, etc., but no further improvement was achieved. The reason could be related to the amount of data used in the fitting procedure, experimental limitations in the data acquisition (temperature, cell-line variability, resolution of electrophysiological recordings), or indicate that the Mmodels should be revisited. It is important to mention that some inconsistencies between the deactivation experimental data and these models were previously discussed by other authors (Fink et al., 2008). Another example can be found in a recently developed Markov model that reproduces biophysical

experimental data at room temperature with CHO cell line includes two closed (C1, C2), one open (O) and corresponding inactivated states (IC1, IC2, IO) (Di Veroli et al., 2013). This model also faces difficulties in fitting deactivation at different voltages. Interestingly, the 6-states model with closed loops can be reduced to a 4-states cyclic model (C1, O, IC, IO) at 37◦C, as different closed states could not be resolved. However, unless explicitly introducing temperature-dependent parameters, all of the available models cannot account for temperaturedependent hERG channel activity changes. A modification of the Di Veroli model was done recently by Li et al. (Li et al., 2016), and can recapitulate macroscopic hERG channel gating behavior for a temperature range from 20 to 37◦C. Providing the better performance for the temperature range, different states and connectivity, it would be interesting to test the performance of this new model in reproducing the experimental data for both isoforms. It is important to emphasize that having a complete and more reliable M-model is of key importance for modeling and predicting differential and temperature dependent effects of drugs on the delayed rectifier potassium "Ikr" current.

## Structural Underpinnings of Isoform Function

The kinetic modeling discussed above isolates principal differences in gating kinetics of hERG a- and hERG b-isoforms. The recent Cryo-EM structures allowed the structural modeling for open- and closed states of hERG1 channel enabling molecular-level description of the determinants of this apparent isoform-specific differences. Homology models (Wacker et al., 2017) and chimera constructs were very useful in the past (Dhillon et al., 2014) for understanding structure-function relationships in K+ channels. However, most of the models were focusing on the trans-membrane section of hERG1 channel only (Wacker et al., 2017). The recently-solved hERG structure shows an open pore, while the EAG1 channel solved by Cryo-EM is captured with the pore closed due to the presence of Ca2+ and calmodulin, which lock the pore closed while the VSD is supposed to be in its depolarized state (Wang and Mackinnon, 2017). The hERG closed model presented here was built using EAG1 structure as a representative template for hERG's closed pore. Given the fact that conformational differences between these two states of VSD are relatively small compared to structures and models of open- and closed states found in K<sup>+</sup> channels from Shaker family (Li et al., 2014); then the question is, if this is a good representation of hERG closed state, what kind of VSD movement could result in that same conformational change in the pore?. As Wang et al. (Wang and Mackinnon, 2017) pointed out, there are key structural differences in the arrangement of the VSD (non-domain swapped) in hERG and EAG1. It seems that an S4 inward movement toward the cytoplasm and centric displacement toward the pore axis driven by the membrane electric field could produce a similar pore closure. In that scenario, there is almost not translation of S4

across the membrane, S5 maintains an extensive antiparallel contact with S6 and the VSD would transmit force through the S5-S6 interface as the movement of S4 would compress the S5 helices and close the S6 gate. This proposed mechanism is different than the lever mechanism proposed for Shaker-like Kv channels and the cytoplasmic domains may play a crucial role in it. It is important to mention that functional measurements also point to substantial differences in the total gating charge, being much less for hERG, which implies that the VSD conformational changes are smaller in hERG channel (Zhang et al., 2004; Li et al., 2014). These rapid developments in hERG structural biology emphasized important roles of PAS and CNBD domains in gating kinetics. As it was shown previously for Kv1.2-Kv2.1 (Morais-Cabral and Robertson, 2015), PAS-CNBD complex published for mEAG1 (Haitin et al., 2013), and all the recent structures; the PAS (**Figure 9**, in orange) domain is far away from the VSD. In stark contrast, hERG structures show (Whicher and Mackinnon, 2016; Wang and Mackinnon, 2017), that the N-terminus of the PAS domain (absent in b-isoform) is directed toward the VSD and S4-S5 linker (**Figure 9B**) and most likely interacts with the gating machinery. NMR studies previously suggested that the N-terminal cap shows a high degree of structural variability and is long enough to reach the voltage sensor, the S4-S5 linker or the C-linker (Muskett et al., 2011; Ng et al., 2011, 2014) (**Figure 9B**). As it was mentioned before, the new structures present new topology of VSD-pore domain packing, which is different from the domain-swapped architecture and might suggest a new paradigm for voltage dependent gating. It was recently proposed for EAG1, a mechanism in which the VSD interacts with the cytoplasmic domains to gate the channel. Combined with the data from isoform kinetic modeling described above, models of hERG in open and closed state may provide better understanding of stabilizing interactions present or missing in a particular isoform.

The arrangement of cytoplasmic domains in the open state and closed state models are shown in **Figure 9**. The PAS domain is interacting with CNBD in a similar way it was found previously for homologous channels (Lee and Mackinnon, 2017; Li et al., 2017; Wang and Mackinnon, 2017). Similar to the previously solved structures for CNBD domains (Ng et al., 2011; Adaixo et al., 2013; Brelidze et al., 2013; Haitin et al., 2013), a portion of the hERG sequence occupies the cyclic nucleotide binding site, which prevents the cyclic nucleotide binding. In addition to that, the N-terminus of PAS Domain (N-cap), which influences the rate of voltage dependent channel opening and closing, is directed toward the VSD (Wang and Mackinnon, 2017) (**Figures 9B**, **10B**). When the channel is in its open state, the C-linker region is packed against the transmembrane domain (**Figure 10A**) interacting with the S4-S5 linker and VSD. A novel interaction pinpointed by the structural analysis is the salt-bridge formed between Glu544 and Arg681 (**Figures 10C,D**). This saltbridge is missing in the closed state model of the channel as the C-linker is slightly rotated with respect to the S4-S5 linker. Hence, we hypothesize that it might be one of the open-state

stabilizing interactions that it is affected in the absence or the PAS domain (b-isoform), note that N-cap (Val 3) is close to E544 and might indirectly affect the E544-R681 interaction. Unfortunately, solved structures are missing significant part of the PAS domain sequence and further refinement of hERG1 PAS domain is essential future goal for structural modeling. Nevertheless, the previously studied E544L mutant (Durdagi et al., 2012) shows an increase in the deactivation rate. Even though is not as much as for the b-isoform (**Figure 10E**), it highlights a potential key role of this residue. When transitioning from closed to open state, the transmembrane and cytoplasmic domains slightly rotate with

respect to each other (**Figures 9**, **10B**), we suggest that the interplay between PAS, VSD: S4-S5, and C-linker during such rotation might be of key importance in modulation the gating.

While more work is still required to decipher gating kinetics of hERG1, the structural models already show enhanced interactions between the cytoplasmic and the transmembrane (TM) domain for the open state of the channel. Analysis of structural differences between open and closed states suggests that a slight rotational movement changing packing of the cytoplasmic domains against the TM part of the channel is required as part of activation/deactivation process. This is in

rotated respects each other. Orange arrow show the rotation direction when transitioning from closed to open states. (B) N-cap PAS interaction with VS (S1 & potentially S4-S5), CNBD, and C-linker for closed in the left panel and open states, right panel.

line with the finding that the conformational change that VSD is undergoing during gating cycle might be small compared to other potassium channels. This would allow the CNBD to close the channel independent of the VSD conformation (as it was observed for EAG1) and provide an added level of regulation through the interaction of intracellular domains with the voltage dependent gating machinery (Whicher and Mackinnon, 2016). These structural insights, although preliminary, lead us to the hypothetic gating mechanism summarized in **Figure 11**. The similar mechanism of gating modulated by soluble domains has been proposed for MolK1, a prokaryotic potassium channel lacking the C-linker and PAS domain (Kowal et al., 2014).

These structural models also raise another point. In other channels, PAS and CNBD domains serve a regulatory function in which the binding of small molecules or signaling proteins is transduced into conformational changes. It is not known whether or not this could be happening for hERG. These new models align to what was suggested previously (Morais-Cabral and Robertson, 2015), and that points to the possibility that the C-linker-CNBD-PAS serves as an anchor to correctly position the N-pas terminal cap during the gating process. Can we explain observed differences in the deactivation kinetics between hERG a- and bisoforms observed with kinetic modeling? Any of the functional alterations due to mutations or truncations in the N-terminal cap or the entire PAS Domain (b-isoform) would ultimately lead to a loss of N-terminal cap position and severely-altered gating kinetics. The lack of stabilizing interactions between soluble and trans-membrane domains is expected to impact the opening probability and stability of the open state. It may explain observed rapid transitions between open and closed states present in the b-isoform.

from experiments previously published by Durdagi et al. for hERG1a, hERG1b, and hERG1a-E544L elicited by the voltage protocol at the top. E544L mutant displays

### Cardiac Cell Models: Functional Implications of Different Isoform Ratios in the Heart

a faster deactivation rates than WT but not as much as hERG1b.

The improved kinetic models allowed us to directly address physiological questions like whether or not hERG isoform composition in ventricular myocytes has a potential to alter QT duration and, hence, to pre-dispose a patient for druginduced QT prolongation. To specifically address the functional implication of having homomeric hERG1a or hERG1b in the heart we conducted simulations including our M-model 1 parameters in the cardiac cell (O'Hara-Rudy human cardiac ventricular myocyte Model) (O'hara et al., 2011; Romero et al., 2015). The final parameters from the fittings were then used as input values in the cardiac cell and tissue model (O'hara et al., 2011) in order to simulate the shape of the action potential and ECG signal for both isoforms (**Figure 12**). The M-model 1 and its parameters from the optimization were introduced in the cardiac cell model in order to test the way in which they affect the shape and duration of action potential. As it was found previously (Larsen and Olesen, 2010), the results of the ventricular cardiomyocyte simulations showed that kinetic changes in Ikr corresponding to homomeric hERG1b resulted in much shorter action potential duration (APD). **Figure 12B** shows the action potential (Dhillon et al.) shape and duration considering the extreme situation of Ikr corresponding only to hERG1 a- or b- isoforms. Intermediate cases, where weighed contributions from both isoforms were considered, are shown in **Figure 12A**. Ikr currents are also shown in **Figure 12A** and, as it can be seen, the currents became larger and peak earlier when transitioning from pure a- to b- isoforms.

Mechanistic inspection of the changes in the channel state occupancy revealed several differences. Figures S9, S11 show the proportion of channels in the different states. The twists in the same direction.

most prominent difference lies in the occupancy of open and inactivated states when comparing a-isoform to b-isoform. The AP shortening is mainly due to an increase in the open state occupancy and a reduction in the inactivated states occupancy for hERG1b compared to hERG1a. Finally, the M-model 1 was also introduced in the tissue model (cable) and the ECG signal was simulated for both homomers (**Figure 12C**). As expected, virtual hERG1b expression resulted in a reduction in the QT interval on the computed pseudo-ECG.

Experimental investigations have revealed many sources of heterogeneity and associated regulation in the heart. Distinct regions with associated cell types that are distinguishable by morphology and action potential duration have been documented. The different cell types have been shown to arise from heterogeneities in ion channel expression, which have been modeled and used in cell-type specific predictive simulations (Viswanathan et al., 1999) (Shimizu and Antzelevitch, 1999). In the left ventricle of the heart, cellular heterogeneity from the endocardium to mid-myocardium to endocardium exists and arises from heterogeneity in potassium currents (Shimizu and Antzelevitch, 1999) (Liu and Antzelevitch, 1995). The differences in stoichiometry between hERG1a and hERG1b likely constitute a novel source of cardiac heterogeneity that may vary in terms of distribution and be subject to regulation by as yet unknown mechanisms.

The kinetic modeling in section Markov Kinetic Models to Describe hERG a- and b-Isoforms shows a profound difference in hERG1a and hERG1b deactivation rates, where the quantitatively fitted parameters to the data suggested that the hERG1b late deactivation rate is between 8 and 15 times faster than hERG1a. One of the most interesting and counterintuitive findings in the results shown above is that this difference did not result in effects on the action potential duration that would expected from the observed changes alone. The dominant presence of the hERG1 bisoform results in faster deactivation, which by itself would result in fewer channels in the open state as the channels close more quickly. The anticipated effect on the action potential duration would be less repolarizing current and consequently, shorter APD. In fact, the opposite was observed both in our modeling predictions with M-model 1 and in a previous experimental study (Larsen and Olesen, 2010). The reason is that the hERG1 bisoform has both faster activation kinetic and faster recovery from inactivation kinetics that results in a net increase current compared to the hERG1 a-isoform.

# CONCLUSIONS

We investigated structural and biophysical properties of hERG1a and 1b homo-tetramers in the context of previously proposed Markov models and new data measured in the HEK cell line. Two M-models were tested and fitted to the experimental data. For the first time a set of parameters were provided for both isoforms. The models' parameters were then used to investigate effects of various homo-tetramers ratios formed by two isoforms in cardiac cells and tissue to track isoform-specific effects on emergent behaviors that occur in higher dimensions. The minimization procedure presented here, allowed assessment of suitability of different Markov model topologies and the corresponding parameters that describe the channel kinetics. In terms of the gating kinetics, we found that both M-models were able to qualitatively capture the kinetics of two isoforms. The kinetic modeling showed a profound difference in hERG1a and hERG1b deactivation rates, where the quantitatively fitted parameters to the data suggested that the hERG1b late deactivation rate is between 8 and 15 times faster than hERG1a.

In order to gain insight and link the observed isoforms' differences to the structure, full channel structural models were developed and analyzed for open and closed states. From the structural point of view, open and closed structural models for the full channel were for the first time compared providing hypothetical structural mechanism for transitions between closed to open states of hERG channel. In line with the kinetic modeling, interactions between soluble domains and the TM part of the channel appeared to be critical determinants of the gating kinetics allowing explanation of apparent differences in the deactivation rates between two isoforms. The model emphasized importance of the electrostatic interactions between N-cap of PAS domain and TM domain. To test the proposed role of stabilizing interactions between N-cap of PAS domain and the gating machinery in TM, we examined gating kinetics of E544L. Introduction of charge neutralizing resulted in significantly enhanced deactivation rates, reminiscent of isoform-specific differences. We attribute it to interactions between E544 and R681 missing in E544L mutant. Importantly, this interaction is present in both hERG1 a-isoform and hERG1 b-isoform, however b-isoform is missing the of PAS domain who might contribute to stabilize that interaction. While this work was under review, another publication by de la Peña et al. (2018) showed that hERG gating profiles can be reconsiled from non-covalently linked VSD and Pore Domain. Their findings, in line to what is presented in this work, challenge the classical view of the S4–S5 linker acting as lever to open the gate, supporting the hypothesis that the S4–S5 linker might integrate signals coming from the cytoplasmic domains (c-linker/PAS). Importantly, those split-channels disconnected at the S4–S5 linker show a destabilization of the closed state, in particular one of the split shown to be near E544 position discussed in our submission. Our structural modeling is providing a first structural glimpse of the structural underpinnings of the peculiar isoforms' gating and suggesting potential key interactions between S4–S5 linker, C-linker and PAS. Equally important question discussed in our study is the potential impact on the Action Potential from different ratios of isoform expression in the myocytes. The AP simulations performed in our study suggest that recovery from inactivation of hERG1 B may contribute to its physiologic role of b-isoform in the action potentials. Both structural and functional models were exploratory in nature aiming to provide a perspective for future multi-scale modeling studies.

In conclusion, the results and in-depth review of modeling, structural and functional data presented here contribute to the growing body of evidence that hERG1b significantly affects the generation of the cardiac Ikr and plays an important role in cardiac electrophysiology.

#### AUTHOR CONTRIBUTIONS

JG: Performed all of the electrophysiological recordings and mutagenesis experiments, analyze results and wrote the manuscripts. LP and PD: Wrote the software; LP, ML, and P-CY: Performed simulations and analyzed the data; CC, SN, and HD: Supervised the research; LP, HD, CC, and SN: Designed the research. All authors wrote the article.

#### ACKNOWLEDGMENTS

This work was supported by the Canadian Institutes of Health Research (to SN); and the Discovery grant from Natural Scientific and Engineering Research Council of Canada (to HD). CC was supported by the National Institutes of Health Grants R01HL128170, U01HL126273 and R01HL128537

#### REFERENCES


(together with SN). The computational support for this work was provided by West-Grid and Compute Canada through a resource allocation award and NSERC-RTI award to SN.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2018.00207/full#supplementary-material

(KCNH2) activator NS1643. J. Pharmacol. Exp. Therapeut. 342, 441–452. doi: 10.1124/jpet.111.189159


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Perissinotti, De Biase, Guo, Yang, Lee, Clancy, Duff and Noskov. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Digging into Lipid Membrane Permeation for Cardiac Ion Channel Blocker d-Sotalol with All-Atom Simulations

Kevin R. DeMarco1,2,3, Slava Bekker 1,4, Colleen E. Clancy 1,2, Sergei Y. Noskov <sup>5</sup> and Igor Vorobyov 1,2 \*

<sup>1</sup> Department of Physiology and Membrane Biology, University of California, Davis, Davis, CA, United States, <sup>2</sup> Department of Pharmacology, University of California, Davis, Davis, CA, United States, <sup>3</sup> Biophysics Graduate Group, University of California, Davis, Davis, CA, United States, <sup>4</sup> Hartnell College, Salinas, CA, United States, <sup>5</sup> Centre for Molecular Simulations, Department of Biological Sciences, Faculty of Science, University of Calgary, Calgary, AB, Canada

#### Edited by:

Blanca Rodriguez, University of Oxford, United Kingdom

#### Reviewed by:

Adam Hill, Victor Chang Cardiac Research Institute, Australia Michela De Bellis, Università degli studi di Bari Aldo Moro, Italy

> \*Correspondence: Igor Vorobyov ivorobyov@ucdavis.edu

#### Specialty section:

This article was submitted to Pharmacology of Ion Channels and Channelopathies, a section of the journal Frontiers in Pharmacology

Received: 22 September 2017 Accepted: 10 January 2018 Published: 01 February 2018

#### Citation:

DeMarco KR, Bekker S, Clancy CE, Noskov SY and Vorobyov I (2018) Digging into Lipid Membrane Permeation for Cardiac Ion Channel Blocker d-Sotalol with All-Atom Simulations. Front. Pharmacol. 9:26. doi: 10.3389/fphar.2018.00026 Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state) or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel Kv11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic) and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD) simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety pharmacology, and identifies some of the challenges that lie therein.

Keywords: hERG, long QT syndrome, cardiotoxicity, CHARMM force field, molecular dynamics, umbrella sampling, lipophilicity, water-membrane partitioning

# INTRODUCTION

The continuing failure to accurately predict the risk of drug toxicity is the primary reason for drug candidates being abandoned or approved drugs being removed from the market (Chi, 2013), illustrating the critical need for a more rational approach to drug development. One example of such a need is the longstanding failure of drug-based treatment of cardiac arrhythmias. The SWORD clinical trial (Waldo et al., 1996) famously showed that the antiarrhythmic drug d-sotalol, which we focus on in this work, actually increased mortality and risk of sudden cardiac death in patients, leading to its removal from the marketplace. Similarly, the gastrokinetic agent cisapride has been removed from the market in many countries due to its arrhythmogenic potential (Quigley, 2011), and a number of such cases for drugs and drug candidates with diverse pharmacological action has been growing over the years. Each year, over 360,000 people die in the US die from cardiac arrhythmias that are often drug-induced, demonstrating that the pharmacological assessment of cardiotoxicity still remains significantly hindered (Benjamin et al., 2017). The proposed Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative is intended to address this shortcoming by improving predictions of pro-arrhythmic drug proclivities through the combination of in vitro assays on several cardiac ion channels and multi-scale modeling and simulation (Colatsky et al., 2016; Fermini et al., 2016). Atomistic MD simulations have the potential to serve as part of such in silico screen (Clancy et al., 2016) for the development of cardiac-safe medicines, and can be used to identify molecular determinants of acquired arrhythmogenesis.

On the molecular level, drug-induced arrhythmogenesis is typically associated with the binding of drugs to cardiac ion channels, membrane proteins responsible for the propagation of electrical signal in cardiomyocytes. It is known that multiple environmental factors, including drug blockade, can modulate the gating and permeation of many ion channels. More specifically, experimental studies aimed at understanding ion channel blockade by drugs often focus on mapping binding sites at or around the intra-cellular cavity of the ion channel. This assumes, either explicitly or implicitly, that a drug (often weakly cationic) is able to diffuse from the intra-cellular space and physically occlude ion permeation. Such a mechanism is supported, for example, by the role of two intra-cavity residues (F656 and Y652) in the drug-induced current block of the voltage gated potassium channel KV11.1 (also known as hERG), which is considered a major drug anti-target due to its promiscuous binding of many drug-like molecules (Vandenberg et al., 2012).

Many of the common ion channel blockers are weak bases with a pK<sup>a</sup> of ∼7.8–8.5. Thus, at a physiological pH of 7.4, up to ∼7–28% of drug molecules remain uncharged, and therefore potentially capable of interacting with the channel by traversing a lipophilic pathway in the plasma membrane toward a binding site, either on the lipid-facing exterior of the channel or within the channel pore via passage through lipid-facing fenestrations. A possible lipophilic access route has been established for ivabradine blockade of hERG in a recent study that implicated a lipid-facing residue (M651) as critical for drug-induced blockade (Lees-Miller et al., 2015). This finding was further substantiated by the recent publication of Cryo-EM structures of hERG (putatively open), and related EAG (putatively closed) channels, suggesting that F656 and M651 can be exposed to lipids in either channel state (Whicher and MacKinnon, 2016; Wang and MacKinnon, 2017). Furthermore, hERG block by the endogenous components of cardiac membranes has also been well-established, with various lipophilic molecules including hormones (Yang et al., 2017), ceramides (Ganapathi et al., 2010; Sordillo et al., 2015), sphingosine-1-phosphate (Sordillo et al., 2015), and polyunsaturated fatty acids (Guizy et al., 2005; Moreno et al., 2012) blocking hERG but without obvious intra-cellular access to the intra-cavity site. Therefore, mapping the lipophilic pathways for common ion channel blockers and understanding the chemistry of drug-lipid interactions remains an unmet pharmacological challenge.

The complexity in understanding the lipophilic access pathways of many blockers arises from their chemical structure. Most drug molecules can coexist in multiple ionization states with different membrane permeabilities or localization on the bilayer surface and consequent access to binding sites in hERG. Hence, significant challenges exist in developing a framework for atomic-scale in silico screening and predictive pharmacology. One example is the lack of robust topologies and parameters defined for most drugs in popular MD force fields, necessitating their de novo development. This task requires computationally expensive calculations of quantum mechanical (QM) optimized molecular geometries and atomic charge distributions, and the time-consuming process of fitting molecular mechanical (MM) parameters to the optimal computed QM data. Here we have developed CHARMM generalized force field (CGENFF) (Vanommeslaeghe et al., 2010) parameters for the hERG blocker d-sotalol, which has high cardiotoxic risk (Colatsky et al., 2016) for the ventricular tachycardia characterized by Torsades de Pointes (TdP) arrhythmias (Waldo et al., 1996; Yap and Camm, 2003). Preliminary parameters for the intermediate-TdP risk compound cisapride (Colatsky et al., 2016), and low-risk compound moxifloxacin (Haverkamp et al., 2012) were developed for the purpose of comparing their membrane affinities, and will be briefly discussed as well.

Computing the free energy cost required for drugs to partition from bulk solution across the cell membrane represents a critical test for drug model viability used in MD simulations. This is because the membrane permeability of a drug not only determines its bioavailability, but is also linked to its medically

**Abbreviations:** aLQTS, acquired Long QT syndrome; CGENFF, CHARMM generalized force field; CHARMM, Chemistry at Harvard Molecular Mechanics; CiPA, comprehensive in vitro pro-arrhythmic assay; CisC, cationic cisapride; COM, center of mass; Cryo-EM, cryo-electron microscopy; DMPC, dimyristoylphosphatidylcholine; ECG, electro-cardiogram; GPU, Graphics Processing Unit; hERG, human Ether-à-go-go-Related Gene; Kv, voltage gated potassium channel; LQTS, Long QT syndrome; MD, molecular dynamics; MM, molecular mechanics; MoxZ, zwitterionic moxifloxacin; PBC, periodic boundary conditions; PMF, potential of mean force; POPC, 1-palmitoyl-2 oleoyl-phosphatidylcholine; POPS, 1-palmitoyl-2-oleoyl-phosphatidylserine; QM, quantum mechanics; SotA, anionic d-sotalol; SotC, cationic d-sotalol; SotN, neutral d-sotalol; SotZ, zwitterionic d-sotalol; US, umbrella sampling; VSD, voltage sensing domain; WHAM, weighted histogram analysis method.

relevant concentration, and pathway to its target. Many drugs are delivered to their targets via a lipophilic pathway, and drug permeation across lipid membranes is crucial for their absorption by tissue, metabolism, extraction from the body, and toxicity (ADME-Tox) (Yu and Adedoyin, 2003). This is especially relevant for predicting propensity for off-target effects of a drug, which is necessarily linked to its tissue permeability. Empirically derived ADME-Tox drug profiles, however, are inherently limited, lacking transferability to different drug classes, and providing no information regarding the structural determinants of membrane-drug distribution or kinetics (Swift and Amaro, 2013). Obtaining these measurements through MD simulation represents a final major challenge: namely, obtaining sufficient sampling of the configurational space in a modeled system to calculate accurate thermodynamic quantities of interest. Ideally, unbiased all-atom MD simulations of drug permeation across large, explicit lipid membranes would provide the most accurate kinetic and thermodynamic profiles for membranedrug interactions (Swift and Amaro, 2013), however the sampling (or simulation time) mandated by such an exhaustive approach makes it computationally prohibitive. Fortunately, more computationally tractable techniques for enhanced sampling exist that allow for the robust calculation of membrane distribution coefficients and permeability measurements of an isolated drug across a small membrane patch. We have employed one such technique, umbrella sampling (US) (Torrie and Valleau, 1977), in this report in order to compute the free energies and diffusion coefficients required for drugs to pass through the cell membrane. Similar approaches have been used for various drug molecules in a number of other studies (Carpenter et al., 2014; Di Meo et al., 2016; Bennion et al., 2017), including previous works by our groups (Boiteux et al., 2014; Yang et al., 2016). The approaches and data presented here serve as preliminary steps in overcoming the many challenges that arise in the messy task of atomistic in silico predictive cardiovascular pharmacology.

# MATERIALS AND METHODS

#### Drug Force Field Parameterization

We obtained starting molecular structures from either PubChem (Kim et al., 2016) (CID 5253 for d-sotalol) or the ZINC (Irwin and Shoichet, 2005) (3775140 for cisapride, 3826253 for moxifloxacin) databases, and used them to generate initial guesses for partial atomic charges and other force field parameters (i.e., bond lengths, bond angles, dihedral angles) using CGENFF program, version 1.0 (Vanommeslaeghe and MacKerell, 2012; Vanommeslaeghe et al., 2012).

Initial topology and parameters for SotC and SotN, were subsequently validated and optimized using QM target data following the suggested CGENFF force field methodology (Vanommeslaeghe et al., 2010). High-quality parameters not already present in CGENFF are assigned from existing parameters based on chemical analogy, with poor chemical analogy corresponding to a high penalty score for use in MD simulation (Vanommeslaeghe et al., 2012). Our optimizations focused on such high-penalty, poorly analogous parameters generated by the CGENFF program. Quantum mechanical (QM) target data for parameter optimization were obtained utilizing Møller–Plesset (MP2) and Hartree-Fock (HF) electronic structure methods and the 6–31(d) basis set using the Gaussian 09 program (Frisch et al., 2009).

MP2/6-31G(d) molecular dipole magnitude and orientation as well as scaled HF/6-31G(d) interaction energies with water were used for partial atomic charge optimization for compatibility with the CHARMM atomistic biomolecular force fields (MacKerell, 2004). The gas-phase MP2/6-31G(d) dipole, along with HF/6-31G(d) interaction energies, should be overestimated by CHARMM (by ∼16% for the latter) in order to account for polarization in aqueous media (MacKerell, 2004; Vanommeslaeghe et al., 2010). Internal bond and angle parameters were validated or modified based on comparison of MP2/6-31G(d) and CHARMM optimized geometries and scaled vibrational frequencies. For bond lengths and angles, respective differences within 0.01 Å and 1◦ between QM and CHARMM values were sought. Dihedral angle parameters were optimized to reproduce MP2/6-31G(d) potential energy scans for rotation around a particular bond. We used the Force Field Toolkit plugin (fftk) (Mayne et al., 2013) for the Visual Molecular Dynamics program (VMD) (Humphrey et al., 1996) in order to generate files for QM reference calculations and to perform parameter optimizations. We were able to achieve substantial improvement over the initial CGENFF generated parameters (highlighted in **Figure 3C** for a selected dihedral angle energy profile), with markedly better agreement between CHARMM and QM geometries, vibrational frequencies, and interactions with water. Final topology and parameters for SotC and SotN are provided in the Supplementary Information. Optimized parameters for charged cisapride and zwitterionic moxifloxacin, obtained using the same methodology, will be subsequently published after additional validation and any necessary improvement.

## Drug Membrane Partitioning: Molecular Systems

Partitioning of charged (SotC) and neutral d-sotalol (SotN), charged cisapride (CisC), and a zwitterionic form of moxifloxacin (MoxZ) were assessed using CHARMM (Brooks et al., 1983, 2009) and NAMD (Phillips et al., 2005) programs. CHARMM-GUI tool (Jo et al., 2008) was used in order to build the simulation systems, which consisted of 128 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) lipids, ∼7,000 water molecules, 21 or 22 K<sup>+</sup> and 22 Cl<sup>−</sup> ions to ensure 0.15 M electrolyte concentration and overall electrical neutrality, and one drug molecule, totaling ∼38,250 atoms.

A separate set of simulations that investigated membrane composition was equilibrated with NAMD and run on Anton 2 supercomputer (Shaw et al., 2014). In these simulations lipid membranes were composed of either pure POPC or a mixture of 85% POPC and 15% of 1-palmitoyl-2-oleoylphosphatidylserine (POPS) lipids. These systems were larger and contained ∼103,000 atoms with 256 lipids, 15 SotC or 16 SotN molecules, ∼22,800 water molecules, 50–88 K<sup>+</sup> and 50–65 Cl<sup>−</sup> ions.

CHARMM biomolecular, and compatible CGENFF forcefields were used throughout all simulations. In particular, C36 lipid (Klauda et al., 2010) and standard CHARMM ion parameters (Beglov and Roux, 1994), newly developed CGENFF drug parameters (see above) along with the TIP3P water model (Jorgensen et al., 1983) were utilized.

## Drug Membrane Partitioning: Molecular Dynamics Simulations

CHARMM simulations of SotC, SotN, CisC, and MoxZ, and NAMD simulations of SotC and SotN in a hydrated 128 lipid POPC membrane were carried out in NPT ensemble with 1 atm of pressure maintained by Langevin piston barostat (Feller et al., 1995) and 310 K temperature controlled by Nosé-Hoover thermostat (Nosé, 1984; Hoover, 1985). Tetragonal cells with periodic boundary conditions (PBC) were used in all the simulations, with P2<sup>1</sup> space group (Dolan et al., 2002) utilized in CHARMM runs. SHAKE algorithm (Ryckaert et al., 1977) was employed to fix the bonds to all hydrogen atoms, allowing a time step of 2 fs for all our simulations. Electrostatic interactions were computed via Particle Mesh Ewald (Darden et al., 1993), with a mesh grid of 1 Å.

For partitioning calculations of each drug we used the US method (Torrie and Valleau, 1977) with 81 independent simulation windows, placing the center of mass (COM) of the drug in 1 Å intervals from −40 Å to 40 Å with respect to COM of the membrane. The COM of the drug was restrained along the z axis with a force constant of 2.5 kcal/mol/Å<sup>2</sup> to provide sufficient sampling with an additional 5 kcal/mol/Å<sup>2</sup> cylindrical constraint applied to prevent the drift of the molecule in the xy plane (Li et al., 2008). Free energy or potential of mean force (PMF) profiles was computed using weighted histogram analysis method (WHAM) (Kumar et al., 1992).

SotC and SotN simulations ran for 15 ns with NAMD and 10 ns with CHARMM per window. To improve sampling, for NAMD runs we used additional US windows from −20 Å to 20 Å, whereas 7 central windows (i.e., for |z| ≤ 3 Å) were used for CHARMM SotC simulations, all running for the same simulation time as the original runs (see Supplementary text). Based on solvation analysis of SotC and SotN (Figure S5), we discarded the first 4 ns to account for equilibration. For consistency, similar procedure was followed for CHARMM simulations of CisC and MoxZ, both of which ran 10 ns/window plus additional 10 ns for the 5 central windows (|z|≤2 Å) of CisC.

Unbiased MD simulations were run for larger membrane systems with several SotC or SotN molecules. First, systems were equilibrated for 50 ns using NAMD and the simulation parameters mentioned above. Then, production simulations were run for 500 or 1000 ns (for SotN system with POPC/POPS mixed membrane) using Anton 2 software (Shaw et al., 2014) version 1.31.0. These simulations were carried out using tetragonal PBC in the NPT ensemble at 310 K, a 2 fs time step with non-bonded long range interactions computed every 6 fs using the RESPA multiple time step algorithm (Tuckerman et al., 1992). The multi-integrator (multigrator) algorithm (Lippert et al., 2013) was used for temperature and semi-isotropic pressure coupling, whereas a novel u-series method (Shaw et al., 2014) was used for handling long-range electrostatic interactions. An electric field in the z direction was applied, gradually increasing from 0 to 160 mV during the first 100 ns of the simulation. A long-range Lennard-Jones (LJ) correction (beyond cutoff) was not used as was suggested for C36 lipid force field (Klauda et al., 2010).

#### Drug Membrane Partitioning: Simulation Analyses

Solvation numbers were computed as number of oxygen atoms of water, lipid phosphate or ester functional groups within 4.25 Å of drug non-hydrogen atoms, with this distance cutoff obtained from an analysis of corresponding radial distribution functions (see Figure S6). Drug orientation was computed based on a polar angle θ between z axis corresponding to a bilayer normal and drug N1...S vector, which is almost anti-parallel to its dipole orientation (see **Figure 3**). Average angles were computed as:

$$<\theta\_{\text{N1\dots S}} \succ = \text{atan2}(<\sin\theta \succ, <\cos\theta \succ) \tag{1}$$

whereas corresponding order parameters were computed as (Vorobyov et al., 2012)

$$S\_{\text{N1\dotsS}} = \mathbb{W}(\text{3 } < \cos^2 \theta > -1) \tag{2}$$

Drug water-membrane partition coefficients were calculated as (Vorobyov et al., 2012):

$$K(\text{wat}\rightarrow\text{mem}) = \frac{1}{z\_2 - z\_1} \int\_{z\_1}^{z\_2} e^{-\frac{\left[W(\varepsilon) - W(\varepsilon\_1)\right]}{k\_B T}} dz\tag{3}$$

where W(z) is the PMF, z<sup>1</sup> and z<sup>2</sup> are points in aqueous solution on opposite sides of the membrane, k<sup>B</sup> is Boltzmann constant, and T is the absolute temperature. Partitioning free energies were calculated as

$$
\Delta G(\text{wat} \rightarrow \text{mem}) = -k\_{\text{B}}T \ln K(\text{wat} \rightarrow \text{mem}) \tag{4}
$$

Error bars were estimated from PMFs by propagation of uncertainties.

To estimate the 1D diffusion constant in the z direction, D(zi), we analyzed the corresponding US windows with Hummer's method (Hummer, 2005):

$$D(z\_i) = \frac{\langle \delta z^2 \rangle\_i}{\mathfrak{r}\_i} \tag{5}$$

where δz 2 i and τ<sup>i</sup> are the mean square deviation from the average position and the position correlation time for US window i.

$$\tau\_i = \lim\_{s \to 0} \tau\_i(s) = \lim\_{s \to 0} \frac{\left\langle \begin{matrix} \mathbb{C}\_z(s; z\_i) \end{matrix} \right\rangle}{\left\langle \delta z^2 \right\rangle\_i} = \lim\_{s \to 0} \frac{\int\_0^\infty e^{-st} \left\langle \delta z(t) \delta z(0) \right\rangle\_i dt}{\left\langle \delta z^2 \right\rangle\_i} \tag{6}$$

Cˆ <sup>z</sup>(s; zi) is the Laplace transform of the position autocorrelation function Cz(t; zi):

$$
\hat{C}\_z(s; z\_i) = \int\_0^\infty e^{-st} C\_z(t; z\_i) \, dt \tag{7}
$$

where Cz(t; zi) = δz(t)δz(0) i , s is the inverse time and δz = z − hzi<sup>i</sup> is the drug COM position displacement.

Values of τi(s) were calculated at s-values 0.01, 0.02, . . . , 0.1, 0.2, . . . , 1.0, 2.0, . . . , 10.0 ps−<sup>1</sup> . τi(s) were extrapolated to s = 0 by fitting the function a/(s+b), where a and b are parameters, in the s range from 0.02 to 1.00 ps−<sup>1</sup> . See our previous study (Vorobyov et al., 2014) for more details.

Based on PMF and diffusion coefficient profiles we computed water-membrane drug permeability rate as,

$$P = \left(\int\_{-L/2}^{L/2} \frac{\exp\{W\_z / k\_B T\}}{D(z)} \,\mathrm{d} \, z\right)^{-1} \tag{8}$$

an integral over the local bilayer resistance (Marrink and Berendsen, 1994), spanning −14≤ z ≤14 Å for SotN and −20≤ z ≤20 Å for SotC (with PMF-values adjusted to be 0 at the borders), where the drug is expected to cross a central barrier; essential for modeling permeation via a single molecule PMF (Roux and Karplus, 1991). This description assumes we are in the diffusion limit, where the mean velocity is proportional to the mean force, which is valid if the drug displacement correlation length is short compared to the spatial variations in the force (Marrink and Berendsen, 1994).

## RESULTS

#### Comparative Ionized Drug Membrane Partitioning

First, we studied membrane partitioning of SotC and compared it to the partitioning of CisC and MoxZ, each drug form representing the dominant protonation state in aqueous solution at the physiological pH. We studied their translocation across POPC membranes using US MD simulations, which allow for more efficient sampling of energetically unfavorable drug distributions across a lipid membrane compared to conventional unbiased MD simulations. US works by restraining drug positions at different values of z across the membrane using a harmonic potential. Thus, we can compute free energy for drug positions along the bilayer normal, with z = 0 corresponding to membrane center.

When all 3 drugs are located near z = 0 (see **Figure 1A**), we observed substantial membrane deformations, where they are coordinated by water molecules and lipid headgroups from one (for CisC) or both (for SotC and especially for MoxZ) membrane interfaces. Not surprisingly, such membrane deformations lead to substantial energetic penalties for ionized drugs to move across the membrane with the peak values at z = 0: around 18 kcal/mol for MoxZ, 10 kcal/mol for SotC and just 5 kcal/mol for CisC. Interestingly, such differences in peak free energy values correlate with computed MM drug dipole moments, which are 41.3 Debye for MoxZ, 15.5 Debye for SotC and 6.8 Debye for CisC for the same drug molecule "standard" positions and orientation (as defined by Gaussian software). For MoxZ, extensive membrane deformation exhibited by both leaflets are due to the positively charged ammonium and negatively charged carboxylate moieties at opposite ends of the molecule (**Figure 1C**). For SotC, a cationic secondary ammonium and polar sulfonamide groups can also attract water molecules or lipid headgroups. Both SotC and MoxZ can stretch along the membrane normal to interact with both bilayer interfaces. However, the situation is different for CisC, which also has several polar functional groups and a positively charged tertiary ammonium functionality at the center of the molecule, but it is floppier than those drugs and seems to be attracted to one membrane interface (see **Figure 1**). Also, CisC has a pronounced binding trough of around −3 kcal/mol at 14 ≤ |z| ≤ 17 Å. This suggests, that unlike SotC and MoxZ it will accumulate at water—membrane interface. The presence of the binding trough will also inadvertently increase a barrier a drug will need to overcome to cross a membrane from ∼5 to 8 kcal/mol (see **Figure 1B**). These calculations suggest fairly high but surprisingly different energetic costs to cross the membrane for this collection of ionized molecules.

#### Models of d-Sotalol

We performed a more detailed analysis of different protonation states of d-sotalol, focusing on the energetics of its membrane crossing. Like many other drugs in aqueous solution, d-sotalol can exist in several protonation states depending on solution pH and other factors, such as proximity to specific protein residues. Data from the literature indicate that aqueous pKa-values for dsotalol are 8.3 and 9.8 attributed to deprotonation of sulfonamide and secondary ammonium functionalities, respectively (Foster and Carr, 1992; Hancu et al., 2014). This indicates that at physiological pH 7.4, SotC is the predominant form (around 89%), while deprotonation of the sulfonamide functionality leads to a second dominant SotZ form (around 11%). At more basic pH, the secondary ammonium functionality will deprotonate as well, leading to a negatively charged, anionic form SotA (**Figure 2**).

However, there is yet another possibility, in which deprotonation of secondary ammonium group occurs first, leading to a neutral d-sotalol form (SotN). In fact, there is likely an equilibrium, and possibly interconversion, between SotN and SotZ forms, in which either one is favored depending on the polarity of the surrounding medium. We expect that a substantially less polar SotN form would be favored in the hydrophobic environment of the lipid membrane interior based on our MoxZ simulations discussed above, whereas a more polar SotZ might be favored in aqueous solution. Unfortunately, there are no experimental data to address this issue for d-sotalol. We performed a series of implicit solvent QM calculations, which seem to indicate slight preference for SotN even in bulk water (see Supplementary text for more information), but their accuracy is very uncertain. However, a recent experimental study using a combination of potentiometric titration and spectrophotometry measurements has suggested around 90% of zwitterionic and 10% of neutral form of moxifloxacin is present at physiological pH range, and that only a neutral form contributes to drug partitioning into a non-polar environment of lipid membranes or 1-octanol often used as a membrane mimetic (Langlois et al., 2005). This suggests that a neutral form of a drug is likely the one to undergo an unassisted membrane translocation.

and lipid tails as wireframes. (B) PMF profiles for POPC membrane crossing for 3 drugs shown in (A). Error bars represent measures of asymmetry. (C) Chemical structures of those drugs drawn using MarvinSketch program.

Since we are particularly interested in lipophilic access of cardiotoxic drugs known to block hERG, we have developed standard CHARMM (Klauda et al., 2010) compatible models of d-sotalol in charged (SotC) and neutral (SotN) forms. The QM and MM dipole moments for those d-sotalol forms and drug water interactions probed for the model optimizations are shown in **Figures 3A**,**B** for SotN and SotC, respectively. Optimized CHARMM charges (Table S3) provide good agreement with QM target dipole values. The optimized MM dipole moments point in same direction (<1 ◦ difference in angle between QM and MM for both SotC and SotN) and are each within 20% difference in magnitude (SotN 6%, and SotC 14%). The water interaction distances were all within 0.4 Å of QM target values (see Tables S4, S5). The dipole moment is significantly higher for SotC (17.64 Debye), than for SotN (5.98 Debye), as is to be expected for charged vs. neutral species and in agreement with QM-values. Interaction energies with water were also in good agreement with QM-values with root mean square (RMS) and maximum errors of 0.8 and 1.5 kcal/mol for SotN (Table S5) as well as 1.6 and 3.0 kcal/mol (see Table S4) for SotC, respectively. No internal (bond, angle, dihedral angle) parameters needed to be optimized for SotC, whereas for SotN there was a high penalty score for the C2-N1-C3 bond angle (shown by blue arrow in **Figure 3C**), and optimization yielded a difference of 0.86◦ (i.e., <1 ◦ as required) between MM and QM values. Also for SotN, 7 dihedral angle parameter optimizations yielded marked improvement over CGENFF initial guesses (illustrated in **Figure 3C** for SotN C8-C3-N1-C2 dihedral angle highlighted in pink, with all the dihedral scan profiles shown in Figure S2), with optimized torsional energy minima within ∼0.5 kcal/mol of QM values. For comparison, raw CGENFF dihedral parameters with high penalties yielded QM energy minima differences sometimes as high ∼2 kcal/mol. These optimized parameters represent a significant improvement over initial guesses and should yield more accurate computed energetics from MD simulations.

At this time, we were not able to develop empirical models of the SotZ and SotA forms of the drug (**Figure 2**), since a negatively charged sulfonamide nitrogen atom type does not exist in either CHARMM biomolecular, or generalized (CGENFF) force fields. The fraction of these forms in aqueous solution or other media is uncertain, but based on a very high free energy barrier for zwitterionic moxifloxacin translocation (**Figure 1** and discussion

above) as well as the very large dipole moments for SotZ and SotA (see Table S1 and Supplementary text), we do not expect them to contribute substantially to the passive diffusion of d-sotalol across a lipid membrane, or the lipophilic access of this drug to hERG or other protein targets.

We should also mention that sotalol has a chiral center at C1 atom (shown by an asterisk in **Figures 2**, **3C**), and in this study we only focused on S-enantiomer, d-sotalol. However, the developed force field parameters can be also used for Renantiomer, l-sotalol, which will be also considered in our subsequent studies.

#### d-Sotalol Solvation and Orientation across the Membrane

We used our SotC and SotN models to investigate their interactions with a lipid membrane as they move across using US MD simulations. For those simulations we applied extensive sampling, especially important for hindered drug reorientation in the membrane interior (see Supplementary text for more information). We also performed those simulations with two popular biomolecular modeling packages, NAMD and CHARMM, with the former being more computationally efficient on our GPU (Graphics Processing Unit) cluster. However, CHARMM allows using P2<sup>1</sup> symmetry to take into account likely changes in the areas of top and bottom bilayer leaflets as a drug moves through the membrane by shuffling lipid molecules between them as it happens. We established that the lipid membrane properties of our simulated systems are in agreement with experimental data in this case (See Supplemental text).

We then started to investigate membrane—drug interactions, first, by looking at equilibrated system snapshots at the membrane center (z = 0 Å) and water/membrane interfacial region |z| = 14 Å, corresponding to free energy minimum for SotN (see **Figure 4**). It can clearly be seen that both charged and neutral drug molecules can adapt different orientations with respect to the membrane normal and can be solvated by both water molecules and lipid head groups even deep in the membrane interior for SotC in agreement with our CHARMM multiple-drug simulations shown in **Figure 1** and discussed above. Interestingly, that in NAMD simulation snapshots shown in **Figure 4**, we observed that SotC while held around membrane center (z = 0) can adopt different long-lasting (see below) orientations "grabbing" water molecules and lipid head groups from either top or bottom membrane interface, but did not observe them making interfacial connections to both leaflets, as was observed in our CHARMM simulations (**Figure 1**).

Next, we performed a quantitative analysis of drug solvation shown in **Figure 5.** While SotC and SotN are found in bulk water regions, for |z| > 25 Å (∼5 Å beyond phosphate groups), they are solvated by ∼5.5 and 5 water molecules, respectively. We defined the interfacial region as 15 < |z| < 25 Å, where 15 Å boundary was established based on an experimentally determined POPC hydrophobic thickness of 28.8 ± 0.6 Å (Kucerka et al., 2011). The water coordination remains the same as in bulk, until the drug reaches inside the core of the membrane, where we observe a bigger drop in the number of water molecules solvating SotN. In the center of the bilayer, at z = 0 Å, almost no water molecules are found coordinating the neutral drug, while at

least 1.2 water molecules continue to coordinate the charged species. Additionally, when SotC is found at the interface or the hydrophobic core of the membrane, it is coordinated by lipid phosphate and carbonyl groups, while SotN remains virtually uncoordinated by these functional groups in the membrane core and has a similar coordination by carbonyl O and smaller by phosphate O atoms in the interfacial region (**Figure 5**).

Such solvation results in the preferential orientation of both SotC and SotN with respect to bilayer normal (coinciding with the z axis) as shown in **Figure 6**. There is no preferred orientation of both drugs in bulk water as expected, which is exemplified by average θ being around 90◦ and order parameter being 0 (see **Figure 6** and top right panels in Figures S7, S8 for time series). There is a strong preference for N1...S vector of both drugs to be aligned with the z axis in the outer interfacial region i.e., at 20 < |z| <25 Å, whereas there is some tendency for drugs to lie perpendicular to the membrane normal i.e., in the membrane plane (with order parameter S < 0) in the inner interfacial and outer core regions at 10 < |z| < 20 Å (see Figures S7, S8 for time series). In the inner core region (|z| < 10 Å) the drugs again become aligned or anti-aligned with the z-axis. Interestingly, the orientation of SotN and SotC in the inner interfacial and core regions seem to be opposite—with SotC favoring parallel orientation and SotN—antiparallel with the membrane normal for the drug positions with the negative zvalues (**Figure 6**). This results from different relative affinities of SotC and SotN functional groups: the cationic ammonium group in SotC strongly attracts water molecules and lipid head groups, whereas its deprotonation makes its sulfonamide functionality a better attractor leading to this functional group re-orientation to be closer to the membrane interface. These interactions lead to hindered rotation (see Figures S7, S8) on the time scale of MD simulations we performed here (10–15 ns for each drug z) leading to difficulties sampling thermodynamics of drug membrane interactions discussed below (see Supplemental text for more details).

## d-Sotalol Energetics and Protonation across the Membrane

We computed free energy profiles for SotC and SotN moving across a POPC membranes based on analysis of drug position fluctuations around restrained z positions in US MD simulations as described above. Those profiles are shown in **Figure 7A** for both NAMD and CHARMM simulations. For SotN, differences between NAMD and CHARMM free energies are within

FIGURE 4 | Representative snapshots of charged (SotC) and neutral (SotN) d-sotalol moving across a POPC membrane from umbrella sampling MD simulations. Reference d-sotalol center of mass (COM) z positions with respect to membrane COM are shown on the top. See Figure 1 caption for molecular representation and coloring information. Two structures for z = 0 for each drug represent final system snapshots from two independent simulations with a different initial drug orientation (see Supplementary text for more information).

uncertainties (shown as error bars in **Figure 7A**), obtained as measures of profile asymmetries (see Figure S9 and Supplemental text). However, for SotC the free energy barrier is ∼3 kcal/mol smaller for CHARMM (11.2 ± 1.1 kcal/mol) compared to NAMD (14.4 ± 0.1 kcal/mol). Such free energy decrease along with a flat free energy profile for |z| < 3 Å can be due to P2<sup>1</sup> point group transformations used in CHARMM simulations. This is also in line with interfacial connections to both bilayer interfaces seen in these simulations (see **Figure 1** and discussion above). However, relatively large asymmetries of up to ∼2 kcal/mol (Figure S9) preclude us from an unambiguous assignment of this difference.

If we compare SotC and SotN free energy profiles shown in **Figure 7A**, we will see differences such as substantially higher central peak for SotC, e.g., 14.4 vs. 5.4 kcal/mol for SotN from NAMD simulations, as well as presence of a deep interfacial minimum of −2.8 kcal/mol for SotN at |z| = 14 Å, similar to one seen for cationic cisapride (**Figure 1** and discussion above). Such minimum indicates a substantial neutral drug accumulation at the water-membrane interface. Interestingly, there is practically no such minimum for SotC, although, a shallow ∼-1 kcal/mol trough can be seen on a not-symmetrized PMF profile in Figure S9. The substantial difference in peak heights for SotC and SotN is not unexpected, however, and was also observed for basic amino acid side chains in our previous simulations (Li et al., 2008, 2013). It can be explained by different molecular mechanisms governing SotC and SotN permeation: substantial membrane deformations for the former and nearly complete drug dehydration for the latter (Vorobyov et al., 2010, 2014; Li et al., 2012, 2013). Based on free energy difference between charged and neutral drug forms we can also approximate pK<sup>a</sup> shift and thus preferred protonation form of a drug across the membrane:

$$
\Delta p K\_{\rm a} = 1/(2.303 k\_{\rm B} T) \quad \{\Delta W\_{\rm SotN}(z) - \Delta W\_{\rm SotC}(z)\} \tag{9}
$$

where k<sup>B</sup> is Boltzmann constant, T—absolute temperature and 1W (z) are position-specific free energies for charged and neutral d-sotalol. Corresponding 1pK<sup>a</sup> profiles are shown in **Figure 7B** and indicate rapid downward 1pK<sup>a</sup> shifts soon after the drug gets into contact with membrane. Near the membrane center 1pK<sup>a</sup> reaches about −6.5 for NAMD and −4.5 for CHARMM based calculations, with the latter estimate being smaller due to a ∼3 kcal/mol smaller SotC free energy barrier discussed above. Qualitatively, both results are similar and indicate rapid drug deprotonation soon after a drug starts moving across a

membrane. In fact, considering its first aqueous pK<sup>a</sup> of 8.3, even getting as close as 20 Å to the membrane center will already lead to drug deprotonation. However, it should be noted that we have not considered a possible role of a zwitterionic d-sotalol form, SotZ, in this equilibrium.

for a few representative RDF profiles. Error bars shown in all the graphs are

computed from profile asymmetries.

#### d-Sotalol Water-Membrane Partitioning and Permeations: Connection to Experiments

Next, we need to attempt connecting our findings to experimental observables such as water—membrane partitioning coefficient K and permeability rate P. All the relevant data are summarized in **Table 1**. There is an experimental estimate for water—dimyristoylphosphatidylcholine (DMPC) membrane K ′ (wat→mem) of 2.50 obtained at 303 K (Redman-Furey and Antinore, 1991). This is an apparent value, which takes into account a pH-dependent fraction of membrane-active drug species at those conditions. However, since we know that only SotN is expected to accumulate in the membrane we can compute an intrinsic K-value at experimental pH = 7.2 using drug aqueous pK<sup>a</sup> = 8.37 and Henderson-Hasselbach equation to obtain K(wat→mem) = 2.50 <sup>∗</sup> 10(8.37−7.20) = 37.0. And corresponding partitioning free energy is 1G(wat→mem) = −RT ln K(wat→mem) = −2.17 kcal/mol. These estimates, again, do not take into account a presence of SotZ form in the drug protonation equilibrium, which will likely further increase K-value and decrease corresponding 1G. Nevertheless, we can compare experimental estimates with values we computed from NAMD US free energy profiles using Equations (3) and (4). Estimated K(wat→mem) and 1G(wat→mem) values for SotN of 13.4 ± 8.6 and −1.6 ± 0.4 kcal/mol (see also **Table 1**), respectively, are in good agreement with experiment also considering a different lipid (POPC vs. DMPC) and temperature

(310 vs. 303 K) used in simulations and experiment. Estimates from CHARMM simulations (Table S6) are similar, within an error of NAMD values. As expected, SotC does not accumulate in the membrane, with K(wat→mem) and 1G(wat→mem) of 0.69 ± 0.36 and 0.23 ± 0.0.28 kcal/mol, respectively (**Table 1**).

computed from profile asymmetries. See Figures S7, S8 for a few

representative θ(N1...S) time series.

MD simulations of water-membrane partitioning are a good test of the drug model accuracy, and can predict how much drug accumulates in the membrane compared to bulk water. However, it does not consider the kinetics of drug movement across a membrane, which is also essential for predicting its pharmacology and toxicology. Permeability rates, P, provide corresponding estimates and are measured experimentally using different cell lines such as caco-2 or artificial membrane systems such as PAMPA (Parallel Artificial Membrane Permeability Assay) (Bermejo et al., 2004). Experimental estimates for dsotalol P are available from a recent study (Liu et al., 2012) with a PAMPA P-value of 3.2 × 10−<sup>7</sup> cm/s. A direct comparison between experimental and computed P values is known to be challenging, with many complicating factors precluding direct quantitative assessment of absolute values (Carpenter et al., 2014;

Di Meo et al., 2016; Bennion et al., 2017). Nevertheless, we computed P estimates for both SotC and SotN using Equation (8) as was done in our previous study (Vorobyov et al., 2014) based on free energy and diffusion coefficient profiles. The latter, shown in **Figure 8**, were obtained based on correlation times and mean fluctuations of drug COM in z direction using Equation (5) as was also done previously (Vorobyov et al., 2014). The computed diffusion coefficient profiles indicate a rapid 10-fold drop of diffusion coefficients for both SotC and SotN as drug molecules start interacting with lipid membranes, similar to many previous observations (Carpenter et al., 2014; Vorobyov et al., 2014). Interestingly, diffusion coefficients for SotC and SotN are similar, both in water and in the membrane interior (**Figure 8** and **Table 1**), despite difference in net charge and very different drug—membrane interactions. Computed Pvalues, presented in **Table 1** as log P of −8.57 for SotC, and −4.43 for SotN encompass an experimental estimate of −6.50. Based on those values alone, we cannot comment on accuracy of our prediction, and comparison with values for other drug molecules (desirably, with similar functionalities) as was done in a recent study (Bennion et al., 2017) would be the best. What our computed values indicate though, that a neutral drug is about

FIGURE 8 | Analysis of d-sotalol diffusion from umbrella sampling MD simulations. Diffusion coefficient profiles are computed as described in the text. Error bars shown are computed from profile asymmetries.

TABLE 1 | Water-membrane partitioning and permeability data from umbrella sampling MD simulations for charged (SotC) and neutral (SotN) d-sotalol translocation across a POPC membrane using NAMD.


<sup>a</sup>Redman-Furey and Antinore (1991) using pK<sup>a</sup> = 8.3 to compute intrinsic values based on observed apparent K′ (wat→mem) of 2.50.

<sup>b</sup>Liu et al. (2012) using measured PAMPA permeability rate.

4-orders of magnitude more permeable compared to a cationic one, and that both values are within few orders of magnitude of an experimentally observed permeability.

#### d-Sotalol—Membrane Interactions: Effect of Anionic Lipids

Thus far, we only considered d-sotalol partitioning across a POPC membrane using US MD simulations for a single drug molecule. However, we also tested if lipid membrane composition affects drug—lipid interactions. In fact, cardiomyocyte lipid membrane is known to host multiple lipid types: in addition to dominant zwitterionic phosphatidylcholine and phosphatidylethanolamine, it also has a substantial fraction of anionic lipids—phosphatidylserine, phosphatidylinositol and

d-sotalol pKa shifts computed from PMFs in (A).

phosphatidic acid [6–13% in human (Post et al., 1995) or 17–18% in feline cardiac cells (Leskova and Kryzhanovsky, 2011) based on total phospholipid content]. Anionic lipids are expected to increase membrane binding affinity for cationic drug forms and other cations, as was evidenced by our previous study where we saw increase in the interfacial binding for a positively charged arginine side chain analog, methyl guanidinium, in the presence of an anionic lipid phosphatidylglycerol (Vorobyov and Allen, 2011). The possible effect of anionic lipids on neutral drug binding is less clear and is worth testing as well. Therefore, we performed simulations of both SotC and SotN in lipid membranes containing 15% POPS and 85% POPC, respectively, and compared the results to corresponding drug simulations with pure POPC membranes.

We used 500 or 1000 ns long unbiased MD simulations with multiple (15–16) drug molecules initially placed in bulk aqueous solution, corresponding to ∼40 mM drug concentration. Most SotN molecules become bound to the lipid membrane within 200 ns for the simulation with pure POPC and around 400 ns with a POPC/POPS mixture (see Figure S11). The equilibrium aqueous concentration of SotN drops to ∼8 mM for POPC/POPS and ∼5 mM for a POPC only system. For systems containing SotC, most drug molecules remain in aqueous solution throughout the simulations with only ∼4 (out of 15) interacting with membrane regardless of the lipid composition (Figure S11). Equilibrated systems are shown in **Figure 9C** demonstrating substantial membrane binding of SotN but not of SotC. Drug probability distributions from those simulations, computed based on simulation data after equilibration (which was achieved in 200 or 400 ns), are shown in **Figure 9A.** These data confirm the picture demonstrating substantial interfacial binding for SotN with well-defined probability maxima around |z| = 15 Å for both POPC and POPC/POPS systems. No interfacial binding was detected for systems containing SotC (**Figure 9A**). In the cationic sotalol system with POPS present, there is a slightly increased accumulation of the drug density in |z| range of 15–30 Å compared to a system with POPC only. This can be due to expected attraction between anionic lipid head groups of POPS and positively charged SotC moieties. However, the effect is small and is thus unlikely to be physiologically significant in this case.

The probability distributions shown in **Figure 9A** can be converted to free energy profiles as 1G(z) = –kBT ln ρ(z), where ρ is probability density, k<sup>B</sup> is Boltzmann constant, and T is the absolute temperature (see also analogous Equation 4 above). Those profiles are shown in **Figure 9B** and are in general agreement with those from US MD simulations shown in **Figure 7A** previously. As expected, we did not observe SotC located near the membrane center during 500 ns of unbiased MD simulations, and therefore free energy profiles are not defined in this region. However, we observe that the slope of the profile is steeper in the presence of POPS, suggesting a higher translocation barrier and hence slower translocation in this case. SotN molecules were distributed throughout the membrane, and thus we could compute complete free energy profiles including central peaks. Interestingly, there are shallower interfacial binding troughs (by 0.5–0.6 kcal/mol at |z| = 14–15 Å), higher central peak (by ∼1.1 kcal/mol) and thus larger translocation barriers in the presence of POPS, indicating less favorable membrane binding and slower translocation rates for SotN. Upon comparison of SotN free energy profiles from US and unbiased MD simulations, shown in **Figure 7A**, **9B**, respectively, we observed a substantially smaller central free energy peak (by 3.7 kcal/mol) and shallower interfacial binding (by 0.6 kcal/mol) in unbiased simulations. There are several factors which can contribute to such differences, including multiple drug molecules, larger membrane patch, and presence of applied electric field in unbiased MD simulations, all of which can possibly lead to smaller permeation barriers. A detailed elucidation of these and other factors is beyond the scope of this study and will be investigated in our subsequent works.

# DISCUSSION

# Exploring Ionized Drug Membrane Partitioning

At physiological pH many cardiac channel blockers exist in aqueous solution mostly in their cationic form for dsotalol and cisapride, and zwitterionic form for moxifloxacin (ionized, but with net zero charge). Our MD simulations have demonstrated that all of them cause substantial membrane deformations, with lipid head groups and water molecules coordinating them deep into the hydrophobic membrane core. Large free energy barriers occur at the center of the membrane as a result of the deformations, making such mode of drug translocation unlikely. Moreover, ionized d-sotalol and moxifloxacin do not demonstrate any interfacial membrane binding, indicating that they will not be accumulating there, and thus limiting their protein target accessibility through this route. Interfacial membrane binding is, however, possible for cationic cisapride, and its accumulation there could play a role in its pharmacological profile. However, to provide a more complete picture for drug membrane translocation and membrane-mediated protein target affinity, additional less-polar drug protonation states should be considered. This is what we did for d-sotalol; a prominent example of high-arrhythmia risk hERG blocker. At a physiological pH of 7.4, 89% of this drug exists in a cationic form, indicating a ∼1.3 kcal/mol energetic penalty for its deprotonation, which can be easily overcome by the hydrophobic environment of lipid membranes that provide a barrier for charged and polar species (Gennis, 1989).

## Computing Charged and Neutral d-Sotalol Membrane Partitioning

In addition to a cationic d-sotalol force field model, we developed parameters for one of the neutral forms of dsotalol. SotN is substantially more lipophilic, as expected, with a free energy penalty near the membrane center of ∼5 kcal/mol, compared to ∼15 kcal/mol barrier for the cationic species, which, interestingly, correlates with the ratio of their dipole moments. Moreover, unlike SotC, SotN accumulates at the water-membrane interface, making it accessible for binding to protein targets through the lipophilic

pathway. Such accumulation, which can be quantified by water-membrane partitioning coefficient, K(wat→mem), is in agreement with experiment (within an uncertainty, see **Table 1**), suggesting a good quality of the developed empirical model.

Also, SotN does not lead to substantial membrane perturbations; it transiently coordinates with only a few water molecules as it moves across a hydrophobic core of a membrane, unlike SotC. This entails different molecular mechanisms of membrane translocation: a traditional "solubilitydiffusion" for SotN governed by drug dehydration, and so called "ion induced defect" for a cationic form, where a cost of membrane deformation plays a major role as was suggested in our previous studies on charged amino acid side chain and small hydrophilic ion translocation (Li et al., 2012; Vorobyov et al., 2014). Thus, we can expect very different dependence of their membrane translocation energetics on lipid membrane composition, such as a strong decrease with a corresponding reduction in membrane thickness for SotC, but not for SotN. This is why we expect good agreement with experiment for SotN water-membrane partitioning despite using a different lipid bilayer (POPC vs. DMPC). Translocation of SotC, however, is expected to be very sensitive to the mechanical properties of membrane such as thickness, as well as the presence of cholesterol, or polyunsaturated fatty acid tails, which can increase or reduce membrane rigidity, respectively (Feller et al., 2002; Pitman et al., 2004). Our computed membrane translocation energetics for charged cisapride and neutral d-sotalol across POPC membrane are very similar, but we expect a larger barrier for cisapride in thicker and/or cholesterol-containing membranes. This will lead to different modulation of drug accessibility for intracellular and membrane-located protein targets. As a first step toward the investigation of lipid composition dependence, we briefly examined the role of anionic lipids in water-membrane d-sotalol partitioning energetics. Despite expected more favorable drug membrane binding in the presence of POPS, we observed an opposite trend with shallower interfacial troughs for SotN and larger translocation barriers for both SotN and SotC. This indicates that such modulation can be due to specific drug—membrane interactions rather than a general electrostatic attraction.

# Estimating d-Sotalol Membrane Permeation Kinetics

For SotC and SotN, we also provide estimates of membrane translocation kinetics, expressed as permeability rates (P). SotN has a translocation rate that is four orders of magnitude faster than SotC (see **Table 1**), which is as expected from the difference in their membrane translocation energetics, and similarly reduced diffusion coefficients in the membrane interior. This is in agreement with our previous estimations for ions (Vorobyov et al., 2014) and other drugs (Boiteux et al., 2014). Based on the computed P-values and the membrane thickness considered in those calculations, we estimate that a single SotN molecule can translocate between interfacial binding sites on opposite sides of the membranes in about 7.5 × 10−<sup>3</sup> s (millisecond time range), whereas for SotC crossing membrane will take around 150 s. SotN is expected to be accumulated in the membrane over 10 fold compared to its equilibrium concentration in bulk aqueous solution, which is why we are considering its permeation, even though it is a minor component in the bulk aqueous solution at the physiological pH, regardless of its unknown ratio to a membrane-impermeable zwitterionic form. An experimental P estimate for d-sotalol based on measurements using PAMPA is in between our computed values for SotC and SotN (see **Table 1** and Liu et al., 2012). Yet, a direct numerical comparison of our computed and experimental P estimates is extremely challenging, as has been indicated in many previous studies (Orsi et al., 2009; Carpenter et al., 2014; Di Meo et al., 2016; Bennion et al., 2017). This is largely because experimentally measured quantities mostly represent so-called apparent values, which typically include contributions from different drug protonation forms at experimental pH, depend on water layer thickness and condition, and may encompass different drug permeation routes (Bermejo et al., 2004; Avdeef et al., 2005; Ottaviani et al., 2006; Orsi et al., 2009). More standardized intrinsic P-values for neutral drug forms are typically harder to get (Bermejo et al., 2004; Orsi et al., 2009), and even then, quantitative agreement with MD computed values remains challenging due to substantial differences between an experimental macroscopic system, and a microscopic molecular model. Therefore, an agreement between relative P-values for different drugs is typically sought (Orsi et al., 2009; Carpenter et al., 2014; Bennion et al., 2017), which will be explored in our future studies.

### Predicting Possible Membrane-Mediated Ion Channel Accessibility Pathways

One mode of ion channel block by drugs is through an intracellular aqueous pathway, where a drug in the cytosol passes through a channel lower gate, when it is open, and occludes a channel pore (Hille, 2001). Another possible mechanism for ion channel block is through a lipophilic route, which was observed in a recent MD study for a local anesthetic, benzocaine, entering a central pore of sodium voltage-gated channel NavAb via lipidfacing channel openings (fenestrations) (Boiteux et al., 2014). In the case of the hERG blocker d-sotalol studied here, SotN would likely to be a dominant drug form binding to the channel via this route, but it could become protonated again once it is in the pore.

Our recent combined experimental/computational studies of pH- and state-dependent hERG block by another high-risk proarrhythmic drug dofetilide (sharing the same functional groups as d-sotalol, but more potent) suggested that drug protonation equilibrium plays a crucial role in its channel binding affinity (Wang et al., 2016). To the best of our knowledge, no such studies have been done for d-sotalol yet. The experimentally measured on-rate of d-sotalol binding to hERG is quite slow, in the range of several minutes (Numaguchi et al., 2000). This is consistent with our computed membrane permeation rate for cationic d-sotalol form. Recent experimental studies using cells pre-equilibrated with sotalol, i.e., after the drug crossing cell membranes, demonstrate faster than 200 ms hERG block (Li et al., 2017; Windley et al., 2017), indicating that drug membrane permeation could be a rate-limiting step considering preferential drug channel access via the intracellular aqueous pore. However, other reasons for such outcome, such as a preponderance of a lipophilic channel access pathway from of a local membrane bound pool of the drug, suggested by our neutral d-sotalol simulations, are possible and can be tested by additional experiments as well as comprehensive drug—channel MD simulations. This along with pH-dependent measurements can help elucidating roles of different drug protonation states and their contribution to channel block.

Moreover, experimental drug—channel on-rates, which are crucial components of functional scale kinetic models used for in silico evaluation of pro-arrhythmia proclivities (as in the CiPA initiative), can be corroborated using atomistic MD simulations, such as those presented in this study. Moreover, atomistic MD simulations can be used to identify different drug—channel interaction pathways not easily discernable via experiment alone. For instance, through comparison of computed rates for drug membrane translocation and binding to the channel via aqueous and lipophilic pathways, we can predict likely rate limiting step, and relative contributions of all those processes to experimentally measured rates, thus informing kinetic models and likely improving their accuracy and predictive power. The spatially resolved ionization-state-specific drug localization profiles and water—membrane permeation rates computed here represent the first crucial step toward this goal.

Further insight into structural determinants of drug-induced channel blockade, including possible drug access pathways, can be provided by comprehensive mutagenesis studies, similar to one done recently for a large set of congenital long QT syndrome 2 associated hERG mutations (Anderson et al., 2014). Though not directly related to drug-induced hERG block, several mutations that were implicated in directly affecting channel gating or permeation were for hERG residues facing the water-membrane interface (Lees-Miller et al., 2015; Saxena et al., 2016), and therefore would be easily accessible by drugs like neutral dsotalol, and cationic cisapride, that we explored in this study.

Even more importantly, similar computational approaches can be used as one of the steps to design drugs, which have similar membrane binding affinities and bind around mutated protein residues that result in altered channel function. Such an approach focusing on a desired drug lipophilicity and spatial arrangement of crucial functional groups was used, for instance, to design selective sodium channel blockers (Muraglia et al., 2007; De Luca et al., 2012; De Bellis et al., 2017). Such a structure-function based approach was shown to improve drug safety profile through mitigation of off-target effects, including hERG block (De Bellis et al., 2017).

#### Limitations and Future Directions

Our study represents just a first step in atomistic-level elucidation of thermodynamics and kinetics of cardiac channel blocking drug translocation across a lipid membrane. We obtained reasonable free energy profiles and water-membrane partitioning coefficients with a moderate amount of sampling (10–15 ns per umbrella sampling window or 0.8–1.2 µs for entire simulations). In some cases, we had to run additional simulations with alternative initial drug orientations to compensate for their slow reorientation in the membrane interior observed in our study. More extensive simulations for other drug membrane partitioning using a different empirical force field and molecular modeling software were reported recently (Bennion et al., 2017). They can potentially provide improved accuracy provided a high quality of an underlying empirical model and sufficient sampling of drug tumbling, and thus can be considered as a viable alternative of our approach. In our future studies we will also test several alternative options for enhanced sampling (Bernardi et al., 2015) such as metadynamics (Barducci et al., 2011), which has been recently used in membrane partitioning simulations to properly sample degrees of freedom orthogonal to the reaction coordinate and thus provide a more accurate energetics (Jambeck and Lyubartsev, 2013).

Alternatively, replica exchange simulations can be employed, which can be especially useful for modeling mixed membrane systems (Huang and Garcia, 2014). In our study, we mostly used a one component lipid membrane containing POPC, whereas lipid composition of cellular membranes is much more complex. For instance, plasma membranes of cardiomyocytes (where hERG channels are mostly located) has substantial fractions of zwitterionic posphatidylcholine, phosphatidyethanolamine, and sphingomyelin, negatively charged phosphatidylserine and non-polar cholesterol with substantial differences in their distribution between inner and outer leaflets (Post et al., 1995). This is without taking into account lateral membrane heterogeneity and existence of functional microdomains such as lipid rafts and caveolae, suggested to influence cardiac ion channel function (Maguy et al., 2006). At this time, however, we are not yet in position to study such complex heterogeneous systems via atomistic simulations, but coarsegrained models, such as a popular MARTINI force field (Marrink and Tieleman, 2013), are well-suited for such investigations and can be potentially used for studying cardiac drug interactions with realistic lipid membranes. In terms of atomistic simulations, we are planning to extend our studies to simulate drug partitioning to binary mixtures of phospholipids and cholesterol, which is expected to substantially influence ionizable drug partitioning and permeation, as discussed above. Another direction, which we already started exploring here, are binary mixtures of two phospholipids with different head groups, possibly influencing drug permeation kinetics and thermodynamics via specific interactions and/or altering membrane physical-chemical properties.

Estimated drug permeation rates and their relation to experimentally measured quantities remain uncertain as was mentioned above. In this study we could only compare relative values for cationic and neutral d-sotalol, which encompass an experimental estimate. However, it is not clear if we can simply relate those values to a measured apparent permeability via computing effective resistances to permeation as was done in a recent study (Carpenter et al., 2014). Another pertinent issue is computing permeability rates for drug molecules with pronounced interfacial binding (such as neutral d-sotalol in this study), which will clearly increase a barrier height a drug will need to hop over to permeate as was noted previously (Orsi et al., 2009). Therefore, an expression for permeability rates (Marrink and Berendsen, 1994) traditionally used for their calculations for polar and ionic species, where free energies are referenced to bulk aqueous solution, might not work anymore. In this study for SotN we used a variant of this expression with free energy set to 0 at the interfacial binding site and computing permeability just across a central barrier. A validity of such approximation remains to be seen in more thorough investigations, e.g., by comparing results with drug translocation rates computed from long unbiased MD simulations. Moreover, this approach does not take into account drug translocation between the interfacial binding site and bulk water. This contribution becomes dominant for hydrophobic drugs such as general anesthetics (Vorobyov et al., 2012), not considered in this study.

For d-sotalol and other hERG blockers with sulfonamide functional group (e.g., dofetilide, ibutilide, E4031), an unresolved issue is its anionic, deprotonated drug fraction, such as one in the zwitterionic d-sotalol (SotZ). A neutral sulfonamide group has been thoroughly parameterized recently and is included in the generalized CHARMM force field (Yu et al., 2012), whereas no atom type for anionic N or any associated parameters are available to the best of our knowledge. For d-sotalol in water at the physiological pH, a cationic form with a neutral sulfonamide group is a dominant form, with SotZ and/or SotN having a ∼11% contribution. Based on our prediction, only SotN can move across a membrane, but we need to know SotZ and SotN ratios in order to relate computed membrane partitioning energetics to experimental observables. Moreover, SotZ can be potentially an important contributor to hERG binding through the interactions of its negatively charged sulfonamide functionality with basic residues in the voltage-sensing domain (VSD) of a channel, for example. Such interactions were revealed in a recent crystallographic/electrophysiological study in a VSD of a voltage gated Nav1.7/NavAb chimera channel, where an anionic sulfonamide "warhead" directly and selectively interacts with a gating charge carrying arginine residue, immobilizing a voltage sensor in its activated state (Ahuja et al., 2015). Whether a similar binding motif is possible for hERG remains to be seen, but it should not be discounted, and thus accurate empirical force field for an anionic sulfonamide functionality will need to be developed and can be validated on predicting an aforementioned drug—channel interaction.

Sotalol is a chiral molecule, and in this work we only studied one enantiomer: d-sotalol, which was used in an infamous SWORD clinical study (Waldo et al., 1996) mentioned above. Sotalol enantiomers can be synthesized and separated (Carr et al., 1991; Foster and Carr, 1992; Brodfuehrer et al., 1997), however, a racemic mixture of d- and l-isomers has been used in many biophysical, physiological and pharmacological experimental studies up to date. l-sotalol is known to have some beta-blocking activities, whereas d-sotalol seems to be inert (Gomoll and Bartek, 1986) (a reason why it was used for SWORD study), but they share very similar electrophysiological properties, including QT prolongation (Touboul, 1993; Manoach and Tribulova, 2001). Even though interaction between two chiral molecules, e.g., sotalol and lipid, can be different for stereoisomers (and used for their separation), we do not expect substantial changes for l-sotalol—membrane interactions as they are mostly governed by dehydration for a neutral drug or membrane deformation by a charged drug electric field. Therefore, simulations with dsotalol should be sufficient, however, a more complex situation will arise for drug—channel interaction simulations, where both stereoisomers might need to be tested.

Nevertheless, despite the limitations of this study, related to tested drug and membrane models, our work demonstrated good agreement between computed and experimental data, and can definitely be used to predict the molecular mechanisms, energetics and kinetics of drug-membrane interactions, and potentially ion channel binding pathways. Moreover, the presented study can be used, for instance, for informing multiscale kinetic models of cardiovascular (and other) drug effects on cellular, tissue and organ levels (Clancy et al., 2016), as was done in our recent study, where we modeled charged and neutral flecainide (cardiac sodium channel blocker with some pro-arrhythmic proclivity) effects (Yang et al., 2016). We are planning a similar extension of the current study along with atomistic structure based investigations of sotalol interactions with hERG using a combination of molecular docking and allatom molecular dynamics simulations. Several other drugs with

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different hERG affinities and pro-arrhythmia proclivities will be investigated as well for both lipid membrane and hERG binding assays.

#### AUTHOR CONTRIBUTIONS

IV, CC, and SN: designed the research; KD, SB, and IV: performed the research and analyzed data; All authors prepared the manuscript and approved the final submitted version.

#### FUNDING

This work was supported by American Heart Association Predoctoral Fellowship 16PRE27260295 (to KD), the National Institutes of Health NHLBI R01HL128537-02 (to CC, SN, SB, and IV), NHLBI U01HL126273-02 (to CC, SB, and IV), NHLBI R01HL128170-03 (to CC), R01GM101928-04 (to CC), the Canadian Institutes of Health Research [Grant 201103MOP-CSA-244888] (to SN). The computational support for this work was provided by University of California, Davis and WestGrid/Compute Canada through a Resource Allocation Award to SN. Anton 2 computer time was provided by the Pittsburgh Supercomputing Center (PSC) through Grant R01GM116961 from the National Institutes of Health. The Anton 2 machine at PSC was generously made available by D.E. Shaw Research.

#### ACKNOWLEDGMENTS

We would like to thank Profs. Heike Wulff, Vladimir Yarov-Yarovoy, and Jon Sack for helpful discussions.

#### SUPPLEMENTARY MATERIAL

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 DeMarco, Bekker, Clancy, Noskov and Vorobyov. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# In Vitro and In Silico Risk Assessment in Acquired Long QT Syndrome: The Devil Is in the Details

William Lee1, 2, Monique J. Windley 1, 2, Jamie I. Vandenberg1, 2 and Adam P. Hill 1, 2 \*

*<sup>1</sup> Molecular Cardiology and Biophysics Division, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia, <sup>2</sup> St. Vincent's Clinical School, University of New South Wales, Sydney, NSW, Australia*

Acquired long QT syndrome, mostly as a result of drug block of the Kv11. 1 potassium channel in the heart, is characterized by delayed cardiac myocyte repolarization, prolongation of the T interval on the ECG, syncope and sudden cardiac death due to the polymorphic ventricular arrhythmia Torsade de Pointes (TdP). In recent years, efforts are underway through the Comprehensive *in vitro* proarrhythmic assay (CiPA) initiative, to develop better tests for this drug induced arrhythmia based in part on *in silico* simulations of pharmacological disruption of repolarization. However, drug binding to Kv11.1 is more complex than a simple binary molecular reaction, meaning simple steady state measures of potency are poor surrogates for risk. As a result, there is a plethora of mechanistic detail describing the drug/Kv11.1 interaction—such as drug binding kinetics, state preference, temperature dependence and trapping—that needs to be considered when developing *in silico* models for risk prediction. In addition to this, other factors, such as multichannel pharmacological profile and the nature of the ventricular cell models used in simulations also need to be considered in the search for the optimum *in silico* approach. Here we consider how much of mechanistic detail needs to be included for *in silico* models to accurately predict risk and further, how much of this detail can be retrieved from protocols that are practical to implement in high throughout screens as part of next generation of preclinical *in silico* drug screening approaches?

Keywords: kv11.1, herg, acquired long QT syndrome, arrhythmia, pharmacology, CiPA, modeling

#### INTRODUCTION

In the past 20 years, a range of structurally unrelated drugs, including antihistamines, antibiotics and antipsychotics, have been withdrawn from the market due to adverse effects on cardiac repolarization - so called acquired long QT syndrome (aLQTS). aLQTS is characterized by prolongation and sometimes morphological deformation of QT segments on the 12-lead electrocardiogram (ECG), syncope and sudden cardiac death due to the polymorphic ventricular arrhythmia Torsade de Pointes (TdP). Theoretically, aLQTS can occur due to unwanted drug induced modulation of any of the ionic channels that contribute to cardiac repolarization either through direct modulation of channel conductance (Cavero et al., 2000; Perrin et al., 2008a) or up/down regulation of channel trafficking and expression on the cell membrane (Dennis et al., 2007; Ballou et al., 2015). In practice however, the overwhelming majority of these drugs cause aLQTS through blockade of the Kv11.1 potassium channel that carries the rapid component of the delayed rectifier current in the heart (IKr) (Perrin et al., 2008b).

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Francis Adriel Ortega, Weill Cornell Medical College, United States Stefano Morotti, University of California, Davis, United States Jon Silva, Washington University in St. Louis, United States*

> \*Correspondence: *Adam P. Hill a.hill@victorchang.edu.au*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *18 August 2017* Accepted: *03 November 2017* Published: *16 November 2017*

#### Citation:

*Lee W, Windley MJ, Vandenberg JI and Hill AP (2017) In Vitro and In Silico Risk Assessment in Acquired Long QT Syndrome: The Devil Is in the Details. Front. Physiol. 8:934. doi: 10.3389/fphys.2017.00934*

**50**

As a result of the prevalence of these proarrhythmic side effects, regulatory guidelines have been put in place as part of preclinical drug development to ensure such dangerous compounds do not get to market. In their current form, these guidelines use simple steady-state measures of Kv11.1 inhibitory concentration and action potential prolongation to estimate arrhythmic risk (E14, 2005; S7B, 2005). However, while these steady-state measures of Kv11.1 block are very sensitive (no new proarrhythmic drugs have knowingly come to market since the inception of these guidelines), they are not specific. The link between Kv11.1 block, repolarization delay, and TdP is poorly understood meaning these measures are poor surrogates for actual risk of TdP. Given that not all drugs that block Kv11.1 are going to be proarrhythmic, this has likely resulted in an unnecessarily high attrition rate of drugs in development (Redfern et al., 2003; Sager et al., 2014).

To address this issue, the Comprehensive in vitro Proarrhythmia assay (CiPA) has been proposed as a new safety paradigm in understanding TdP and assessing proarrhythmia risk (Sager et al., 2014). CiPA has two primary objectives: (1) Detailed in vitro electrophysiological characterization of drug interaction with Kv11.1 (and other cardiac ion channels) and integration of this data into in silico models to predict proarrhythmia in simulations of the cardiac action potential and (2) Validation of in silico models using human induced pluripotent stem cell derived cardiac cardiomyocytes (Fermini et al., 2016). Central to the first of these objectives is our understanding of the mechanistic subtleties of how drugs interact with Kv11.1. There are several key factors that contribute to a drug's pharmacological profile and hence contribute to proarrhythmic risk, including the kinetics of drug binding and unbinding, gating-state preference and temperature dependence. These factors are not easily quantified by simple steady-state measures, yet can have significant effects on the measured potency of a drug as well as profound impact on the degree of repolarization delay and the emergence of proarrhythmic markers seen in in silico simulations. For example, **Figure 1** demonstrates an in silico simulation of 6,561 theoretical drugs that block Kv11.1 all at calculated IC<sup>50</sup> doses and yet the simulated action potential prolongation is significantly varied. Furthermore, whilst Kv11.1 is the major repolarizing current in the cardiac action potential, there are multiple other currents that contribute to repolarization, a concept known as repolarization reserve (Roden, 1998). In this context, the evolution of drug induced TdP may involve block of multiple ion channel currents and a drug's affinity for a variety of targets may modify the proarrhythmic risk associated with its block of Kv11.1. Determination of the proarrhythmic risk profile of Kv11.1 blocking drugs is therefore a multifaceted problem that goes beyond simple measures of potency. As a result, using in silico means to predict the risk associated with individual drugs is a complex process for which the optimal implementation remains to be decided upon. In this article we will consider what level of mechanistic detail describing the interaction between drug and ion channel target needs to be included for in silico models to accurately predict risk and further, how much of this detail can be retrieved from protocols that are practical to

#### FIGURE 1 | Continued 0.01–100 s-1 using half-logarithmic increments. An IC50 dose of each drug, calculated *in silico* using a simulated direct drug application of the drug at a holding potential of 0 mV, was applied to the O'Hara Rudy action potential at 1000 ms pacing cycle length. Drugs with higher affinity for the open state are shown on the right (*K*o / *K*i > 1) and drugs with higher affinity for the inactivated state are shown to the left (*K*o / *K*i < 1). The green line shows the APD90 for IKr50 (a 50 % conductance block of Ikr) of 428 ms. *Adapted from* Lee et al. (2016). (B–E) Drug binding kinetics contribute to reverse rate dependence. (B) Action potentials simulated at 500 ms pacing interval in response to an IC50 dose of the drugs selected in (A). Black line represents a control action potential with no drug applied. (C) Action potentials at 1,000 ms pacing interval. (D) Action potentials at 2,000 ms pacing interval. (E) Pacing cycle dependence of 1APD90.

implement in high throughout screens as part of preclinical development?

#### COMPLEXITY OF THE KV11.1/DRUG INTERACTION

In many cases, a drug's interactions with its ion channel pharmacological target can be described as a simple bimolecular reaction according to the equation:

$$\mathbf{O} \xrightleftharpoons[]{\text{ $\mathbb{A}^\*$ }} \mathbf{O} \mathbf{D} \tag{1}$$

Where O represents the open ion channel, D is drug, and k<sup>f</sup> and k<sup>b</sup> are the rates of association and dissociation respectively. A dissociation constant (KD), describing the affinity of binding can then be defined as the quotient of k<sup>b</sup> from k<sup>f</sup> :

$$K\_D = \frac{k\_b}{k\_f} \tag{2}$$

In the scenario where this binding results in block of the ion channel current, the IC50, the drug concentration at which 50% of channels are blocked, approximates the KD. Whilst Kv11.1 interaction with drugs does not follow this simple rule (Windley et al., 2016), it nevertheless provides a useful framework for discussion of drug binding to Kv11.1. A detailed consideration of the factors that contribute to the complexity of block of these channels is presented in the following sections.

#### Drug Binding Kinetics

The inclusion of drug binding kinetics in in silico simulations has been demonstrated to significantly alter predictions of cardiac action potential prolongation (Di Veroli et al., 2014; Lee et al., 2016). Specifically, drugs of equivalent affinity for Kv11.1 demonstrate varying degrees of action potential prolongation (**Figures 1B–D**). In some experiments, up to 4-fold increased difference in prolongation can be observed when comparing equipotent drugs with fast kinetics (τon = 0.1 s) to those with slow kinetics (τon = 100 s) (Di Veroli et al., 2014), which is within the range of time constants for drug binding observed for known drugs (Windley et al., 2017). Moreover, this differential prolongation is accentuated at different pacing frequencies; fast drugs cause greater prolongation at lower pacing frequencies while the opposite is true for slow drugs. At a pacing cycle length of 1,000 ms this leads to a difference in prolongation of APD<sup>90</sup> of 52 ms when these parameters are incorporated into in silico simulations (**Figure 1C**; Lee et al., 2016).

These rate dependent effects therefore contribute to one of the most commonly measured indicators of proarrhythmic propensity—reverse rate dependence (RRD)—where an inverse relationship exists between action potential prolongation and depolarization frequency (Hondeghem et al., 2001a,b). The implied mechanism of this is that drugs with different kinetics of binding reach different levels of steady state block as a function of the relative rates of drug binding, unbinding and cycle length. Specifically, for the drugs shown in **Figures 1B–D**, this manifests as a maximal 30% block of Kv11.1 achieved with application of slow drugs at an IC<sup>50</sup> dose during 1 Hz pacing, compared to 50% block for fast drugs under the same conditions (Lee et al., 2016). While it is known that other factors including genetic background and environmental factors including adrenergic upregulation of IKs (Sanguinetti et al., 1991; Bosch et al., 2002; Bányász et al., 2009) contribute to RRD, it is clear that the kinetics of the drug/channel interaction are also central to this established measure of proarrhythmia.

Another characteristic of drug interaction with Kv11.1 that is at least partially underpinned by the kinetics of binding and unbinding is that of "trapping" (Carmeliet, 1992; Yang et al., 1995; Mitcheson et al., 2000b; Perry et al., 2004; Stork et al., 2007). For some drugs, this phenomenon is due to true drug trapping. In these cases the drug molecule remains within the channel pore, sterically prevented from diffusing out as a result of closing of the cytoplasmic gate when the channel deactivates (Mitcheson et al., 2000b; Stork et al., 2007). Other compounds however, are more likely to display "virtual trapping," where drug unbinding is significantly slower than the rate of channel deactivation (Perry et al., 2004). In these cases, depending on the voltage protocol used, the drug will appear to be "virtually trapped" if the interpulse time is insufficient for complete drug dissociation. (Lee et al., 2016; Windley et al., 2017). However, the extent to which the degree and type of trapping can be measured in vitro using simple voltage protocols is limited. For example, in the step depolarization protocol used by Windley et al. (2017) and Li et al. (2017), the degree of trapping is estimated with a fixed 15 s interpulse interval. The limitations of this approach are twofold. First, it is not possible to distinguish between true trapping and virtually trapped drugs. In practical terms, in silico simulation has demonstrated that true trapping results in significantly greater APD<sup>90</sup> prolongation and greater pro-arrhythmic risk, Di Veroli et al. (2014) and therefore it is important to distinguish between the two. Second, any virtually trapped drug that dissociates quicker than 15 s will be described as non-trapped. Even if there was significant residual block evident at 5 or 10 s, the protocol cannot test this. In the context of cardiac cycle, where a typical diastolic interval might be on the order of 600 ms, this might be a significant shortcoming. Even so, Li et al. have shown that including an approximation of trapping and kinetics based on this protocol in their in silico models is useful in improving proarrhythmic prediction. For example, discrimination between drugs with low, medium and high risk of proarrhythmia using the metric ability of the "cqInward" (which represents the net inward current during the cardiac action potential) is incrementally improved when descriptions of trapping and kinetics are included in simulation as compared to simple IC<sup>50</sup> measures of drug potency (Li et al., 2017; **Figure 2**). This is therefore clearly an important factor to consider, even if it is described with some degree of simplicity.

training compounds. (High risk drugs are labeled in red, intermediate risk in blue and low risk in green) x-axis is the ratio between the simulated concentration and free *C*max; y-axis is the cqInward metric. Stars indicate the threshold dose, which is the highest dose that did not elicit an early afterdepolarization (EAD). The metric cqInward is the net inward current for each drug and is calculated as (INaL\_AUC\_drug/INaL\_AUC\_control+ICaL\_AUC\_drug/ICaL\_AUC\_control)/2, where AUC is the integrated area under the curve of the late sodium (INaL) and L-type calcium (ICaL) current traces during steady-state action potential simulation with (\_drug) or without (\_control) drugs. (A) Simulations are performed using instantaneous block of Kv11.1 base on dose response curves. (B) Simulations are performed using a dynamic model of Kv11.1-drug binding with incremental improvement in arrhythmia risk stratification. Reproduced from Li et al. (2017).

In summary, the kinetics of binding and unbinding of drugs to Kv11.1 play an important role in accurate prediction of prolongation of repolarization and proarrhythmic propensity. The addition of greater complexity, such as variability in ionic channel densities/function seen in different layers of the ventricular myocardium (Saiz et al., 2011) or congenital LQTS mutants (Romero et al., 2014), will further compound these effects. Consequently, in pursuit of a robust and comprehensive risk prediction assay, detailed understanding of these baseline measures of drug binding kinetics are likely an important component for in silico risk prediction and inaccurate estimation will likely lead to compounding errors as we continue to build and refine prediction models.

#### State Dependent Binding

The vast majority of drugs which target Kv11.1 require channel opening in order to gain access to the receptor site within the inner cavity of the channel pore (Kiehn et al., 1996; Walker et al., 1999; Vandenberg et al., 2012). However, a drug's affinity can be relatively greater for either the open state (Ko) or inactivated state (Ki) resulting in a state preference in drug binding. To date, there are no studies that have been able to demonstrate drug binding in the closed state. Several studies have demonstrated that some, but not all, drugs with high affinity binding to Kv11.1 show preferential binding to the inactivated state (Suessbrich et al., 1997; Ficker et al., 1998; Numaguchi et al., 2000; Perrin et al., 2008a; Du et al., 2014). These studies show that Kv11.1 binding potency in certain high affinity drugs is reduced by using inactivation attenuated mutants, such as N588K or S631A (Perrin et al., 2008a; Du et al., 2014), or the inactivation deficient mutant S620T (Suessbrich et al., 1997; Ficker et al., 1998; Perrin et al., 2008a; Wu et al., 2015). The inference being that these drugs favor binding to the inactivated state, hence channel mutants which reduced inactivation are less likely to bind the drug in question.

However, it is important to note that it is not always the case that there is a direct correlation between the extent of inactivation and the affinity of drug binding, even for state-dependent blockers. Electrophysiological studies using concatenated Kv11.1 tetramers containing variable number of inactivation deficient subunits have demonstrated changes in drug binding affinity that occur independent of inactivation (Chen et al., 2002; Wu et al., 2015). The major molecular determinants for drug binding to Kv11.1 are two aromatic residues Y652 and F56 in the S6 helix (Mitcheson et al., 2000a; Chen et al., 2002; Wu et al., 2015). In addition to these two S6 aromatics, Thr623, Ser624, and Val625 at the base of the selectivity filter, and Phe557 on the S5 helix also contribute to drug binding at least for some drugs (Mitcheson et al., 2000a,b; Saxena et al., 2016). It is likely that conformational changes that accompany inactivation, but that are not strictly necessary for the open to inactivated state transition, alter the arrangement of these residues within the pore cavity to allow for additional close molecular interactions that result in preferential binding to the inactivated state (Durdagi et al., 2012). This is supported by evidence from molecular dynamics simulations, albeit those limited to using homology models of Kv11.1, which demonstrate these conformational changes (Durdagi et al., 2012).

Of course, there are also non-state dependent drugs whose potencies are not affected by inactivation deficient mutants. These drugs include: quinidine, erythromycin, perhexiline (Perrin et al., 2008a), and clozapine (Hill et al., 2014). Moreover, studies have suggested that some compounds may also have an open state preference with minimal binding to the inactivated state (Kamiya et al., 2001; Park et al., 2002; Su et al., 2004). However, the contention with these studies is that rather than using mutagenesis to manipulate state occupancy, they utilize complex non-standardized voltage protocols to demonstrate state preference since an open deficient Kv11.1 mutant is not useful due to an absence of current. It is likely that the recent advent of high resolution structures of Kv11.1 (Wang and MacKinnon, 2017) and the potential this presents to generate more structures of drugs interacting with inactivation deficient Kv11.1 channels, will allow more accurate molecular dynamic simulations to probe these questions around state-dependent drug binding in more detail.

How important then is the consideration of state dependent binding for in silico prediction of arrhythmic risk? The data in **Figures 3A,B** shows that an IC<sup>50</sup> dose of two drugs with opposite state preferences differ in the degree of observed APD prolongation by 56 ms—clearly a significant amount in predicting their proarrhythmic potential. However, this relationship also needs to be considered through the prism of the limitation that the measured IC<sup>50</sup> is itself influenced by the state preference and how this manifests as a function of the voltage protocol used to measure the potency. Current safety guidelines mandate equilibrium testing of drugs to estimate potency to estimate arrhythmic risk (S7B, 2005). However, measures of drug potency vary between voltage protocols for some drugs but not for others (Kirsch et al., 2004; Yao et al., 2005; Milnes et al., 2010). These differences, which can be an order of magnitude in disparity, are in part due to using voltage protocols which favor occupancy of either the open or inactivated state, so favoring drug binding to that state (Milnes et al., 2010). Therefore, how can one measure state preference for incorporation into in silico simulations? The processes of channel opening and inactivation occur over overlapping voltage ranges, so it is almost impossible to tease out the relative affinities for the two states from a single, relatively simple voltage protocol. One potential approach to this might be to examine multiple protocols, that each sample the state occupancy of open vs. inactive differently, and attempt to infer information about state preference from the differences in IC50s measured using each. However, this is a relatively complex task that may not be amenable to high throughput screens.

### Temperature Dependence

The temperature dependence of potency of Kv11.1 block is a phenomenon that has been described in the literature for many drugs (Guo et al., 2005; Yao et al., 2005; Alexandrou et al., 2006; Hill et al., 2007). For instance, Guo et al. (2005) and Alexandrou et al. (2006) demonstrate an increase in potency with respect to increasing temperature from 22 to 37◦C for fluoroquinolone antibiotics (erythromycin and moxifloxacin respectively), although not to the same magnitude. In contrast, other drugs, including loratadine and bepridil, exhibit reduced

shown in red-dash. (B) Ventricular action potentials corresponding to the two drugs in (A) in comparison to IKr50. (C–F) Effect of pacing cycle length on cardiac action potential prolongation. 2 drugs with equal and opposite ratio of affinity for the open vs inactivated state and equal APD90 at a pacing cycle length of 1,000 ms were selected from (A). The inactivated state preference drug (*K*<sup>o</sup> /*K*<sup>i</sup> <sup>=</sup>10−<sup>4</sup> ) is shown in blue-solid. The open state preference drug (*K*<sup>o</sup> / *<sup>K</sup>*<sup>i</sup> <sup>=</sup>10<sup>4</sup> ) is shown in red-solid. (C) Action potentials at 500 ms pacing interval. (D) Action potentials at 1,000 ms pacing interval. (E) Action potentials at 2,000 ms pacing interval. (F) Pacing cycle dependence of 1APD90

potency at physiological temperatures (Kirsch et al., 2004). Larger scale studies have also established that a range of different drugs have a variable degree of Kv11.1 blockade when examined at ambient temperature compared to physiological temperatures (Kirsch et al., 2004; Yao et al., 2005). Moreover, differences in temperature sensitivity can be accentuated by different voltage protocols (Kirsch et al., 2004).

In relation to gathering data to constrain in silico models, this problem is further complicated by recent studies by Windley et al. (Windley et al., 2016), that revealed some mechanistic insights into the temperature dependence of drug binding to Kv11.1. Using a direct measurement of kinetics at 0 mV rather than a pulsed voltage protocol, Windley et al. demonstrated that for cisapride, increasing temperature from 22 to 37◦C did not affect affinity of binding, but significantly altered kinetics. In silico the temperature dependence of binding and unbinding kinetics could not be described by a simple bi-molecular interaction, but required inclusion of an "encounter-complex"; a conducting intermediary state between unblocked and blocked channels states. This change in kinetics could also be used to potentially explain apparent differences in drug potency when using varying pulsed voltage protocols as discussed in the following section For example: at 20 nM comparing 22–37◦C, Windley et al. observed a 5.5-fold increase in cisapride binding rates to Kv11.1. Based on the analysis in Lee et al. (2016), this could account for a ∼20 ms increase in drug-induced APD<sup>90</sup> prolongation, despite no change in affinity. In addition to these effects of temperature on drug binding, the gating of the Kv11.1 channel itself is sensitive to temperature. Specifically, at 37◦C there are increases in channel conductance, a hyperpolarizing shift in activation and a depolarizing shift in inactivation (Vandenberg et al., 2006), resulting in an overall increase in in open state that will also influence the measured potency of drugs that display state dependent binding (see Section State Dependent Binding).

The implications of these studies are that for some drugs, measures of potency and kinetics made at ambient temperatures may not be useful in constraining in silico models used to predict proarrhythmia at physiological temperatures (Windley et al., 2016). This is potentially a concern for large scale, highthroughput drug screening as many of the current generations of automated patch clamp platforms are limited to recording at ambient temperature (Fermini et al., 2016). However, efforts are currently underway, through the CiPA in silico Working Group and High Throughout stream to establish the practical importance and consequences of this issue.

## MEASURING AND MODELING DRUG BINDING TO KV11.1

The complexity of Kv11.1-drug interactions therefore has clear implications for how the field should approach both measuring of these phenomena in vitro, as well as how we describe them using in silico models that can be used for risk prediction. Current guidelines stipulate the IKr current should be assayed but do not specify voltage protocols, or details, such as temperature or cellular expression systems. As a result there is a lack of standardization in how block of IKr current is measured (Fermini et al., 2016). Redfern et al. (2003) proposed a 30-fold safety margin between the measured IC<sup>50</sup> of a drug and its maximum unbound plasma concentration (Cmax) to distinguish between safe and unsafe drugs. However, many studies have shown variance in drug potency dependent as a function of temperature and voltage protocol (Kirsch et al., 2004; Yao et al., 2005; Milnes et al., 2010) and this safety margin becomes unreliable if a true IC<sup>50</sup> value cannot be agreed upon. For example, the reported IC<sup>50</sup> values for cisapride, span a 60-fold range (Potet et al., 2001; Rezazadeh et al., 2004). One approach therefore is to use in silico modeling to "fine-tune" in vitro experimental protocols to more closely mimic in vivo conditions (Ellinwood et al., 2017). However, even if a standardized protocol could be agreed upon, such as using a physiological cardiac action potential to reproduce the state transitions of Kv11.1 that are seen during the cardiac cycle, this would not take into account the impact of variations in heart rate or action potential prolongation which are paramount to the highly dynamic binding kinetics of the drug/Kv11.1 interaction. For example the data in **Figures 3C–F** shows two drugs with equal and opposite gating state preference. At 1,000 ms pacing cycle length the APD<sup>90</sup> differs by 1 ms. However, at 500 ms pacing cycle length the open state preference drug prolongs the APD<sup>90</sup> by 35 ms more than the inactivated state preference drug; while at 2,000 ms pacing cycle length the open state preference drug prolongs the APD<sup>90</sup> by 53 ms less than the inactivated state preference drug. (**Figures 3C–F**) Moreover, these standardized conditions also lack the ability to predict variations in physiological conditions, such as hyper/hypokalaemia (Wang et al., 1997) or low pH (and the consequent changes in protonation of drug compounds) (Moreno et al., 2011; Wang et al., 2016), all of which are known to affect the statedependence of drug binding. An alternative therefore, is to use non-physiological voltage protocols to accurately constrain in silico models of drug binding (Hill et al., 2014; Beattie et al., 2017) that can then be used in silico to evaluate a limitless range of physiological conditions.

This approach however brings with it a new set of challenges. There exists a wide variety of models of Kv11.1/drug interaction in the literature, each with different structures and each constrained by different in vitro datasets. Furthermore, they differ substantially in their ability to describe the key features of Kv11.1/drug binding dynamics discussed above, such as kinetics and state dependence (**Figures 4A,B**; Di Veroli et al., 2013; Hill et al., 2014), drug trapping (**Figure 4C**; Li et al., 2017) and temperature dependence (**Figure 4D**; Windley et al., 2016). While each of these models represents a good description of drug binding under certain conditions, they differ significantly in their predicted state occupancies over any given voltage protocol (**Figures 4Aii,Cii**), so will result in a difference in statedependent drug binding. As yet, no Markov model provides a universal solution that we can be sure would be useful for prediction of proarrhythmic risk. As a result, further complexity may need to be added, or the existing models constrained with new in vitro data, to improve the model's predictive accuracy (Fermini et al., 2016). The issue of what is the optimum approach to measuring and modeling drug binding to Kv11.1 is therefore an open question and the optimum balance between how much and what type of data is required to constrain in silico models and what is practical to do in the context of high throughput data acquisition is yet to be determined.

### MULTICHANNEL PHARMACOLOGY

The final piece of the puzzle that needs to be considered in developing ventricular cell simulations for in silico risk prediction is the role of multichannel pharmacology, and how this contributes to characteristics of the cellular action potential. Whilst Kv11.1 blockade is certainly critical to understanding aLQTS and drug induced TdP, it is not the sole determinant of arrhythmogenesis since drugs that block Kv11.1 can often also block other cardiac ion channels (Bril et al., 1996; Aiba et al., 2005; Wu et al., 2008; Vicente et al., 2015) to suppress or promote arrhythmogenesis (Fermini et al., 2016). An evaluation of the potency of a panel of 30 drugs against the seven major currents that contribute to repolarization demonstrated that the primary pharmacological targets that determine proarrhythmia were IKr (Kv11.1), ICaL (Cav 1.2), and INaL (Nav1.5-late). Furthermore,

FIGURE 4 | Example Markov models of drug binding to Kv11.1. (Ai) Kinetic and gating-state dependent model a*dapted from* Lee et al. (2016). (Aii) State occupancies of the combined closed (C-black), open (O-red) and inactivated (I-blue) states using the Markov model in (Ai), simulated in an O'Hara Rudy action potential at 1 Hz. (B) Kinetic and gating-state dependent model a*dapted from* Di Veroli et al. (2013). (Ci) Drug trapping model *adapted from* Li et al. (2017). (Cii) State occupancies of the combined closed (C-black), open (O-red) and inactivated (I-blue) states using the Markov model in (Ci), simulated in an O'Hara Rudy action potential at 1 Hz. (D) Temperature dependent model *adapted from* Windley et al. (2016). C0, C1, C2, Closed states; IC1, IC2, Inactivated-closed states; I, IO, Inactivated states; O, Open state; ID, IOD, Drug bound-inactivated states; OD, Drug bound-open state; CD, Drug trapped state.

drugs with high TdP risk tended toward unopposed Kv11.1 block, while drugs with low TdP risk had similar or higher potency for the inward currents (ICaL and INaL) in conjunction with Kv11.1 block (Crumb et al., 2016). These multichannel pharmacological profiles are reflected in the morphology of the AP waveform (and hence the surface ECG). The AP waveform is formed through summed contribution of all the individual ionic currents in the cardiac myocytes. As a result, varied drug block of different ionic currents will result in a spectrum of AP morphologies and durations, which is idiosyncratic to individual drugs that manifests in vivo as differences in QT duration as well as T wave morphology (**Figures 5Ci**–**Cii**; Vicente et al., 2015). Critically for in silico risk prediction, this "AP morphology signature" is in turn linked to the drug's pro-arrhythmic potential and potentially can be used to predict TdP.

In this regard, drug induced morphological changes in the cardiac AP have been shown to correlate with risk of TdP (Hondeghem et al., 2001a). Specifically, this study suggested the presence of AP "triangulation" (slow repolarization, without a distinct plateau or rapid repolarization phase) was a marker of risk of drug induced TdP. Several single drug studies exemplify this point and support the link with multichannel pharmacology. Drugs that block Kv11.1 without significant inward current block, such as Sotalol (Milberg et al., 2004) and dofetilide (Osadchii, 2012; **Figure 5Aii**), produce AP triangulation in addition to prolongation, (**Figure 5Bii**) and are considered high TdP risk drugs. Conversely, Verapamil, a potent blocker of Cav1.2 as well as Kv11.1 (**Figure 5Ai**), does not manifest in triangulation or prolongation of the AP (**Figure 5Bi**) and is considered a low TdP-risk drug (Aiba et al., 2005). Similarly, other drugs with multichannel pharmacological profiles, such as ranolazine (Jia et al., 2011) and tolterodine (Martin et al., 2006) demonstrate dose dependent AP prolongation without AP triangulation and are also considered low risk. It is clear therefore, that multichannel pharmacology, and its manifestation in morphology of the AP, is an important detail that must be considered for risk prediction.

In silico modeling again provides an ideal solution to integrating pharmacological data from multiple cardiac ion channels. Indeed, recent studies by Li et al. (2017) and Dutta et al. (2017) have shown the value of this approach and demonstrated that incorporating Cav1.2 and Nav1.5-late block into action potential simulations improves arrhythmia risk prediction (Yang et al., 2016; Li et al., 2017). However, in a similar vein to that discussed above for models of the Kv11.1/drug interaction, there are several models of the ventricular cardiac action potential that have been proposed in the literature including the ten Tusscher 2006 (TT06) (Ten Tusscher and Panfilov, 2006), Grandi-Bers 2010 (GB10) (Grandi et al., 2010), and O'hara Rudy 2011 (ORD11) models (O'Hara et al., 2011). Population based studies using these cell models have allowed interrogation of how the variation in repolarization reserve that occurs as a result of differential expression of ion channels between individuals can influence predicted drug effects as well as develop our understanding of multichannel pharmacology (Sobie, 2009; Lancaster and Sobie, 2016). However, each of the models is considerably different in relation to the conductance levels of

and 2.5 h post injection of 120 mg verapamil or 500 ug dofetilide. Verapamil demonstrates no change in prolongation or T-wave morphology while Dofetilide shows marked changes in prolongation and T-wave notching between the 2 time points. Reproduced from Vicente et al. (2015).

individual cardiac ion channels. As a result, predictions around APD prolongation and emergence of proarrhythmic markers that each of the models make in response to drug block are significantly different (Mirams et al., 2014) and do not reproduce in vivo data (Britton et al., 2017). For example, Mann et al showed that 50% inhibition of Kv11.1 caused 113, 22, and 34 ms prolongation of APD<sup>90</sup> for ORD11, TT06 and GB10 respectively (Mann et al., 2016). This issue is being considered by the field and recent efforts have focused on refining cell models by rescaling their ionic conductances using either patient data from subjects with various subtypes of the long QT syndrome (Mann et al., 2016) or published drug data (Britton et al., 2013; Dutta et al., 2016). Even so, significant disparity still exists between the "optimized" versions of the cell models, meaning the differences in predicted risk that result from using different models are likely to outweigh, or at least match, the differences associated with descriptions of the drug/channel interaction. It may also prove to be true that similar mechanistic descriptors that are becoming routine for drug binding to Kv11.1, such as kinetics and state dependence, also need to be incorporated for other cardiac ion channels for optimum risk prediction. However, the benefit of this relative to the cost of acquiring the data may preclude such an approach. What is clear, is that each of these facets of in silico risk prediction—the Markov descriptions of drug/channel interaction as well as the model of the ventricular cell in which they are incorporated, should each be considered as a priority for the field.

# CONCLUSION

Understanding the intricacies of the Kv11.1/drug interaction and optimizing our approaches to measuring and modeling these characteristics is critical to developing better preclinical in silico risk prediction. In doing this it is important to remember that all models are simplifications. Therefore, the challenge is to determine how much information needs to be included to make them useful rather than how much information is needed to make them accurate for every drug scenario, which would potentially necessitate the collection of very large amounts of data that may be redundant for many drugs. Given the potential significance of factors, such as drug binding kinetics, temperature dependence, state dependence and multichannel pharmacology discussed above, it seems clear that these factors need to be included at some level in models of drug binding. The major challenge faced by the field in the short term is determining what level of detail is necessary, and balancing this against the practicalities of data acquisition in high throughout screens.

#### AUTHOR CONTRIBUTIONS

WL, MW, JV, and AH all contributed to planning, writing and editing of the manuscript and figures contained herein.

#### FUNDING

WL is supported by a National Heart Foundation of Australia Health Professional Scholarship (101552). AH is supported by an Australian National Health and Medical Research Council

#### REFERENCES


project grant (1088214). JV is supported by an Australian National Health and Medical Research Council Fellowship (1019693).

#### ACKNOWLEDGMENTS

Special thanks to Dr. Melissa Mangala and Dr. Matthew Perry for intellectual input in the editing of this manuscript; and to Dr. Jose Vicente and Dr. Zhihua Li for providing data for figures.


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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer SM and handling Editor declared their shared affiliation.

Copyright © 2017 Lee, Windley, Vandenberg and Hill. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# In Silico Assessment of Efficacy and Safety of IKur Inhibitors in Chronic Atrial Fibrillation: Role of Kinetics and State-Dependence of Drug Binding

Nicholas Ellinwood<sup>1</sup> , Dobromir Dobrev <sup>2</sup> , Stefano Morotti <sup>1</sup> \* and Eleonora Grandi <sup>1</sup>

<sup>1</sup> Department of Pharmacology, University of California, Davis, Davis, CA, United States, <sup>2</sup> West German Heart and Vascular Center, Institute of Pharmacology, University Duisburg-Essen, Essen, Germany

Current pharmacological therapy against atrial fibrillation (AF), the most common cardiac

#### Edited by:

Domenico Tricarico, Università degli studi di Bari Aldo Moro, Italy

#### Reviewed by:

Adam Hill, Victor Chang Cardiac Research Institute, Australia Clemens Möller, Hochschule Albstadt-Sigmaringen, Germany

> \*Correspondence: Stefano Morotti smorotti@gmail.com

#### Specialty section:

This article was submitted to Pharmacology of Ion Channels and Channelopathies, a section of the journal Frontiers in Pharmacology

Received: 07 August 2017 Accepted: 23 October 2017 Published: 07 November 2017

#### Citation:

Ellinwood N, Dobrev D, Morotti S and Grandi E (2017) In Silico Assessment of Efficacy and Safety of IKur Inhibitors in Chronic Atrial Fibrillation: Role of Kinetics and State-Dependence of Drug Binding. Front. Pharmacol. 8:799. doi: 10.3389/fphar.2017.00799 arrhythmia, is limited by moderate efficacy and adverse side effects including ventricular proarrhythmia and organ toxicity. One way to circumvent the former is to target ion channels that are predominantly expressed in atria vs. ventricles, such as KV1.5, carrying the ultra-rapid delayed-rectifier K<sup>+</sup> current (IKur). Recently, we used an in silico strategy to define optimal KV1.5-targeting drug characteristics, including kinetics and state-dependent binding, that maximize AF-selectivity in human atrial cardiomyocytes in normal sinus rhythm (nSR). However, because of evidence for IKur being strongly diminished in long-standing persistent (chronic) AF (cAF), the therapeutic potential of drugs targeting IKur may be limited in cAF patients. Here, we sought to simulate the efficacy (and safety) of IKur inhibitors in cAF conditions. To this end, we utilized sensitivity analysis of our human atrial cardiomyocyte model to assess the importance of IKur for atrial cardiomyocyte electrophysiological properties, simulated hundreds of theoretical drugs to reveal those exhibiting anti-AF selectivity, and compared the results obtained in cAF with those in nSR. We found that despite being downregulated, IKur contributes more prominently to action potential (AP) and effective refractory period (ERP) duration in cAF vs. nSR, with ideal drugs improving atrial electrophysiology (e.g., ERP prolongation) more in cAF than in nSR. Notably, the trajectory of the AP during cAF is such that more IKur is available during the more depolarized plateau potential. Furthermore, IKur block in cAF has less cardiotoxic effects (e.g., AP duration not exceeding nSR values) and can increase Ca2<sup>+</sup> transient amplitude thereby enhancing atrial contractility. We propose that in silico strategies such as that presented here should be combined with in vitro and in vivo assays to validate model predictions and facilitate the ongoing search for novel agents against AF.

Keywords: ultra-rapid delayed-rectifier K<sup>+</sup> current, atrial fibrillation, mathematical modeling, ion channel blockers

**Abbreviations:** AP, action potential; APD, AP duration; APD40, APD to 40% repolarization; APD90, APD to 90% repolarization; AF, atrial fibrillation; C, closed state; cAF, chronic AF; CaT, Ca2<sup>+</sup> transient; CaTamp, CaT amplitude; CL, cycle length; EAD, early afterdepolarization; Em, membrane potential; ERP, effective refractory period; GKur, maximal conductance of the ultra-rapid delayed-rectifier K<sup>+</sup> current; I, inactivated state; IKur, ultra-rapid delayed-rectifier K<sup>+</sup> current; nSR, normal sinus rhythm; O, open state.

# INTRODUCTION

Atrial fibrillation (AF) is characterized by rapid, irregular heart contractions following fast, disorganized electrical signals in the atria. AF is the most common cardiac arrhythmia, occurring in 1–2% of the general population and projected to increase dramatically in the coming decades (to 4% by 2050) with an aging westernized population (Andrade et al., 2014). The most effective current treatment for preventing recurrence of AF in the clinic is radiofrequency ablation. Pharmacological therapy against AF is limited by low efficacy and substantial adverse side effects including an increased risk of lethal ventricular tachyarrhythmias.

To maximize efficacy and minimize proarrhythmic risk, an AF-selective drug should exert potent effects on fibrillating atria without significantly impacting ventricular tissue function during normal sinus rhythm (nSR) (Ehrlich et al., 2008; Van Wagoner et al., 2015). A potential strategy to achieve this goal is to target ion channels that are predominantly expressed in atria vs. ventricles, such as KV1.5, carrying the ultra-rapid delayedrectifier K<sup>+</sup> current (IKur). Genetic mutations causing both lossand gain-of-function of IKur have been associated with atrial arrhythmias in human (Olson et al., 2006; Christophersen et al., 2013; Colman et al., 2017). In a previous investigation, we used an in silico strategy to define optimal KV1.5-targeting drug characteristics, including kinetics and state-dependent binding, that maximize AF-selectivity (i.e., fast pacing-rate selectivity) in human atrial cardiomyocytes (Ellinwood et al., 2017). Because this work was conducted in atrial cardiomyocytes under nSR conditions, the best-performing drug properties identified would have relevance for patients with paroxysmal AF that have not undergone extensive AF-related electrical remodeling (Grandi et al., 2012; Nattel and Dobrev, 2016).

Building on our previously established simulation framework, the major goal of this investigation was to determine the optimal drug characteristics of IKur inhibitors in long-standing persistent (chronic) AF (cAF) conditions. Although not a universal finding (Yue et al., 1997; Bosch et al., 1999; Grammer et al., 2000; Workman et al., 2001), previous reports showed that IKur is strongly diminished in cAF patients (Van Wagoner et al., 1997; Brandt et al., 2000; Van Wagoner and Nerbonne, 2000; Dobrev and Ravens, 2003; Christ et al., 2008; Caballero et al., 2010), making the therapeutic potential of inhibitors targeting this current uncertain (Ravens et al., 2013; Grandi and Maleckar, 2016). Indeed, evidence of anti-arrhythmic efficacy of KV1.5 inhibitors in clinical trials is lacking (Ravens et al., 2013). However, recent studies have suggested an anti-arrhythmic potential of IKur-targeting drugs in cAF (Christ et al., 2008; Ford et al., 2013, 2016; Loose et al., 2014), as they can prolong action potential (AP) and effective refractory period (ERP) in atrial cardiomyocytes of cAF patients. Moreover, experimental evidence suggests that block of IKur enhances force of contraction of isolated human atrial trabeculae in cAF (Wettwer et al., 2004; Schotten et al., 2007). Our human atrial cardiomyocyte model confirmed that block of IKur results in prolongation and elevation of the AP plateau, which augments the Ca2<sup>+</sup> transient (CaT) amplitude (CaTamp), thereby eliciting a positive inotropic effect (Grandi et al., 2011). Thus, IKur might be a useful atrialselective target to potentially prevent reentry and related atrial hypocontractility in cAF. We propose that our computational approach, combined with in vivo and in vitro validation, might be useful to facilitate the identification of atrial-selective antiarrhythmic drugs against AF (Bers and Grandi, 2011; Grandi and Maleckar, 2016).

# METHODS

#### Atrial AP Model and Simulations

APs and CaTs were simulated with the Grandi et al. model of the human atrial cardiomyocyte in nSR and cAF (Grandi et al., 2011; Morotti et al., 2016b). IKur gating was described by a 6-state Markov type model (**Figure 1A**) as in Ellinwood et al. (2017), and IKur maximal conductance (GKur) in cAF was reduced by 50% compared to nSR (Grandi et al., 2011).

Simulations were equilibrated for 300 beats at 1-Hz pacing or 900 beats at 3-Hz pacing. After the 300th or 900th beat, the time to 40 and 90% repolarization of the AP (APD<sup>40</sup> and APD90) were calculated, along with diastolic intracellular Ca2<sup>+</sup> concentration ([Ca2+]i), CaTamp and time to 50% CaT decay. The atrial ERP was determined using a standard S1-S<sup>2</sup> premature stimulation protocol (Wang et al., 1996; Shinagawa et al., 2000; Christ et al., 2008; Zhao et al., 2009), where the S<sup>1</sup> basal stimulus (5 ms in duration) was applied to a steadystate human atrial cardiomyocyte model. As previously described (Ellinwood et al., 2017), ERP was determined by applying the premature S<sup>2</sup> stimulus (5 ms in duration, 2-fold the diastolic threshold of excitation) at progressively smaller S1-S<sup>2</sup> intervals from 700 ms to refractoriness by decrements of 2 ms. The longest S1-S<sup>2</sup> interval that failed to elicit an AP was taken as the local ERP (i.e., maximum upstroke velocity ≥5 V/s and AP with an amplitude ≥50% of the amplitude of the preceding AP elicited by S1).

An irregular pacing protocol was run for 20 s, starting from steady-state conditions at the fixed 3-Hz pacing. The cycle length (CL) was allowed to vary randomly following a uniform distribution between 285.7 and 400 ms, corresponding to a minimum pacing frequency of 2.5 Hz and a maximum pacing frequency of 3.5 Hz, with a mean of 333.3 ms (corresponding to 3- Hz pacing). The time course of membrane potential (Em), APD90, and CL was tracked over the course of the simulation.

All simulations and analysis were performed in MATLAB (The MathWorks, Natick, MA, USA) using the stiff ordinary differential equation solver ode15s. The model code is available for download at the following webpages: https://somapp.ucdmc. ucdavis.edu/Pharmacology/bers/ and http://elegrandi.wixsite. com/grandilab/downloads.

#### Parameter Sensitivity Analysis

Parameter sensitivity analysis was performed with the population-based approach described in Sobie (2009), Morotti et al. (2017), and Morotti and Grandi (2017) to investigate the role of various currents and transporters in the regulation of AP duration (APD), ERP, and CaT characteristics. Two populations of 900 atrial cardiomyocyte models were generated by randomly

varying the values of 18 parameters (see list in the Supplementary Materials) in the baseline nSR and cAF models. Specifically, the default value of each conductance or maximal transport rate was independently varied with a log-normal distribution (with standard deviation of 0.1). Multivariable regression (non-linear iterative partial least squares method) on log-transformed values was performed for 30 random subsets of 300 model variants from the 900-variant population to correlate the variation in each parameter to the consequent effect on each output. In **Figure 1C** and Figures S1–S6 bars represent the mean regression coefficients and error bars represent one standard deviation.

# KV1.5 Drug-Binding Model

We utilized our recent IKur Markov formulation and approach to describe various drug-KV1.5 channel binding schemes (**Figures 2A,F**; Ellinwood et al., 2017), as done by Lee et al. (2016). We previously showed that open state (O) blockers and open and inactivated state (O & I) blockers that target KV1.5 display fast pacing-rate selectivity (Ellinwood et al., 2017). Thus, we focused on these two types of inhibitors when examining the relationship between electrophysiological parameters and drugbinding kinetics in cAF. We considered different theoretical drugs with variable forward (kon) and reverse (koff) drugbinding rates to the open and inactivated states of the KV1.5 channel in the predicted physiological range of 0.01–100 s−<sup>1</sup> (Lagrutta et al., 2006) using half-logarithmic increments resulting in nine transition rates for each drug state transition (0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100 s−<sup>1</sup> ). For a particular state of the channel, dissociation constants (Kd) for our drug scenarios were calculated as koff/kon, and affinity constants were calculated as kon/koff. To investigate the effects of these drug characteristics, for a given state-dependent binding inhibitor, we varied kon and koff together (kon = koff) or considered all permutations of the nine different rates of drug binding (producing a total of 81 different drug scenarios). For drugs that could bind to multiple states of the KV1.5 channel, we also varied the relative affinity to open (KO) vs. inactivated state (KI). For O & I blockers, we included transitions between drug-bound states (orange transitions in **Figure 2F**) when specified. All drugs were simulated at the concentration causing a 50% reduction in peak IKur (i.e., IC50). IC<sup>50</sup> values were computed as described previously (Ellinwood et al., 2017), using a 200-ms down-ramp voltage-clamp protocol from +30 to −60 mV. After the application of a given [drug] (range: 1 nM−1 M), we allowed sufficient time for the degree of block to reach equilibrium. IC<sup>50</sup> values were calculated at 1 and 3-Hz pacing rates as the [drug] causing a 50% reduction in peak IKur compared to drug-free conditions. We chose the down-ramp, as compared to a typical square pulse, because it more closely resembles the relative state occupancies of the closed states, open state, and inactivated state of the KV1.5 channel during a physiological atrial AP, as we have shown in (Ellinwood et al., 2017).

# RESULTS

#### Role of IKur in nSR and cAF Atrial Electrophysiology

We built 900 variations of our nSR and cAF human atrial cardiomyocyte models (Grandi et al., 2011) at 1- and 3- Hz pacing, and performed parameter sensitivity analysis on 30 random subsets of 300 model variants to determine how alterations in each maximum ionic conductance/transport rate differentially (in cAF vs. nSR) affect electrophysiological properties including APD40, APD90, ERP, CaTamp, diastolic [Ca2+]<sup>i</sup> , and time to 50% CaT decay (Figures S1–S6). Simulated APs and CaTs in a representative group of 300 cAF cardiomyocyte model variants are shown in **Figure 1B**, and the average regression coefficients for GKur in nSR and cAF conditions at 1- and 3-Hz pacing are in **Figure 1C**. The values are negative because an increase in IKur shortens APD40, APD90, and ERP on average according to the regression algorithm. The analysis revealed that, while at a slow pacing rate APD<sup>90</sup> and ERP

FIGURE 2 | Effect of state-dependence and kinetics of drug binding on APD90. APD90 was determined for open (schematic in A, B, 1-Hz and D, 3-Hz pacing rate) and open and inactivated (schematic in F, G 1-Hz and I, 3-Hz pacing rate) state blockers given nine different rates of binding kinetics between 0.01 and 100 s−<sup>1</sup> using half-logarithmic increments, whereby koff = kon, K<sup>d</sup> = 1µM. For O & I blockers, we either allowed or prevented transitions between drug-bound states (orange vs. black traces in G,I). Simulations were also run in nSR and cAF drug-free conditions, and in cAF given a 50 and 100% reduction in GKur (dotted and dashed lines in B,D,G,I). Simulations were equilibrated for 300 beats at 1-Hz pacing or 900 beats at 3-Hz pacing using a [drug] equal to the IC50 value. (C,E,H,J) show the closed, open, inactivated and drug-bound (dB, i.e., Od or Od+Id) state occupancies during an AP for three different drug-binding kinetics (koff <sup>=</sup> <sup>k</sup>on <sup>=</sup> 0.01, 3, and 100 s−<sup>1</sup> ).

are more sensitive to changes in GKur, APD<sup>40</sup> is similarly sensitive in nSR and cAF (**Figure 1C**). At 3-Hz pacing, GKur impacts AP and ERP prolongation more in cAF vs. nSR despite the fact that GKur is smaller in cAF conditions. This points to IKur inhibition as a promising approach to counteract the abbreviated APD and ERP in cAF, while having a more moderate effect at physiological pacing rates. Therefore, we next ran simulations to reveal IKurtargeting drug properties that exhibit anti-AF selectivity and efficacy along with minimized proarrhythmic risk in cAF.

### Effect of Conformational State Specificity and Binding/Unbinding Kinetics on Human Atrial Cardiomyocyte APD at Normal and Fast Pacing Rates in cAF Conditions

**Figure 2** shows changes in APD caused by O and O & I inhibitors at varying drug-binding kinetics, whereby kon is set equal to koff (i.e., K<sup>d</sup> = 1µM). These are compared to no block, 50, and 100% reduction in GKur in cAF conditions, as well as no block in nSR conditions. Similar to our findings in nSR (Ellinwood et al., 2017), both types of inhibitors display a biphasic relationship between APD and drug-binding kinetics at 1- and 3-Hz pacing. At 1-Hz pacing, APD in the presence of drug is comparable to a 50% reduction in GKur at slow and fast drug-binding kinetics (**Figures 2B,G**). Significant APD prolongation is only seen for intermediate drug-binding kinetics (0.3–30 s−<sup>1</sup> for the open state blocker and 1–30 s−<sup>1</sup> for the open and inactivated state blocker), and goes well beyond the little APD prolongation resulting from a constant 50% reduction in GKur. However, even the maximal APD prolongation produced by an O or O & I inhibitor in cAF is still ∼50 ms less than the APD in nSR in drug-free conditions, which we interpret to suggest that such drugs would have limited toxicity at 1-Hz pacing rate.

At 3-Hz pacing, the two types of inhibitors cause stronger relative prolongation as compared to 1-Hz pacing across the same range of drug-binding kinetics (**Figures 2D,I**). Notably, all simulated drugs caused APD prolongation at 3-Hz pacing, but the maximal prolongation produced by these theoretical inhibitors did not match the APD prolongation caused by a 100% reduction in GKur. However, drugs with intermediate drugbinding kinetics (3–30 s−<sup>1</sup> for the O blocker and 10–30 s−<sup>1</sup> for the O & I blocker) did extend the APD at 3-Hz pacing above the APD in nSR conditions given no block of IKur. Thus, even though GKur is reduced by 50% in cAF as compared to nSR, **Figure 2** illustrates that IKur inhibitors can still prolong APD in cAF, particularly at 3-Hz pacing.

**Figures 2C,H,E,J** display the closed (red), open (blue), inactivated (green), and drug-bound (gray) state occupancies during the steady-state AP for the slowest (0.01 s−<sup>1</sup> ), intermediate (3 s−<sup>1</sup> ), and fastest (100 s−<sup>1</sup> ) drug-binding rates. In general, for the slowest drug-binding kinetics, the inhibitors do not bind readily during the AP, and the drug-bound state stays level below 0.4. At intermediate drug-binding kinetics, the inhibitors bind readily during the AP, thus significantly shrinking the open state occupancy. In addition, the off-rate of drug binding is slow enough to achieve maintenance in the drug-bound state during the AP. This allows for considerable AP prolongation, almost mimicking complete block of IKur. Finally, for the fastest drug-binding kinetics, the drugs again bind readily during the AP, but the off-rate of drug binding is so fast as to cause cycling between the drug-free open state and the drug-bound open state during a single AP. This results in prolongation of the drug-free open state occupancy later in the AP that limits AP prolongation. These results are consistent with our previous simulations in nSR. However, given the more positive plateau in the cAF cardiomyocyte AP, KV1.5 channels stay open longer, and inactivate more markedly (especially at 3-Hz pacing) as compared to nSR (Figure S7).

Given not only the rapid, but irregular electrical activity seen with AF, we sought to determine how the kinetics of drug binding of IKur inhibitors affected the time course of E<sup>m</sup> (**Figure 3B**) and APD<sup>90</sup> (**Figure 3C**) in cAF cardiomyocytes with a randomly variable CL (**Figure 3A**). Results in drug-free conditions and for an O & I blocker (modeled as in **Figure 2F**, black) with kon = koff (K<sup>d</sup> = 1µM) in **Figure 3** again demonstrate a biphasic relationship between drug-binding kinetics and average APD<sup>90</sup> (**Figure 3D**), as seen with constant pacing (**Figure 2I**). Thus, for all future simulations, we used a constant pacing interval that can more easily be standardized in a high-throughput drug-screening process.

#### Effect of Conformational State Specificity and Binding/Unbinding Kinetics on Human Atrial Cardiomyocyte ERP at Normal and Fast Pacing Rates in cAF Conditions

The desired effect of IKur inhibitors is prolongation of atrial ERP (Amos et al., 1996; Christ et al., 2008; Sanchez et al., 2012; Loose et al., 2014; Ford et al., 2016), particularly during fast pacing rates typifying AF. Thus, we assessed the effects of binding/unbinding kinetics on the ERP for O (**Figures 4A,B**) and O & I (**Figures 4C,D**) blockers. Simulations reveal a similar biphasic relationship between ERP and drug-binding kinetics at 1- and 3-Hz pacing for both types of inhibitors, which mirror the drugs' effects on APD (**Figure 2**).

At 1-Hz pacing, IKur inhibitors cause minimal ERP prolongation at slow drug-binding rates (≤0.3 s−<sup>1</sup> for O blockers and ≤1 s−<sup>1</sup> for O & I blockers) and fast drug-binding rates (100 s−<sup>1</sup> ). Although substantial ERP changes are predicted at intermediate drug-binding rates (1–30 s−<sup>1</sup> for O blockers and 3–30 s−<sup>1</sup> for O & I blockers), ERP prolongation remains ∼62 ms lower than the ERP in nSR given no block of IKur for both inhibitors.

At 3-Hz pacing, however, IKur inhibitors appear to be more effective at extending ERP than APD, which is a favorable drug property as previously demonstrated for Class I antiarrhythmic drugs which cause clinically relevant postrepolarization refractoriness. For all drug-binding kinetics, ERP prolongation is at least equivalent to that caused by a constant 50% reduction in GKur (**Figures 4B,D**). Notably, for intermediate drug-binding kinetics (3–30 s−<sup>1</sup> for O inhibitors and 10–30 s−<sup>1</sup> for O & I inhibitors), drug-induced ERP prolongation extends above the ERP in nSR in drug-free conditions, and the fastest drug-binding kinetics prolong the ERP to a point that closely

whereby kon = koff, K<sup>d</sup> = 1µM. These results are compared to 50, and 100% reduction in GKur (dotted lines) given the same irregular pacing protocol in (A).

resembles that in nSR in drug-free conditions. These drugs showing substantial ERP prolongation at 3-Hz pacing in cAF (with APD at slow pacing rates being well below that in nSR, see **Figure 2**) might represent suitable compounds for AF-selective therapy.

#### Effects of Drug Binding/Unbinding Kinetics with Variable K<sup>d</sup> on APD, ERP, and Ca2<sup>+</sup> Handling

**Figures 2**, **3**, **4** show the results from drug scenarios where the on- and off-rate of drug binding are equal to one another (kon = koff, K<sup>d</sup> = 1µM), but even closely related IKur inhibitors can have dissimilar K<sup>d</sup> values (Lagrutta et al., 2006). Thus, we simulated all permutations of the nine different rates of drug binding (0.01 to 100 s−<sup>1</sup> ), yielding 81 different combinations of kon and koff for the O & I state inhibitors (assuming equal affinities for open and inactivated states) at 1- and 3-Hz pacing. We assessed the effects of these drugs (at their IC<sup>50</sup> concentration) on APD, ERP, CaTamp, and diastolic [Ca2+]<sup>i</sup> . **Figure 5** shows the output of the simulations for an O & I inhibitor (modeled as in **Figure 2F**, black) in the form of a heatmap, where the diagonals of the squares from the bottom left to the top right corner correspond to drug scenarios where kon = koff (K<sup>d</sup> = 1µM). Except for the drugs with the largest K<sup>d</sup> values (koff >> kon), when kon is held constant, APD, ERP, and Ca2<sup>+</sup> handling are not very sensitive to changes in koff. Thus, the effects of IKur inhibitors on atrial electrophysiology and Ca2<sup>+</sup> handling are largely driven by kon rates as compared to koff rates.

In cAF conditions, ideal IKur inhibitors exhibiting AFselectivity will prolong atrial refractoriness (ERP prolongation at 3-Hz pacing), have limited toxicity (minimal to no APD prolongation at 1-Hz pacing), and have a positive inotropic effect (an increase in CaTamp at 1-Hz pacing). O & I inhibitors with a large K<sup>d</sup> do not display any of the desired favorable drug properties including prolongation of ERP at 3-Hz pacing (**Figure 5B**) or increase in CaTamp (**Figures 5C,D**), as their effects on APD, ERP, and Ca2<sup>+</sup> handling are minimal, resembling drug-free conditions. Intermediate kon rates (3–30 s−<sup>1</sup> for 1- Hz pacing and 10–30 s−<sup>1</sup> for 3-Hz pacing) cause the most significant increase in all the outputs displayed in **Figure 5**. For example, drugs with a kon rate equal to 10 s−<sup>1</sup> cause the greatest ERP prolongation at 3-Hz pacing (**Figure 5B**) and increase in CaTamp and diastolic [Ca2+]<sup>i</sup> (**Figures 5C,E**). Note, there is also significant APD prolongation at 1-Hz pacing when kon is in the intermediate drug-binding range (**Figure 5A**), but none of the 81 permutations of the simulated open and inactivated state inhibitor cause the APD to get close to the APD in nSR at 1-Hz

pacing (320 ms). Thus, the APD prolongation seen in **Figure 5A** does not necessarily disqualify any of these theoretical drug candidates for AF therapy. Likewise, at 3-Hz pacing, the increase in CaTamp and diastolic [Ca2+]<sup>i</sup> mirrors the prolongation in APD and ERP at 3-Hz pacing (**Figures 5D,F**). While an excessive increase in diastolic [Ca2+]<sup>i</sup> might be deleterious, we find it to remain well below the predicted value in the nSR human atrial cardiomyocyte model (∼360 nM).

In our previous study in nSR (Ellinwood et al., 2017), we found that O & I inhibitors with the fastest drug-binding kinetics (30–100 s−<sup>1</sup> ) cause ERP prolongation at 3-Hz pacing and no APD prolongation at 1-Hz pacing. These same inhibitors display favorable fast pacing-rate selectivity in atrial cardiomyocytes from cAF according to our simulations shown in **Figures 5A,B**. However, if we are not as concerned with APD prolongation in cAF conditions at 1-Hz pacing, then drugs with a kon rate in the intermediate drug-binding range (3–30 s−<sup>1</sup> ) would also be efficacious and perhaps more efficacious since they cause a positive inotropic effect at 1-Hz pacing (**Figures 5C,E**).

#### Effect of Relative State-Specific Drug Binding

Because many IKur inhibitors bind to multiple states of KV1.5 with variable affinity (Bouchard and Fedida, 1995; Lagrutta et al., 2006; Ford et al., 2016), we allowed kon for the open state (kon,O), koff for the open state (koff,O), kon for the inactivated state (kon,I), and koff for the inactivated state (koff,I) to have any of the three binding rates (0.01, 3, and 100 s−<sup>1</sup> ), and varied them independently to yield 81 different drug combinations. We studied the effects of these IKur blockers in cAF conditions using a [drug] equal to their IC<sup>50</sup> value at 1-Hz pacing for APD and 3-Hz pacing for ERP. Then, we compared the outputs of APD and ERP to no block, 50, and 100% reduction in GKur in cAF conditions (**Figure 6**, dotted lines), along with no block in nSR conditions (**Figure 6**, dashed lines).

**Figures 6A,B** display the relationship between APD (at 1-Hz pacing) and KO/K<sup>I</sup> . Data points in **Figure 6A** are separated by IC<sup>50</sup> cutoffs of 0.1µM, 10µM, and 1 mM, and show that when KO/K<sup>I</sup> < 1, we almost always obtain maximal AP prolongation (this also corresponds to larger IC<sup>50</sup> values). In **Figure 6B**, we separated the points according to the drug's koff,O rate (0.01, 3, or 100 s−<sup>1</sup> ), which revealed that when KO/K<sup>I</sup> > 1, we only obtain significant AP prolongation when koff,O is equal to 3 s−<sup>1</sup> (i.e., the intermediate drug-binding rate). These results in the cAFremodeled atrial cardiomyocyte correspond well with the results from our previous study of IKur inhibitors in nSR (Ellinwood et al., 2017). Nevertheless, none of the 81 simulated O & I inhibitors in **Figure 6** prolong the AP beyond the APD found in nSR at 1-Hz pacing.

**Figures 6C,D** present the relationship between APD at 1- Hz pacing and ERP at 3-Hz pacing for the O & I inhibitors with a variable KO/K<sup>I</sup> ratio. In **Figure 6C**, light gray symbols correspond to KO/K<sup>I</sup> ≤ 1, and dark symbols correspond to KO/K<sup>I</sup> > 1). The O & I blockers displaying favorable pacing-rate selectivity, i.e., producing ERP prolongation at 3-Hz pacing while having moderate effect on APD (and ERP) at 1-Hz pacing, are the ones with KO/K<sup>I</sup> > 1, except if koff,O equals 3 s−<sup>1</sup> . However, as none of the 81 simulated O & I inhibitors in **Figure 6** prolong the APD beyond that found in nSR at 1-Hz pacing, one could argue that none of the drugs is expected to cause harmful AP prolongation when AF is terminated. To try and enrich our metric, in **Figure 6D** we also categorize the drugs according to

3 Hz), (C,D) CaTamp (at 1 and 3 Hz), and (E,F) diastolic [Ca2+] i (at 1 and 3 Hz) are plotted for open and inactivated state blockers with varying binding kinetics, which were simulated via permutations of nine different drug-binding rates of (from 0.01 to 100 s−<sup>1</sup> ) while keeping kon,O = kon,I and koff,O = koff,I. CaTamp is 103.6, 109.4, and 120.4 nM at 1 Hz, and 103.4, 120.4, and 135.9 nM at 3 Hz for drug-free, 50 and 100% IKur block, respectively. Diastolic [Ca2+] i is 157.6, 160.0, and 165.2 nM at 1 Hz, and 253.3, 266.9, and 286.9 nM at 3 Hz for drug-free, 50 and 100% IKur block, respectively.

percent increase in CaTamp. The best-performing drugs will cause ERP prolongation at 3-Hz pacing in cAF (above nSR), and have a positive inotropic effect (**Figure 6D**, black). Corresponding with the results showcased in **Figure 5**, drugs with intermediate binding rates (e.g., koff,O = 3 s−<sup>1</sup> ) may thus be favorable given their stronger inotropic effect.

inactivated state IKur blockers with varying affinities to the open and inactivated states were simulated via permutations of three different rates of binding kinetics (0.01, 3, and 100 s−<sup>1</sup> ). Simulations were equilibrated for 300 beats at 1-Hz pacing or 900 beats at 3-Hz pacing using a [drug] equal to the IC50 value. (A,B) report APD90 values (at 1 Hz) plotted as a function of the ratio of the open to the inactivated state affinity (KO/K<sup>I</sup> ) used in each simulation. (C,D) report APD90 (at 1 Hz) and ERP values (at 3 Hz). Color code in (A) is for IC<sup>50</sup> levels. Symbols in (B,C,D) indicate various koff,O. Shades in (C) reflect either higher affinity to the open or the inactivated state. Color code in (D) corresponds to the variable degree of CaTamp increase (at 1 Hz) induced by IKur block. Horizontal and vertical lines represent APD90 and ERP values obtained in cAF in drug-free conditions, and 50 and 100% reduction in GKur (dotted lines), and in nSR in drug-free conditions (dashed lines).

#### DISCUSSION

In this study, we sought to determine if IKur is a suitable anti-AF target despite it being downregulated in cAF patients, and, if so, what are the kinetic and state-dependent binding properties that maximize anti-AF efficacy and limit potential cardiotoxicity. Building off our previous study in nSR conditions (Ellinwood et al., 2017), we implemented an in silico assessment of IKur inhibitors in cAF atrial cardiomyocyte models, and identified metrics for delineating ideal KV1.5 blockers against AF. Our results point to IKur inhibition as a valid strategy to prolong atrial refractoriness also generating a positive inotropic effect in cAF conditions. Although increasing force generation may not be a useful therapeutic goal at the high atrial rates seen during AF, it can be important to counteract atrial hypocontractility after cardioversion of AF to nSR. Interestingly, our simulations suggest that electrophysiological properties in cAF cardiomyocytes, such as shorter AP and more depolarized plateau potential, both might act to increase efficacy and dampen cardiotoxicity of potential KV1.5-targeting drugs as compared to nSR (Ellinwood et al., 2017; **Figure 7**).

#### IKur Role in APD and ERP Regulation Is Preserved Despite Its Downregulation in cAF

Figure S7 shows the differences in the time courses of Em, IKur, and closed, open, and inactivated state occupancies of KV1.5 in cAF and nSR during the AP. Despite the reduced peak current, the channel stays open later in cAF (at both 1- and 3- Hz pacing) because of the more depolarized AP plateau. Thus, the consequences of IKur inhibition, including the extent of AP

and ERP prolongation, depend not only on IKur magnitude (i.e., maximal conductance), but also on other fluxes affected by AFinduced remodeling, which affect E<sup>m</sup> and thus Em-dependent properties of IKur (**Figure 7**). For example, our group and others have hypothesized that the extent of AP and ERP prolongation due to IKur blockade depends on the AF-induced remodeling of other K<sup>+</sup> currents (Lagrutta et al., 2006; Morotti et al., 2016a; Aguilar et al., 2017; Colman et al., 2017), and relative strengths of ICaL and IKur (Wettwer et al., 2004; Grandi and Maleckar, 2016). Our sensitivity analysis (**Figure 1C** and Figures S1–S6) revealed that APD<sup>90</sup> and ERP are more sensitive to changes in GKur at fast vs. slow pacing rates. Aguilar et al. recently determined that the relative contribution of IKur to AP repolarization increases at higher frequencies because of reduced activation of the rapid delayed-rectifier current IKr (Aguilar et al., 2017). Our results concur with these findings, as our sensitivity analysis shows that APD<sup>90</sup> and ERP are less sensitive to changes in GKr at 3-Hz pacing as compared to 1-Hz pacing in nSR conditions (Figures S2, S3). Most importantly, we also found that GKur impacted the duration of AP repolarization and refractoriness more in cAF vs. nSR (even though this parameter was halved in the cAF model) at 3-Hz, but not at 1-Hz pacing (i.e., fast pacing-rate selectivity). This is a favorable drug property to avoid harmful AP prolongation (which is also limited by the reduced basal APD) if AF is terminated. Similar to Aguilar et al. (2017), our results suggest that the APD- (and ERP)-prolonging effect of IKur block is not affected by IKur downregulation.

#### Enhanced Efficacy and Safety of IKur Inhibitors in cAF vs. nSR

We focused here on O and O & I blockers because we have previously shown that these inhibitors display fast pacing-rate selectivity in nSR (Ellinwood et al., 2017). This choice was also supported by the increased occupancy of open and inactivated states in cAF conditions (**Figure 7**). In our previous report in nSR (Ellinwood et al., 2017), we found that when kon = koff (i) slow drug-binding kinetics caused minimal APD changes and modest ERP prolongation; (ii) intermediate drug-binding kinetics led to substantial AP and ERP prolongation; and (iii) fast drug-binding kinetics failed to produce substantial AP or ERP prolongation at normal pacing rate, but increased the ERP at 3-Hz pacing. While in cAF the overall biphasic relationship between APD/ERP and drug-binding kinetics was maintained (see **Figures 2**–**4**), notably, at 1-Hz pacing rate, even the maximal AP prolongation induced by IKur inhibition in cAF is not sufficient to reach the APD observed in nSR in drug-free conditions. This might indicate that there are less safety concerns for KV1.5 block in cAF patients. At 3-Hz pacing, ERP prolongation is at least equivalent to that caused by a constant 50% reduction in GKur, and, for intermediate and fast drug-binding kinetics, the ERP is equal to or greater than the one obtained in nSR in drugfree conditions. These observations suggest that O and O & I inhibitors have a broader range of efficacy in cAF vs. nSR. We assessed whether closed state inhibitors, which displayed reverserate dependence in terms of potency (Ellinwood et al., 2017), may also be effective and safe anti-AF agents in cAF conditions (Figure S8). We found that these blockers prolong ERP at 3-Hz pacing (Figure S8G) while minimally prolonging the cAF AP at 1-Hz pacing at the fastest drug-binding kinetics (≥30 s−<sup>1</sup> , Figure S8B). However, they had a smaller maximal effect and kinetic range for prolonging the ERP at 3-Hz pacing beyond nSR conditions as compared to O and O & I blockers.

We enriched our metric for quantifying anti-AF efficacy and safety of IKur inhibitors by also accounting for changes in Ca2+-handling parameters, namely CaTamp and diastolic [Ca2+]<sup>i</sup> (Tsujimae et al., 2008; Cavero and Holzgrefe, 2014; Lancaster and Sobie, 2016; Li et al., 2017), which provided additional detail to refine the search for best-performing drugs. In identifying the ideal drug characteristics, we looked for inhibitors that prolong ERP (especially at fast pacing rates), limit APD prolongation at slow pacing-rates, and improve atrial inotropy, i.e., increase CaTamp. Increasing force generation might be a useful outcome after cardioversion to nSR.

When K<sup>O</sup> = K<sup>I</sup> , the best-performing O & I inhibitors were those with intermediate kon rates (3–30 s−<sup>1</sup> ), because they prolonged ERP at 3-Hz pacing and increased CaTamp and diastolic [Ca2+]<sup>i</sup> at 1-Hz pacing (**Figure 5**). These inhibitors also prolonged the AP at 1-Hz pacing and increased CaTamp and diastolic [Ca2+]<sup>i</sup> at 3-Hz pacing—thus potentially predisposing to harmful AP prolongation and Ca2<sup>+</sup> overload. However, we note that such cardiotoxicity is unlikely considering the fact that the maximum increases of APD and CaTamp still remain far below the corresponding values obtained in nSR in drug-free conditions. In our previous study, we highlighted that the bestperforming drugs in nSR were the O & I inhibitors with the fastest drug-binding kinetics (Ellinwood et al., 2017). While these drugs are still efficacious at prolonging ERP at 3-Hz pacing in cAF, they have limited effect on Ca2<sup>+</sup> handling.

When K<sup>I</sup> and K<sup>O</sup> were varied, the relationships between APD at 1-Hz pacing and affinity ratio (KO/KI) are similar to those in nSR (**Figures 6A,B**; Ellinwood et al., 2017), except none of the 81 simulated O & I inhibitors prolonged the AP beyond the duration found in nSR in drug-free condition. Likewise, the relationship between APD at 1-Hz pacing and ERP at 3-Hz pacing is similar to nSR (**Figures 6C,D**; Ellinwood et al., 2017), but none of the drugs exhibit obvious toxicity. The same O & I inhibitors simulated in cAF conditions were more effective at prolonging ERP at 3-Hz pacing rates as compared to nSR conditions. Thus, on average, the same inhibitors in **Figure 6** exhibit less toxicity and greater efficacy in cAF vs. nSR.

In their simulation study, Aguilar et al. concluded that the ability of (simple pore) IKur block to terminate simulated AF was greatly attenuated by remodeling, because the block-induced AP prolongation was insufficient to counteract the strong effects of cAF-induced remodeling (Aguilar et al., 2017). Notably, here we show that depending on the drug-binding kinetics, certain IKur inhibitors can markedly counteract the effect of cAF-associated remodeling, and bring AP and ERP parameters close to nSR values, i.e., have a greater effect than simple pore blockers.

#### Limitations and Future Directions

We presented a theoretical study of the effects of IKur inhibitors in cAF, and compared our results to our previous study in nSR atrial cardiomyocytes. We acknowledge several limitations to the described approach, which provide opportunities for further extensions. First, we only considered direct drug effects on KV1.5, and future analysis should consider multi-channel effects of IKur inhibitors (Ford and Milnes, 2008; Li et al., 2017), as this realistically occurs in vivo in the clinical setting. We only considered cardiotoxicity at the atrial level, assuming that the absence of IKur in ventricles prevents ventricular proarrhythmia. However, this might not be true for real IKur blockers with off-target effects. Here, we simulated IKur block at the cellular level with no contribution of structural tissue remodeling and defined IKur inhibitors' efficacy and toxicity by tracking only electrophysiological properties such as APD, ERP, CaTamp, and diastolic [Ca2+]<sup>i</sup> . While this is an important first step in defining metrics for AF-selectivity, other arrhythmia indices and integration of such simulations into tissue and organ level models would improve our ability to discern bestperforming drug characteristics of IKur inhibitors against AF. Since many antiarrhythmic drugs lose anti-AF efficacy with the progression of the arrhythmia, particularly in patients with atrial cardiomyopathy and comorbidities (Goette et al., 2016), IKur block might be less efficient against AF in the structurally remodeled atrium. Further studies including 2- and 3-dimensional tissue simulations are needed to address this clinically relevant issue. In addition, machine-learning methods have begun to be implemented to analyze AP metrics after the application of a drug and classify the risk (e.g., torsadogenic risk) of the candidate drug (Lancaster and Sobie, 2016). Such methods can also highlight which ion channels contribute most to such risk. Furthermore, this study revealed that the efficacy and toxicity of IKur inhibitors is modulated by the extent of atrial ionic remodeling, and likely by the relative expressions of many ion channels and transporters (Figures S1–S6). Thus, given the differences in AP properties and ion channel expression in patients with AF (Heijman et al., 2014), and differences in IKur remodeling in the right vs. the left atria (Dobrev and Ravens, 2003; Caballero et al., 2010), we hypothesize that certain subpopulations of nSR and cAF patients may be more responsive to therapy with IKur inhibitors, i.e., degree and heterogeneity of IKur remodeling in atrial tissue might impact safety and anti-AF efficacy of drugs. Future studies could identify which cell characteristics lead to more favorable responses to anti-IKur therapy utilizing sensitivity analysis and variations of nSR and cAF models similar to the methods discussed in **Figure 1** and in (Sobie, 2009; Lee et al., 2013; Cummins et al., 2014; Devenyi and Sobie, 2015; Morotti and Grandi, 2017). This information could be useful for a personalized (precision) medicine approach to AF treatment or helpful in suggesting potential combination therapies with IKur inhibitors.

Finally, advancements in high-throughput screening methods (Obergrussberger et al., 2016; Picones et al., 2016; Molokanova et al., 2017) provide functional drug screening capabilities that can be coupled with in silico investigations such as the one described here to help identify actual candidate compounds for in vivo testing. Such technologies can potentially be implemented to simultaneously screen many KV1.5-selective compounds for the desired kinetics, state-dependence, and rate-dependence of IKur block. In addition, multi-parallel recordings from atrial-like cardiomyocytes from induced human pluripotent stem cells is also emerging as a preclinical model for evaluating drugs targeting atrial-specific ion channels, such as KV1.5 (Devalla et al., 2015), particularly in combination with APclamp experiments. These could be coupled with in silico studies such as this one for delineating the ideal properties of AF-selective drugs and gaining a more comprehensive understanding of the arrhythmic risk of candidate compounds.

#### CONCLUSIONS

In this study, efficacy and cardiotoxicity on cAF atrial cardiomyocytes of theoretical IKur inhibitors were assessed in silico. We concluded that IKur is a promising anti-AF target, even if strongly downregulated in cAF condition. We confirmed that steady-state IC<sup>50</sup> values are insufficient to predict how candidate compounds will interact with a dynamically changing electrophysiological substrate, thus emphasizing the importance of accounting for kinetic and state-dependent drug-binding properties. This approach could aid experimental and screening

#### REFERENCES


efforts to identify the complex net impact of IKur inhibition in different AF-remodeling conditions during the pre-clinical drug development process.

#### AUTHOR CONTRIBUTIONS

Designed simulation experiments: NE, SM, EG. Performed modeling and simulations: NE, SM. Wrote the manuscript: NE, DD, SM, EG.

#### ACKNOWLEDGMENTS

The authors would like to thank Dr. Lucía Romero Pérez, Polytechnic University of Valencia, for her critical reading of this manuscript. This work was supported by the National Institute of Health grant R01-HL131517 (to EG and DD), the American Heart Association grant 15SDG24910015 (EG), the Heart Rhythm Society post-doctoral fellowship 16OA9HRS (SM), the Bill Bertken Sudden Death Prevention Fund, and the National Center for Advancing Translational Sciences, National Institutes of Health, through grant number UL1 TR001860 and linked award TL1 TR001861 (NE).

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphar. 2017.00799/full#supplementary-material

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Ellinwood, Dobrev, Morotti and Grandi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Global Optimization of Ventricular Myocyte Model to Multi-Variable Objective Improves Predictions of Drug-Induced Torsades de Pointes

Trine Krogh-Madsen1, 2, 3, Anna F. Jacobson<sup>3</sup> , Francis A. Ortega<sup>4</sup> and David J. Christini 1, 2, 3 \*

*<sup>1</sup> Greenberg Division of Cardiology, Department of Medicine, Weill Cornell Medicine, New York, NY, United States, <sup>2</sup> Institute for Computational Biomedicine, Weill Cornell Medicine, New York, NY, United States, <sup>3</sup> Cardiovascular Research Institute, Weill Cornell Medicine, New York, NY, United States, <sup>4</sup> Physiology, Biophysics and Systems Biology Graduate Program, Weill Cornell Graduate School, New York, NY, United States*

#### Edited by:

*Stefano Morotti, University of California, Davis, United States*

#### Reviewed by:

*Jamie Vandenberg, Victor Chang Cardiac Research Institute, Australia Thomas Hund, The Ohio State University, United States Kelly C. Chang, United States Department of Health and Human Services, United States*

> \*Correspondence: *David J. Christini dchristi@med.cornell.edu*

#### Specialty section:

*This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology*

Received: *07 October 2017* Accepted: *04 December 2017* Published: *19 December 2017*

#### Citation:

*Krogh-Madsen T, Jacobson AF, Ortega FA and Christini DJ (2017) Global Optimization of Ventricular Myocyte Model to Multi-Variable Objective Improves Predictions of Drug-Induced Torsades de Pointes. Front. Physiol. 8:1059. doi: 10.3389/fphys.2017.01059* *In silico* cardiac myocyte models present powerful tools for drug safety testing and for predicting phenotypical consequences of ion channel mutations, but their accuracy is sometimes limited. For example, several models describing human ventricular electrophysiology perform poorly when simulating effects of long QT mutations. Model optimization represents one way of obtaining models with stronger predictive power. Using a recent human ventricular myocyte model, we demonstrate that model optimization to clinical long QT data, in conjunction with physiologically-based bounds on intracellular calcium and sodium concentrations, better constrains model parameters. To determine if the model optimized to congenital long QT data better predicts risk of drug-induced long QT arrhythmogenesis, in particular Torsades de Pointes risk, we tested the optimized model against a database of known arrhythmogenic and non-arrhythmogenic ion channel blockers. When doing so, the optimized model provided an improved risk assessment. In particular, we demonstrate an elimination of falsepositive outcomes generated by the baseline model, in which simulations of nontorsadogenic drugs, in particular verapamil, predict action potential prolongation. Our results underscore the importance of currents beyond those directly impacted by a drug block in determining torsadogenic risk. Our study also highlights the need for rich data in cardiac myocyte model optimization and substantiates such optimization as a method to generate models with higher accuracy of predictions of drug-induced cardiotoxicity.

Keywords: cardiac modeling, model optimization, safety pharmacology, long QT, in silico drug trial, cardiotoxicity

# 1. INTRODUCTION

Mathematical models of cardiac electrophysiology are at the cusp of usage in a variety of clinical and pre-clinical applications, including safety pharmacology (Mirams et al., 2012; Zhang et al., 2016). In particular, mathematical modeling forms a central component in the Comprehensive in Vitro Proarrhythmia Assay (CiPA) initiative, a proposed strategy for progressing drug safety testing (Sager et al., 2014; Colatsky et al., 2016; Fermini et al., 2016; Gintant et al., 2016).

In terms of cardiotoxicity, drug safety testing aims to avoid Torsades de Pointes (TdP), a life-threatening ventricular tachycardia. Indeed, occurrences of drug-induced TdP in patients have

lead to regulatory bans and market withdrawals of several drugs (Mirams et al., 2011). TdP risk is associated with prolongation of the QT interval on the electrocardiogram, in particular due to block of the hERG channel, which carries the rapid delayed rectifier current (IKr; Sanguinetti et al., 1995; Straus et al., 2005; Hoffmann and Warner, 2006). However, multiple other currents and dynamics are of importance to torsadogenesis, and including measured effects of drugs on multiple channels, rather than just hERG, into TdP risk stratification improves risk prediction (Kramer et al., 2013; Mistry et al., 2015). Mechanistically, TdP initiation is linked to early afterdepolarizations (EADs) at the cellular level. Triggering of these EADs may depend directly on multiple different ionic currents, including the L-type calcium current (ICaL) and the late sodium current (INaL) (Lankipalli et al., 2005; Hale et al., 2008), and may also depend on intracellular calcium and sodium dynamics (Terentyev et al., 2014; Kim et al., 2015; Xie et al., 2015; Krogh-Madsen and Christini, 2017), implying that the levels of the ionic transporters that control these concentrations (e.g., the sodium-calcium exchanger and the sodium-potassium pump) are important for torsadogenesis. Indeed, recent in silico work have pointed to the magnitudes of these two transporters as having large impact on TdP risk (Lancaster and Sobie, 2016).

Despite the proposed usage of mathematical models in safety pharmacology, even recent and sophisticated models of human ventricular myocyte electrophysiology perform poorly when simulating each of the most typical congenital long QT (LQT) syndromes (Mann et al., 2016). This naturally raises concerns about the ability of these in silico models to predict drug-induced LQT and TdP. However, using a global optimization strategy, in silico models can optimized to reproduce repolarization delays consistent with those seen clinically in the congenital LQT patient datasets, providing optimism for clinically-related model usage (Mann et al., 2016). A concern remains, however, as to whether these in silico models, optimized in terms of action potential properties, replicate dynamics of intracellular ionic concentrations well enough to reliably predict TdP risk. For example, when optimizing a model in terms of its electrical activity only, it can be difficult to correctly identify parameters that mainly control ionic concentrations (Groenendaal et al., 2015). Indeed, previous modeling studies have shown how identical-looking action potentials, modeled using different combinations of model parameters, can have differing calcium transients (Sarkar and Sobie, 2010).

To investigate this possible limitation, we therefore carried out a multi-variable optimization, using both clinical congenital LQT data and constraints on the concentrations on intracellular Ca2<sup>+</sup> and intracellular Na<sup>+</sup> ([Ca2+]<sup>i</sup> and [Na+]i). We then asked whether optimized models that better represent the congenital LQT syndromes might allow for more accurate and more reliable modeling of acquired LQT and TdP risk. To this end, we simulated 86 cases of multi-channel drug block with known TdP risk level (Lancaster and Sobie, 2016) and found that the model optimized in terms of both action potential and [Ca2+]<sup>i</sup> , and [Na+]<sup>i</sup> data, better predicts TdP risk.

# 2. METHODS

# 2.1. Cell Model and Drug Simulations

Simulations were performed using the O'Hara-Rudy (ORd; O'Hara et al., 2011) human ventricular ionic model as the baseline model, as this is the model proposed to be used in the CiPA initiative (Colatsky et al., 2016; Fermini et al., 2016). We used endocardial myocyte parameter settings except where otherwise noted (**Figure 4A**). We used a 1 Hz pacing rate and corresponding steady-state initial conditions (O'Hara et al., 2011). For each perturbation to the model (simulating drug block or LQT syndromes and parameter changes during the optimization; detailed below), the model was simulated for 500 beats prior to collecting data. We quantified action potential duration to 90% (APD90) or 50% (APD50) repolarization, as indicated. Calcium transients were characterized by diastolic level (the minimum [Ca2+]<sup>i</sup> attained within an action potential cycle cycle) and systolic concentration (the peak [Ca2+]<sup>i</sup> reached during an action potential). The [Na+]<sup>i</sup> varies little within a single action potential and was measured as the maximum value.

For our drug simulations, we used the datasets of Kramer et al. (2013) and Mirams et al. (2011) as curated by Lancaster and Sobie (2016) with an associated yes/no risk of torsadogenesis. For each drug, the dataset gives its estimated effective free therapeutic plasma concentration (EFTPC), along with IC<sup>50</sup> values for block of the channels generating IKr, ICaL, and the fast sodium current (INa). Drug effect on each channel type was modeled as a conductance block based on a Hill equation with a coefficient of 1:

$$G\_{\rm x,drug} = G\_{\rm x} \left( 1 + \frac{\rm EFTPC}{IC\_{50,x}} \right)^{-1},\tag{1}$$

where Gx,drug is the maximal conductance of channel x in the presence of the drug. The dataset contains 86 entries, with some duplicate drugs modeled differently by the two original sources. There are therefore 68 different compounds in the set, covering a variety of intended clinical use, including anti-arrhythmics, anti-histamines, antipsychotics, hypertension/angina drugs, and others.

## 2.2. Drug Classification

To classify model output generated by these drug simulations we used a Support Vector Machine (SVM; Ben-Hur et al., 2008). We used linear decision boundaries separating two categories of data: TdP risk and no TdP risk. These decision boundaries were computed as the solution to a minimization of an error (E) calculated as the sum of squared distances between the location of miscategorized points and the boundary. Because the two variables used in the classification (APD<sup>50</sup> and diastolic [Ca2+]i) have very different absolute values, we normalized them to baseline (i.e., no drug) values.

In general, the minimum value of E will take on different values when using different cell models to simulate drug effects, indicating that the separation of data points by category is better for some models than others. Therefore, to compare goodness of the classification between models and also to determine sensitivity of the decision boundaries, we calculate regions for which E remains below a threshold value (E<sup>∗</sup> ), which we set to twice the value of the lowest value of E found among the four tested models.

#### 2.3. Model Optimization

We optimized the baseline ORd model based on clinical data from LQT patients, following a similar strategy as Mann et al. (2016) and using their QT interval data for control patients and patients with one of the three most prevalent congenital LQT syndromes: LQT1, LQT2, or LQT3. The QT interval data from LQT1 and LQT2 patients came from a patient cohort with heterozygote nonsense mutations only, as that can be mimicked in the model by decreasing the conductances of IKs and IKr by 50%, respectively. The LQT3 cohort data is more heterogenous and the subtype was simulated by increasing the conductance of INaL by a factor that was allowed to vary as part of the optimization process. The amount of QT interval prolongation in these patient groups was 12.2% for LQT1, 16.6% for LQT2, and 16.2% for LQT3. Mapping the delayed repolarization measured clinically as QT interval prolongation directly to APD<sup>90</sup> prolongation in the cell model, the objective data set was 267.97 ms (control), 301.14 ms (LQT1), 312.20 ms (LQT2), and 311.55 (LQT3).

In its simplest setup, the optimization was designed to minimize a sum-of-squares error from the APD<sup>90</sup> objective when subjecting the model to control conditions and each of the LQT subtypes 1, 2, and 3. We refer to this as the "APDLQT" optimization. In other optimizations, we included [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> information in the objective to improve the optimization outcome. This "multi-variable" optimization was done by adding a hefty error (200 ms squared) if [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> fell outside a certain range during the control condition. We used a range of 0.05–0.15µM for diastolic [Ca2+]<sup>i</sup> , 0.3– 0.7 µM for systolic [Ca2+]<sup>i</sup> , and 7–10 mM for [Na+]<sup>i</sup> based on measurements in human ventricular myocytes and recent modeling work (Beuckelmann et al., 1992; Piacentino et al., 2003; Grandi et al., 2010).

For the optimization method, we used a genetic algorithm (GA), which is a global optimization method that has been successful in optimizing cardiac ionic models to experimental and simulated data (Syed et al., 2005; Bot et al., 2012; Kaur et al., 2014; Groenendaal et al., 2015). We used a population size of 200 individual model instantiations and ran each GA for 50 generations. All other settings specific to the GA (detailing selection, crossover, mutation, and elitism) were defined as detailed previously (Bot et al., 2012). Because of the stochasticity inherent to the GA, each optimization was run ten times. We used the run resulting in the lowest error as the optimized model.

The parameters to be determined in the optimization process are scaling factors for the currents IKr, ICaL, INaL, the slow delayed rectifier current (IKs), the sodium-calcium exchange current (INCX), the sodium-potassium pump current (INaK), and the extent of INaL increase with simulated LQT3. All scaling parameters were allowed to vary from 0.1% to 10-fold their values in the baseline model.

Note that for ease and consistency we will refer to current scaling factors as scaling of maximal conductances (and use GKr, GCaL, GNaL, GKs, GNCX, and GNaK for the currents defined above), although some currents are technically scaled by a permeability or a maximal charge carried.

# 3. RESULTS

#### 3.1. Sensitivity of APD, [Ca2+]<sup>i</sup> , and [Na+]<sup>i</sup> in Baseline Model

To help guide our optimization procedure, we first did a sensitivity analysis to the major conductances as parameters with low sensitivity are problematic to determine in an optimization.

In the baseline ORd model, the action potential duration of the ORd model is highly sensitive to changes in IKr (**Figure 1A**). For example, when decreasing GKr by 50% to simulate LQT2, the response is a prolongation of APD<sup>90</sup> by 117 ms (44%), substantially larger than the QT interval prolongation of 68 ms (16.6%) seen in LQT2 patients with heterozygote nonsense mutations (Mann et al., 2016). The APD has an intermediate sensitivity on GCaL, but shows little sensitivity to variations in GKs and GNaL, the currents associated with LQT1 and LQT3, respectively. For example, reducing GKs by 50% to mimic LQT1, gives a modest 8-ms (3%) APD<sup>90</sup> prolongation, much shorter than the 51 ms (12%) QT interval prolongation seen clinically (Mann et al., 2016).

As expected, the calcium transient has a very different parameter sensitivity dependence. It depends strongly on the conductances of ICaL and INCX, with a 50% increase in GCaL or a 50% reduction of GNCX increasing systolic [Ca2+]<sup>i</sup> by almost 0.2 µM (**Figure 1B**). The calcium dynamics also has a significant dependence on GNaK, which only controls [Ca2+]<sup>i</sup> indirectly via [Na+]<sup>i</sup> changes that regulate INCX. Indeed, [Na+]<sup>i</sup> depends sensitively on GNaK, with a 50% reduction in GNaK resulting in a 1.7 mM increase in [Na+]<sup>i</sup> (**Figure 1C**). Variations in the remaining key conductances have little influence on [Na+]<sup>i</sup> levels.

These results are consistent with those presented previously for ±10 and ±20% parameter variations in the ORd model (O'Hara et al., 2011).

# 3.2. Model Optimization

As it is difficult to estimate parameters to which an output is not sensitive, the above analysis suggests that if optimizing the baseline ORd model to APD data only, it will be problematic to estimate many of the conductance parameters. Including repolarization delay data from LQT types 1, 2, and 3 as additional information to the objective may help determine the scaling of GKs, GKr, and GNaL. Further, pinpointing these parameters may narrow down other conductances that correlate with these more directly determined parameters (Groenendaal et al., 2015). The sensitivity analysis also indicates that inclusion of calcium transient data to the optimization objective should help determine GNCX and GNaK scaling, and that incorporation of [Na+]<sup>i</sup> may further help determination of GNaK scaling.

We therefore optimized the baseline ORd model to both clinical QT interval data from LQT patients and [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> as detailed in section 2.3. The model optimized to this multi-variable objective produces APD<sup>90</sup> values that are within 3% of their target values (**Figure 2**). The optimized parameter

calcium transient (quantified here as systolic [Ca2+] *i* ) depends sensitively on GCaL, GNCX, and GNaK. (C) The level of [Na+] *i* depends mainly on GNaK. Conductances were varied by ±20% (light blue/red) and ±50% (dark blue/red) of baseline values.

FIGURE 2 | APD values of optimized models. Horizontal lines give control APD90 (black) as well as APD90 surrogates for QT interval prolongation in LQT patients (colored). These APD values form the optimization objective in the simplest case ("APDLQT"). For the multi-variable optimization ("multi-var"), the objective also include constraints on [Ca2+] *<sup>i</sup>* and [Na+] *i* . Dots give APD90 values under control simulations (black) and during LQT simulations (LQT1, red; LQT2, blue; LQT3, green). The overestimation of the LQT2 response and the underestimation of the LQT1 response in the baseline ORd model are eliminated in the optimized models. Relative APD90 prolongation in the baseline model is 3.0, 43.8, and 15.8%, for LQT1, LQT2, and LQT3, respectively. For the multi-variable optimized model, relative APD90 prolongation is 14.9, 22.9, and 18.6% for LQT1-3, while for the APDLQT-optimized model the corresponding values are 14.5, 19.4, and 17.0%. The target QT interval values are 12.2, 16.6, and 16.2%.

scaling factors are given in **Table 1**. The optimized model has a much increased GKs, resulting in a larger response to the simulated LQT1 condition, matching the target data (**Figure 2**).

Optimizing the baseline model to APD values only (i.e., omitting the [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> constraints) results in slightly better matching of the objective (**Figure 2**; errors with 2%). Optimized parameter values are very different, with large increases in scaling of GCaL and GNaK in addition to the enhanced GKs scaling (**Table 1**).

TABLE 1 | Scaling factors for optimized models.


*The optimization gave estimated parameters for scaling of the currents IKs, IKr, ICaL, INCX , INaK, and INaL, and for the increase of INaL during simulated LQT3. Optimizing to APD values only (APDLQT ) resulted in a very different parameter set compared to the multivariable optimization that include of [Ca2*+*]<sup>i</sup> and [Na*+*]<sup>i</sup> constraints. In particular, it resulted in much increased scalings for ICaL and INaK.*

Despite the diversity in parameter scalings among the baseline and the optimized models, the action potential morphology is quite similar across these differently parameterized models (**Figure 3A**). We also include for comparison the action potential generated by Mann et al. in an optimization to clinical LQT data under both baseline and β-adrenergic conditions ("APDLQT±βAdr" optimization, Mann et al., 2016). The main difference among the action potential waveforms is a depolarization of phase 2 of the action potential, the amount of which correlates with the upscaling of GCaL from the baseline model (about 2–4 in the multivariable and APDLQT±βAdr models, and almost 10 in the APDLQT model).

However, calcium transients and [Na+]<sup>i</sup> levels are vastly different across models (**Figures 3B,C**). When including [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> constraints in the optimization, the optimized calcium transient and [Na+]<sup>i</sup> level are very close to those of the baseline model, despite the allowed ranges being relatively large (0.05–0.15 µM for diastolic [Ca2+]<sup>i</sup> , 0.3–0.7 µM for systolic [Ca2+]<sup>i</sup> , and 7–10 mM for [Na+]i). In our optimizations, when optimizing to APD only, the calcium transient is significantly enhanced. This is consistent with the much boosted GCaL and the decreased GNCX scaling (relative to the multi-variable optimization) both of which favor a larger calcium transient. In addition, the GNaK scaling is much increased when optimizing to APD only, consistent with the lower [Na+]<sup>i</sup> . For the

the different parameter sets underlying the different solutions give rise to some waveform variation. (B) Despite having comparable action potentials, models optimized without constraints on [Ca2+] *<sup>i</sup>* and [Na+] *<sup>i</sup>* can have widely different calcium transients. Shaded areas give constraints on minimum and maximum [Ca2+] *i* (0.05–0.15 and 0.3–0.7µM, respectively). (C) Without constraints on [Ca2+] *<sup>i</sup>* and [Na+] *i* , optimization can result in models with very low [Na+] *i* levels. Shaded area indicate constraint on [Na+] *i* (7–10mM). "APDLQT±βAdr" designates the original optimization to clinical LQT data under normal and β-adrenergic stimulation conditions by Mann et al. (2016).

APDLQT±βAdr optimized model (Mann et al., 2016), both GNCX and GNaK were much increased relative to baseline (scaling of 2.95 and 9.12, respectively), resulting in a small-amplitude calcium transient and a low [Na+]<sup>i</sup> .

#### 3.3. TdP Prediction

To test how well the optimized models predict TdP risk, we used a dataset consisting of drugs blocking IKr, ICaL, and INa to varying degrees, and their associated risk of torsadogenesis (TdP positive or TdP negative; Lancaster and Sobie, 2016). As demonstrated previously, while many of the drugs in this dataset that carry a TdP risk do prolong APD, some drug simulations predict an increased APD for TdP negative drugs (**Figure 4A**, Lancaster and Sobie, 2016). In particular, in the baseline model, simulations of three non-torsadogenic drugs results in action potential prolongation of 15–25 ms (one of these is noted by a black dot in **Figure 4A**). As demonstrated by Lancaster and Sobie, simulations of those three drugs also led to a decreased diastolic [Ca2+]<sup>i</sup> , which was not seen in the TdP positive drugs. Therefore, including diastolic [Ca2+]<sup>i</sup> as a second metric (APD<sup>50</sup> being the first) by which to classify the drugs, allows for a correct TdP risk categorization of these three otherwise false positives (**Figure 4A**, Lancaster and Sobie, 2016). Indeed, using APD<sup>50</sup> and diastolic [Ca2+]<sup>i</sup> in combination correctly classifies drugs in the dataset with high specificity and sensitivity (**Figure 4A**, Lancaster and Sobie, 2016).

For the APDLQT±βAdr optimized model (Mann et al., 2016), qualitatively similar results are observed (**Figure 4B**). The particular values of diastolic [Ca2+]<sup>i</sup> over which TdP positive drugs are separated from TdP negative drugs are shifted, reflecting baseline differences. The same three TdP negative compounds that resulted in APD prolongation in the baseline model, give increased APD<sup>50</sup> in this optimized model as well.

When simulating drug application in the multi-variable optimized model, predictions are improved (**Figure 4C**). In particular, none of the TdP negative drugs result in APD<sup>50</sup> prolongation beyond 5 ms, implying that APD<sup>50</sup> prolongation in itself is a strong predictor of torsadogenic risk in this model. In addition, many of the TdP negative compounds result in more substantial reductions in APD<sup>50</sup> and/or diastolic [Ca2+]<sup>i</sup> compared to the baseline and the APDLQT±βAdr optimized models. There is therefore an increased flexibility to the positioning of the decision boundary separating the TdP positive from the TdP negative drugs (dashed lines in **Figure 4C** mark off area within which the categorization error remains less than the threshold value, E<sup>∗</sup> ).

For the APDLQT optimized model, the classification is less successful (**Figure 4D**). The same three TdP negative drugs that resulted in false positive APD prolongation in the baseline and in the APDLQT±βAdr optimized model do so here. Further, simulation of several TdP positive drugs result in decreased diastolic [Ca2+]<sup>i</sup> without much change in APD and therefore form false negatives in this categorization. The presence of these false positives and negatives pose a challenge to the classification and prevents the categorization error from getting below the threshold value regardless of the location of the decision boundary.

What are the ionic mechanisms underlying the improvement in predictive ability by the multi-var model? The simulated drugs that give the false positive APD prolongations for the baseline and APD-optimized models are piperacillin and verapamil (note that two independent measurements for verapamil are included in the dataset). These drugs block both ICaL and IKr. We investigated the ionics of verapamil (black dots in **Figure 4**) in more detail, as verapamil is a well-known example of an IKr-blocking agent that does not prolong the QT-interval and is not torsadogenic (Redfern et al., 2003).

A simulation of verapamil application in the baseline model is shown in **Figure 5A**. Drug-induced reductions in outward IKr and inward ICaL are seen to be of similar amplitude and

here as it was determined to give the best classification in Lancaster and Sobie, 2016. Using the endocardial baseline model yields very similar results). (B) APDLQT±βAdr optimized model. (C) Multi-variable optimized model. (D) APDLQT optimized model. Dotted lines indicate no-drug control values of APD<sup>50</sup> and diastolic [Ca2+] *i* . Colors for the different models correspond to the color scheme in Figure 3. Solid lines give decision boundaries between torsadogenic (open circles) and non-torsadogenic drugs (filled circles). Dashed lines demarcate regions within which the categorization error remains below a threshold value (E\*). Using the multi-variable optimized model, all drugs that prolong APD50 by more than 5 ms are known TdP risk drugs. Verapamil (marked by black dot) is an example of a TdP negative drug that significantly prolongs the AP in the baseline and APD-optimized models but not in the multi-variable optimized model.

balance each other during the first 200 ms of the action potential. When ICaL inactivates at this time, the loss of outward IKr is largely unopposed, leading to a decreased rate of repolarization and APD prolongation. In the multi-variable optimized model, the non-drug action potential is generated through a near-balance between a much increased ICaL and a larger INCX providing inward current against the outward currents IKr and IKs, with IKs now being of similar size as IKr (**Figure 5B**). When simulating verapamil application in the multi-var optimized model, there is a loss of inward current by the direct effect of ICaL conductance block and because of a reduction of INCX due to the decreased calcium transient. As both ICaL and INCX are increased in the multivariable optimized model relative to the baseline model, the loss of inward current with verapamil application is amplified, preventing repolarization delays. Further, the increased IKs in the multi-var model helps maintain repolarization under verapamil application. Thus, factors beyond the scaling of the directly blocked currents IKr and ICaL contribute to the drug-induced response.

# 4. DISCUSSION

We investigated optimization of conductance parameters in a human ventricular myocyte model to match clinical data from LQT patients using constraints on the concentrations of intracellular calcium and sodium ions. Without these constraints, parameter optimization can lead to models with unphysiological calcium transient and [Na+]<sup>i</sup> . To test the hypothesis that the optimization would allow the model to make improved predictions of drug-induced arrhythmogenesis, we investigated the ability of the model to determine TdP risk in a large set of known drugs. We found that using the optimized model improves TdP prediction in two complementary manners. First, simulations of three TdP negative drugs that result in APD prolongation using the baseline model result in no or minimal APD prolongation when using the optimized model. Second, when using both diastolic [Ca2+]<sup>i</sup> and APD<sup>50</sup> for the modelbased drug classification, the optimized model gives an improved separation between the TdP positive and negative drugs, measured as an increased flexibility in the positioning of the

a scaling of GCaL by 0.64, a scaling of GKr by 0.55, and a scaling of GNa by 0.998) decrease IKr by similar amounts in the baseline and in the multi-variable optimized models. However, due to the up-regulated ICaL and INCX in the optimized model, it sustains a larger loss of inward current than the baseline model. Further, the increased IKs in this model provides a repolarization reserve. Together, these effects lead to a maintained APD50 value and an only slightly increased value of APD90.

decision boundary. Based on these findings, our main conclusion is that intracellular ionic concentrations are important for safety pharmacology modeling.

#### 4.1. In Silico TdP Prediction

Other studies have investigated ionic-model-based TdP prediction using different approaches. It is clear from these studies that a range of strategies can be applied to improve TdP prediction. First, there is improvement to the baseline model, which in itself can involve a number of approaches. One is to optimize a model to clinical LQT data, as done here or previously (Mann et al., 2016). Conceptually, fitting a cellular model to clinical ECG data rather than to experimental cellular-level data may appear counter-intuitive, but it makes sense given that the model is used to predict an organ-level, rather than a cellularlevel, arrhythmia risk. Another model optimization approach is to tune the model to experimental data obtained with ion channel blockers. Such data can be additional to the data used originally to build the baseline model, as in the example of a canine model that upon optimization delivered improved prediction of test drug data (Davies et al., 2012). In another article in this Research Topic, Dutta et al. (2017) used drug data presented in the original ORd model paper to reparameterize the ORd model. This optimization was done in conjunction with another model improvement strategy: re-casting the IKr description as a Markov model with state- and voltage-dependent drug block (Li et al., 2017). An alternative strategy to optimizing a model is to generate a population of models to represent inter-individual and/or inter-cell variability, potentially recapitulating variability in drug response across a heterogeneous population (Lancaster and Sobie, 2016; Britton et al., 2017). Another contribution to this Research Topic demonstrates that such population models predict TdP risk better than using a single baseline model (Passini et al., 2017). Population models may also be used to gain mechanistic insights into arrhythmogenesis. For example, Passini et al. determined that different sub-populations of models had different propensities to repolarization abnormalities, with low conductances for the outward currents IKr and INaK and increased levels of ICaL and INCX making models more prone to repolarization abnormalities, emphasizing that currents other than IKr are important in this aspect.

Second, TdP prediction may be improved by selection of better risk measures. While repolarization delay (APD or QT interval prolongation) has high sensitivity to TdP positive drugs, its specificity is more limited, with some drugs prolonging QT interval, yet carrying only low TdP risk (e.g., amiodarone; Sager et al., 2014). Measures that may be useful in risk stratification include diastolic [Ca2+]<sup>i</sup> (Lancaster and Sobie, 2016) as employed here. While this measure was selected, in combination with APD50, from a range of action potential and calcium transient biomarkers through a machine learning process, there is a mechanistic basis as to why [Ca2+]<sup>i</sup> levels may be associated with TdP risk, as abnormal intracellular calcium dynamics and spontaneous calcium release is associated with EAD formation, a cellular-level trigger of TdP (Lancaster and Sobie, 2016; Nemec et al., 2016 ˇ ). Another risk measure proposed from in silico work is the net charge carried during the action potential by six major ionic currents (Dutta et al., 2017; Li et al., 2017). This measure may also be mechanistically linked to TdP arrhythmogenesis, as it is indicative of robustness against EAD generation under a GKr-reduction challenge (Dutta et al., 2017). Use of repolarization abnormality occurrence (i.e., EADs or incomplete repolarization) in simulations as a metric for TdP risk may also present a viable stratification pathway (Passini et al., 2017). Given the direct link to arrhythmogenesis, this seems like a promising risk marker, but a possible limitation lies in its use of highly elevated drug concentrations to trigger the repolarization abnormalities, which may lead to an overestimation of the number of false negatives. Use of this metric rather than APD prolongation improves TdP prediction in a population of models, but not in the baseline ORd model (Passini et al., 2017).

In summary, it is clear that in silico cell models can be improved to better predict TdP risk and that measures beyond APD prolongation are helpful to this end, but it also apparent that significant uncertainties remain as to how to best carry out the modeling and the arrhythmia risk prediction.

#### 4.2. Kr/Ks Balance

Our optimization resulted in significant rescaling of many parameters, in particular GKs, which was increased approximately eight-fold. This is comparable to the scaling of 5.75 found in Mann et al. (2016). In the baseline ORd model, IKs is relatively small under control conditions, its peak value during an action potential being roughly 10 times smaller than peak IKr. Significant upscaling of this current is therefore necessary to recapitulate the clinical LQT1 phenotype showing substantial QT interval prolongation with loss of IKs. Likewise, the Grandi-Bers model, another recent human ventricular myocyte model (Grandi et al., 2010) that has little reliance on IKs under control conditions, requires sizeable upscaling of GKs (about 25-fold) to reproduce the LQT1 clinical data (Mann et al., 2016). In contrast, the ten Tusscher-Panfilov human ventricular myocyte model (ten Tusscher and Panfilov, 2006) which has similarly sized IKs and IKr, requires increased GKr (2.65-fold) and decreased GKs (0.41-fold) to reproduce the clinical LQT dataset (Mann et al., 2016).

These substantial increases in GKs required for the ORd and the Grandi-Bers models to reproduce the clinical LQT data are at odds with the IKs ranges recorded experimentally. Factors that may contribute to this disagreement include: (1) Differences between levels of β-adrenergic-dependent kinases and phosphorylation which regulate IKs and exacerbate LQT1 (Wu et al., 2016); (2) Transmural or other intra-heart heterogeneity with some regions having especially delayed repolarization; (3) Methodological experimental limitations with IKs rundown and/or damage of the IKs channel due to enzymatic digestion—however, the recordings that formed the basis of GKs in the ORd model were done in small tissue preparations using microelectrodes for the express purpose of mitigating these complications (O'Hara et al., 2011).

The IKs conductance was also increased (by 87%) in the recent optimization of the ORd model with the Markov IKr formulation to the original O'Hara et al. data (Dutta et al., 2017). While this approximately doubled IKs at baseline, IKs remained much smaller than IKr (by about five-fold) and would not be expected to be able to reproduce the LQT1 phenotype. Because the particular balance between IKr and IKs can be important for action potential stability and EAD generation (Devenyi et al., 2017), one may expect a model with large GKs to behave differently from a model with smaller GKs model in terms of arrhythmogenesis. Because the reasons for the discrepancy between the experimental and the clinical IKs data are not known, it will likely be useful to the field to have both a model with large GKs, replicating the clinical LQT data, and a model with smaller GKs, replicating the experimental data.

The mismatch between the experimental and the clinicallybased estimations of GKs also raises broader questions regarding how to best handle inconsistent data in model development. Our approach here has been to use data of perceived highest relevance to the particular type of predictions made, i.e., to use clinicallybased parameter estimations to predict clinical arrhythmia risk. This approach is in line with the general strategy of using data specific to a particular system (e.g., a cell or a patient) to generate a model specific to that system. However, the best way forward may be to couple rigorously uncertainty in model parameters to uncertainty in model predictions using uncertainty quantification tools (Johnstone et al., 2016).

# 4.3. Effect of Verapamil on Action Potential Duration

The balance between different currents is also important for determining a model's response to simulated drug block. The anti-hypertension and anti-angina drug verapamil blocks ICaL and IKr, does not prolong the QT interval, and does not prolong APD in recordings from human trabeculae (Redfern et al., 2003; Britton et al., 2017). However, different human in silico models give different responses to simulated verapamil application. The Grandi-Bers and the ten Tusscher-Panfilov models predict action potential shortening in response to verapamil (Mirams et al., 2011, 2012). In variations of the ORd model, verapamil almost always prolongs the APD, but the response varies depending on drug concentration, on how block is modeled, and on whether a Markov model is used for IKr (Britton et al., 2017; Dutta et al., 2017; Passini et al., 2017).

One hypothesis as to why verapamil does not prolong APD is that its block of IKr is compensated for by block of ICaL. Using our multi-var optimized model, we show here that in addition to the block of ICaL, a secondary reduction in INCX (due to the decreased calcium transient) is important in offsetting the IKr block by verapamil. The size of the IKs current is also important in determining APD under IKr block conditions as IKs provides a repolarization reserve. However, IKs level in itself is not predictive of APD shortening with verapamil since in the APDLQT optimized model, which has a much increased repolarization reserve in IKs, verapamil leads to APD prolongation.

#### 4.4. Limitations

There are several limitations to our modeling and optimization approach. We allowed large ranges of the scaling (0.1% to 10-fold) of the parameters to be estimated in the optimization. Consequentially, the conductance scalings may be unphysiologically large, with, e.g., GKs becoming larger than estimated experimentally. However, we are explicitly not attempting to make the best model of a single cell or small tissue, but, rather, a model capable of making clinically relevant predictions. We did not include the clinical data from control and LQT types 1, 2, and 3 patients during β-adrenergic stimulation (Mann et al., 2016) in the optimization objective

#### REFERENCES


as preliminary optimizations with this addition resulted in adrenergically stimulated action potentials having unsmooth repolarization profiles, characterized by slow late repolarization. Due to experimental difficulties in determining absolute values of [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> , we based the allowed ranges of these mainly on modeling work, particularly the ORd and the Grandi-Bers models. While experimental measurements of [Ca2+]<sup>i</sup> in human ventricular myocytes are consistent with the simulated values (Beuckelmann et al., 1992; Piacentino et al., 2003), reported measurements of [Na+]<sup>i</sup> are much higher (∼20 mM), but may be overestimated (Pieske et al., 2002; Grandi et al., 2010). While the inclusion of bounds on [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> provided additional information to constrain conductance parameters, it is likely that inclusion of more data into the objective would help constrain parameters further. Such data could include more repolarization markers, further calcium transient features, and drug block data.

We modeled the drug application using a simple conductance block, although some drugs are known to block in a statedependent manner (Mirams et al., 2011; Di Veroli et al., 2014; Britton et al., 2017; Dutta et al., 2017). However, use of this simpler approach allowed us to simulate a larger drug data set. We used a single model for the drug simulations. It might be valuable in future work to generate a population of models around the optimized model to potentially improve predictions and to give insights into ionic mechanisms underlying population heterogeneity in drug responses.

# AUTHOR CONTRIBUTIONS

TK-M: Designed study, carried out simulations, and analyzed data; AFJ and FAO: Implemented the optimization software. All authors contributed to critical revision of the manuscript.

# FUNDING

This work was supported by funding from the National Institutes of Health grant U01HL136297 (to DJC). AFJ acknowledges funding from the Weill Cornell Medicine & Memorial Sloan Kettering Cancer Center Computational Biology Summer Program.


calcium precipitate arrhythmic storms? Prog. Biophys. Mol. Biol. 120, 210–221. doi: 10.1016/j.pbiomolbio.2015.11.00


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Krogh-Madsen, Jacobson, Ortega and Christini. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment

Sara Dutta, Kelly C. Chang, Kylie A. Beattie, Jiansong Sheng, Phu N. Tran, Wendy W. Wu, Min Wu, David G. Strauss, Thomas Colatsky † and Zhihua Li\*

*Division of Applied Regulatory Science, Office of Clinical Pharmacology, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, MD, United States*

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Eric A. Sobie, Icahn School of Medicine at Mount Sinai, United States Colleen E. Clancy, University of California, Davis, United States*

\*Correspondence:

*Zhihua Li zhihua.li@fda.hhs.gov*

#### † Present Address:

*Thomas Colatsky, Marshview Life Science Advisors, Seabrook Island, SC, United States*

#### Specialty section:

*This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology*

Received: *31 March 2017* Accepted: *09 August 2017* Published: *23 August 2017*

#### Citation:

*Dutta S, Chang KC, Beattie KA, Sheng J, Tran PN, Wu WW, Wu M, Strauss DG, Colatsky T and Li Z (2017) Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment. Front. Physiol. 8:616. doi: 10.3389/fphys.2017.00616* Drug-induced Torsade-de-Pointes (TdP) has been responsible for the withdrawal of many drugs from the market and is therefore of major concern to global regulatory agencies and the pharmaceutical industry. The Comprehensive *in vitro* Proarrhythmia Assay (CiPA) was proposed to improve prediction of TdP risk, using *in silico* models and *in vitro* multi-channel pharmacology data as integral parts of this initiative. Previously, we reported that combining dynamic interactions between drugs and the rapid delayed rectifier potassium current (IKr) with multi-channel pharmacology is important for TdP risk classification, and we modified the original O'Hara Rudy ventricular cell mathematical model to include a Markov model of IKr to represent dynamic drug-IKr interactions (IKr-dynamic ORd model). We also developed a novel metric that could separate drugs with different TdP liabilities at high concentrations based on total electronic charge carried by the major inward ionic currents during the action potential. In this study, we further optimized the IKr-dynamic ORd model by refining model parameters using published human cardiomyocyte experimental data under control and drug block conditions. Using this optimized model and manual patch clamp data, we developed an updated version of the metric that quantifies the net electronic charge carried by major inward and outward ionic currents during the steady state action potential, which could classify the level of drug-induced TdP risk across a wide range of concentrations and pacing rates. We also established a framework to quantitatively evaluate a system's robustness against the induction of early afterdepolarizations (EADs), and demonstrated that the new metric is correlated with the cell's robustness to the pro-EAD perturbation of IKr conductance reduction. In summary, in this work we present an optimized model that is more consistent with experimental data, an improved metric that can classify drugs at concentrations both near and higher than clinical exposure, and a physiological framework to check the relationship between a metric and EAD. These findings provide a solid foundation for using *in silico* models for the regulatory assessment of TdP risk under the CiPA paradigm.

Keywords: Torsade-de-Pointes (TdP), Comprehensive in vitro Proarrhythmia Assay (CiPA), rapid delayed rectifier potassium current (IKr), in silico cardiac cell model, drug block, proarrythmia risk, model optimization

# INTRODUCTION

Drug-induced Torsade-de-Pointes (TdP) is a lethal arrhythmia that has caused removal of several drugs from the market (Gintant, 2008). The current cardiac safety paradigm (described by the ICH E14 and S7B guidelines) focuses on two markers to assess TdP risk: in vitro block of the hERG (human Ether-à-go-go-Related Gene) channel (representing the rapidly activating delayed rectifier potassium current, or IKr), and prolongation of the QTc interval in clinical studies (Sager et al., 2014). However, while eliminating the incidence of TdP in marketed drugs, this testing regime primarily aims at detecting delayed ventricular repolarization rather than the clinical end point TdP, and may be assigning proarrhythmia liability to drugs that could in fact be safe (Sager et al., 2014). Therefore, the Comprehensive in vitro Proarrhythmia Assay (CiPA) was proposed as a new regulatory paradigm that assesses drug TdP risk by combining measurements of drug effects on multiple cardiac ionic currents in vitro with in silico modeling of drug effects on the ventricular myocyte (Sager et al., 2014). The O'Hara Rudy cardiac cell model (ORd) (O'Hara et al., 2011) was chosen as the consensus base in silico model and a set of 28 drugs with known levels of clinical TdP risk (high, intermediate, low/none) were identified for the development and evaluation of the CiPA paradigm (Colatsky et al., 2016; Fermini et al., 2016). The three TdP risk categories were assigned by a Clinical Translation Working Group comprised of clinical cardiologists, safety pharmacologists, and clinical electrophysiologists according to published and publically available data and expert opinion. The 28 CiPA drugs were separated into a training set of 12 compounds to be used for calibration of the in silico model and the remaining 16 compounds are to be used later for validating the model. Both the training and validation compound sets comprise drugs that cover the full range of TdP risk categories and demonstrate varied electrophysiological profiles.

Previous studies have presented computational frameworks to assess TdP risk (Mirams et al., 2011; Kramer et al., 2013; Lancaster and Sobie, 2016), but their use within the CiPA framework is limited due to their differing TdP risk categories from those defined in CiPA. In addition, prior studies simulated drug effects using the half-maximal blocking concentration (IC50) for different drugs, which assumes simple pore block of the ion channels and neglects any intricacies of drugion channel interactions that may be important factors in predicting relative TdP risk. The importance of incorporating a kinetic representation of drug-ion channel interactions has been demonstrated in previous publications (Di Veroli et al., 2013, 2014; Li et al., 2017). In the Li et al. (2017) study we recently reported the development of a novel IKr dynamic model that can capture drug-channel dynamic interactions, and the integration of this IKr model into the ORd cardiac model with multi-channel pharmacology data. This IKr-dynamic ORd model (hereinafter referred to as the original IKr-dyn ORd model) was calibrated based on the original ORd model so that it can reproduce experimentally recorded adult human left ventricular cardiomyocyte action potential (AP) morphology and rate dependency under control (drug-free) conditions. However, this model calibration process in our previous work did not include experimental AP changes under the influence of different channel blocking drugs. This may negatively affect the model's predictive power as this model is intended for simulating drug effects under channel blocking conditions.

In this study we further optimized the original IKr-dyn ORd model by adjusting channel conductance values of major ionic currents according to human ventricular cardiomyocyte experimental data in the presence and absence of various drugs with different channel blocking activities. We show that this optimization procedure allowed the model (hereinafter referred to as optimized IKr-dyn ORd model) to quantify more accurately the impact of each individual current on the AP. We then screened a series of published and novel metrics computed by this model based on their capability of stratifying CiPA training compounds into their corresponding TdP risk categories using drug-IKr binding kinetics and multi-channel pharmacology data collected earlier through manual patch clamp systems (Li et al., 2017). The best metric identified to date is based on drug-induced changes to the net charge carried by ionic currents (qNet) during the AP, which can stratify the 12 CiPA training drugs into three TdP risk levels across various conditions. We also show that the increased predictive power of this metric is mechanistically linked to the incorporation of IKr-drug binding dynamics and the improved representation of the block effects of individual currents, two important features of the optimized IKr-dyn ORd model. Finally, we developed a framework to evaluate a cell's robustness against EAD generation, and demonstrated that the new qNet metric is correlated with the system's repolarization robustness to external pro-EAD perturbations that could reduce the membrane density of the hERG channel (IKr conductance).

#### METHODS

#### Optimization of the IKr-Dynamic ORd Model

The original IKr-dyn ORd model (described in Li et al., 2017 and Expanded Methods in the Supplemental Material) was further modified (optimized IKr-dyn ORd) by scaling five ionic current conductances [IKr, the slow rectifier potassium current (IKs), inwardly rectifying potassium current (IK1), the L-type calcium current (ICaL) and the late sodium current (INaL)] so that the model provides a good fit to published APD rate dependence experimental data for control and five channel blockers (O'Hara et al., 2011). The optimization was performed using the model parameterization algorithm described in Li et al. (2014). Briefly, an initial set of scaling factors was defined within a certain range (between 0.001 and 9) and their goodness of fit was assessed using an objective cost function defined as the weighted sum of the squared errors between model simulations

**Abbreviations:** CiPA, Comprehensive in vitro proarrhythmia assay; TdP, Torsadede-Pointes; ORd, O'Hara Rudy dynamic cell model (O'Hara et al., 2011); IKr-dyn ORd, ORd model with dynamic IKr; Inet, net current (sum of currents ICaL, INaL, IKr, IKs, IK1, Ito); qNet, charge passed by Inet from the beginning to the end of the AP beat (same for qCaL and ICaL, qNaL and INaL...); cqInward, change in charge passed by ICaL and INaL; Cmax, free maximum plasma clinical drug exposures.

and experimental measurements. The set of scaling factors then underwent iterative changes (i.e., mutation and recombination) to create new generations of parameters and this process was continued until the convergence criterion was met (when the change in the minimum error of the new parameters is less than 5% over the last 30 generations). The experimental data used for fitting were taken from Figure 8 of the ORd model paper (O'Hara et al., 2011) and comprise APD rate dependence data for control and 5 drug blocking conditions: 1 µM E-4031 (70% IKr block), 1 µM HMR-1556 (90% IKs block), 1 µM nisoldipine (90% ICaL block), 100 µM BaCl2 (90% IK1 block), 10 µM mexiletine (54% INaL, 9% IKr, and 20% ICaL block). The simulated percentage of block for all drugs was kept the same as in the ORd model paper (O'Hara et al., 2011), apart from mexiletine, which used new pharmacology data from manual patch clamp systems at physiological temperatures (Crumb et al., 2016). The algorithm was run using in-house developed R scripts (R Core Team, 2014) and C programs using the Snow, Rmpi and deSolve packages (lsoda solver with a 10−<sup>6</sup> relative and absolute tolerance) (Yu, 2002; Soetaert et al., 2010; Tierney et al., 2015) on the FDA High Performance Computer (HPC) with 160 cores.

#### Simulation Protocol for Metric Evaluation

All simulations were run from control steady state conditions (after 1,000 beats) at varying cycle lengths (CLs) 1,000, 2,000, and 4,000 ms and stimulus of −80 µA/µF for 0.5 ms (as in the original model). Block of ion channels at various concentrations were simulated and run for another 1,000 beats to reach a new steady state with drug. The last two beats were analyzed to check for alternans, which was observed in the presence of early afterdepolarizations (EADs), defined as having a positive derivative during the repolarization phase of the AP. The pharmacology data for the 12 CiPA training compounds (the full list and their corresponding risk categories can be found in Supplemental Table 1) were the same as in our previous report (Li et al., 2017), where drug-IKr binding kinetic parameters were estimated using an in vitro IKr dynamic protocol and IC50/Hill coefficients based on Crumb et al. (2016) were used for the remaining channels [the peak sodium current (INa), INaL, ICaL, IK1, IKs and transient outward potassium current (Ito); all the parameters can be found in the Supplemental Tables 2 and 3]. Simulations were run for a range of drug concentrations: from 0.5x up to 25x free maximum plasma clinical drug exposures (Cmax). Simulations were run in R and C using the deSolve package (Soetaert et al., 2010).

We assessed a range of standard metrics as also considered in Mirams et al. (2011), Lancaster and Sobie (2016): resting membrane potential (resting Vm), maximum upstroke velocity (dV/dtmax), peak membrane potential (peak Vm), APD at 50% of the amplitude (APD50), APD at 90% of the amplitude (APD90), APD triangulation (APDtri) defined as APD90- APD50, diastolic intracellular calcium concentration ([Ca2+]i) (diastolic Ca), peak [Ca2+]<sup>i</sup> (peak Ca), calcium transient duration at 50% (CaD50) and 90% (CaD90) of the amplitude, calcium transient triangulation (Catri) defined as CaD90-CaD50, as well as the cqInward metric that quantifies the change in the amount of charge carried by INaL and ICaL, which demonstrated good separation between risk categories in our previous report (Li et al., 2017). In addition, we considered a new metric (qNet) calculated as the net charge constituting (the integral or area under the curve of) the net current (Inet) from the beginning to the end of the simulated beat (defined as Inet = ICaL + INaL + IKr + IKs + IK1 + Ito). The currents making up Inet within our study play an important role in modulating arrhythmic risk and have been chosen based on input from pharmaceutical company scientists and safety pharmacology experts as the main currents of interest within the CiPA paradigm, as outlined in Fermini et al. (2016).

To assess the robustness of a cell against EAD generation, we simulated an added perturbation by reducing the maximum conductance of IKr and reporting the minimum IKr reduction needed to trigger an EAD. Simulations were run for varying degrees of IKr conductance reduction (using a binary search algorithm) at a CL of 2,000 ms with a precision of 0.01%. For each IKr reduction tested, EADs were defined as having a positive differential (dV/dt) during the plateau phase of the AP (between APD30 and APD90) after 100 beats. The cell model was pulsed for a 100 beats before checking for EADs to allow the system to reach quasi-steady state, as in Kurata et al. (2017). The minimum IKr conductance reduction needed to trigger an EAD was named IKr reduction threshold, which reflects the system's repolarization robustness against, or distance from, EADs. To assess the relationship between the metric and the repolarization robustness, we calculated the correlation coefficients (using the pearson method) between the metric at steady state after 1,000 beats (without added IKr reduction) and the IKr reduction threshold for each drug across a series of concentrations (0.5x– 25x Cmax). Situations where no IKr reduction threshold could be calculated (no EADs could be induced for the highest IKr reduction tested) or IKr reduction threshold is 0 (an EAD occurred without any added perturbation) were excluded from the correlation calculation.

# Classification Methods

To assess the ability of the metrics to identify each drug's TdP risk level, we performed a proportional odds logistic regression classification and a leave-one-out validation, as in Mirams et al. (2011). If EADs were observed, the metric value at the concentration prior to EAD generation was used for the classification. We used the R lrm function from the rms package (https://CRAN.R-project.org/package=rms) and calculated the classification training error for each metric as follows: the mean (across 12 drugs) of the absolute error (difference between predicted and known risk categories), with the risk categories defined as 1 = low risk, 2 = intermediate risk and 3 = high risk. The proportional odds logistic regression model is a regression model for ordinal dependent variables, and accounts for the ordering by using cumulative probabilities defined as the odds of (Y ≤ i) = P(Y ≤ i)/(1 − P(Y ≤ i)) for each risk category i, where Y is the variable that represents a drug's risk category and P(X) is the probability of X. The function uses maximum likelihood estimates to calculate the probability of each drug being a member of each risk category, and the drug is assigned to the risk category corresponding to its highest probability. We then performed a leave-one-out validation by removing one drug from the data set and then predicting its risk category based on the classification of the remaining drugs. This was performed in turn for each drug within the data set and its leave-one-out prediction error was calculated the same way as the training error.

#### RESULTS

#### Optimized IKr-dyn ORd Model

The optimized IKr-dyn ORd model was built by scaling the conductance of the main ion currents (IKr, IK1, IKs, INaL, ICaL) of the original IKr-dyn ORd model (presented in Li et al., 2017) to fit the APD rate dependence experimental data in control and drug block conditions from O'Hara et al. (2011). The set of scaling factors that gives the best fit for the optimized model is as follows: scaling IKr by 1.013, IKs by 1.870, IK1 by 1.698, ICaL by 1.007, and INaL by 2.661, as summarized in **Table 1**. A comparison of the simulation results from both the original and optimized models to the experimental data is shown in **Figure 1** and the corresponding sum of squares errors (between simulation and experimental data) are shown in **Table 2**. Sum of squares error for the original ORd model as presented in their paper (O'Hara et al., 2011) are also shown in **Table 2** for comparison purposes. We see that although for control and some current blocking conditions the original IKr-dyn ORd model has errors similar to the original ORd model, for other conditions the errors were worsened (IK1 and ICaL blocking experiments), resulting in an average error bigger than the original ORd model (72.33 vs. 57.77). However, the discrepancy between simulations and experiments was significantly reduced in the new optimized IKr-dyn ORd model.

As can be seen in **Figure 1A**, under control conditions both the original IKr-dyn ORd and optimized IKr-dyn ORd models display similar behavior. Although for control data points, the optimized IKr-dyn ORd model fitting is slightly worse than the original IKr-dyn ORd model (fitting error 22.63 vs. 18.82 in **Table 2**), the average fit across both control and all drug block conditions is much better for the optimized IKr-dyn ORd

TABLE 1 | Conductance scaling factors for the original and optimized IKr-dynamic O'Hara-Rudy models (original and optimized IKr-dyn ORd): current conductances of the rapid (IKr) and slow (IKs) rectifier potassium current, inwardly rectifying potassium current (IK1), L-type calcium current (ICaL) and late sodium current (INaL) in the model are multiplied by the corresponding scaling factor.


*Note that the IKr conductance in the original IKr-dyn ORd model was scaled as described in Li et al. (2017).*

model compared to the original IKr-dyn ORd model (fitting error 30.81 vs. 72.33). The main improvements in the quality of fit to the experimental data are observed for drug blocking conditions, especially with mexiletine (INaL blocker) and E-4031 (IKr blocker) (**Figures 1B,E** respectively). In the case of mexiletine, a reduction in the fitting error from 91.09 (original IKr-dyn ORd model) to 18.36 (optimized IKr-dyn ORd model) was achieved (**Table 2**). **Figure 1B** shows that, with the original IKr-dyn ORd model, the simulated APD prolongation with mexiletine is significantly longer than experimental data. A similar pattern can be seen for the IKr blocker E-4031 (**Table 2** and **Figure 1E**). Due to the opposite roles of INaL and IKr in prolonging AP (Johannesen et al., 2016), this suggests that block of INaL is underestimated and that of IKr is overestimated in the original IKr-dyn ORd model. The optimized model corrected these inaccuracies with better fitting to the experimental data, which is important for TdP risk assessment as it is known that INaL block plays an important role in counteracting proarrhythmic APD prolongation of IKr block (Orth et al., 2006; Johannesen et al., 2016).

To further understand the contribution of various ionic currents to AP profile after the optimization process, we compared the simulated AP traces and the ionic currents over the time course of the steady state AP between the original and our optimized IKr-dyn ORd model at different cycle lengths. As described earlier in this section all of the current conductances are increased in the optimized IKr-dyn ORd model (**Table 1**). However, the AP shapes from both models under control conditions are very similar, as shown in **Figure 2A**. This is consistent with the fact that both models fit the control AP morphology parameters (**Figure 1A**) reasonably well. On the other hand, while only a small change in current amplitude is observed for ICaL (**Figure 2C**), which only has a 0.7% change in conductance (**Table 1**), clear differences are observed for all other currents (IKr, INaL, IKs and IK1) with the biggest changes occurring for INaL (conductance is increased by 166.1% between the optimized and original models as shown in **Table 1**). This further demonstrates that INaL plays a bigger role in the optimized model than the original IKr-dyn ORd model.

#### Candidate Metrics

We then investigated whether the optimized IKr-dyn ORd model could be used to stratify proarrhythmia risk levels. As a first step we explored the changes in AP and individual currents induced by three representative drugs (one taken from each one of the CiPA TdP risk categories), using pharmacology data as used in Li et al. (2017). Since it is known that the subtle balance between inward (such as INaL and ICaL) and outward (such as IKr, IKs, IK1, and Ito) currents underlies the generation of EADs, a mechanistic precursor to TdP (Vos et al., 1995; Volders et al., 2000; Wu et al., 2002; Weiss et al., 2010), we also examined the net current between inward and outward currents (Inet) in addition to individual currents. **Figure 3** shows simulations of AP, Inet, ICaL, INaL, IKr, IKs, IK1, and Ito for ranolazine (low risk), cisapride (intermediate risk) and dofetilide (high risk), for a CL of 2,000 ms and a dose of 25x Cmax

TABLE 2 | Sum of squares error (divided by 100) between experimental action potential duration (APD) rate dependence mean data (from Figure 8 in O'Hara et al., 2011) and the original O'Hara Rudy model (original ORd) (O'Hara et al., 2011), the original IKr-dyn ORd (Li et al., 2017) as well as the optimized IKr-dyn ORd under different conditions: control, mexiletine (blocks mainly INaL), HMR 1556 (blocks IKs), E-4031 (blocks IKr), BaCl2 (blocks IK1) and nisoldipine (blocks ICaL).


\**Error was calculated using the updated mexiletine IC50 data (Crumb et al., 2016); using the block suggested in the ORd paper of 90% INaL block (O'Hara et al., 2011), the sum of squares error is of 38.48, changing the average error to 48.70.*

using our optimized model. A slow pacing rate (CL 2,000 ms) is used here because bradycardia is a known risk factor for TdP (Kurita et al., 1992; Kallergis et al., 2012), and a high concentration (25x Cmax) is used to highlight the potential differences between various risk levels. The amount of electronic charge carried by each current is calculated as the area under the curve (AUC) of the individual current trace and is plotted for Inet in **Figure 3C**.

We see in **Figure 3A** that all three drugs cause prolongation of APD and the low risk drug, ranolazine, shows a greater prolongation of APD compared to the intermediate risk drug, cisapride (266.78 vs. 176 ms). The performance of APD90 as a metric for all the drugs from 0.5 to 25x Cmax, can be seen in Supplemental Figure 1. In fact, verapamil and ranolazine (both low risk) display APDs greater than most intermediate risk drugs over a wide range of doses. Therefore, the amount of APD prolongation is not a good indicator of the TdP risk of a drug, demonstrating the unsuitability of APD alone as a marker for TdP risk. However, we notice that Inet (**Figure 3B**), calculated as the sum of the five main currents that modulate the plateau phase of the action potential (ICaL, INaL, IK1, IKr, IKs, and Ito, shown in **Figures 3D–I**), does correlate with the TdP risk category. As shown in **Figure 3C**, the order of qNet (charge carried by Inet integrated from the beginning to the end of the AP beat) is consistent with the rank order of TdP risk levels for the three drugs. At the end of the CL, ranolazine has a qNet of 0.061 µC/µF while cisapride and dofetilide have a qNet of 0.037 µC/µF and 0.013 µC/µF, respectively. A detailed

examination of the individual current profiles reveals why ranolazine caused the least amount of qNet decrease. As shown in **Figures 3D, G**, ranolazine (green lines) caused a marked decrease of the absolute amount of charge carried by IKr (qKr decrease of 0.119 µC/µF) and INaL (qNaL decrease of 0.07 µC/µF) at the end of the AP beat compared to control (black lines). Because the outward current IKr and inward current INaL have opposite directions, ranolazine-induced reduction (in absolute values) of the two currents balanced each other and resulted in only a small change of the net charge at the end of the AP (qNet, **Figure 3C**). In contrast, dofetilide (**Figure 3D**, red lines) and cisapride (**Figure 3D**, blue lines) caused a significant reduction of qKr (0.135 and 0.063 µC/µF respectively) through direct channel blocking, and a slight increase of qNaL through prolonged APD. These two effects changed Inet in the same direction and worked together to decrease qNet significantly, with dofetilide causing the biggest decrease due to more significant blocking of IKr. Note that these drugs have some effects on other currents (Ito, IKs, and IK1) as well, but those changes are relatively small and will not change the rank order of qNet values significantly for the three drugs tested here. However, these other currents may become important for drugs that directly block them. For example, the effects on ICaL may be critical in determining the qNet change and risk level for a calcium blocker.

These initial promising results prompted us to calculate this new Inet-based metric, qNet, for all 12 CiPA training compounds and systematically compare its capability of separating the three TdP risk levels to a range of commonly tested metrics (described in the Methods section). The risk categories, IC50 and IKr dynamic parameters for each drug are listed in Supplemental Tables 1–3. Included in the comparison is also the cqInward metric, described in our previous study and defined as the normalized drug-induced change of the charge carried by the inward currents INaL and ICaL (Li et al., 2017). As shown in **Figure 4**, we calculated the classification training error for each metric over a range of doses (0.5–25x Cmax) and a range of CLs (1,000, 2,000, and 4,000 ms) for the 12 CiPA training compounds. This error quantifies the mean (across the 12 CiPA drugs) difference between known and predicted risk levels for each metric. We can see that across the full range of concentrations and all CLs the qNet metric shows the smallest classification training error. Notably, the qNet metric shows a classification training error of 0 for concentrations greater than or equal to 1x Cmax, meaning it consistently classifies each of the 12 CiPA training compounds into the correct TdP risk category. The cqInward metric performance is comparable to that of qNet at low pacing rates (4,000 ms) and high drug concentrations. All of the other standard metrics we considered show training errors that never come down to 0, which fluctuate across the range of doses.

The results presented in **Figure 4** are consistent with the leaveone-out validation described in **Table 3** performed on a subset of the doses tested (1, 10, and 20x Cmax) for a CL of 2,000 ms; the cqInward and qNet show the smallest prediction errors with values of 0.33 and 0.08 respectively at 20x Cmax. The other next best performing metrics are peak Vm with an error of 0.42 and APD50, APD90 with errors of 0.5 at Cmax 20x. Of note, at 1x Cmax, qNet and APD90 all have the same prediction error of 0.17. This is because at lower concentrations (1x Cmax) the effects of each drug are harder to differentiate due to there often being only subtle effects on the AP morphology. However, the CiPA paradigm assumes that the assessment of TdP risk may occur at any time during drug discovery and development, even prior to the time the clinical effective drug concentrations are known with any certainty. In addition, the incidence of clinical TdP is limited and not necessarily related strictly to normal (1x) clinical exposure (i.e., concomitant factors may play a role in expressing clinical TdP events). Therefore, we propose that a metric should be evaluated under multiple physiological and pharmacological conditions. The overall evidence suggest

that qNet is the best among all the metrics tested, because it has a training error of 0 across a wide range concentrations (1–25x Cmax) at various pacing frequencies (2,000 and 4,000 ms), and the lowest leave-one-out error at all concentrations tested.

# The Impact of IKr-Drug Binding Kinetics and Channel Conductance Optimization on Risk Level Stratification

Compared to the original ORd (i.e., the consensus base model for CiPA), the optimized IKr-dyn ORd model presented in this work has two important changes: the incorporation of a dynamic IKr model to capture drug binding kinetics (Li et al., 2017), and an improved set of channel conductances to better represent the contribution of individual currents to AP (**Figures 1**, **2**). In order to shed light on possible mechanistic differences among the drugs tested, we used the best candidate metric qNet as a benchmark, and compared the performance of the optimized IKr-dyn ORd model with model variations where each of the changes was removed in turn. **Figure 5** shows computed qNet values for the 12 CiPA training drugs calculated over a range of drug doses from 0.5x to 25x Cmax when using the optimized IKr-dyn ORd model (**Figure 5A**), a model variation without incorporating the IKr dynamic model (**Figure 5B**) and a model variation incorporating the IKr dynamic model but without optimizing channel conductances (**Figure 5C**). In line with results from **Figure 4** and **Table 3**, the metric qNet shows clear separation between the 3 TdP risk categories across the range of doses tested with the optimized IKr-dyn ORd model (**Figure 5A**); however, this is not the case for the other two model variations (**Figures 5B,C**).

The first model variation we tested does not have the IKr dynamic model incorporated but instead uses simple IC50s to represent channel block (**Figure 5B**). Note that this model variant has gone through a channel conductance optimization process similar to that presented in this article, as described in Dutta et al. (2016), so the difference observed between this model variant (**Figure 5B**) and the full optimized IKr-dyn ORd model (**Figure 5A**) is mainly due to the different representation of IKr block (dynamic vs. IC50s). From **Figure 5B** we can see that there are two intermediate risk drugs that are not correctly categorized: cisapride that is mixed with the high risk drugs, and chlorpromazine that is mixed with the low risk drugs. Cisapride is a potent and selective IKr blocker (IC50 10.1 nM and Cmax 2.6 nM see Supplementary Material), with a safety margin (IKr IC50/Cmax) of 3.8 (Redfern et al., 2003), which is close to that of the high risk drug dofetilide (IC50 4.87 nM and Cmax 2 nM, safety margin 2.4) for example. So if IC50 data are used with an assumption of simple pore drug block, cisapride is grouped with the high risk drugs. However, when we consider the IKr-drug binding dynamic data (Li et al., 2017), cisapride, but not high risk drugs like dofetilide, can rapidly dissociate from the hERG channel during diastolic intervals because it is not trapped in the closed channel. Consequently, cisapride has an actual block potency lower than high risk drugs despite similar IKr IC50/Cmax ratio, which may explain why it belongs to the intermediate rather than high risk level. On the other hand, chlorpromazine is not a potent IKr blocker (safety margin 24.4, similar to other low risk drugs) so when we look at IC50 only it is classified closer to the low risk drugs. But when IKr dynamic data are considered, chlorpromazine is highly trapped in the closed hERG channel and very slow in unbinding during diastolic intervals (Li et al., 2017). This makes it more dangerous than its IKr IC50 suggests and thus classified as an intermediate rather

TABLE 3 | Leave-one-out prediction error for a range of metrics at a CL of 2,000 ms and 3 doses (1, 10, and 20x Cmax): resting membrane potential (resting Vm), maximum upstroke velocity (dV/dtmax), peak membrane potential (peak Vm), APD at 50 and 90% of the amplitude (APD50 and APD90), action potential (AP) triangulation (APDtri), diastolic intracellular calcium concentration ([Ca2+] i ) (diastolic Ca), peak [Ca2+] i (peak Ca), calcium transient duration at 50 and 90% of the amplitude (CaD50 and CaD90), calcium transient triangulation (Catri), change in amount of charge carried by INaL and ICaL (cqInward) (Li et al., 2017) and charge carried by the net current (qNet).


than low risk drug. This demonstrates that including a dynamic representation of IKr-ion channel interactions is important for categorizing TdP risk of drugs and IC50 data alone are not sufficient.

The second model variation we tested has the IKr dynamic model included, but without optimized channel conductances to reproduce AP changes under channel blocking conditions (**Figure 5C**). Note that this model variant is the same as the original IKr-dyn ORd model (Li et al., 2017) and, as demonstrated in **Figure 1**, has an inaccurate quantification of the block effects of individual currents compared to experimental data. In this scenario the low risk drug ranolazine is misclassified as a high risk compound (**Figure 5C**). Ranolazine is a potent IKr and INaL current blocker and these two effects can balance each other to reduce ranolazine's TdP risk (Antzelevitch et al., 2004; Johannesen et al., 2016; Saad et al., 2016). Because the INaL effect is underestimated and the IKr effect is overestimated without channel conductance optimization (**Figure 1**), ranolazine has a dominant IKr block effects when simulated by this model variant and thus will be mistakenly put in the high risk category (**Figure 5C**). Taken together, this suggests that the two added features are both important for TdP risk stratification and may mechanistically explain why a certain drug belongs to a specific TdP risk level.

## Physiological Significance of qNet

In order to assess the physiological significance of the metric, we borrowed some concepts from non-linear dynamic theory, where EADs appear as membrane voltage oscillations when the equilibrium state at the plateau phase (membrane voltage between 0 and −40 mV) changes its stability via bifurcation (Qu et al., 2013; Kurata et al., 2017). The robustness of the system could be evaluated by applying a specific perturbation with a series of strengths and measuring the range of the perturbation

FIGURE 5 | qNet for the 12 CiPA training compounds for a range of doses (0.5–25x Cmax) at a pacing rate of 2,000 ms. (A) Optimized IKr-dyn ORd; (B) A model variation without the incorporation of the IKr dynamic model (note this is the same model as in Dutta et al., 2016) and; (C) A model variation without the optimized channel conductances to accurately quantify block effects of individual currents (note this is the same model as in Li et al., 2017). Different TdP risk levels are color coded (high risk in red, intermediate risk in blue and low/no risk in green). Results are not shown once drug concentrations are high enough to induce early after depolarizations (EADs) (i.e., quinidine).

the system can tolerate without changing stability (i.e., emergence or annihilation of oscillations) (Kurata et al., 2008). We applied this concept to our model using IKr maximum conductance reduction as a perturbation. In this case the minimum IKr reduction required to induce an EAD (IKr reduction threshold) reflects the system's robustness against, or distance from, EADs.

Therefore, for each drug over a range of concentrations from 0.5 to 25x Cmax we calculated the IKr reduction thresholds, and checked their correlation with the metrics qNet, APD90, and cqInward respectively. Detailed correlation plots for each metric can be found in the Supplemental Figures 2–4. **Table 4** shows the correlation coefficients for each drug across all concentrations for IKr reduction threshold vs. qNet, APD90 and cqInward respectively. We see that qNet shows a strong correlation across all drugs (close to 1). As qNet increases the IKr reduction threshold (and the system's robustness against EAD) increases and vice versa as qNet decreases. The bigger the qNet value the safer the system is and the harder it is to induce EAD.

For APD90, in most cases there is a strong negative correlation with IKr reduction threshold (close to −1) as expected, indicating the longer the APD the lower the repolarization robustness (i.e., the closer to EAD) and vice versa (**Table 4**). However, this trend reverses completely for some drugs like verapamil and mexiletine, where the correlation is positive (**Table 4**), suggesting the longer the APD90 the higher the repolarization robustness (the further away from EAD). This is contradictory to the general perception that longer APD90 (and QTc) signals a higher EAD/TdP liability. These unexpected relationships between APD and EAD can be seen more clearly in **Figure 6**, where the AP traces before and after the perturbation are shown. As can be seen from **Figure 6A** (left panel), using APD90 as a metric a cell under mexiletine at 1x Cmax seems safer (APD less prolonged) than at 10x Cmax, while qNet suggests otherwise (1x Cmax is more dangerous due to a smaller qNet value). When the same perturbation was applied (95% IKr reduction), the cell with 1x Cmax of mexiletine but not 10x, generated an EAD (**Figure 6A** right panel), indicating the cell with lower mexiletine concentration is actually closer to EAD generation, consistent with the prediction of qNet but not APD90. The same pattern can be seen in **Figure 6B**, where verapamil at 1x Cmax is shown to be closer to EAD than at 3x Cmax through perturbation assays (right panel), contradictory to the prediction using APD90 but not qNet (left panel). This pattern holds true when comparing ranolazine and cisapride as compared in **Figure 3**. As described earlier, a cell under ranolazine has a longer APD90 (indicating higher risk) and also a higher qNet value (indicating lower risk) than cisapride at 25x Cmax (**Figure 6C** left panel). An added perturbation of 75% IKr reduction will trigger an EAD with cisapride but not ranolazine (**Figure 6C** right panel), supporting the prediction of qNet but not APD90. Note that here we used 25x Cmax to match the concentrations used in **Figure 3**. When 1x Cmax was used, the same pattern was seen for the two drugs (see Supplemental Figure 5). This suggests under most circumstances qNet is a better metric than APD90 in marking the repolarization robustness to added perturbation of IKr reduction.

Finally, cqInward does not correlate well with robustness against EAD generation, measured as IKr reduction threshold



(**Table 4**), despite a good performance (next to only qNet) on separating the risk categories for the training compounds (**Figure 4**). This suggests cqInward does not indicate the repolarization robustness to a perturbation of hERG channel density decrease. Whether cqInward is correlated with the robustness to another perturbation, or its separating power on the 12 training drugs is a non-physiological artifact, remains to be investigated. If the latter this highlights the importance to assess a metric in not only a pre-defined drug classification system, but also a physiological framework to quantitatively evaluate the correlation between the metric and EAD.

#### DISCUSSION

In this study we present an optimized version of the ORd model (O'Hara et al., 2011), which incorporates a dynamic representation of IKr to allow modeling of drug-IKr channel interactions (Li et al., 2017) as well as providing a better fit to experimental data in both control and drug blocking conditions by rescaling ionic current conductances. Most notably, INaL current is increased compared to the original model. We also demonstrate that our optimized model, used in combination with a mechanistic net charge metric (qNet), enables good separation of 12 CiPA training compounds into their respective risk categories over a range of drug concentrations and pacing rates. Furthermore, we show that this is because qNet is correlated with a system's repolarization robustness to external perturbation of hERG channel density decrease, or IKr maximum conductance reduction.

#### Optimization of the O'Hara Rudy Model

To optimize the model we rescaled ionic current conductances in the model presented by Li et al. (2017). We demonstrate in **Figure 2** that recalibration of the model conductances leads to very little changes in the AP in control conditions across a range of pacing frequencies. It did however shift the effect of some of the different currents in the cardiac cell model, most notably increasing the role of INaL in contributing to AP. A recent study also optimized the ORd model to fit various LQTS profiles (Mann et al., 2016). Mann et al. present an optimized version of the ORd model by scaling the conductances of IKs (by 5.75), IKr (by 1.00), ICaL (by 2.01), INaL (by 1.00), INaCa (by 2.95), and INaK (by 9.12). The scaling factors are different to the ones observed in our model: IKs is increased in both models although ours is increased by a smaller amount 1.87, in their model IKr is unchanged while it is slightly increased in our model, ICaL is increased significantly in their model but only very slightly in ours and INaL is unchanged in their model while it is scaled by 2.661 in our model. The differences in INaL can be explained by the differences in context of use of the model: Mann et al. investigate the effects of increased INaL (LQTS3) as opposed to drug block of INaL, as in this study. Furthermore, a key difference between our model optimization process and Mann et al. is that we used human cardiomyocyte experimental data with various channel blockers, while they used clinical LQTS data. However, one of their findings was that the ORd model over predicts the effect of IKr block (50% IKr block produced a 42% increase in APD90 as opposed to the 16.5% observed clinically), which is concurrent with our findings. An awareness of this property of the ORd model is important as the model is often considered a consensus gold standard model for simulating drug effects on cardiac cells, and properties such as the over prediction of block of IKr may lead to inaccurate predictions of drug effects on cardiac electrophysiology. Our manuscript further highlights this point and provides an alternative model with improved balance of the effect of the different ionic currents in drug block conditions.

## Performance of the qNet Metric Using the Optimized Model

Using pharmacology data for the 12 CiPA training compounds (Li et al., 2017), we assessed the suitability of a range of standard metrics based on AP morphology properties, as well as the recently published cqInward metric (Li et al., 2017) and our new qNet metric. We demonstrated that the commonly used AP-based metrics are poor indicators of TdP risk and found that our qNet metric allowed best separation of the CiPA training compounds into their risk categories. Our new metric outperformed the cqInward metric presented in Li et al. which may be a consequence of optimized channel conductances to better quantify the block effects of individual currents.

Our optimized IKr-dyn ORd model has two important features compared to the original ORd model: incorporation of modeling drug-IKr interaction kinetics based on dynamic hERG binding data (Li et al., 2017) and better characterization of individual currents' role in AP based on channel blocking data. We demonstrate the importance of simulating drug-IKr dynamics and accurate drug block conditions by providing rationale for misclassification of compounds when either one of the features were removed during TdP risk classification (**Figure 5**). This highlights the need for more precise model representation to simulate drug effects and stratify TdP risk levels. Additional human cardiomyocyte data may help to further refine this model.

## qNet Correlates with the System's Robustness against EADS

Based on ideas from non-linear dynamic theory and studies demonstrating mechanisms of EAD generation (Guo et al., 2007; Weiss et al., 2010; Xie et al., 2010; Chang et al., 2013; Kurata et al., 2017), we established a theoretical framework to quantitatively evaluate the physiological consequences of the change of the qNet (and in principle any) metric. A key concept here is the system robustness (Kurata et al., 2008), which is defined as the level of a specific perturbation the system can tolerate without a qualitative change of stability (e.g., emergence or annihilation of oscillations). We applied that concept here using IKr maximum conductance reduction as a perturbation. Note that in our model all drugs' hERG/IKr block is modeled as binding to different channel states without changing the IKr conductance. Thus the IKr conductance decrease applied here reflects extra pro-EAD perturbations independent of each drug's direct ion channel block activities, for example inter-subject variability (hERG channel density variation due to genetic background), intra-subject variability (regional difference in hERG channel density), chronic drug effects (to block hERG maturation), or drug-drug interaction. We found that qNet is correlated with the cell's repolarizing robustness to the perturbation of IKr conductance reduction. When qNet increases, the cell's IKr reduction threshold also increases, meaning the cell is moving away from EAD and needs a more severe perturbation of IKr conductance reduction to trigger an EAD. The opposite happens when qNet decreases. This positive correlation is consistent across all the compounds tested in this study. In contrast, APD90 does not show a consistent correlation with the repolarization robustness across all the drugs, suggesting for some drugs (mainly compounds with balanced inward and outward current blocking activities) APD90 may not be a good indicator of distance from EAD.

The concept of robustness to pro-EAD perturbations is highly related to that of repolarization reserve, developed by Roden (1998) to describe the redundant cellular mechanisms to effect orderly and rapid repolarization, which can be disrupted by an added stressor (perturbation), resulting in APD prolongation and/or EAD. We chose to use the term robustness instead of repolarization reserve because the latter has been widely used to describe a cell's repolarization mechanism against both delayed repolarization (APD prolongation) and voltage oscillation (EAD), which we show in **Figure 6** are not necessarily correlated with each other. In contrast, robustness of a system, a concept borrowed from non-linear dynamic theory (Kurata et al., 2008), is directly related to emergence or annihilation of oscillations (EADs) in the presence of perturbations. There are different types of perturbations that could be used to test a system's robustness, for instance an applied bias current (Gray and Huelsing, 2008; Kurata et al., 2008), or an increased conductance for ICaL and/or INaL. We chose IKr conductance

to assess the system's robustness against EADs (see Results section).

reduction as a perturbation because it is independent of the direct drug effects (the dynamic IKr model allows us to model IKr blockers without changing IKr conductance), and also it naturally reflects many physiological and pharmacological factors (hERG channel density variability, hERG channel trafficking block, etc.). It is possible that using different perturbations the same system can show different robustness against EADs. For example, the second best metric cqInward in terms of risk category separation does not correlate with the robustness to IKr conductance reduction, but could potentially correlate with the robustness to other perturbations. We also note that even qNet is not perfectly correlated with the robustness to IKr reduction. The correlation between qNet and IKr reduction threshold was checked only for 12 drugs at selected concentrations (0.5–25x Cmax), and it is not known if the strong correlation holds true beyond the drugs and concentrations tested. Even within the concentrations tested, some drugs (for instance ranolazine) do not have a consistent correlation across all the concentrations (Supplemental Figure 2). This suggests it may be beneficial to use the repolarization robustness (for instance IKr reduction threshold) directly as a metric so that it has clear and direct physiological meaning. However, this method is much more computationally intensive: for each drug at each concentration, the computing time for the IKr reduction threshold is more than 10 times that for qNet, as multiple levels of perturbations are needed to find the threshold. In addition, it is hard to define the metric if different perturbations to the same system lead to different thresholds (robustness). Thus, using a highly correlated surrogate metric qNet is a practical choice currently.

#### Limitations and Ongoing Work

While the model and metric combination presented here have been able to separate all the CiPA training compounds into their respective TdP risk categories, we have yet to test this approach on the CiPA validation compounds or any compounds that were not used in the training of the model, which would provide an independent validation of this framework. A key limitation of this approach that prevents an independent validation study is that we have not provided thresholds for the qNet metric, which could be used to place an unknown compound within a specific TdP risk category. Instead we would only be able to group together compounds which would be expected to pose similar TdP risk.

As suggested in previous studies the sodium potassium pump (Lancaster and Sobie, 2016; Britton et al., 2017) and the sodium calcium exchanger (Armoundas et al., 2003; Nagy et al., 2004) play an important role in EAD generation. Simulations of hypothetical drugs by Lancaster and Sobie (2016) show that both the sodium potassium pump and sodium calcium exchanger were ranked as having the greatest influence on TdP risk, above IKs, IK1, and Ito (but excluding IKr, ICaL, and INa). Further experiments and simulations are needed to assess how CiPA drugs affect these currents and whether they should be directly taken into account in our net current calculation to improve TdP risk prediction.

Another key factor to consider is that while we have demonstrated the success of our approach using gold standard manual patch clamp data. At least in a pre-regulatory setting, the CiPA framework will likely rely on the use of high-throughput ion channel screening data acquired from different platforms routinely used within the pharmaceutical industry. We would therefore need to further refine this model to fit to highthroughput system generated data and demonstrate that the model and metric combination identified perform equally well in this case. Furthermore, dynamic modeling of other channels (such as ICaL) may be needed as the project moves forward; however, at this stage detailed kinetic drug block data for other channels is not available, nor are the protocols to extract the necessary parameters. A priority of CiPA is to keep the framework simple and constrain the cost of data generation; therefore, we use only IC50 data for other channels as, based on our current knowledge, they provide enough information to correctly separate drugs into their TdP risk categories. Additionally, calcium transient properties in the ORd model differ from other models, such as the Grandi et al. model (Grandi et al., 2010); therefore, changes to the calcium transient could improve prediction of TdP risk. In fact, Cummins et al. incorporated the Grandi et al. model [along with the ORd and the ten Tusscher et al. model (ten Tusscher and Panfilov, 2006)] in their TdP risk classification and found diastolic intracellular calcium and APD to be good markers of TdP risk (Cummins et al., 2014). However, as mentioned earlier in this study Cummins et al. define a binary TdP risk stratification that does not follow the same categorization as defined by CiPA.

A number of different avenues for further improvement of the model and TdP risk prediction approach presented here are currently being explored. We are examining the use of thresholds for TdP risk level classification, as well as incorporating both variability and uncertainty within the model predictions. In conclusion, in this manuscript we present an optimized version of the IKr-dyn ORd model presented in Li et al. (2017) that is able to accurately separate the CiPA training compounds into their respective risk categories and correlates well with the system's robustness against EADs. An independent validation of this approach is limited, but more ongoing work will see further refinement of this model and increasing its suitability to be used routinely within the CiPA paradigm.

## AUTHOR CONTRIBUTIONS

JS, PT, MW, and WW contributed to the acquisition of data and provided experimental data guidance. SD and ZL contributed to designing the work and carried out simulations. TC and DS contributed to revising the manuscript. SD, ZL, KC, and KB contributed to the analysis and interpretation of the data and writing of the manuscript.

#### FUNDING

This project was funded by the FDA Critical Path Initiative.

#### ACKNOWLEDGMENTS

We would like to thank Drs. Thomas O'Hara, Norman Stockbridge, Richard Gray, Leonid Livshitz, Jules Hancox, Najah Abi-Gerges, Jamie Vandenberg, Gary Mirams, Bernard Fermini, Adam Hill, Meisam Hosseini and Jose Vicente for useful discussions and input.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fphys. 2017.00616/full#supplementary-material

### REFERENCES


in predicting torsade de pointes. Sci. Rep. 3:2100. doi: 10.1038/srep 02100


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer CC and handling Editor declared their shared affiliation, and the handling Editor states that the process met the standards of a fair and objective review.

Copyright © 2017 Dutta, Chang, Beattie, Sheng, Tran, Wu, Wu, Strauss, Colatsky and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Corrigendum: Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment

#### Edited and reviewed by:

*Eleonora Grandi, University of California, Davis, United States*

> \*Correspondence: *Zhihua Li zhihua.li@fda.hhs.gov*

#### Specialty section:

*This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology*

Received: *22 November 2017* Accepted: *27 November 2017* Published: *06 December 2017*

#### Citation:

*Dutta S, Chang KC, Beattie KA, Sheng J, Tran PN, Wu WW, Wu M, Strauss DG, Colatsky T and Li Z (2017) Corrigendum: Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment. Front. Physiol. 8:1025. doi: 10.3389/fphys.2017.01025* Sara Dutta<sup>1</sup> , Kelly C. Chang<sup>1</sup> , Kylie A. Beattie<sup>1</sup> , Jiansong Sheng<sup>1</sup> , Phu N. Tran<sup>1</sup> , Wendy W. Wu<sup>1</sup> , Min Wu<sup>1</sup> , David G. Strauss <sup>1</sup> , Thomas Colatsky <sup>2</sup> and Zhihua Li <sup>1</sup> \*

*<sup>1</sup> Division of Applied Regulatory Science, Office of Clinical Pharmacology, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, MD, United States, <sup>2</sup> Marshview Life Science Advisors, Seabrook Island, SC, United States*

Keywords: Torsade-de-Pointes (TdP), Comprehensive in vitro Proarrhythmia Assay (CiPA), rapid delayed rectifier potassium current (IKr), in silico cardiac cell model, drug block, proarrythmia risk, model optimization

#### **A corrigendum on**

#### **Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment**

by Dutta, S., Chang, K. C., Beattie, K. A., Sheng, J., Tran, P. N., Wu, W. W., et al. (2017). Front. Physiol. 8:616. doi: 10.3389/fphys.2017.00616

In the original article, there was a mistake in **Figure 6** as published. In the top left panel the qNet gray value should be 0.109 instead of 0.011. The corrected **Figure 6** appears below. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Dutta, Chang, Beattie, Sheng, Tran, Wu, Wu, Strauss, Colatsky and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

FIGURE 6 | AP traces for mexiletine (A) at 1x Cmax (black solid line) and 10x Cmax (gray dashed line) without (left panel) and with 95% IKr reduction (right panel); verapamil (B) at 1x Cmax (black solid line) and 3x Cmax (gray dashed line) without (left panel) and with 98% IKr reduction (right panel); and ranolazine (black solid line) and cisapride (dashed gray line) (C) at 25x Cmax without (left panel) and with 75% IKr reduction (right panel) for a CL of 2,000 ms. Corresponding APD90 (ms) and qNet (µC/µF) values are reported in black for mexiletine 1x Cmax, verapamil 1x Cmax and ranolazine 25x Cmax and in gray for mexiletine 10x Cmax, verapamil 3x Cmax and cisapride 25x Cmax. Note the IKr reduction (simulated by scaling the IKr maximum conductance) is applied in addition to the drug block effect and is used to assess the system's robustness against EADs (see Results section).

# Uncertainty Quantification Reveals the Importance of Data Variability and Experimental Design Considerations for in Silico Proarrhythmia Risk Assessment

#### Edited by:

*Stefano Morotti, University of California, Davis, United States*

#### Reviewed by:

*Sebastian Polak, Jagiellonian University, Poland Michelangelo Paci, Tampere University of Technology, Finland Alexandre Lewalle, King's College London, United Kingdom*

> \*Correspondence: *Zhihua Li Zhihua.Li@fda.hhs.gov*

#### Specialty section:

*This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology*

Received: *01 August 2017* Accepted: *30 October 2017* Published: *21 November 2017*

#### Citation:

*Chang KC, Dutta S, Mirams GR, Beattie KA, Sheng J, Tran PN, Wu M, Wu WW, Colatsky T, Strauss DG and Li Z (2017) Uncertainty Quantification Reveals the Importance of Data Variability and Experimental Design Considerations for in Silico Proarrhythmia Risk Assessment. Front. Physiol. 8:917. doi: 10.3389/fphys.2017.00917* Kelly C. Chang<sup>1</sup> , Sara Dutta<sup>1</sup> , Gary R. Mirams <sup>2</sup> , Kylie A. Beattie<sup>1</sup> , Jiansong Sheng<sup>1</sup> , Phu N. Tran<sup>1</sup> , Min Wu<sup>1</sup> , Wendy W. Wu<sup>1</sup> , Thomas Colatsky <sup>3</sup> , David G. Strauss <sup>1</sup> and Zhihua Li <sup>1</sup> \*

*<sup>1</sup> Division of Applied Regulatory Science, Center for Drug Evaluation and Research, Office of Translational Sciences, Office of Clinical Pharmacology, Food and Drug Administration, Silver Spring, MD, United States, <sup>2</sup> Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom, <sup>3</sup> Marshview Life Science Advisors, Seabrook Island, SC, United States*

The Comprehensive *in vitro* Proarrhythmia Assay (CiPA) is a global initiative intended to improve drug proarrhythmia risk assessment using a new paradigm of mechanistic assays. Under the CiPA paradigm, the relative risk of drug-induced Torsade de Pointes (TdP) is assessed using an *in silico* model of the human ventricular action potential (AP) that integrates *in vitro* pharmacology data from multiple ion channels. Thus, modeling predictions of cardiac risk liability will depend critically on the variability in pharmacology data, and uncertainty quantification (UQ) must comprise an essential component of the *in silico* assay. This study explores UQ methods that may be incorporated into the CiPA framework. Recently, we proposed a promising *in silico* TdP risk metric (qNet), which is derived from AP simulations and allows separation of a set of CiPA training compounds into Low, Intermediate, and High TdP risk categories. The purpose of this study was to use UQ to evaluate the robustness of TdP risk separation by qNet. Uncertainty in the model parameters used to describe drug binding and ionic current block was estimated using the non-parametric bootstrap method and a Bayesian inference approach. Uncertainty was then propagated through AP simulations to quantify uncertainty in qNet for each drug. UQ revealed lower uncertainty and more accurate TdP risk stratification by qNet when simulations were run at concentrations below 5× the maximum therapeutic exposure (Cmax). However, when drug effects were extrapolated above 10× Cmax, UQ showed that qNet could no longer clearly separate drugs by TdP risk. This was because for most of the pharmacology data, the amount of current block measured was <60%, preventing reliable estimation of IC50-values. The results of this study demonstrate that the accuracy of TdP risk prediction depends both on the intrinsic variability in ion channel pharmacology data as well as on experimental design considerations that preclude an accurate determination of drug IC50-values *in vitro*. Thus, we demonstrate that UQ provides valuable information about *in silico* modeling predictions that can inform future proarrhythmic risk evaluation of drugs under the CiPA paradigm.

Keywords: uncertainty quantification, experimental variability, cardiac electrophysiology, action potential, Torsade de Pointes, ion channel, pharmacology, computational modeling

#### INTRODUCTION

Drugs that block cardiac ion channels encoded by the humanether-à-go-go Related Gene (hERG) and consequently prolong the QT interval are associated with increased risk of Torsade de Pointes (TdP), a potentially lethal arrhythmia that caused several drugs to be withdrawn from market (Gintant et al., 2016). In 2005, the International Council on Harmonisation (ICH) S7B and E14 guidelines were established to address the issue of TdP liability for new drugs. As stated in these guidelines, their intent was to be used as a screening method to identify drugs that would require more intensive electrocardiographic monitoring of patients in late phase (e.g., phase 3) clinical trials. However, hERG block or QT prolongation does not necessarily correlate with TdP risk, and as a result of these guidelines, many novel compounds are screened out of development because of detected hERG block or QT prolongation without further evaluation of actual TdP risk. Additional insight into TdP risk for hERG-blocking and QT-prolonging drugs can be determined by also assessing whether drugs block inward currents such as, L-type calcium or late sodium (Duff et al., 1987; January and Riddle, 1989; Chézalviel-Guilbert et al., 1995; Guo et al., 2007). The Comprehensive in vitro Proarrhythmia Assay (CiPA) is a global initiative to revise the current guidelines with a new set of mechanistic assays that improve the specificity of the proarrhythmia screening process (Fermini et al., 2016).

The CiPA in silico assay will test new compounds for the potential to cause TdP by incorporating in vitro pharmacology data on multiple ion channels into a mathematical model of the cardiac action potential (AP). The AP model will be used to predict drug effects related to early afterdepolarizations (EADs), which are a known cellular trigger of TdP (Yan et al., 2001). Numerous studies have shown that when outward repolarizing currents such as, IKr (the current carried by hERG-encoded channels) are blocked in cardiac cells, the resulting imbalance of inward and outward currents prolongs the AP and can, at extreme levels, lead to inward current reactivation and EADs (January and Moscucci, 1992). However, EADs may not occur if a drug also significantly blocks inward currents, leading to a balanced block scenario where the AP is prolonged but inward currents cannot reactivate (Antzelevitch et al., 2004). Because it is difficult to know how much inward vs. outward current block is safe, or how dynamic effects might impact EAD propensity, the purpose of the CiPA in silico model will be to assess the integrated effects of multiple ion channel block on TdP risk. As with any model built on inherently variable experimental data, however, confidence in model predictions will depend on the level of uncertainty in model inputs (here, the drug-specific parameters) and the corresponding uncertainty in model outputs (Pathmanathan et al., 2015; Johnstone et al., 2016b). In order for CiPA to provide useful guidance to the drug development and regulatory process, it will be necessary to incorporate uncertainty quantification (UQ) into modeling predictions (Pathmanathan and Gray, 2013; Mirams et al., 2016).

The CiPA in silico ventricular AP model and a mechanismbased metric for TdP risk stratification have been trained on a designated set of 12 CiPA compounds with known TdP risk levels (High, Intermediate, or Low, see **Table 1**). These compounds were selected and categorized by a team of expert clinicians, safety pharmacologists, and electrophysiologists based on adverse event data and published reports (Colatsky et al., 2016). The current CiPA AP model was developed through a series of modifications to the O'Hara-Rudy (ORd) human ventricular AP model (O'Hara et al., 2011). Li et al. (2016) first developed a Markov model of the hERG channel that included temperature-sensitive gating, which was subsequently modified to recapitulate IKr from the original ORd model, with an added pharamacological component (Li et al., 2017). The hERG/IKr model was then incorporated into the ORd AP model to produce the IKr-dynamic ORd model. In the CiPAORdv1.0 model, we further optimized the IKr-dynamic ORd model by scaling ionic current conductances to better reflect changes in AP duration observed in human ventricular myocytes when ionic currents were blocked (referred to as the optimized IKr-dynamic ORd model in Dutta et al., 2017). With this model, we derived a new in silico biomarker for TdP risk, the qNet metric, which correlated well with in silico cell "distance" to EADs and thus provided a continuous marker for EAD susceptibility. Although we showed that the qNet metric could correctly stratify the 12 CiPA training drugs by known TdP risk, uncertainty in these modeling predictions was not evaluated.

In this study, methods for applying UQ to the CiPA in silico assay are presented. For the 12 CiPA training compounds, we examine the uncertainty in drug-specific kinetics parameters for drug binding and trapping in the IKr-dynamic model. In addition, we examine uncertainty in dose-response curve IC<sup>50</sup> and Hill coefficients for the remaining six CiPA-selected ionic currents, as this can also be considerable (Elkins et al., 2013). We thereby characterize uncertainty in drug effects on ion channels due to variation in experiments, whatever the cause of this variation may be. We then sample from these probability distributions for the drug effects and run forward simulations to examine the subsequent uncertainty in qNet and TdP risk stratification.



#### MATERIALS AND METHODS

#### Human Ventricular Action Potential Model

The CiPAORdv1.0 model (the optimized model from Dutta et al., 2017) was used for all simulations in this study, in order to evaluate TdP risk for the set of 12 CiPA training compounds listed in **Table 1**. Parameter values for the model are listed in Tables S1, S2.

#### Multiple Ion Channel Pharmacology

Pharmacological effects of the 12 CiPA training compounds on ionic currents were modeled as in Li et al. (2017) and Dutta et al. (2017). The kinetics of hERG block were modeled with the IKr Markov model from Li et al. (2017), which was fit to voltage clamp data obtained at the U.S. Food and Drug Administration (FDA; parameters listed in **Table 2**). For six other ionic currents (L-type calcium, ICaL; late sodium, INaL; fast sodium, INa; transient outward, Ito; slowly activating delayed rectifier, IKs; and inward rectifier, IK1), drug effects were represented by a simple pore blocking model in which maximal current conductances were reduced according to the Hill equation. Hill equation parameters (**Table 3**) were fit to data from Crumb et al. (2016). Some of the data have been updated since publication and are available online (see section Software and Data).

#### Numerical Methods and Data Analysis

Model equations were written in C and compiled for use with version 3.3 of the R programming language (R Core Team, 2016) and version 1.14 of the deSolve package (Soetaert et al., 2010). Equations were integrated using the lsoda solver with relative and absolute error tolerances of 10−<sup>6</sup> and other solver settings as default. For computationally intensive bootstrap simulations (see section Drug-hERG Binding Kinetics), a relative tolerance of 10−<sup>3</sup> was used. Data analysis was performed in R, and figures were produced with version 2.2.0 of the ggplot2 package (Wickham, 2009).

#### Simulation Protocol for TdP Risk Evaluation

The CiPAORdv1.0 model was used to simulate APs at a cycle length (CL) of 2 s (stimulus amplitude = −80 µA/µF, duration = 0.5 ms). The model was initialized from control (no drug) steady-state values (Table S3) and paced for 1,000 beats. Drugs were simulated at multiples of their maximum therapeutic concentrations (Cmax, Table S4), ranging from 1 to 10× Cmax (1× increments) and from 15 to 25× Cmax (5× increments). At each concentration, TdP risk was evaluated using the metric qNet, defined as the net charge carried by six major currents (IKr, ICaL, INaL, Ito, IKs, and IK1) over an entire beat (Dutta et al., 2017). The qNet metric was computed by integrating the sum of the six currents from the start of the stimulus (t = 0 s) until the end of the beat (t = 2 s) using lsoda (see section Numerical Methods and Data Analysis).

Analysis was performed only on the last 250 beats of the pacing protocol to allow drug effects to reach quasi-steady state for simulations with beat-to-beat instability. Beats in which transmembrane potential (Vm) failed to depolarize above 0 mV were excluded from analysis, and simulations in which every beat failed to depolarize were excluded from TdP risk evaluation. The maximum slope during repolarization (dV/dtrepol) was defined as the maximum change in V<sup>m</sup> (dV/dt) between 30 and 90% repolarization for beats that fully repolarized; as the maximum dV/dt between 30% repolarization and the end of the beat (t = 2 s) when V<sup>m</sup> repolarized by 30% but not 90%; or as the maximum dV/dt between the AP peak and the end of the beat when V<sup>m</sup> failed to repolarize by 30%. An EAD was defined to have occurred on any beat in which dV/dtrepol was greater than zero. Out of the last 250 beats, the beat with the steepest reactivation of the membrane potential (maximum dV/dtrepol) was used to calculate qNet, whether or not an EAD had occurred.

#### Uncertainty Characterization Drug-hERG Binding Kinetics

In Li et al. (2017), time series measurements of the fractional hERG current in the presence of drug were obtained using a modified Milnes voltage clamp protocol (Milnes et al., 2010; Li et al., 2017). Because of the long duration of the protocol, each cell could only be tested at a single drug concentration, and the drug-hERG binding and trapping parameters (see **Table 2**) were fit to the fractional current traces measured during a voltage step to 0 mV, averaged across cells by concentration. Specifically, each dataset y consisted of a set of fractional current time series observations xc,i(t) (c = 1, 2, . . . , m, where m is number of the concentrations tested; i = 1, 2, . . . , n<sup>c</sup> , where n<sup>c</sup> is the number of cells tested at the cth concentration; and xc,i(tj) were independent between concentrations). The mean drug response at the cth concentration was x¯<sup>c</sup> (t) = 1 nc Pn<sup>c</sup> i=1 xc,<sup>i</sup> (t) (i.e., the average of fractional current traces across cells), and the overall mean response y¯ = x¯<sup>1</sup> (t), x¯<sup>2</sup> (t), . . . , x¯<sup>m</sup> (t) (i.e., the set of average fractional current traces at each concentration) was used to fit the optimal drug-hERG kinetics parameters (θˆ(y¯)). Parameters were fitted using the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) (Hansen, 2006), with version 1.0-11 of the cmaes package (Trautmann et al., 2011). Details on the CMA-ES implementation can be found in the Supplemental Methods. Bounds for the dynamic drug-hERG binding parameters used to fit bootstrap samples can be found in Table S5.



*The optimal values are shown with 95% CIs obtained with bootstrapping. Units are as follows: Kmax (unitless), K<sup>u</sup> (ms*−*<sup>1</sup> ), EC*<sup>50</sup> *(nM), n (unitless), and Vhalftrap (mV).*

The non-parametric bootstrap method was used to characterize uncertainty in the fitted parameters (Efron and Tibshirani, 1986). Observations x ∗ c,i (t) were randomly drawn with replacement from xc,i(t) to obtain a bootstrap sample y ∗ b of the same size as the original dataset, with an identical number of observations per concentration. A total of 2,000 bootstrap samples (b = 1, 2, . . . , 2000) were generated using version 1.3-18 of the boot package (Davison and Hinkley, 1997; Canty and Ripley, 2016). The mean response y¯ ∗ b for each bootstrap sample was then computed in the same manner as y¯ and used to refit the drug-hERG kinetics parameters (θˆ(y¯ ∗ b )), yielding a joint sampling distribution of drug-hERG parameters.

#### Dose-Response Curves

For other ionic currents, uncertainty in dose-response curves was characterized using a Bayesian inference approach. Version 1.3.5 of the FME package was used to fit Hill equation parameters and to characterize uncertainty, using Markov-chain Monte Carlo (MCMC) simulation with the delayed rejection and adaptive Metropolis algorithm (Soetaert and Petzoldt, 2010). The percentage of ionic current block was assumed to be a normal random variable located at the Hill equation response curve with unknown variance σ 2 . Log-transformed IC50-values [pIC<sup>50</sup> = −log10(IC50/c0), where c<sup>0</sup> = 10<sup>9</sup> nM] were bounded to the range [−1, 19] for fitting and MCMC simulation (bounding IC50-values between 10−<sup>10</sup> and 10<sup>10</sup> nM). Hill coefficients (h) were bounded to the range [0, 10]. Optimal IC<sup>50</sup> and Hill coefficient (h)-values were fit using non-linear least squares (see **Table 3**). The joint probability distribution of IC<sup>50</sup> and h was estimated using MCMC simulation. A uniform prior distribution was used for pIC<sup>50</sup> and h. The error variance σ <sup>2</sup> was considered a nuisance parameter and was sampled as conjugate priors from an inverse gamma distribution during MCMC simulation. The proposal distribution was multivariate normal. A total of 2,000 MCMC samples (pIC50, h) were saved for each drugcurrent combination to form a joint sampling distribution of Hill equation parameters (see Supplemental Methods for implementation details).

#### Credible Intervals

Variability of model inputs (parameters) or outputs (predicted responses) was summarized with 95% credible intervals (95% CIs, the 2.5–97.5% quantiles of the marginal distributions).

#### Uncertainty Propagation

Samples from the joint distribution of drug-hERG parameters and the joint distributions of Hill equation parameters for a

#### TABLE 3 | Hill equation parameters for the 12 CiPA training compounds.


*The optimal fitted values are shown with 95% CIs obtained using Markov-chain Monte Carlo simulation. IC50-values are log-transformed as pIC<sup>50</sup>* = −*log10(IC50/c0), where c<sup>0</sup>* = *10<sup>9</sup> nM. Not applicable (N/A) indicates that IC50-values were not defined in Li et al. (2017), so the amount of block was assumed to always be 0%.*

particular drug were assumed to be independent and were combined in AP simulations to assess the uncertainty in qNet (see section Simulation Protocol for TdP Risk Evaluation). One sample from each distribution was selected in sequential order (e.g., the first sample from each distribution) to form a set of parameters that defined a single sample from the drug-effect probability distribution. This was repeated until all parameter samples were exhausted, generating a sampling distribution of 2,000 drug-effect samples per drug (referred to as uncertainty inputs), which. Each input was simulated with the CiPAORdv1.0 model to assess variability in AP model outputs (qNet, see section Simulation Protocol for TdP Risk Evaluation). Variability in qNet was quantified with 95% CIs. Sampling distributions of qNet were visualized with violin plots.

#### Cross Validation

Leave-one-out cross validation (LOOCV) (Hastie et al., 2009) was used to assess the accuracy of TdP risk stratification at each simulated concentration relative to Cmax. The CiPA Low, Intermediate, and High TdP risk levels (**Table 1**) were given numerical category values of 0, 1, and 2, respectively. At each concentration (1−25× Cmax), a classifier was trained on all samples from the qNet distributions of all but one of the training drugs. The classifier was based on proportional odds logistic regression using the lrm function from version 4.5-0 of the rms package (Harrell, 2016). The numerical tolerance was set to 10−<sup>10</sup> and the maximum number of iterations was set to 10<sup>6</sup> for fitting. Each sample of the remaining, "left out" drug was then assigned to the category with the highest probability based on logistic regression results. The predicted probability of each category [P(x), where x is 0, 1, or 2] for the "left out" drug was computed as the fraction of samples assigned to that category, and the prediction error for that drug was computed as the mean absolute difference between the assigned and actual TdP category over all samples. This procedure was repeated for all 12 training drugs, and the mean and standard deviation of prediction errors at each concentration were computed to evaluate overall TdP risk stratification performance.

#### Software and Data

The software and data used in this study are available at https:// github.com/FDA/CiPA.

# RESULTS

#### Uncertainty in Drug-hERG Binding Kinetics

Bootstrapping was performed with voltage clamp data from Li et al. (2017) in order to estimate the joint probability distribution of fitted drug-hERG dynamic binding parameters. The 95% CIs of hERG binding parameters for the 12 CiPA training drugs (**Table 1**) are listed in **Table 2**. Parameter fitting results for bepridil are illustrated in **Figure 1A**. The rate of bepridil unbinding (Ku) had a relatively narrow 95% CI [10−3.8713, 10−3.671 ms−<sup>1</sup> ], indicating that this parameter was well-constrained by the experimental data and uncertainty in its value was low. In contrast, the pairwise scatter plot of log10(Kmax) and log10(EC<sup>50</sup> n ) revealed a strong correlation between the two parameters, and their fitted ranges spanned several orders of magnitude. The pairwise scatter plots for other training drugs displayed similar correlations between log10(Kmax) and log10(EC<sup>50</sup> n ) (panel A in Figures S1–S11).

The large uncertainty in Kmax and EC<sup>50</sup> <sup>n</sup> did not produce a similar degree of variability in the kinetics of hERG block, however. In **Figure 1B** and panel B of Figures S1–S11, shaded areas indicate the 95% CI of the block predicted by parameters in **Figure 1A** and panel A of Figures S1–S11. The variability in hERG block was much more limited than the variability in Kmax or EC<sup>50</sup> n , which was not surprising because Li et al. (2017) showed that for most of the 12 training drugs, there was a near-linear relationship between drug concentration and binding rate, occurring when the fitted EC50-value was much greater than the maximum drug concentration tested. For example, the optimal EC50-value of bepridil was 108.7 nM, and the bootstrapestimated 95% CI was [107.0, 109.7], but the maximum bepridil concentration tested was 300 nM, or roughly 102.5 nM. In such cases, the Emax equation defining the sigmoidal dose-response relationship of drug binding [Emax = Kmax ∗ (D<sup>n</sup> /(Dn+EC<sup>50</sup> n ))] was linearly approximated by Emax≈(Kmax/EC<sup>50</sup> n ) <sup>∗</sup>D<sup>n</sup> , and the ratio Kmax/EC<sup>50</sup> n effectively becomes a single identifiable parameter. Thus, the 95% CIs for log10(Kmax/EC<sup>50</sup> n ) were much narrower than the 95% CIs for log10(Kmax) and log10(EC<sup>50</sup> n ) (**Table 2**). The Emax equation was chosen to model drug binding because of its flexibility in accommodating both linear and sigmoidal dose-response relationships. As a result, for those compounds whose drug binding mode is actually linear, the ratio but not the individual values of the two correlated parameters were identifiable (Li et al., 2017).

In addition, multimodality (the presence of multiple peaks in the sampling distribution) was frequently observed in other hERG kinetics parameters (Figures S1–S11), in particular with Vhalftrap. In the hERG binding model, Vhalftrap is a drug trapping parameter that determines the steady-state fraction of openbound (untrapped) to close-bound (trapped) channels. Li et al. (2017) demonstrated that the High- and Low-risk CiPA training drugs could be separated by this single parameter (Vhalftrap > −65 mV for High-risk drugs, while Vhalftrap < −85 mV for Lowrisk drugs). The multimodality identified in Vhalftrap sampling distributions raised the question of whether this trend still holds under uncertainty analysis. As shown in **Figure 2**, the 95% CIs of Vhalftrap were quite wide for most drugs, but much of this variability covered ranges where the ratio of open- to close-bound channels (Obound/Cbound) at −80 mV was relatively flat, near 1 for Low-risk drugs (green bars) or near 0 for High-risk drugs (red bars). In the steepest region of the Obound/Cbound curve, Vhalftrap distributions of High- vs. Low-risk drugs were wellseparated (upper credible bounds < −77 mV for Low-risk drugs, lower credible bounds > −75 mV for High-risk drugs). Thus, UQ identified consistently low or high levels of trapping for Low- vs. High-risk drugs, respectively, providing increased confidence in the Vhalftrap trend identified by Li et al. (2017). Note that with or without UQ, the Vhalftrap-values of Intermediate-risk drugs (blue bars and points) other than chlorpromazine were generally indistinguishable from Low-risk drugs, and chlorpromazine was indistinguishable from High-risk drugs, indicating that the

scatter plots of the fitted parameters for 2,000 bootstrap samples. (B) Kinetics of hERG block during 10 sweeps of a modified Milnes voltage-clamp protocol (Milnes et al., 2010; Li et al., 2017). Shaded areas show the range of block produced by the parameters from (A). Lines show the experimental results used to fit the data (down-sampled 5× for clarity).

degree of drug trapping is not sufficient to stratify compounds into the three CiPA risk levels.

#### Uncertainty in Dose-Response Curves

Bayesian inference was used to estimate the joint probability distribution of Hill equation parameters characterizing steadystate INa, ICaL, INaL, Ito, IKs, and IK1 block by each of the 12 CiPA training drugs. MCMC simulation was not performed for drug-current combinations that did not have defined IC50 values in Li et al. (2017), which were assumed to have 0% block. Parameter fitting results are summarized in **Table 3**. Some MCMC simulations produced joint sampling distributions with a single well-defined peak, such as, that of ranolazine-INaL (**Figure 3A**). The mean parameter values of this distribution (pIC<sup>50</sup> = 5.0958, h = 0.9594) were close to the optimal fitted values (pIC<sup>50</sup> = 5.1033, h = 0.945), and the 95% CIs [pIC<sup>50</sup> (4.9859, 5.2079), h (0.7247, 1.256)] were relatively narrow, indicating that uncertainty in these parameters was low. Consequently, the variability in dose-response curves defined by these parameters was also low. At any given concentration, uncertainty in ranolazine-INaL block (i.e., the width of its 95% CI) was <16% (**Figure 3B**, shaded area), reflecting the variability observed in experiments (circles). Note that uncertainty in ranolazine- INaL block did not increase at concentrations beyond the highest tested (23µM) because the well-constrained doseresponse curve allowed for extrapolation beyond experimentally tested concentrations.

For other MCMC simulations such as, dofetilide-INaL, an inverse relationship of possible IC50- and h-values was observed, without a defined peak (**Figure 3C**). Furthermore, many MCMC samples reached near the bounds imposed on IC<sup>50</sup> and h during fitting [95% CIs for pIC<sup>50</sup> (−0.754, 7.8227] and h [0.1543, 9.49)]. This was symptomatic of having insufficient experimental data to constrain IC50-values, as the maximum measured INaL block was 12.1% at 3× Cmax, the highest concentration tested (**Figure 3D**, circles). Although an optimal fit could be defined using least squares (solid line), confidence in the fitted parameters was low, and uncertainty in predicted block increased abruptly above 3× Cmax. At 10× and 25× Cmax, the 95% CIs of predicted block were [0, 82.8%] and [0, 99.8%], respectively, reaching close to the maximum possible range (shaded area). Thus, under circumstances where insufficient current block was achieved in experiments, uncertainty in the dose-response relationship became very high when extrapolating beyond the tested concentrations. Similar findings were obtained with other drug-current combinations (**Table 3** and Figures S12–S62).

The amount of uncertainty in predicted block (measured as the width of the 95% CI) was examined as a function of the mean block achieved at the highest tested concentration (Chigh). **Table 4** lists the mean block measured in experiments at 1× Chigh for the 12 CiPA training drugs (some drugs had a different Chigh for different channels). The resulting uncertainty in the amount of drug block at concentrations above Chigh is depicted in **Figure 4**. At 1× Chigh, uncertainty was <25% for all drug-current combinations, indicating that variability in the experimental observations was low. When uncertainty was quantified at extrapolated concentrations (2×, 3×, and 10× Chigh), differences were observed between experiments with low and high amounts of block at 1× Chigh. When <30% mean block was measured at 1× Chigh, uncertainty was >25% for most dose-response curves and reached close to 100% in several cases. But when >60% mean block was measured at 1× Chigh, uncertainty at the extrapolated concentrations was <16%. Thus, UQ results for this dataset suggest that >60% block should be achieved experimentally if dose-response curves are to predict drug effects beyond the tested concentrations. Although >60% block was achieved in hERG experiments with the 12 CiPA training drugs, none of the training drugs were tested at concentrations producing >60% block for all six non-hERG ionic currents (which would be unlikely other than for quinidine, given the selectivity of these compounds). This analysis therefore suggested that drug effects could only be reliably predicted at the highest experimentally tested concentration for which data on all six non-hERG ionic currents were available (**Table 4**).

# Propagation of Uncertainty to AP Simulations

Uncertainty in drug-hERG kinetics and dose-response curves was propagated to AP simulations to explore its impact on TdP risk stratification for the 12 CiPA training drugs. For each drug, the optimal drug-hERG parameters and Hill equation parameters (referred to as fixed inputs) were used to simulate APs, as in previous studies (Dutta et al., 2017; Li et al., 2017). In addition, a total of 2,000 drug-effect uncertainty samples per drug (referred to as uncertainty inputs) were simulated in order to estimate the distribution of drug effects derived from uncertainty characterization (see section Uncertainty in

Drug-hERG Binding Kinetics–Uncertainty in Dose-Response Curves). Individual beats were classified as having normal APs, EADs, or depolarization failure (**Figure 5A**), and each simulation was classified as having EADs, complete depolarization failure, or normal otherwise (see section Simulation Protocol for TdP Risk Evaluation). As drug concentration increased from 1 to 25× Cmax in uncertainty-input simulations, repolarization and depolarization abnormalities became more frequent for some training drugs. EADs occurred in quinidine, dofetilide, and ranolazine simulations (**Figure 5B**), and depolarization failure occurred in quinidine, dofetilide, ranolazine, and verapamil simulations (**Figure 5C**). However, the frequency of these events was generally low except in quinidine simulations, which had EADs in >90% of simulations at 3–10× Cmax and depolarization failure in >50% of simulations at ≥20× Cmax. While EADs are mechanistically linked to TdP, depolarization failure constitutes a different type of rhythm disturbance; therefore, simulations with depolarization failure were removed from further analysis. The remaining simulations represented the conditional distribution of drug effects, given that depolarization failure did not occur at a particular concentration.

# Impact of Uncertainty on TdP Risk Stratification

Although EADs are a mechanistic marker for TdP risk, stratification based on EADs was not possible because they occurred very rarely in simulations, and not at all for many High Risk compounds at free Cmax. Instead, Dutta et al. (2017) proposed to use the in silico metric qNet (the net charge carried by major AP currents during one paced beat at steady state) as

in AP simulations (1−25× Cmax).



*Concentrations are also expressed as multiples of the maximum therapeutic concentration (*× *Cmax ). Because some ionic current experiments used different test concentrations, verapamil and ranolazine both have two entries in the table.*

an indicator of how far a cell is at a particular drug concentration from producing an EAD. The qNet metric was used in the present study as a marker of TdP risk because it successfully stratified the 12 CiPA training drugs at a range of concentrations in the previous study by Dutta et al. (2017). The calculation of qNet was updated to include simulations in which EADs occurred (see section Simulation Protocol for TdP Risk Evaluation) so that the sampling distributions of qNet would accurately reflect the uncertainty in drug parameters (excluding those that produced depolarization failure). As expected, the values of qNet obtained

with uncertainty-input simulations trended according to TdP risk (**Figures 6A,B**). At a given concentration, median qNetvalues decreased between the Low, Intermediate, and High TdPrisk drugs, indicating that outward currents were diminished and inward currents became increasingly dominant at higher risk levels. Note also that extreme negative values of qNet occurred when EADs were present (**Figure 6B**), reflecting the higher TdP risk evident in these simulations.

Variability in qNet increased as uncertainty in drug effects increased. At 1× Cmax, the distribution of qNet-values for each drug was relatively narrow, and as a result, only a small amount of overlap was observed between adjacent TdP risk levels (**Figure 6A**). At 10× Cmax, however, the distribution of qNet-values for dofetilide (a High-risk drug) contained several outliers, which encompassed the values for all other drugs except the most negative quinidine values (**Figure 6B**). These outliers resulted from the high degree of uncertainty in dose-response curves for dofetilide above the highest concentration tested (3× Cmax), particularly with inward currents. As discussed in section Uncertainty in Dose-Response Curves, uncertainty in INaL block by dofetilide increased dramatically above 3× Cmax (**Figure 3D**, shaded area). A similar pattern occurred for ICaL block by dofetilide (Figure S12), with high uncertainty in predicted block at 10× Cmax [95% CI (0%, 97.6%)]. Because qNet reflects the

balance of inward currents (INaL and ICaL) and outward currents (mainly IKr), the effects of IKr block by dofetilide were offset in simulations with significant block of INaL or ICaL, resulting in the "safe" outliers for dofetilide at 10× Cmax with very high qNetvalues. On the other hand, simulations with very little INaL or ICaL block led to "dangerous" outliers with very low or negative qNet-values.

results. For all panels, High TdP-risk drugs are in red, Intermediate-risk drugs are in blue, and Low-risk drugs are in green.

Poor separation of qNet between TdP risk levels was apparent at higher drug concentrations, due primarily to the increased uncertainty in drug effects. Dutta et al. (2017) showed that with fixed model simulations, perfect separation in qNet occurred for the 12 CiPA training drugs at 1–25× Cmax. However, our analysis of dose-response uncertainty in section Uncertainty in Dose-Response Curves suggests that qNet may be highly variable above experimentally tested concentrations. In **Figure 6C**, fixed-input simulation results are shown for concentrations up to (solid lines) and including (point) the maximum simulated concentrations for which complete drug block data on all six non-hERG ionic currents was available; above these concentrations, fixed-input results are plotted as dotted lines. At 1× Cmax, data were available for all 12 CiPA training drugs. Above 1× Cmax, however, some data were unavailable for quinidine (>1.7× Cmax), mexiletine (>2.4× Cmax), dofetilide (>3× Cmax), verapamil (>6.2× Cmax), and ranolazine (>11.8× Cmax; see **Table 4**). Nevertheless, near 1× Cmax, the 95% CIs of qNet remained largely separated between TdP risk levels, indicating that uncertainty at these concentrations was low enough to stratify the training drugs (shaded areas). At >4× Cmax, however, overlap between different risk levels increased due to the higher variability in qNet sampling distributions, particularly for verapamil and dofetilide. However, increased uncertainty in qNet was not the sole factor affecting TdP risk separation. The qNet-values for verapamil and ranolazine (Low-risk drugs) also drifted closer to those of chlorpromazine (Intermediate-risk) at >4× Cmax, further increasing the overlap between these risk levels, though qNetvalues for fixed-input results remained separate.

The accuracy of TdP risk stratification as a function of concentration was assessed using LOOCV. At each concentration relative to Cmax, a classifier was trained on qNet uncertainty samples for 11 of the 12 training drugs and then used to predict the probabilities of each TdP risk level for the remaining drug (see section Cross Validation). At 1× Cmax, the maximum probability always occurred at the correct TdP risk level, but several drugs had non-zero probabilities for the incorrect TdP risk level (**Table 5**). In contrast, when LOOCV was performed at 1× Cmax in Dutta et al. (2017), two drugs (terfenadine and chlorpromazine) were misclassified on the basis of fixedinput results (equivalent to a predicted 100% probability of the drug being in the wrong category). As a result, although LOOCV prediction errors were non-zero for more drugs when uncertainty was considered, the overall mean prediction error was lower as compared to fixed-input results (0.09 vs. 0.17). At 10× Cmax, however, mean prediction error was higher when the classifier was trained on uncertainty-input results rather than fixed-input results (0.23 vs. 0.08) because of increased prediction errors for dofetilide, sotalol, cisapride, and verapamil. This was due to the low level of block achieved experimentally for many non-hERG currents, which led to high uncertainty in qNet when drug effects were extrapolated above the tested concentrations. Thus, uncertainty analysis produced more robust TdP risk predictions near concentrations with experimental data for all currents but less robust predictions at concentrations for which extrapolation of drug effects was unreliable due to insufficient levels of block (<60%) measured experimentally.

LOOCV results for the 12 training drugs at 1–25× Cmax are summarized in **Figure 7A**. As concentration increased, prediction errors improved for some drugs and worsened for others. Terfenadine's prediction error was the highest of all drugs at 1× Cmax (0.4545) but decreased to <0.01 at 4× Cmax (blue diamonds). On the other hand, prediction errors for chlorpromazine (blue circles), sotalol (red triangles), verapamil (green triangles), cisapride (blue × s), and dofetilide (red squares) all generally increased from 1 to 10× Cmax. Above 10× Cmax, prediction errors for dofetilide and ranolazine (green crosses) increased, while prediction errors for sotalol decreased. As a result of these trends, both the mean and the standard deviation of prediction errors were lowest at 1–4× Cmax (**Figure 7A**, black points and error bars), near the concentrations for which experimental data on all currents were available for the 12 training drugs.


*The TdP risk levels were assigned category values of 2 (High), 1 (Intermediate), and 0 (Low). A classifier was trained on 11 of 12 drugs and then used to predict the category probabilities [P(x), where x is the category value] and to obtain an overall prediction error for the remaining drug (see section Cross Validation). Uncertainty model simulations were used for training and prediction. For comparison, probabilities, and prediction errors from Dutta et al. (2017) are shown in parentheses when they differed from uncertainty results.*

FIGURE 7 | Cross validation of TdP risk stratification with uncertainty quantification. LOOCV was performed at each concentration to assess TdP risk stratification performance. Prediction error for each drug was obtained by training on qNet distribution samples from all other drugs and calculating the mean classification error of the test drug's samples. (A) LOOCV at 1−25× Cmax. Markers show the prediction errors for each drug when it was "left out," as indicated in the legend. Black points and error bars are the mean + standard deviation (SD) of prediction errors at each concentration. High TdP-risk drugs are in red, Intermediate-risk drugs are in blue, and Low-risk drugs are in green. (B) LOOCV at 1−4× Cmax was repeated with the drug effects for a particular ionic current removed. Black points are the mean prediction errors from (A). Markers show the mean prediction errors that resulted when drug effects on the ionic current indicated in the legend were omitted from simulations.

To explore the impact of different ionic currents on TdP risk stratification, LOOCV was repeated for a set of simulations in which drug effects on a particular ion channel were removed. This analysis was limited to 1–4× Cmax in order to avoid concentrations at which uncertainty was due primarily to the lack of experimental data. When drug effects on INa, Ito, IKs, or IK1 were removed, prediction errors were virtually unchanged (**Figure 7B**). However, when drug effects on ICaL, INaL, or IKr were removed, prediction errors increased dramatically, indicating that TdP risk stratification of the 12 CiPA training compounds depended primarily on the drug effects for these three currents. Because most of the training compounds (other than quinidine) did not block INa, Ito, IKs, or IK1 substantially at 1−4× Cmax, their resulting impact on TdP risk stratification was expected to be minimal.

#### DISCUSSION

Although many potential sources of uncertainty exist within the CiPA paradigm, the primary concern for the in silico component is uncertainty related to in vitro measurements of pharmacological effects on ionic currents. This study presents methods for conducting UQ within the framework of the CiPA in silico assay. Previously, Dutta et al. (2017) showed that the metric qNet, derived from fixed-input AP simulations incorporating multiple ion channel pharmacology, could be used to stratify the CiPA training set of 12 compounds by relative TdP risk. This study examined the impact of uncertainty in drug effects on simulation predictions. Bootstrapping and Bayesian inference were used to estimate the joint probability distributions of drug parameters in order to quantify the variability in mean drug effects. This variability was then propagated to a set of uncertainty-input AP simulations to assess the robustness of risk stratification with qNet. UQ revealed that some drug effects were insufficiently constrained at higher concentrations to be able to stratify TdP risk with high confidence. Near therapeutic concentrations, however, TdP risk stratification was robust to the uncertainty in drug effects. This study illustrates the benefits of applying UQ under the CiPA paradigm, both during model validation and when model-based predictions are used in regulatory decision making.

UQ helped to identify challenges concerning model calibration and parameter identification that will inform future model development. Such issues are frequently encountered in models of cardiac electrophysiology but are not often addressed during model development (Fink and Noble, 2009; Shotwell and Gray, 2016). In the Li et al. (2017) IKr Markov model, drug-hERG binding kinetics was characterized by six parameters, but one parameter (drug trapping rate, Kt) was fixed at a value of 3.5× 10−<sup>5</sup> ms−<sup>1</sup> . UQ revealed that three of the remaining five parameters (Kmax, EC<sup>50</sup> n , and Vhalftrap) could not be precisely estimated based on the available data. Although the current model structure was designed to allow for both linear and sigmoidal drug binding as well as drug trapping, this flexibility comes at the expense of parameter identifiability and presents difficulties for UQ. To address these issues, model recalibration and/or simplification may be warranted, as was done for a model of INa inactivation in Pathmanathan et al. (2015).

On the other hand, for some drugs, the observed hERG block kinetics could not be accurately captured by the IKr Markov model. For instance, at 10 nM cisapride, hERG block developed more slowly in the experimental traces than in fitted model, even when uncertainty was considered (Figure S4B). This suggests that alternative (and possibly more complex) model structures might be needed to characterize certain drugs. Thus, the challenge for CiPA is to define a one-size-fits-all model that is simple enough to be estimable but still accurate enough to predict TdP risk. The current approach attempts to strike an appropriate balance between the two concerns, combining the flexible dynamic representation of IKr block with a simplified pore-block approach for other currents. The final assessment of the model will depend on its validation with an additional 16 compounds, which will determine its suitability for CiPA (Colatsky et al., 2016).

Many IC50-values could not be reliably estimated from the current data, an issue raised previously by Johnstone et al. (2016a). This occurred when fitted IC50-values were well above the tested concentrations, resulting in high levels of uncertainty in the upper concentration ranges simulated by Li et al. (2017) and Dutta et al. (2017). The impact of this uncertainty is illustrated in results for the High-risk drug dofetilide, which is known to be a selective hERG blocker. Because its hERG selectivity could not be confirmed above 3× Cmax with the current dataset (see **Figure 3D** and Figures S12– S15), uncertainty-input simulations of dofetilide above 10× Cmax resulted in highly variable qNet-values, including very "safe" values similar to Low-risk drugs (**Figure 6B**). Although the impact of dofetilide on non-hERG currents is likely small, such assumptions cannot be made for new compounds, particularly if such currents and higher concentration ranges are deemed relevant for TdP risk prediction. To avoid these assumptions, in silico model predictions should be limited to concentrations less than or equal to the highest tested experimentally, unless the amount of drug block can be reliably extrapolated from data at lower concentrations (generally, if >60% block is achieved experimentally, see **Figure 4**). Thus, UQ highlights the importance of obtaining the appropriate data for generating reliable model predictions within the CiPA paradigm. For the current training set, TdP risk prediction appeared to depend solely on ICaL, INaL, and IKr data (**Figure 7B**), so this "60% rule" may potentially only need apply to these three currents. However, the importance of INa, Ito, IKs, and IK1 cannot be discounted entirely because most of the training compounds did not substantially affect these currents. Further sensitivity analysis of qNet and testing with additional compounds may provide insight into the importance of these currents for TdP risk prediction.

Hierarchical UQ approaches may account for some of the discrepancies between observed experimental variability and the estimated variability of model outputs in the present study. For example, at the highest bepridil concentration (300 nM), the kinetics of IKr block in a few cells was noticeably faster than that of other cells and the fitted bootstrap traces. Although it is unlikely that any single method could capture all observed variability, hierarchical approaches to quantify inter-individual variability may provide a more accurate representation of the true physiological variability than do population-averaged approaches (Pathmanathan et al., 2015). Recently, Johnstone et al. (2016a) used a hierarchical statistical model to assess the inter-experiment variability of drug block data from Crumb et al. (2016). Such an approach could be explored in the future if complete doseresponse data for all ionic currents become available. In the present study, however, the IC<sup>50</sup> of most currents could not be reliably estimated, so a further hierarchical analysis was not warranted. For the Li et al. (2017) IKr Markov model, hierarchical methods would be more experimentally and computationally challenging. Experimentally, this would require obtaining hERG block data for each cell at multiple concentrations in order to estimate individual dose-dependent kinetics. However, due to stability and time limitations associated with the current experimental protocol, cells were only recorded at a single concentration. The computational demands of estimating hierarchical model parameters for dynamic models would also be very high because of the need to integrate differential equations. Addressing these difficulties may be unnecessary for CiPA, however, if a population-averaged approach to UQ is shown to provide sufficient information for robust TdP risk prediction.

The UQ results presented in this study illustrate the need to evaluate model predictions in the context of uncertainty. Previously, Dutta et al. (2017) demonstrated that qNet could separate the CiPA training drugs by TdP risk better than metrics based on AP or Ca2<sup>+</sup> transient morphology. In addition, the mean LOOCV prediction error of qNet was lower when drugs were simulated at 10× and 20× Cmax than at 1× Cmax, suggesting that higher concentrations could provide better risk separation. However, this assessment was based only on fixedinput simulations. When uncertainty inputs were used to classify drugs, mean LOOCV prediction error was lowest at 1–4× Cmax and worsened as concentration increased above 4× Cmax (**Figure 7A**). In part, the differences in LOOCV results for fixed vs. uncertainty inputs were due to the high uncertainty in qNet for drugs such as, dofetilide and verapamil above 4× Cmax (**Figure 6C**). However, these differences also arose because when uncertainty was low, classification with qNet probability distributions was more robust than with fixed qNet-values, which improved the mean LOOCV prediction error at 1× Cmax (**Table 5**). UQ also provided an indication of the degree to which drugs could be separated, so LOOCV was more sensitive to subtle changes in qNet. Risk stratification of the training drugs at >4× Cmax may be improved if additional in vitro data are obtained at higher concentrations and incorporated into the model. However, it is important to keep in mind that the CiPAassigned TdP risk levels for the 12 training and 16 validation compounds are not absolute; these relative risks are mainly based on years of clinical evidence and expert opinion rather than a quantitative measure of real-world data. Effort is ongoing within the CiPA framework to develop more objective and quantitative TdP risk categorization systems based on postmarket data, which will help to refine the model and metric for more accurate TdP risk assessment.

This study did not address the issue of model uncertainty related to physiological variability because the focus of CiPA is on drug screening and obtaining an estimate of proarrhythmic risk that can be used to assess overall drug safety, not on predicting risk in specific individuals or subpopulations. However, this is an important topic for many safety pharmacology applications involving mathematical modeling. In pharmacokinetics, nonlinear mixed effects (NLME) models have routinely been applied to quantify intersubject variability (Fitzmaurice et al., 2008). However, methods for quantifying physiological variability in more complex cardiac electrophysiology models are not wellestablished. One approach has been to use a "population" of in silico cardiac cell models, generated by randomly varying model parameters, to explore mechanisms underlying physiological variability and to predict the resulting variability in drug responses, such as, hERG block-induced changes in APD (Sarkar and Sobie, 2011; Britton et al., 2013). The aim of UQ is to estimate model parameters within a statistical framework and then to give probabilistic predictions. Pathmanathan et al. (2015) used data from 10 to 16 cells and NLME modeling to perform a thorough UQ analysis of a single model parameter, steady-state INa inactivation. But applying similar approaches to whole cell models, which typically have dozens of parameters, would require large amounts of data and, most likely, simpler models, as discussed by Pathmanathan et al. (2015). Nevertheless, such studies on physiological variability can be considered in complement with the results in this study concerning UQ of drug effects, providing insight into how multiple sources of uncertainty may impact variability in drug responses.

One additional issue that was not explored in this study was the effect of the number of experimental repeats on parameter uncertainty. For the manual patch clamp data used in this study, 4–10 repeats were obtained per drug concentration for the hERG experiments, and 3–4 repeats were obtained for nonhERG experiments. Thus, based on the current dataset, 3–4 experimental repeats appeared sufficient to constrain the model parameters for TdP risk prediction. However, data obtained from multiple labs or using automated, high-throughput systems can be much more variable, and more experimental repeats may be needed to accurately estimate the mean drug effect with these types of data (Elkins et al., 2013). These issues may be addressed in the future CiPA in silico validation phase.

In summary, risk stratification of the CiPA training drugs with the currently available data was most reliable near the maximum clinical concentration. This was because most of the

# REFERENCES


in vitro experiments were designed around known therapeutic concentrations that often did not block the major ionic currents, and measurements at significantly higher concentrations were not consistently obtained for all drugs. The lack of experimental data produced a large degree of uncertainty in drug effects, which negatively impacted the ability to distinguish between drugs of different TdP risk at higher concentrations. Hence, our findings suggest that for new compounds, the CiPA in silico assay will require in vitro measurements at much higher drug concentrations that can achieve significant ionic current block if the model is expected to provide TdP risk predictions with high confidence. Whether this will be necessary for all seven ion channels that have been suggested as part of CiPA, however, remains to be determined.

# AUTHOR CONTRIBUTIONS

KC designed and carried out the study and wrote the manuscript. SD, GM, KB, and ZL contributed to the study design and analysis. ZL supervised the project. ZL, DS, SD, GM, KB, and TC revised the manuscript. JS, PT, MW, and WW collected the data and provided guidance on interpretation of the data.

# FUNDING

This project was supported by an appointment to the Research Participation Program at CDER, administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the US Department of Energy and the FDA. The perspectives presented in this work are those of the authors and do not represent the views of the FDA or its employees. GM gratefully acknowledges personal support from a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and The Royal Society (Grant Number 101222/Z/13/Z).

# ACKNOWLEDGMENTS

The authors would like to thank Dr. Norman Stockbridge for his helpful discussions and feedback on the manuscript.

# SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.00917/full#supplementary-material


and multichannel pharmacology. Circ. Arrhythm. Electrophysiol. 10:e004628. doi: 10.1161/CIRCEP.116.004628


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Chang, Dutta, Mirams, Beattie, Sheng, Tran, Wu, Wu, Colatsky, Strauss and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Composite Biomarkers Derived from Micro-Electrode Array Measurements and Computer Simulations Improve the Classification of Drug-Induced Channel Block

#### Eliott Tixier 1, 2, Fabien Raphel 1, 2, Damiano Lombardi 1, 2 and Jean-Frédéric Gerbeau1, 2 \*

1 Inria Paris, Paris, France, <sup>2</sup> Sorbonne Universités, Université Pierre et Marie Curie—Paris 6, UMR 7598 LJLL, Paris, France

#### Edited by:

Esther Pueyo, University of Zaragoza, Spain

#### Reviewed by:

Ksenia Blinova, United States Food and Drug Administration, United States Jan Pavel Kucera, University of Bern, Switzerland Andrew Tinker, Queen Mary University of London, United Kingdom

Andrea Buccarello and Echrak Hichri contributed to the review of Jan Pavel Kucera

> \*Correspondence: Jean-Frédéric Gerbeau jean-frederic.gerbeau@inria.fr

#### Specialty section:

This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology

Received: 31 July 2017 Accepted: 13 December 2017 Published: 04 January 2018

#### Citation:

Tixier E, Raphel F, Lombardi D and Gerbeau J-F (2018) Composite Biomarkers Derived from Micro-Electrode Array Measurements and Computer Simulations Improve the Classification of Drug-Induced Channel Block. Front. Physiol. 8:1096. doi: 10.3389/fphys.2017.01096 The Micro-Electrode Array (MEA) device enables high-throughput electrophysiology measurements that are less labor-intensive than patch-clamp based techniques. Combined with human-induced pluripotent stem cells cardiomyocytes (hiPSC-CM), it represents a new and promising paradigm for automated and accurate in vitro drug safety evaluation. In this article, the following question is addressed: which features of the MEA signals should be measured to better classify the effects of drugs? A framework for the classification of drugs using MEA measurements is proposed. The classification is based on the ion channels blockades induced by the drugs. It relies on an in silico electrophysiology model of the MEA, a feature selection algorithm and automatic classification tools. An in silico model of the MEA is developed and is used to generate synthetic measurements. An algorithm that extracts MEA measurements features designed to perform well in a classification context is described. These features are called composite biomarkers. A state-of-the-art machine learning program is used to carry out the classification of drugs using experimental MEA measurements. The experiments are carried out using five different drugs: mexiletine, flecainide, diltiazem, moxifloxacin, and dofetilide. We show that the composite biomarkers outperform the classical ones in different classification scenarios. We show that using both synthetic and experimental MEA measurements improves the robustness of the composite biomarkers and that the classification scores are increased.

Keywords: cardiac electrophysiology, numerical simulations, bidomain model, micro-electrode array, classification, drug safety evaluation

# INTRODUCTION

One of the main goals of safety pharmacology studies is to anticipate how drugs affect cardiomyocytes. Among other adverse effects, it focuses on predicting arrhythmic behaviors which may lead to torsades de pointes (TdP). The most common risk factors under consideration are QT prolongation and hERG block. However these risk factors are now considered insufficient and the guidelines need to be improved (Fermini et al., 2016). For instance, an observed QT

**120**

prolongation is not necessarily associated with TdP risk (Antzelevitch et al., 2004). Several advances in technology and computational modeling may favor the emergence of new methods for more efficient drug safety evaluation. On the hardware side, the Micro-Electrode Array (MEA) technology<sup>1</sup> (Meyer et al., 2004) enables high-throughput electrophysiology measurements that are less labor-intensive than patch-clamp based techniques. This device has been successfully used in large drug studies (Blinova et al., 2016). On the biological side, the use of human-induced pluripotent stem cells (hiPSC) has developed (Scott et al., 2013) and their recent large-scale production makes it a viable human model replacement. The combined use of the MEA technology and hiPSC cardiomyocytes (hiPSC-CM) represents a new and promising paradigm for automated and accurate in vitro drug safety evaluation (Clements and Thomas, 2014; Cavero et al., 2016). The CIPA initiative (Cavero et al., 2016; Fermini et al., 2016) promotes disruptive drug safety guidelines, in particular the use of hiPSC-CM and in silico modeling. In parallel of these technological breakthroughs, several efforts have been recently made toward promoting the use of computational tools in drug safety evaluation (Davies et al., 2016; Lancaster and Sobie, 2016). In this context, a framework for drug safety evaluation using in silico models and experimental measurements using a MEA device is hereby presented. The device considered in the present work is a six-well nine-electrode MEA but, as shown in Raphel et al. (2017), the approach is general enough to be extended to other types of MEA.

The framework aims at predicting the effect of a drug onto the cardiomyocytes ion channels activities from the knowledge of MEA experimental recordings. More precisely, the goal is to determine which ion channels are affected by a given drug. Note that the aim of the present study is not to predict the drugs propensities to induce cardiac arrhythmias but rather to identify which ion channel is primarily blocked. This represents a first step toward the use of the MEAhiPSC-CM platform in arrhythmogenicity studies. Even though patch-clamp experiments are the gold standard to assess druginduced channel block, it was shown in a recent study (Raphel et al., 2017) that it is possible to do so also using MEA field potential measurements. The approach is based on an in silico model of the MEA and the hiPSC-CM tissue, a feature selection algorithm and a classification model. The in silico model is based on a simple ionic model (Bueno-Orovio et al., 2008) for the cardiomyocytes electrical activity and on the bidomain equations (Tung, 1978) for the spatial propagation of the electrical potentials. The ionic model counts three different currents (fast inward, slow inward, slow outward), each being associated with an ionic species (respectively sodium, calcium, potassium). The activity of each current is controlled by a scaling parameter that is referred to as conductance in the following. In the present work, the drugs considered are assumed to affect one of those three currents. Thus, the inactivation of a current caused by a drug is modeled by a diminution of the corresponding conductance in the ionic model. The conductances and some other parameters of the model can be varied in order to replicate the variability observed in the experimental measurements. The in silico model is used to generate what is later referred to as synthetic MEA measurements. The experimental data set itself consists of MEA electrode recordings which come in the form of time series. Each recording is done in control conditions (no drug) and with different drug concentration levels. The experimental data is also labeled, meaning the affected ionic channels are known for each drug.

As explained above, the MEA measurements, whether synthetic or experimental, come in the form of time series. For classification purposes, it is more efficient to extract features from these time series. Some features, also called biomarkers, are already widely used in the community such as the field potential duration (Clements and Thomas, 2014) which may be associated with the QT segment in ECGs. These common features are referred to as classical biomarkers. We propose a way to automatically extract features from the MEA measurements that are designed to perform well in a classification context. First a set of biomarkers is built. The set is referred to as dictionary and each biomarker is referred to as an entry in the following. Then we define new features, referred to as composite biomarkers, as linear combinations of the dictionary entries. The weights of these linear combinations are found by solving a sparse optimization problem. The optimization procedure uses a data set which consists of experimental MEA measurements, simulated ones or a combination of both.

To predict the effects of drugs onto channel block, we propose to adopt a Machine Learning approach. Machine Learning is a family of statistical methods whose aim is to build predictive models given a (ideally large) data set. There exists a wide variety of such methods: neural networks (Kiranyaz et al., 2016), Support Vector Machine (Hua and Sun, 2001), decision trees (Arikawa et al., 1993), etc. All these methods have proved their performances in many different scenarios of regression and classification, in particular when applied to biological data. In the present work, we propose to use Support Vector Classification (SVC) (Boser et al., 1992) which derives from Support Vector Machine. This method seeks a hyperplane that separates the data samples with a maximum margin. The samples are then classified according to their position with respect to the separating hyperplane.

The paper is organized as follows. First, the methods are described. The in silico model is presented and the generation of synthetic data is explained. The algorithm that computes the composite biomarkers is described and the classification tools are presented. Second, the performance of the composite biomarkers and of the classification tools are studied in different drug classification scenarios. The composite biomarkers are compared to the classical ones using two different classification strategies. Finally, composite biomarkers computed with experimental data only and with a mixed set of experimental and synthetic data are compared.

<sup>1</sup> Systems, M. Microelectrode array (mea) manual. http://www. multichannelsystems.com/sites/multichannelsystems.com/files/documents/ manuals/MEA\_Manual.pdf.

#### METHODS

#### Equations

#### Bidomain Equations and Ionic Model

Let be the domain representing a MEA's well. The thickness of the layer of cells being small compared to the size of the well, the problem is assumed to be two-dimensional. We denote by Am, C<sup>m</sup> the surface area of membrane per unit volume of tissue, the membrane capacitance, and the thickness of the cell layer, respectively. The intra and extra-cellular conductivity tensors σ<sup>i</sup> and σ<sup>e</sup> are assumed to be scalar. The parameters values are reported in **Table 1**. The propagation of the transmembrane potential V<sup>m</sup> and the extracellular potential φ<sup>e</sup> are modeled in with the bidomain model (Tung, 1978):

$$\begin{cases} A\_{\rm m} \mathbf{C}\_{\rm m} \frac{\partial \operatorname{V}\_{\rm m}}{\partial t} + A\_{\rm m} I\_{\rm ion} (\operatorname{V}\_{\rm m}, \boldsymbol{\omega}) - \nabla \cdot (\boldsymbol{\sigma}\_{\rm i} \nabla \operatorname{V}\_{\rm m}) - \nabla \cdot (\boldsymbol{\sigma}\_{\rm i} \nabla \boldsymbol{\phi}\_{\rm c}) = A\_{\rm m} I\_{\rm app}, \\\\ - \nabla \cdot ( (\boldsymbol{\sigma}\_{\rm i} + \boldsymbol{\sigma}\_{\rm c}) \nabla \boldsymbol{\phi}\_{\rm c} ) - \nabla \cdot (\boldsymbol{\sigma}\_{\rm i} \nabla \boldsymbol{V}\_{\rm m}) = \frac{1}{\boldsymbol{\varepsilon}\_{\rm i\rm k\rm c}} \sum\_{c\_{\rm k}} \frac{I\_{\rm c1}^{k}}{|\boldsymbol{\varepsilon}\_{\rm k}|} \boldsymbol{\chi}\_{\rm c}. \end{cases} $$

In the second equation, I k el is the electric current which goes through the electrode located at e<sup>k</sup> , |e<sup>k</sup> | is the electrode surface and χe<sup>k</sup> is the characteristic function of e<sup>k</sup> (which takes the value 1 on the electrode and 0 elsewhere). An imperfect model for the electrode is used to compute I k el and described in the Supplementary Material. The activation is assumed to be triggered by a current Iapp that is applied in an arbitrary region of the well with a cycle length of 1,200 ms. The locations of the stimulations are randomized to model the uncertainties of the spontaneous stimulus locations in in vitro measurements. This is further explained in the Heterogeneity modeling subsection. The computational domain corresponds to one well of the MEA device as shown in **Figure 1**. Let **n** be the outward normal to the boundary of the domain . Equations (1) are completed with the following boundary conditions: σi∇φ<sup>i</sup> · **n** = 0 (where φ<sup>i</sup> = V<sup>m</sup> + φe), and either φ<sup>e</sup> = 0 on the region connected to the ground or σe∇φ<sup>e</sup> · **n** = 0 elsewhere. The ground location is indicated in **Figure 1**.

The transmembrane ionic current Iion is described with the Minimal Ventricular (MV) model (Bueno-Orovio et al., 2008) which includes three currents: fast inward (fi), slow inward (si) and outward (so) currents. The reader is referred to the original publication for more details. Schematically, Iion depends on V<sup>m</sup> and on gating variables **w** = (wj)1≤j≤3, solution of a system of three non-linear ordinary differential equations. A conductance coefficient g<sup>s</sup> , with s = fi,si or so, controls the activity of the idealized channels associated with each of three currents of the model.

The partial differential equations are discretized in space by means of P1 finite elements, and in time by using backward differentiation formula (BDF) schemes with adaptive time steps


and order provided by Sundials' CVODE library (Hindmarsh et al., 2005). The quantity of interest is the extra-cellular potential, also referred to as field potential (FP). It is a function of time and recorded at the electrodes locations.

#### **Synthetic measurements**

In the present work, the computational model is used to generate synthetic MEA measurements. The main idea is to enrich the experimental data set with in silico measurements to make the classification more robust, in particular by exploring regions of the parametric space that are not covered by the experience. For a given set of conductances, the model is evaluated and the electrodes FPs are recorded. The conductances are chosen as to represent meaningful scenarios, as explained later in the Results section. To mimic experimental measurements, a zero-mean Gaussian noise of standard deviation 10 µV is added to the FPs (see **Figure 2**). A heterogeneity model of some ionic parameters is also considered to replicate the variability exhibited by the experimental measurements. This model is described later in this section. The stimulation location is also varied to model the uncertainty of the spontaneous stimulus location in the experiments. **Figure 3** shows examples of synthetic recordings generated using the aforementioned in silico model. The FPs are simulated for three different scenarios. The scenarios consist in simulating the effects of sodium, calcium and potassium antagonist drugs, in each case with five different concentrations. In Supplementary Figure 1 a simulated FP recorded on an electrode is shown with the simulated action potential recorded on the same electrode.

#### **Steady-state regime**

Because the initial conditions of the ionic model do not correspond to those of a steady-state regime, several beats may need to be simulated before reaching a regime where there is negligible beat-to-beat variations. A numerical experiment was carried out to determine when this regime is reached. **Figure 4** shows superimposed consecutive simulated FPs and the normalized beat-to-beat variations in the FP. When considering noisy synthetic measurements as described above, the steadystate is assumed to be reached when the beat-to-beat variations are comparable to variations induced by noise only. The beatto-beat variability observed after this beat may be imputed to the coarseness of the mesh, the time discretization errors and the fluctuations of the ionic model itself. In the present work, the steady-state is assumed to be reached at the second beat. Therefore, the simulations are run for two cardiac cycles and the second beat is recorded to be used as a synthetic measurement.

#### Drug Modeling

We chose to model the action of drugs on the ion channels by the conductance-block formulation of the pore block model (Bottino et al., 2006; Mirams et al., 2011; Zemzemi et al., 2013). This simple approach, which relies on a small number of parameters, was shown in Abbate et al. (2017) to be able to reproduce the expected effects of several drugs on MEA signals. The conductance of a

FIGURE 1 | (A) Schematic of one well of the nine-electrode MEA device. The bidomain equations are solved in the domain with homogeneous Neumann boundary conditions on ŴN: ∇φ<sup>e</sup> · nE = 0 and homogeneous Dirichlet boundary conditions on ŴD: φ<sup>e</sup> = 0 where the ground is located. (B) Corresponding finite element mesh.

FIGURE 2 | Experimental recording of MEA field potential. Eight biomarkers are extracted from the time series: DA, depolarization amplitude; DW, depolarization width; RA, repolarization amplitude; FPD, field potential duration; AUCr, area under repolarization curve; RC, repolarizarion center; RW, repolarization width; FPN, field potential notch.

given channel s is given by:

$$\mathbf{g}\_s = \mathbf{g}\_{control,s} \left[ 1 + \left( \frac{[D]}{\mathrm{IC}\_{50}} \right)^n \right]^{-1},\tag{2}$$

where gcontrol,<sup>s</sup> is the drug-free maximal conductance, [D] is the drug concentration, IC<sup>50</sup> is the value of the drug concentration at which the peak current is reduced of 50%, n is the Hill coefficient. In this work, n will be assumed to be equal to 1.

#### Heterogeneity Modeling

A typical experimental MEA FP measurement exhibits both a depolarization spike and a repolarization wave (see **Figure 2**). Using the computational model described above, the repolarization wave is usually too small compared to what is observed in experiments. As noted in Abbate et al. (2017), the repolarization wave provided by this model is larger when the domain includes cells with different APDs. In Abbate et al. (2017), the cell heterogeneity was defined on a checkerboard arbitrarily chosen in the MEA's well. We propose here a different approach, based on a probabilistic description of the

simulated MEA FPs (right). (B) Effect of diltiazem (assumed to be mainly calcium antagonist in this study) on experimental recordings (left) and effect of a virtual calcium antagonist drug on simulated MEA FPs (right). (C) Effect of moxifloxacin (potassium antagonist drug) on experimental recordings (left) and effect of a virtual potassium antagonist drug on simulated MEA FPs (right).

heterogeneity. The tissue is supposed to be a continuous mixture of two cell types: A and B. We make the assumption that the transition between these two types can be described by a single space dependent parameter c(x, y) as follows:

$$\mathbf{p}(\mathbf{x},\boldsymbol{\uprho}) = (1 - c(\mathbf{x},\boldsymbol{\uprho})) \mathbf{p}^{(A)} + c(\mathbf{x},\boldsymbol{\uprho}) \mathbf{p}^{(B)},\tag{3}$$

where c is a random process with values in [0, 1] and **p** (A) (resp. **p** (B) ) the set of 19 parameters of the MV model corresponding to cell type A (resp. B). The values of **p** (A) and **p** (B) are given in Supplementary Table 1. The APs corresponding to different realizations of c are shown in **Figure 5**. We make the hypothesis that the spatial variations of c are structured by a normal correlation function f<sup>c</sup> :

$$f\_{\mathfrak{c}}\left[\binom{\mathfrak{x}}{\mathsf{y}}, \binom{\mathsf{x}'}{\mathsf{y}'}\right] = \exp\left[-\frac{(\mathsf{x}-\mathsf{x}')^2 + (\mathsf{y}-\mathsf{y}')^2}{2l\_{\mathfrak{c}}^2}\right],\tag{4}$$

where l<sup>c</sup> is the correlation length, set to l<sup>c</sup> = 0.25 mm in the present work. To discretize the random process c, we compute the correlation matrix on the finite element mesh used for the discretization of the bidomain equations. The correlation matrix

FIGURE 4 | Steady-state analysis: the Bidomain equations are solved for 100 consecutive beats. Qualitatively, a satisfactory steady state is reached at the second beat (left). The beat-to-beat relative difference of the FP is monitored (right) and is to be compared to the relative difference between two identical solutions, each polluted by an independent noise (right).

parameter is a function of space and its pattern differs from one well to another (see Figure 6).

**C** = [Ci,j] ∈ R <sup>N</sup>mesh×Nmesh reads:

$$\mathbf{C}\_{i,j} = f\_c \left[ \begin{pmatrix} \hat{\mathbf{x}}\_i \\ \hat{\mathbf{y}}\_i \end{pmatrix}, \begin{pmatrix} \hat{\mathbf{x}}\_j \\ \hat{\mathbf{y}}\_j \end{pmatrix} \right], \tag{5}$$

where Nmesh is the total number of mesh nodes and (xˆ<sup>i</sup> , yˆi) are the coordinates of the ith node. The eigenpairs of **C** are denoted by (λ<sup>i</sup> , 8i), and ordered by decreasing order of the eigenvalues λi . By a convenient abuse of notation, we denote by (xˆ, yˆ) → 8i(xˆ, yˆ) the function of the finite element space associated with the eigenmode 8<sup>i</sup> . Finally, the discretized heterogeneity field is approximated by the following truncated expansion:

$$\mathcal{L}(\hat{\boldsymbol{x}}, \hat{\boldsymbol{y}}, \boldsymbol{\xi}) = \sum\_{i=1}^{n\_{\boldsymbol{\xi}}} \xi\_i \Phi\_i(\hat{\boldsymbol{x}}, \hat{\boldsymbol{y}}) \tag{6}$$

where ξ = (ξi)i=1...n<sup>c</sup> is a random vector and n<sup>c</sup> a truncation index chosen so that the truncation explains at least 99% of the variance. In other words, n<sup>c</sup> is the smallest index n such that the following criterion is verified:

$$\frac{\sum\_{i=1}^{n} \lambda\_i}{\sum\_{i=1}^{N\_{\text{mesh}}} \lambda\_i} > 0.99\,\text{.}\tag{7}$$

In our case, the choice of l<sup>c</sup> and the domain geometry yields n<sup>c</sup> = 14. Heterogeneity fields can now be generated simply by sampling the random variable ξ . In the present work, N<sup>h</sup> = 128 heterogeneity fields were generated by sampling ξ from an uncorrelated uniform distribution over [−1, 1]n<sup>c</sup> , and each sample is rescaled to range between 0 and 1. An example of heterogeneity field is presented in **Figure 6**.

The observed variations in the experimental MEA FP recordings are also attributable to fluctuations in the stimulation location. In practice, the hiPSC-CM are not electrically stimulated: a stimulus arises spontaneously in the medium, probably due to the presence of pacemaker cells. The location of the spontaneous stimulation is not known to the experimentalist. We make the assumption that the location is random and therefore model it with a random uniform law over the square [0.15, 0.85]<sup>2</sup> where = [0, 1]<sup>2</sup> is the complete domain.

To conclude, in a given experimental setting, we know neither the stimulation position nor the cell distribution inside the well and we would like the classification method to be robust with respect to all these unknown, random elements. This is why, when generating synthetic MEA FPs using our in silico model, we introduce two sources of uncertainty: the heterogeneous CM field and the stimulation location.

#### Biomarkers

Biomarkers may be defined as quantities extracted from a signal that convey information about hidden quantities of interest. In our case, the biomarkers are features extracted from the MEA FP which would ideally provide information about the conductances of interest: gfi, gso, gsi. In this section, we present different choices of biomarkers to be used in a classification context.

#### "Classical" Biomarkers

The MEA FP can be split into two regions of interest: the depolarization and the repolarization. The depolarization observed at one electrode corresponds to the local depolarization of the cardiomyocytes. The depolarization amplitude (DA, referred to as spike amplitude in Clements and Thomas, 2014) may be qualitatively linked to the AP upstroke velocity. This biomarker is commonly associated with the activity of the fast sodium channel (gfi for the MV model). The repolarization amplitude (RA) may be qualitatively linked to some extent to the AP repolarization slope and to a bigger extent to spatial heterogeneities in AP durations. Once the depolarization and repolarization have been detected, it is possible to measure the FP duration (FPD), simply as the difference between the repolarization and depolarization times. The FPD is a commonly used biomarker (Navarrete et al., 2013; Clements and Thomas, 2014) which may be seen as a surrogate for APD in patch clamp experiments and QT interval in electrocardiograms. Both biomarkers RA and FPD are associated with the activity of the potassium and calcium currents (gso and gsi in the MV model). As explained above, each (real or numerical) experiment is performed both in drug-block conditions and in control condition. Because of the significant variability of measurements in MEA, it is important to consider the variations observed in the FP in drug block conditions with respect to the control conditions to isolate the effect of the drug from other sources of variability: tissue variability, stimulation protocol, etc. Therefore, as proposed in Raphel et al. (2017), the features of interest are the biomarkers in drug block condition divided by the biomarkers in control conditions. For instance, the depolarization amplitude is actually the following ratio:

$$\text{DA}\_{\text{ratio}} = \frac{\text{DA}\_{\text{drug}}}{\text{DA}\_{\text{control}}} \tag{8}$$

For the sake of clarity in the notation, the subscript "ratio" is omitted in the following and any biomarker actually refers to a ratio with the control value. For each MEA measurement, the FP is recorded at each of the nine electrodes. Again, the important variability in the measurements motivates the use of robust features. Since the behavior of the FP may greatly vary from one electrode to another, the median of the biomarkers over all electrodes is in practice a good choice of features. In the following, the set of biomarkers {DA, ˜ RA, ˜ FPD˜ } is referred to as the classical biomarkers, where the ˜ operator denotes the median over all nine electrodes.

#### Composite Biomarkers

The rationale behind the choice of biomarkers described above is only qualitative and oftentimes does not represent the best set of features in a classification context. Here, we adopt a more automatic strategy to select the best set of biomarkers for a given experimental scenario. First, the set of features to be extracted from a given FP is enriched with other features.

It is indeed possible to extract additional quantities from the FP other than DA, RA, and FPD. We propose to compute also, for each electrode of the MEA, the following features: the area under curve of the repolarization wave (AUCr), the repolarization center (RC), the repolarization width (RW), the FP notch (FPN), and the depolarization width (DW). The details on how to compute these additional biomarkers are described in Appendix A (Supplementary Material) and illustrated in **Figure 2**. Ratios of these quantities are also added to the dictionary of features: RA/DA, DA/RA, RA/FPD, FPD/RA, DA/FPD, FPD/DA, RA/RW, RW/RA. Each feature is actually a ratio with its control counterpart as described in Equation (8). To include the information of all nine electrodes, the median (denoted by the˜operator), mean (denoted by the <> operator) and maximum values (denoted by a max subscript) over the electrodes are retained in the dictionary. We finally add the conduction velocity (CV) which is not an electrode-wise quantity but defined using all nine electrodes signals as explained in Appendix A (Supplementary Material). This amounts to a total of N<sup>b</sup> = 41 features reported in **Table 2**. The extended set of features is referred to as the dictionary or the biomarkers dictionary. Each biomarker is referred to as an entry, denoted by bj , 1 ≤ j ≤ N<sup>b</sup> , in the following.

Before going into further details about the numerical methods, let us now explain the purpose of the composite biomarkers. The purpose of the method is to associate each conductance gfi, gsi, gso with a composite biomarker that is maximally correlated with it and minimally correlated with the others. For instance, the composite biomarker, denoted by y1, associated with gfi is maximally correlated with gfi while being minimally correlated

TABLE 2 | Indices of the biomarkers dictionary entries.


with gsi and gso. The main idea is that by observing y<sup>1</sup> we have good information about the hidden variations of gfi which is not tampered by simultaneous variations of gsi or gso. The composite biomarkers are defined as weighted linear combinations of the dictionary entries. We also require that the weights are sparse, meaning there are a lot of zero weights. This makes the composite biomarkers more easily interpretable. Indeed, they can be seen as a combination of only a small subset of the dictionary entries, ideally including the classical biomarkers as seen in **Figure 7**.

The weights of such a combination are solution of an optimization problem. First, let us introduce some notation. We denote by y<sup>1</sup> (resp. y2, y3) the composite biomarker (to be determined) associated with gfi (resp. gsi, gso). From now on, the conductances (gfi, gsi, gso) are denoted by θ = (θ1, θ2, θ3). Each dictionary entry is considered as a function of θ. The composite biomarkers are sought as a linear combination of the dictionary entries:

$$\wp\_h(\theta) = \sum\_{j=1}^{N\_b} w\_j^{(h)} b\_j(\theta), \quad 1 \le h \le 3,\tag{9}$$

where the weights **w** (h) = (w (h) j ) ∈ R <sup>N</sup><sup>b</sup> are the unknowns of the problem. These weights are sought so that yh(θ) is maximally correlated with θ<sup>h</sup> and minimally correlated with θ<sup>k</sup> , ∀k 6= h. This may be stated as follows:

$$\begin{cases} \max\_{\mathcal{Y}\_{\text{h}}} & \text{cov}\left(\mathcal{Y}\_{\text{h}}(\boldsymbol{\theta}), \boldsymbol{\theta}\_{\text{h}}\right) \\\\ \min & |\_{\text{cov}\left(\mathcal{Y}\_{\text{h}}\left(\boldsymbol{\theta}\right), \boldsymbol{\theta}\_{\text{h}}\right)|} \quad \forall k \neq h \end{cases} \tag{10a}$$

$$\forall h \in \{1, \ldots, 3\}, \quad \left\{ \min\_{\mathcal{Y}\_h} \quad \left| \text{cov} \left( \wp\_h(\theta), \theta\_k \right) \right|, \quad \forall k \neq h \quad \text{(10b)} \right. $$

$$\text{s.t.} \quad \text{var} \left( \wp\_h(\theta) \right) = 1 \tag{10c}$$

where cov(·, ·) and var(·) are respectively the covariance and variance operators. In the following, we assume that each

FIGURE 7 | Example of composite biomarkers weights. The three highest weights (in absolute value) are highlighted by a red dot for each composite biomarker. Note that some classical biomarkers are selected by the method: DA for ˜ <sup>g</sup>fi , RC (closely related to the FPD) for ˜ <sup>g</sup>si and RA in the ratio (DA/RA) for <sup>g</sup>so.

component of θ is a zero-mean unit-variance random variable. This is achieved in practice by a simple rescaling of the conductances samples. We also adopt the following notation:

$$
\tilde{b}\_j(\theta) = b\_j(\theta) - \mathbb{E}\left[b\_j(\theta)\right], \tag{11}
$$

where E[·] is the expectation operator. The problem may now be recast into an optimization problem where the cost function to be minimized reads:

$$\mathcal{J}(\mathbf{w}^{(h)}) = \mathcal{J}\_{\mathbb{C}}(\mathbf{w}^{(h)}) + \mathcal{J}\_{\mathbb{N}}(\mathbf{w}^{(h)}) + \mathcal{J}\_{\mathbb{P}}(\mathbf{w}^{(h)}),\tag{12}$$

where

$$\mathcal{L}\mathbf{C}(\mathbf{w}^{(h)}) = \frac{1}{2} \|\mathbf{C}\mathbf{w}^{(h)} - \mathbf{e}^{(h)}\|^2 \text{ where } \quad \mathbf{C}\_{kj} := \mathbb{E}(\theta\_k \tilde{b}\_j), \ e\_k^{(h)} := \delta\_{kh,j} \tag{13a}$$

$$\mathcal{L}\_N(\mathfrak{w}^{(h)}) = \frac{\xi}{2} \left( \mathfrak{w}^{(h)T} \mathbf{G} \mathfrak{w}^{(h)} - 1 \right)^2 \quad \text{where} \quad \mathcal{G}\_{\vec{l}\vec{l}} := \mathbb{E}(\tilde{b}\_l \tilde{b}\_{\vec{j}}), \tag{13b}$$

$$\mathcal{L}\_P(\mathfrak{w}^{(h)}) = \frac{\lambda\_h}{N\_b} \|\mathfrak{w}^{(h)}\|\_1. \tag{13c}$$

Let us now explain each term of Equation (13). JC(**w** (h) ) corresponds to Equations (10a,b). It measures the discrepancy to the ideal situation where cov yh(θ), θ<sup>h</sup> = 1 and cov yh(θ), θ<sup>k</sup> = 0, ∀k 6= h.

JN(**w** (h) ) is a relaxation of the constraint in Equation (10c). ξ is a regularization parameter that is set to 1 in practice.

JP(**w** (h) ) is a regularization term by penalization of the 1– norm of **w** (h) , where λh, 1 ≤ h ≤ 3, are regularization parameters. ℓ<sup>1</sup> penalized cost functions tend to promote sparse solutions (Tibshirani, 1996). Sparse solutions for **w** (h) are interesting in that they offer a more interpretable decomposition onto the dictionary entries (since most weights are zero) than what an ℓ<sup>2</sup> penalization would yield.

We now discretize the problem by considering N samples of the parameters θ drawn over a parameter space 2 ⊂ R 3 . The expectation operator is approximated using a quasi-Monte-Carlo quadrature rule and the cost function in Equation (12) is minimized using a Nesterov accelerated gradient descent (O'Donoghue and Candes, 2015). The Monte-Carlo samples may come from synthetic or experimental measurements. For synthetic measurements, the conductances are known, but this is not the case for experimental measurements. In that case, an approximation of these conductances is computed using Equation (2). Note that the solution weights depend strongly on the choice of samples used for the Monte-Carlo approximations.

An example of the obtained weights is shown in **Figure 7**. Interestingly, the classical biomarkers are still among the most weighted features. The correlation between the conductances of interest and the composite biomarkers is compared to the correlation with the classical biomarkers in **Figure 8**. The correlation between two quantities u and v is defined as follows:

$$\text{cov}(u,\nu) = \frac{\text{cov}(u,\nu)}{\sqrt{\text{var}(u)\text{var}(\nu)}}.\tag{14}$$

As expected, each composite biomarker is well correlated with its associated conductance whereas uncorrelated with the others. This is not the case for the classical biomarkers. The results in the next section show that such a choice of features improves the classification performance.

#### Experimental Data Set

The MEA considered in the present work is a 6-well MEA with nine electrodes per well. Its geometry as well as the corresponding finite element mesh is shown in **Figure 1**. The MEA measurements come in the form of FP recordings corresponding to the different electrodes of the different wells of the MEA. These recordings come in the form of time series where several cardiac cycles, or beats, are recorded. The time resolution of the MEA recordings is 10 kHz. We extracted several beats on each electrode from each well of the MEA. Data were provided by Janssen Pharmaceutica NV using MC\_Rack (Multi Channel Systems GmbH) and post-processed by NOTOCORD Systems (NOTOCORD-FPS 3.0 software). The hiPSC-CM used in this study are a commercially available line of cells (iCell Cardiomyocytes) and were provided by the CDI (Cellular Dynamics International) company.

After thawing, the hiPSC-CM were precultivated for 7 days before being plated on the MEA. Then the cells were cultivated again from 6 to 7 days. Prior to the experiments, the cells rested for 15 min inside the MEA. The recordings come in series of 2 min each and a wash-in period of 5 min was allocated before changing compound concentrations. Up to two different hiPSC-CM cultures were used and each experiment was repeated from 5 to 12 times.

As explained earlier the recordings were made in control conditions (no drug) and with different drugs at different concentrations levels. **Figure 3** shows examples of experimental recordings in control conditions and with five different concentrations of flecainide, diltiazem and moxifloxacin. The drugs used for the present study are summarized in **Table 3**. The corresponding concentrations are presented in **Table 4**. The IC<sup>50</sup> values that were used in the study are also reported and are in the range of those reported in Crumb et al. (2016). Note that the diltiazem was recorded in two different wells (A and B) since it was the only calcium-antagonist drug in the experimental data that were made available to the authors. The experimental process consists in adding five times a compound at increasing concentrations in a given well. Thus, including the control condition record, we finally obtain field potentials for six contexts in each well. Equation (2) was used to obtain an approximation of the conductances values associated with the experimental measurements which are needed for the composite biomarkers calculations. The Hill coefficients and IC<sup>50</sup> values are given in the Supplementary Material of Kramer et al. (2013) and Mirams et al. (2011). Concerning the dictionary of features, a few adjustments need to be made in some cases. Indeed, it appears that at some high concentration levels of mexiletine, there is simply no action potential (because the sodium channels are too blocked) and therefore the field potential is a flat line. To take this into account, the values of dictionary entries are set to the ones at the last concentration where an action potential was observed. In addition, all features where DA is in the numerator position in a ratio are set to zero for this concentration.

#### Classification

#### Support Vector Classification

Support vector classification (Boser et al., 1992) (SVC) is an adaptation of the support vector machine (SVM) method in a classification setting. Classification generally consists in attributing labels to inputs. The available data set, comprising both inputs and labels, is generally split into a training set used to build the classifier and a validation set to test the classifier. The inputs are often multidimensional and in our case


The ID is used in the data set splitting (see Table 5). The SVC class label corresponds to the associated blocked channel conductance.


TABLE 4 | Summary of the drugs information constituting the experimental measurement set.

Five concentrations were studied for each drug. The IC<sup>50</sup> values are reported as well as the main channel blocked by each drug (in the scope of the single channel block assumption).

correspond to the biomarkers, whether classical or composite. The labels are integers that represent the classes to which the inputs are assigned. These classes are mutually exclusive, meaning one sample can only belong to a single class. SVC belongs to the so-called supervised methods since the labels are known, at least for the training set. The main idea behind SVC is to maximize the margin between the inputs and the decision boundary (Boser et al., 1992). In the linear case, the decision boundary is a hyperplane of the input space. In general, however, this is not sufficient to properly separate the samples according to their classes. A common way to obtain more complex boundary decisions is to use a so-called "kernel trick" (Schölkopf and Smola, 2002) which is based on a mapping from the input space to a higher-dimensional space where the existence of a separating hyperplane is more likely. In the present case, the labels are "sodium antagonist," "calcium antagonist," and "potassium antagonist," respectively associated with labels 0, 1, and 2. Among various possible choices of kernels, a Gaussian kernel is employed in this work.

We used a Python implementation of SVC through the Scikitlearn (Pedregosa et al., 2011) machine learning library which itself uses the LIBSVM library (Chang and Lin, 2011). For a given training set, a so-called classifier is built. The classifier is then called to predict the labels of the validation set samples. The predictions are finally compared to the true labels. There exist several metrics to quantify the prediction quality. Two different metrics are considered here: the Cohen's kappa and the receiver operating characteristic area under curve (AUC). The Cohen's kappa is a single scalar designed to measure the performance of multi-class classifiers. Its value ranges from −1 (worst possible classifier) to 1 (perfect classifier), 0 corresponding to a coin-flip classifier. The AUC is defined for each class and measures how a classifier performs with respect to a given class. Its value ranges from 0 (worst) to 1 (best), 0.5 being a coin-flip. Because the classification is repeated several times with different data set splittings, the classification metrics are summarized using their means and standard deviations. The "averaged AUC" corresponds to the average of all AUCs (one AUC per class).

Both metrics are described in detail in the Supplementary Material. We now present two different strategies to employ SVC in the context of drug classification.

#### **3-vs.-3 classification**

Since there are three distinct classes in the experimental set, those three classes need to be included in the training set, preferably in equal proportions. The strategy of 3-vs.-3 (3v3) classification consists in dividing the experimental set into a training set and validation set that both include samples from the three classes. Each class is divided into two sub-classes. This is naturally done for the sodium and potassium antagonist classes since they are each comprised of data from two different drugs. For the calcium antagonist class, the diltiazem data is artificially split into two drugs "diltiazem A" and "diltiazem B" (see **Table 3**). Each subclass is associated with an identification number (ID) from 0 to 5. Therefore, there are 8 possible choices for the training and validation set combinations as summarized in **Table 5**.

#### **One-vs.-all classification**

The One-vs.-All (OvA) classification strategy consists in training one classifier for each class. For each class j, the training set labels are modified to take the value 1 for samples in class j and 0 otherwise and a classifier is trained on this relabeled training set. In other words, the classifier for class j is only trained to recognize whether or not a sample belongs to class j. For the validation step, the classifiers do not predict a class label but a probability for a given sample to be in their respective class. Each sample of the validation step goes through each of the three classifiers and the predicted class corresponds to the classifier returning the highest probability. The splitting between training and validation sets is done in the same way as in the 3-vs.-3 classification strategy.

#### RESULTS

# Comparison between Classical and Composite Biomarkers

Here the performance of the composite biomarkers in a classification context is compared to that of the classical biomarkers for two different classification strategies. The data set is composed of 880 experiments, each counting one control measurement and 5 measurements at different drug concentration levels. For each experiment, the conductances values and FP features are computed as explained in the Methods section and the labels are defined according to **Table 3**. The classification results are summarized in the following and more detailed results may be found in Supplementary Tables 3, 4.


TABLE 5 | Different possible splittings of the experimental data set.

The statistical significance of the potential improvements in the classification scores attributable to the use of composite biomarkers is studied using an analysis of variance (ANOVA) with a significance level of 0.05.

#### 3v3 Classification

The performance of the composite biomarkers compared to the classical ones is evaluated using the 3v3 classification strategy. The classification procedure is carried out for each different splitting of the data set as summarized in **Table 5**. First, the classification inputs are the 3 classical biomarkers for each drug concentration level:

$$\left\{ \mathbf{D}\mathbf{\tilde{A}}\_{\mathrm{c1}}, \mathbf{R}\mathbf{\tilde{A}}\_{\mathrm{c1}}, \mathbf{F}\mathbf{\tilde{P}}\mathbf{D}\_{\mathrm{c1}}, \dots, \mathbf{D}\mathbf{\tilde{A}}\_{\mathrm{c5}}, \mathbf{R}\mathbf{\tilde{A}}\_{\mathrm{c5}}, \mathbf{F}\mathbf{\tilde{P}}\mathbf{D}\_{\mathrm{c5}} \right\},\tag{15}$$

where c<sup>k</sup> is the k-th concentration level. Then, the classification inputs are the composite biomarkers for each concentration, computed as explained in the Methods section using the classification training set as samples for the Monte-Carlo approximations. The inputs now read:

$$\left\{ \mathcal{Y}1, \mathcal{c}1, \mathcal{Y}2, \mathcal{c}1, \mathcal{Y}3, \mathcal{c}\_1, \dots, \mathcal{Y}1, \mathcal{c}5, \mathcal{Y}2, \mathcal{c}5, \mathcal{Y}3, \mathcal{c}\_5 \right\}.\tag{16}$$

In both cases, the inputs are therefore of dimension 15. Note that for each splitting of the data set, new weights for the composite biomarkers are computed. The classification procedure is carried out in both cases and the results are summarized in **Table 6**. Regardless of the chosen classification score, the results are significantly better using the composite biomarkers as inputs.

#### OvA Classification

The same procedure as in the 3v3 case is applied to the OvA strategy. The classification procedure is carried out with both classical and composite biomarkers as inputs and the results are summarized in **Table 7**. The prediction of slow outward current block is significantly improved using the composite biomarkers as inputs. Furthermore, the results are overall better when using the OvA approach rather than the 3v3 one.

In the next section, the addition of synthetic measurements in the computation of the composite biomarkers is investigated. To test whether potential improvements are due to the nature of the added data and not to the increase in the size of the data set, the classification framework was applied to a smaller data set of 440 experiments (i.e., half of the previous data set) for which the results are reported in Supplementary Tables 5, 6. The conclusions of this additional study being similar, this suggests that the classification results are weakly impacted by the size of the data set.

TABLE 6 | Comparison between classical and composite biomarkers with the 3v3 classification strategy.


Variation (+increase, <sup>−</sup>decrease) in the classification scores attributable to the composite biomarkers. ANOVA study: \*significant at the 0.05 probability level.



Variation (+increase, <sup>−</sup>decrease) in the classification scores attributable to the composite biomarkers. ANOVA study: \*significant at the 0.05 probability level, † non-significant at the 0.05 probability level.

# Using Combined Experimental and Synthetic Measurements for the Composite Biomarkers Computation

Having established that composite biomarkers outperform classical ones in two different classification scenarios, we now investigate the addition of synthetic measurements for the computation of the composite biomarkers weights. To enrich the set of experimental samples used to compute the composite biomarkers, a set of synthetic measurements is built. First, conductances samples are chosen to mimic the effect of drugs as shown in **Figure 9**. Depending on the most affected conductance, these samples are associated with a synthetic sodium (resp. calcium and potassium) antagonist drug called "synth A" (resp. B and C). 775 samples per drug are chosen which amounts to 155 experiments per drug. and their repartition is summarized in **Table 3**. This approximately corresponds to a 50/50% split between experimental and synthetic measurements. For each conductance sample, the computational model described in the

Methods section is evaluated and the dictionary entries are computed from the simulated FPs. For each experiment, the computational model is also evaluated in control conditions, i.e., with gfi = gsi = gso = 1 in order to compute the ratios as defined in Equation (8). The in silico measurements are incorporated in the experimental set to create an augmented set. This augmented set is then used to compute the composite biomarkers weights. The same data set splitting procedure as described before is carried out. Note that the synthetic measurements are only used for the composite biomarkers computation and are included neither in the training set nor in the validation set. Again, two classification strategies are explored.

#### Classification Results

The classification is carried out using both 3v3 and OvA approaches. The results are summarized in **Tables 8**, **9** and reported in detail in Supplementary Tables 4, 7. The statistical significance of the modifications in the classification scores standard deviations attributable to the use of synthetic data is assessed using the F-test with a significance level of 0.05.

In the 3v3 case, the Cohen's kappa standard deviation is significantly decreased when using the mixed set of experiments and synthetic data. In the OvA case, the standard deviation of the gsi AUC is significantly decreased while that of the gso AUC is increased.

TABLE 8 | Comparison between composite biomarkers computed from experiments only and combined experiments and synthetic measurements.


3v3 classification strategy.

Variation (+increase, <sup>−</sup>decrease) in the classification scores standard deviations attributable to the use of numerical simulations in the composite biomarkers computation. F-test of variances: \*significant at the 0.05 probability level, † non-significant at the 0.05 probability level, <sup>=</sup>no variation.

# DISCUSSION

In this study, a framework for an automatic classification of drugs from MEA measurements has been presented. The framework relies on an in silico model of a MEA device, on a feature selection algorithm and on state-of-the-art machine learning tools. The in silico model is a PDE model (the bidomain equations) coupled with an ionic model that describes the transmembrane current of the cardiomyocytes. The ionic model is a phenomenological model consisting of a set of coupled non-linear ODEs. The feature selection algorithm proposes a way to compute a so-called



OvA classification strategy.

Variation (<sup>+</sup> increase, <sup>−</sup> decrease) in the classification scores standard deviations attributable to the use of numerical simulations in the composite biomarkers computation. F-test of variances: \* significant at the 0.05 probability level, † non-significant at the 0.05 probability level.

composite biomarker for each conductance of interest, designed to perform better in a classification context than classical biomarkers. The composite biomarkers are linear combinations of the entries of a dictionary of features which is given. The calculation of the weights involves Monte-Carlo approximations which use experimental or synthetic (or both) conductances and FP samples. It has been applied to drug classification problems using experimental MEA recordings. The classification was carried out using the Scikit-Learn Python library (Pedregosa et al., 2011) which includes several classification tools. In the present work a Support Vector Classification was used. The data used for the classification consist in FP features extracted from experimental measurements and their associated labels corresponding to the type of drug that is considered.

The purpose of the present work is twofold. First, it intends to establish that the classically used biomarkers may be improved, at least in a classification context, by using composite biomarkers instead. Second, it intends to show that the classification performance may benefit from the addition of synthetic measurements in the calculation of the composite biomarkers. More generally, the authors intend to show that numerical simulations are useful to cardiac electrophysiology in general, beyond the sole scope of drug classification.

First, a comparison between classical and composite biomarkers was carried out. The comparison consists in classifying drugs from experimental measurements using two different strategies: 3v3 and OvA. For each strategy, the classification is performed using classical or composite biomarkers as inputs. As expected, the classification results in both cases are improved when using the composite biomarkers. The latter were indeed designed to be maximally correlated to their associated conductance and minimally correlated to the others. As a consequence, they are more revealing of the underlying conductances than the classical biomarkers. In the 3v3 case, all classification scores significantly increase when using composite biomarkers instead of classical ones. In the OvA case, the improvement is less clear, mainly because most variations in the classification scores are not statistically significant. Nevertheless, the improvement is significant for the gso AUC and overall the OvA strategy yields better classification results than the 3v3 strategy.

Second, the use of combined experimental and synthetic measurements to compute composite biomarkers is investigated. The composite biomarkers are computed using Monte-Carlo approximations that require conductances and FP features samples. In the previous case, these samples are experimental. The idea is to improve the robustness of the composite biomarkers by incorporating synthetic measurements which better span the parameters (i.e., conductances) space. This approach is meant to compensate the scarcity of experimental data and more generally the fact that the experiments do not cover every possible drug block scenario. The in silico measurements allow for a more thorough exploration of the parameter space. Conductances samples were drawn and the computational model was evaluated to generate noisy FPs. From these FPs, the entries of the dictionary of features were computed. The composite biomarkers weights are then computed using a mixed set of experimental and synthetic samples. These composite biomarkers are compared to the ones computed using only experimental data. The same two classification strategies as before are used to compare both approaches. In the 3v3 case, the standard deviation of the Cohen's kappa is significantly decreased, which suggests that this approach makes the classification more robust, at least when considering this metric. The variations of the other classification scores are not statistically significant. In the OvA case, the Cohen's kappa seems to increase in average while its standard deviation decreases. This finding must however be mitigated by the fact that it is not statistically significant. As for the AUC scores, the same observation can be made concerning the gfi AUC. The standard deviation of the gsi AUC is significantly decreased but the standard deviation of the gso AUC is increased. Overall, the use of mixed experimental and synthetic measurements seems to improve the classification and make it more robust even though the statistical significance of the results is not conclusive. The use of a larger experimental data set could help assessing the statistical significance of the previous findings.

The use of FP features in a classification context is now discussed. In classification problems, and in machine learning in general, a large number of inputs tend to provoke an overfitting of the model. This means that the classifier tends to have satisfactory training scores but generalizes poorly on a validation test. This is in part solved by the regularization used but the number of inputs still remains important. When dealing with experimentally recorded FPs, the different signals are often not perfectly synchronized, making timestep-wise comparisons meaningless. Furthermore, an important variability of the signal amplitudes is observed in practice, making even perfectly synchronized signals difficult to compare. Using features extracted from the FP that are do not depend on time shifts and amplitude variations are therefore more robust in a classification context.

#### Limitations

The limitations of the proposed approach are now discussed. First we discuss the heterogeneity modeling. In the present work, we make the assumption that the hiPSC-CM medium is a continuous mixture of two cell types ("A" and "B") based on a ventricular endocardium cell model, modified to match the action potential duration of the experimental recordings. The actual nature of the hiPSC-CM types is still quite unknown, to the authors knowledge, even though some studies suggest it is a mixture of atrial, ventricular and pacemaker cells (Matsa et al., 2011). Even if the medium can be well characterized in a particular setting, it varies greatly from one cell line to another. In the present work, we propose a general method to generate heterogeneous media and for the sake of simplicity we restricted our study to a continuous mixture of two cell types. The approach is easily generalizable to more realistic heterogeneities, including for instance atrial, ventricular and pacemaker cells. Second, the conductances values associated with the experimental measurements are not known and are therefore approximated using Equation (2). This approximation is, however, subject to several sources of uncertainty such as the IC<sup>50</sup> whose value for a given drug may vary according to the source considered (Mirams et al., 2011; Kramer et al., 2013). The uncertainties also come from the Hill's equation which is an imperfect model. Knowing the exact values for the conductances is, however, not critical since those values are only needed to derive the composite biomarkers and are not directly used during the classification procedure. Furthermore, the drugs studied in the present work are assumed to be single channel blockers. In reality, some drugs (e.g., diltiazem) are known to target more than one ion channel. In fact, it can be considered that any drug affects every ion channel with different IC<sup>50</sup> values. In the present work, we make the strong assumption of single channel blocking as a first step toward a finer description of the drugs effects. This assumption is also motivated by the simplicity of the considered ionic model which only counts three different currents. Note also that mexiletine primarily blocks the late sodium channel current and not the fast one. In the MV model, there is no distinction between these two currents.

Another limitation comes from the computational model used in the present work. The sources of error are multiple: space and time discretizations, conductivities errors, modeling errors, etc. These errors are not critical either since the computational model is only used to compute the composite biomarkers weights. This study shows that, despite the modeling errors, adding synthetic measurements simulated by the computational model leads to a better and more robust classification. In the present study, we based our in silico modeling on the MV ionic model. It is a very simplistic model which is not able to reproduce complex behaviors such as early after depolarizations for instance. Furthermore, the hiPSC-CM are spontaneously excitable cells in our case while the MV model is not sophisticated enough to reproduce such a behavior. For this reason, it is not suited to the study of drug arrhythmogenicity. However, in the scope of the present work, we have established that it is suited to the characterization of drug-induced channel block, at least for a coarse description of it. Furthermore, it was also established in Raphel et al. (2017) that it is possible to identify which of the three main currents is affected by a drug using the MV model. Other limitations come from the classification strategies. Both classification strategies are nonexhaustive in that they do not explore every possible way of splitting the data set. Furthermore, the classification metrics used to compare the different approaches are not flawless. In some cases comparing AUCs for instance is not the best way to compare classifiers (Adams and Hand, 2000). Other metrics exist, such as the mean squared error, but were not investigated in this work. Finally, the composite biomarkers derived in the present work are not optimal in the sense that their correlation with their associated conductances is not equal to one, as seen in **Figure 8**.

The limitations of the study also arise from the MEA measurements themselves. Variations of the repolarization wave morphology and the depolarization amplitude from one experiment to another constitute a technical challenge when one tries to extract meaningful information from the measurements. In the present study, we propose to model the heterogeneities of the experimental settings (CM cell types and stimulation location) to account for the observed variability in the data. Furthermore, considering ratios of biomarkers with their control counterparts makes the approach more robust and less dependent on fluctuations from one experiment to another.

#### Perspectives

We now discuss some perspectives that could lead to interesting future works. Other classification methods than SVC exist, such as neural networks or random forests for instance. It would be interesting to assess whether the findings of this work are still valid when considering other classification tools. It would also be interesting to evaluate which classification tool generally performs best in the present drug classification context. Other perspectives concern the composite biomarkers computed using a mixed set of synthetic and experimental measurements. In the present work, the mixed set is roughly composed of half synthetic and half experimental measurements. However, other proportions could be investigated and an optimal proportion with respect to the classification score could be found. In the present work, only sodium, potassium and calcium antagonists drugs are considered but other types of drugs exist. Drugs that affect other ionic channels or even simultaneously several of them could be investigated. In parallel, more sophisticated ionic models including more current types would need to be used to model these new drugs. This would, of course, come at the expense or more computationally intensive simulations. Another interesting perspective would be to train the classifiers with only synthetic measurements instead of experimental ones. This would be very useful when experimental data are insufficient or even not available. The classifiers could also be trained with a mixed set of synthetic and experimental data just like it is done in this work for the computation of composite biomarkers. Finally, as explained earlier, the point of the present work is not the direct assessment of drugs arrhythmogeneicity but rather the identification of the main channel block induced by the drugs. This is, in the author's opinions, a necessary first step toward a better understanding of MEA measurements and in fine its use in drug safety evaluation. Considering a larger set of drugs and more realistic ionic models in order to perform drugs classification based on their arrhythmogenicity (or TdP risk) will be the purpose of future works.

# ETHICS STATEMENT

The MEA recordings were made using a commercially available line of hiPSC-CM provided by the CDI (Cellular Dynamics International) company.

#### DATA ACCESSIBILITY

The implementation (in Python) of the composite biomarkers algorithm is available at this URL: https://github.com/eltix/ numbio.

# AUTHOR CONTRIBUTIONS

All authors listed have made substantial, direct and intellectual contribution to the work, and approved it for publication.

## REFERENCES


#### FUNDING

ET was funded by a doctoral grant from the French Ministry of Research and Higher Education. FR was funded by Instem. This work was partially supported by the Agency for Interaction in Mathematics with Business and Society (AMIES).

#### ACKNOWLEDGMENTS

We would like to thank Janssen Pharmaceutica NV for providing us with the raw experimental data and Philippe Zitoun for many fruitful discussions.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.01096/full#supplementary-material

(CIPA) proposed ion channel panel. J. Pharmacol. Toxicol. Methods 81, 251–262. doi: 10.1016/j.vascn.2016.03.009


**Conflict of Interest Statement:** The authors declare that this study received funding from Instem. The funder was not involved in the study design or collection, analysis, or interpretation of the data.

Copyright © 2018 Tixier, Raphel, Lombardi and Gerbeau. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Novel Two-Step Classifier for Torsades de Pointes Risk Stratification from Direct Features

Jaimit Parikh, Viatcheslav Gurev and John J. Rice\*

*IBM T. J. Watson Research Center, Yorktown Heights, NY, United States*

While pre-clinical Torsades de Pointes (TdP) risk classifiers had initially been based on drug-induced block of hERG potassium channels, it is now well established that improved risk prediction can be achieved by considering block of non-hERG ion channels. The current multi-channel TdP classifiers can be categorized into two classes. First, the classifiers that take as input the values of drug-induced block of ion channels (direct features). Second, the classifiers that are built on features extracted from output of the drug-induced multi-channel blockage simulations in the *in-silico* models (derived features). The classifiers built on derived features have thus far not consistently provided increased prediction accuracies, and hence casts doubt on the value of such approaches given the cost of including biophysical detail. Here, we propose a new two-step method for TdP risk classification, referred to as Multi-Channel Blockage at Early After Depolarization (MCB@EAD). In the first step, we classified the compound that produced insufficient hERG block as non-torsadogenic. In the second step, the role of non-hERG channels to modulate TdP risk are considered by constructing classifiers based on direct or derived features at critical hERG block concentrations that generates EADs in the computational cardiac cell models. MCB@EAD provides comparable or superior TdP risk classification of the drugs from the direct features in tests against published methods. TdP risk for the drugs highly correlated to the propensity to generate EADs in the model. However, the derived features of the biophysical models did not improve the predictive capability for TdP risk assessment.

Keywords: Torsades de Pointes, machine-learning, classification and prediction, cardiac modeling, early afterdepolarization

# 1. INTRODUCTION

In-vitro examination of drug effects on multiple cardiac ion channels and in-silico reconstruction of cardiac electrical activity from in-vitro experiments are two coupled components in the new paradigm of TdP risk assessment (Sager et al., 2014). At the molecular/ionic level, pharmacological TdP genesis is associated with drug-induced reduction in the net repolarizing current (Antzelevitch, 2007), which is manifested in prolongation of the QT interval in the body-surface ECGs. Drug-induced block of hERG (human Ether-à-go-go-Related Gene) channels, which gate the primary repolarizing current IKr, is an acknowledged marker for TdP risk prediction. However, recent studies have shown that the classification that is based on the safety margins from the hERG channel assays has moderate concordance with QTc prolongation (Gintant, 2011)

#### Edited by:

*Blanca Rodriguez, University of Oxford, United Kingdom*

#### Reviewed by:

*Elisa Passini, University of Oxford, United Kingdom Sara Dutta, United States Food and Drug Administration, United States Michelangelo Paci, Tampere University of Technology, Finland*

> \*Correspondence: *John J. Rice johnrice@us.ibm.com*

#### Specialty section:

*This article was submitted to Predictive Toxicology, a section of the journal Frontiers in Pharmacology*

Received: *10 August 2017* Accepted: *27 October 2017* Published: *14 November 2017*

#### Citation:

*Parikh J, Gurev V and Rice JJ (2017) Novel Two-Step Classifier for Torsades de Pointes Risk Stratification from Direct Features. Front. Pharmacol. 8:816. doi: 10.3389/fphar.2017.00816* and TdP risk (Mirams et al., 2011; Kramer et al., 2013). Druginduced modulation of non-hERG channels either mitigates (i.e., block of L-type voltage regulated calcium channel current ICaV and inward late sodium current INaL) or enhances (i.e., block of slow activating potassium current IKs or increase of INaL) the pro-arrhythmic effects of hERG channel block (Bril et al., 1996; Antzelevitch, 2004; Lacerda et al., 2008; Towart et al., 2009; Fermini et al., 2016). Several multi-channel TdP risk classifiers have already been created (Mirams et al., 2011; Christophe, 2013, 2015; Kramer et al., 2013; Mistry et al., 2015; Okada et al., 2015; Lancaster and Sobie, 2016; Abbasi et al., 2017). **Table 1** lists previously published classifiers that are based on several in-vitro ion channel assays.

The drug-induced changes in the ionic currents result in altering of action potential and calcium transient at the cellular level. These modulations can further trigger events in the cardiac cells, such as early or delayed afterdepolarizations (EADs or DADs), and increase heterogeneity in the electrical activity across the myocardium [i.e., increase in transmural dispersion of repolarization (TDR)]; both effects are thought to be the key determinants for TdP genesis (Wu et al., 2002; Antzelevitch, 2007). In-silico reconstruction of drug-induced responses of action potential and calcium transient at cellular or electrical activity at tissue levels could potentially provide better mechanistic insight. The classifiers that use the features from the in-silico simulations (derived features) have shown the capability to make good predictions (**Table 1**) of torsadogenic risk (Mirams et al., 2011, 2014; Christophe, 2013, 2015; Okada et al., 2015; Lancaster and Sobie, 2016; Abbasi et al., 2017; Li et al., 2017). However, in spite of providing better biological insights for TdP genesis, the role of computational models in improving TdP risk prediction is controversial as machine-learning/statistical analysis of the in-vitro ion channel measurements (direct features) have been shown to produce equally accurate TdP risk assessment (Kramer et al., 2013; Mistry et al., 2015).

The amount of drug-induced block of the channels depends on the compound's effective free therapeutic plasma concentration (EFTPC). Unfortunately, reported EFTPC values are highly variable (Redfern et al., 2003). The maximum EFTPC values, which is used to determine the ion channel block, also vary across the datasets (e.g., Moxifloxacin 3.5 µM in Crumb et al., 2016, 10.9 µM in Kramer et al., 2013). In addition, the actual free plasma concentrations of drugs in subjects could also differ because of inter-individual variations, impaired metabolism, and interactions with other drugs. In fact, drug concentrations could potentially be much larger than reported maximum EFTPC values. Researchers have employed different strategies to address the uncertainty in EFTPC. Direct and derived features have been evaluated at the drug's EFTPC, at supra-therapeutic drug concentrations (which is several times above maximum EFTPC), or across a wide range of drug concentrations (Christophe, 2013, 2015; Kramer et al., 2013; Mirams et al., 2014; Mistry et al., 2015; Okada et al., 2015; Lancaster and Sobie, 2016; Abbasi et al., 2017; Ando et al., 2017; Li et al., 2017). The range is obtained by titrating up the drug concentrations until a fixed threshold, until a predetermined increase in action potential prolongation is reached, or until EADs are triggered.

Here, we propose a new two-step method for TdP risk classification, referred to as Multi-channel Blockage at Early After Depolarization (MCB@EAD). The MCB@EAD classifier employs as inputs direct or derived features obtained at drug concentrations that produce critical hERG block (∼60% block that generates pause-induced EADs in the biophysical models). We test the proposed classifier on several previously published datasets derived from in-vitro screening of the ion channels and on a large composite dataset comprising of all datasets. Finally, we examine the connection between TdP risk of the drugs and drug propensity to induce pause-dependent EADs. Our results show that MCB@EAD classification from the direct features performs better or equivalently to previously suggested methods including the classifiers built on derived features from biophysical models. We also highlight the link between the direct and derived feature based classifiers and demonstrate that TdP risk for the drugs highly correlates to the likelihood to produce EADs in the model.

# 2. METHODS

**Table 2** provides a brief summary for each of the analyzed datasets. More extensive descriptions of the datasets is provided in the Supplemental Material.

# 2.1. Torsadogenicity Definition

The definition of drug groups according to their torsadogenic risk is critical for the development of the TdP risk classifiers. Different torsadogenic definitions from previous classification studies are listed below.

Redfern et al. assigned drugs to five categories based on the number of reports of TdP in humans, QT prolongation and TdP associated withdrawal from the market (Redfern et al., 2003). The five categories are:


Arizona Center for Education and Research on Therapeutics (AZCERT) maintains a list of drugs associated with QT prolongation/TdP risk (Woosley et al., 2017) (https://crediblemeds.org/) and has categorized the drugs into three groups:


#### TABLE 1 | TdP classifiers based on *in-vitro* ion channel assays.


*LDA, Linear Determinant Analysis; LR, Logistic Regression; SVM, Support Vector Machine; PCA, Principal Component Analysis; Cdrug*,*EAD, concentration of the drug that produces EAD; BP<sup>x</sup> , % block of the x (x* = *Na*, *fast, CaV, hERG) ion channels; TDR, transmural dispersion of repolarization; Cdrug*,*Arrhythmia, concentration of the drug that produces arrhythmia in the model; EAD, early after depolarizations; AUCIx*,*drug*/*control, area under the curve of the x (x* = *CaV, NaL) current transient at steady state action potential in the presence (drug) or absence of the drug (control). Table also lists the number of compounds analyzed in the study (NTotal) and the number of correctly classified compounds (Ncorrect).*

• CM3: Drugs with conditional risk of TdP. These drugs are associated with TdP but only under certain conditions of their use.

Champeroux et al. assigned drugs into three categories based on the number of reports of TdP cases associated with the drug (Champeroux et al., 2005):


Based on a general consensus, a working group formed under the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative picked 28 compounds and categorized them into three groups (Colatsky et al., 2016; Fermini et al., 2016) for testing/training of the classifiers under the new CiPA paradigm:


To consistently compare with other methods we attempt to use the binary TdP definitions [i.e., a drug is either torsadogenic (TdP+) or non-torsadogenic (TdP−)] as in the original publications (see **Table 2** and the Supplemental Material for further details regarding the exact risk definition used for the particular datasets). For dataset 7 where tertiary definition is reported, binary TdP definition was defined by placing CP1 and CP2 drugs into torsadogenic (TdP+) and CP3 drugs to non-torsadogenic (TdP−) categories. In the case of the merged dataset or the datasets that lacked binarized TdP definitions (Crumb et al., 2016), we assigned drugs as TdP+ or TdP− using a similar approach as in Lancaster and Sobie (2016). The drugs which fell in the known risk category (CM1) in the CredibleMeds database, R1, R2, and R3 category in Redfern et al. (2003) or drugs with several reports for TdP (CH1) (Champeroux et al., 2005) were assigned to TdP+. For the remaining drugs we categorized the drug as TdP+ if a warning for TdP associated with QT prolongation appeared on its package label (http://dailymed.nlm.nih.gov/). The risk categorization for the drugs are provided in the Supplemental Material. Paroxetine has a warning for TdP in the label and Imipramine was assigned to CH1 category in Champeroux et al. (2005). These two drugs were also assigned as TdP+ in Lancaster and Sobie (2016). Here, we defined them as TdP− as these two compounds are not directly associated

TABLE 2 | Datasets analyzed for TdP risk. The total number of drugs in each dataset is listed in the "Number compounds" column.


*"Risk categorization tested" column refers to the TdP risk definition (see more info on definitions in the text) used to test/train the particular datasets, and the "Figure/Table" column list the corresponding Figure and Table numbers where the results of the particular dataset and risk categorization pair are reported. The IC<sup>50</sup> values and risk category of individual drug for each datasets are also reported in the Supplemental Material.*

with QT prolongation or TdP. These drugs inhibit CYP2D6 and increase plasma concentrations of TdP positive drugs such as Thioridazine (http://dailymed.nlm.nih.gov/). Sometimes alternative definitions were also considered and are explicitly defined in the manuscript.

#### 2.2. Drug-Induced Ion Channel Block

The in-vitro ion channel assay data is converted to drug-induced block of ion channel (direct features) using

$$Block\_{channel} = 100 \times (\frac{\text{C}\_{Drug}{}^{h}}{\text{IC}\_{50,channel}{}^{h} + \text{C}\_{Drug}{}^{h}}),\tag{1}$$

where IC50,channel is the drug concentrations at which the wholecell current through particular channels is reduced by half, CDrug

is the concentration of the drug and h is the Hill-coefficient. The Hill coefficient values were taken as reported in the original datasets. The IC50, Hill coefficients, and EFTPC values for each of the datasets are given in the Supplemental Material. Note that Hill coefficient values had little impact, and even fixing Hill coefficient to 1 for all the drugs did not significantly alter the observed classification accuracies (results not shown). The drug-induced blocks of ion channels are used as input features for the machinelearning based classifiers or utilized to scale the maximum conductance (gchannel) of the particular ion channels in the in-silico models, assuming that drug-induced effect on multiple ion-channels are well represented by a simple conductance-block model (Mirams et al., 2011),

$$g\_{channel,drug} = (1 - Block\_{channel} / 100) \times g\_{channel}.\tag{2}$$

The effects of drug-induced modulation of multi-channel conductance (Equation 2) on the action potentials (AP) and calcium transients are simulated for all of the compounds using two versions of human ventricular myocyte models (O'Hara et al., 2011; Dutta et al., 2016). Ohara et al. model (OHR) (O'Hara et al., 2011) was picked as it has been chosen as the consensus base model for proarrhythmic risk assessment (Colatsky et al., 2016). OHR model was also shown to have the best predictive capability for TdP risk classification among the few tested models in Lancaster and Sobie (2016). We also utilized the modified version of the OHR model (OHRmv) which has been shown to better fit APD-rate dependence experimental data under drug block conditions, particularly improving the effect of INaL block on action potential prolongation (Dutta et al., 2016). Several derived features are extracted from AP and calcium transients, and TdP risk classifiers are constructed using these derived features. The details on the simulation protocols and the computations of the derived features are reported in section 2.6 that describes in-silico simulations.

#### 2.3. Two-Step Classifier—Multi-Channel Blockage at hERG EAD(MCB@EAD)

We propose a two-step approach for TdP risk prediction. In the first step, we classified the drugs into non-torsadogenic and potentially torsadogenic categories. We performed the classification in the first step considering solely the block of hERG channels. Using a Redfern-like criteria (Redfern et al., 2003), we obtained the ratio between the drug concentration that produces 60% block of the hERG channel current (IC60,hERG) and the drug EFTPC (i.e., hERGratio = IC60,hERG EFTPC ). The motivation for using IC60,hERG was that the 60% block of hERG channel currents triggers pause-induced EAD in the mid cell type of OHR and OHRmv models (2 Hz pacing rate) at a quiescent interval greater than 700 ms. For example, a drug with hERG IC<sup>60</sup> of 500 nM and EFTPC of 1 nM would yield a threshold of 500. Since this drug's EFTPC would be far from the critical hERG block concentration, we would classify this compound as non-torsadogenic. Previous classifiers based on EAD appearance for different datasets have shown a wide range of thresholds (approximately 30×−200× EFTPC) for achieving best TdP risk predictions (Christophe, 2013; Okada et al., 2015). Hence, we tested four different thresholds for hERG ratio of 50, 100, 150, and 200 for all the datasets and chose the one that gives the best classification accuracy. For the remaining drugs with EFTPC above the critical hERG block concentrations (hERG ratio less than the threshold), the role of multi-channel block was examined in the second step using logistic regression classifiers ignoring the EFTPC values of the drugs. The regression classifiers employed as inputs either the Blockchannel of additional nonhERG ion channels (direct features) or the features derived from the simulated calcium transient and the AP in the ventricular myocyte models, at drug concentrations equal to IC60,hERG. Such two-step classifier partially solves the problem of EFTPC variability, restricting EFTPC usage only to the first step to primarily discard the drugs that produce insufficient hERG block at extremely high concentrations by classifying them as non-torsadogenic. Therefore, the moderate variations in EFTPC values of the drugs would only matter for a very small population of the drugs with hERG ratio close to the threshold in the classification. A summary of the two-step approach is given in **Figure 1**.

In order to compare the performance of the classifiers based on the two-step approach to the performance of the classifiers based on features obtained at actual drug EFTPC concentrations, we also constructed TdP risk classifiers using the direct and derived features at reported maximum EFTPC of the drugs. They are referred in the current paper as one-step classifiers (hERG ratio is not utilized for these classifiers).

#### 2.4. Classifiers

We utilized statistical/machine-learning models for binary classification of the drugs into TdP+ or TdP− categories. The binarized torsadogenic definitions for each drug were used to train/test the classifier models. Here, we used Logistic regression model. SVM and neural network models were also tested and resulted in comparable classification accuracies (results are shown in the Supplemental Material). Python's scikit-learn package (Pedregosa et al., 2011) (http://scikit-learn.org/stable/) was used to train/test different models. Here, we present results for logistic regression models only as other methods produced similar results. The generalized model equation is described as

$$\text{logit(TdP)} = \frac{1}{1 + \exp^{-(\beta\_0 + \sum\_{i}^{n} \beta\_i \text{Feature}\_i)}},\tag{3}$$

where Feature represents the input metrics to the model (either direct feature or the derived feature), n is the number of input features used to train/test the model, and β<sup>0</sup> and βi (i = 1, 2, .., n) are the parameters to be determined. The predictive power of the model was evaluated by the leave-one-out (LOO) cross validation technique.

#### 2.5. Two-Dimensional TdP Risk Map

A two-dimensional TdP risk map with hERG ratio (IC60,hERG EFTPC ) on the x-axis and summation of one or more features (block of ICaV and INaL) on the y-axis were constructed for visualization of the two-step (MCB@EAD) classifier. The hERG ratio threshold and regression coefficients from the two-step classifier are used to generate the two-dimensional risk maps. The hERG ratio (step 1 in the two-step classifier) that provides the best classification in the two-step classifier is used to set the threshold along the x-axis. Drugs that fall in the region above the hERG ratio threshold are considered to be non-torsadogenic. For the drugs with hERG ratio less than the threshold, the coefficients of the logistic regression model in step 2 of the two-step classifier are used to determine the threshold along the y-axis of the risk map. An example of separating hyperplane that would be obtained from the second step of the two-step classifier is given by

$$\begin{aligned} \beta\_{\text{CaV}} \text{block}\_{\text{CaV}} &+ \quad \beta\_{\text{NaL}} \text{block}\_{\text{NaL}} &+ \sum\_{i=3}^{n} \beta\_{\text{feature},i} \text{feature} \\ &+ \quad \beta\_{\text{intercept}} = 0 \end{aligned} \tag{4}$$

where blockICaV and blockINaL are the blocks of ICaV and INaL, respectively. feature<sup>i</sup> are additional input features of the model, such as drug trapping parameters. βICaV , βINaL , and βfeature,<sup>i</sup> represent the regression coefficients. The regression coefficients obtained from the step 2 are normalized to the coefficient βICaV for the ICaV block. This gives

$$blockk\_{I\_{\rm CdV}} + \frac{\beta\_{I\_{\rm NaL}}}{\beta\_{I\_{\rm CdV}}} block\_{I\_{\rm NaL}} + \sum\_{i=3}^{n} \frac{\beta\_{\rm feature,i} feature\_i}{\beta\_{I\_{\rm CaV}}} = -\frac{\beta\_{\rm intercept}}{\beta\_{I\_{\rm CdV}}}.\tag{5}$$

Thus, the left hand side of Equation (5) is plotted on the y-axis, and the ratio <sup>β</sup>intercept βICaV determines the threshold along this axis. For example, if only block of ICaV is taken into consideration, the risk map has the values of ICaV along the y-axis and hERG ratio along the x-axis.

Ternary classification for Dataset 7 requires multiple hyperplanes with different regression coefficients to separate the high, low and intermediate risk drugs. To represent the ternary classification in a two-dimensional risk map similar to the binary classification, we summed the different features (Featuresum) assuming identical weights for each of the features (i.e., β<sup>1</sup> = β<sup>2</sup> = .. = β<sup>n</sup> equal to β<sup>f</sup> ) reducing the classification model to <sup>1</sup> 1+exp <sup>−</sup>(β0+β<sup>f</sup> Featuresum) . For Dataset 7, assuming identical weights for different features resulted in similar accuracy to a multinomial logistic regression classifier while providing a simpler visualization in one two-dimensional plot as in the binary classification. The ratio <sup>−</sup>β<sup>0</sup> βf obtained after training the model is used to set the two thresholds along the y-axis. Along the x-axis arbitrary hERG ratio of 25, the value slightly greater than the maximum hERG ratio observed for high risk drugs in Li et al. (2017) and Fermini et al. (2016), was utilized to separate low and intermediate risk drugs from the high risk drugs. The hERG ratio of 150 obtained from the merged dataset was utilized to separate the high and intermediate risk drugs from the low risk drugs.

#### 2.6. In-Silico Simulations

The alteration in the action potential and calcium transients at the cellular level arising from drug-induced multi-channel block were simulated for all the compounds (Dataset 8) using the OHR model. Using a similar approach as in Lancaster and Sobie (2016), simulations were carried out at three pacing rates (0.5, 1, and 2 Hz) for each of the endo, mid and epi cell types resulting in 9 simulations per drug, and 13 metrics were obtained from the AP and Ca2<sup>+</sup> transients. Simulations were carried out for 1,000 beats to allow the models to reach the steady state. The 13 metrics obtained from the in-silico models are listed below:


We systematically construct the classifiers on each of the 13 derived features extracted from the action potentials and calcium transients at two different drug concentrations (i.e., at CDrug = EFTPC and CDrug = hERG IC60).

The onset of TdP is usually preceded by a sudden reduction of the heart rate (i.e., by pauses or long cycle lengths) (Neal Kay et al., 1983; Viskin et al., 2000). Here, we test the generation of pause-induced EADs, that are implicated as triggers of TdP (Viswanathan and Rudy, 1999; Liu and Laurita, 2005), in simulations of drug-induced multi-channel blockage in the ventricular myocytes models (O'Hara et al., 2011; Dutta et al., 2016). The basic protocol was similar to that in Viswanathan and Rudy (1999), where stimulation of the cell is carried out 200 times at a constant cycle length of 500 ms. After 200 stimuli, an additional stimulus was applied following a pause of 1,000 ms. Drug-induced EAD development was tested at drug concentrations = IC60,hERG in the mid cell type. EAD analysis was also performed at Cdrug = IC60,hERG for combinations of ICaV, INaL, and IKs blocks ranging from 0–100% with step of 10% resulting in a set of 1,000 simulations. TdP risk prediction was carried out using ability of drugs to induce EADs as a classification criteria (EAD+: drugs that induce EADs at 60% hERG block concentrations, EAD−: drugs that do not induce EADs at 60% hERG block concentrations). **Figure 1** illustrates the classification based on the drug EAD risk. The drugs with hERG ratio greater than the hERG ratio threshold determined for the particular dataset (using the two-step approach on the direct features) were considered EAD−. For the remaining drugs the block of ion-channels was calculated at drug concentration equal to IC60,hERG and overlaid on the parametric space obtained from EAD analysis at varying combinations of ICaV, INaL and IKs blocks (**Figure 2A**), for both the OHR and OHRmv models, to determine whether a drug will induce EAD or not at 60% hERG block concentrations.

The system of ordinary differential equations were solved using the rapid integration scheme (a combination of forward Euler, Rush-Larsen method, Rush and Larsen, 1978 and adaptive time-step) proposed in the original model (O'Hara et al., 2011). For the EAD simulations rapid integration scheme proposed in O'Hara et al. (2011) yielded different results to gold standard simulations with fixed time step of 0.001 ms. Hence, for the EAD simulations we utilized forward Euler method with a time step of 0.001 ms. Execution scripts were written in C++.

#### 3. RESULTS

#### 3.1. Drugs TdP Risk Highly Correlates to EAD Propensity

A short-long cycle length (i.e., pause) often precedes the onset of TdP (Neal Kay et al., 1983; Viskin et al., 2000). The pause is known to facilitate the formations of EADs (Viswanathan and Rudy, 1999; Liu and Laurita, 2005). Here, we test the effects of drug-induced block of different channels on triggering of pauseinduced EADs. Block of hERG channel causes prolongation of action potential and can result in the generation of EADs. In the OHR and the OHRmv models, the amount of hERG block required to induce pause-induced EADs is reduced with increase in the duration of the pause. hERG block by 57 and 55% induced EADs in the mid-cell paced at 2 Hz (500 ms pacing cycle length) following a 700 ms pause in the OHR and OHRmv models, respectively. The amount of hERG block required to induce EADs in the OHR and OHRmv model following 1,000 ms pause is reduced to a 47 and 46% block, respectively. Under these critical blocks of hERG channel, modifications of other channels may promote or inhibit the EADs. First, we tested individually the effects of block of six ion-channel currents (ICaV, INaL, IKs, IK1, INa,fast, and Ito) in promoting or inhibiting pause-induced EADs at fixed blocks of hERG channels that are marginally above (60%) and below (40%) the critical value (48%) of hERG block that is required to induced EADs in the models. At 60% hERG block, block of ICaV (> 30% for both the OHR and OHRmv models) and INaL (> 60% for the OHRmv model) resulted in suppression of EADs. The remaining five channels had no inhibitory effects. At 40% hERG block, blocks of IKs and IK<sup>1</sup> led to induction of EADs with lower block of IKs currents promoting triggering of EADs compared to IK1. The block of remaining five channels did not result in EADs at 40% hERG block.

For visualization of combined effects of the channels on EAD induction, we performed EAD analysis for varying combinations of block of the three most sensitive non-hERG channels (ICaV, INaL, and IKs) regulating EAD generation, each ranging from 0 to 100% at Cdrug = IC60,hERG. **Figure 2A** represents the EAD test for the models. The red region represents the set of combinations of blocks for these currents that resulted in the EADs in the OHR model (EAD+ region). The region in green covers the parameter subspace where no EADs were observed in the OHR model (EAD− region). Separation of the EAD+ region and EAD− region is outlined by the blue and yellow surfaces for the OHR and OHRmv model, respectively (**Figure 2A**). Among the non-hERG channels, block of ICaV had the highest modulatory effects on EAD generation under normal

simulation of six drugs in the OHR model. Red and green traces show that the drug is defined as TdP+ and TdP−, respectively.

conditions. Under critical hERG block (60%), block of ICaV by more than 30% resulted in suppression of the EADs in both the OHR and OHRmv models (**Figure 2A**). Block of INaL in the absence of the block of ICaV did not result in suppression of the EADs in the OHR model. Even in the OHRmv model with improved INaL formulation, block of more than 60% of the late sodium current was required to suppress pause-induced EADs. Block of IKs currents increased the amount of block of INaL and ICaV currents required to prevent EADs. A similar parametric space for EAD generation was also analyzed under enhanced late sodium currents (**Figure 2B**), associated with LQT3. In the OHRmv model the conductance of the late sodium current was doubled. Block of the hERG channel by 30% was enough to induce EADs in the OHRmv model under enhanced late sodium currents. EAD generation was examined at this 30% hERG block and is shown in **Figure 2B**. For the simulations with enhanced late sodium currents, the difference in the effects of INaL and ICaV was significantly reduced. At 30% hERG block in the OHRmv model, block of greater than 20 and 30% was required for EAD suppression by ICaV and INaL, respectively (**Figure 2B**).

**Table 3** lists the accuracy of TdP risk prediction using EADs as the classification criteria. As an illustration, the data points for the drugs in one of the datasets (Dataset 5) are overlaid on the the parametric space in **Figure 2A** at hERG blocks of 60% to visualize the agreement between drugs EAD and TdP risks. The drugs with positive TdP risk are shown in red, while the drugs with negative TdP risk are shown in green. Actual AP profiles were also simulated for drugs in Datasets 5 and 7 at 60% hERG block concentrations taking into account the block of all seven channels. **Figure 2C** gives representative examples of the AP profiles for the multi-channel block of six of the drugs from Dataset 7 simulated in the OHR model. Our results show a good concordance between drugs torsadogenic risk and its propensity to induce EADs (i.e., most of the torsadogenic drugs resulted in pause-induced EADs in the models while no EADs are observed for majority of the non-torsadogenic drugs at 60% hERG block drug concentrations) across all the datasets. Majority of the datasets (Datasets 1, 2, 4, 6) contains values of blocks for two non-hERG channels (ICaV, INa,fast) of which only ICaV had an impact on EAD occurrence in the OHR and OHRmv models. Hence, for these datasets, OHR



and OHRmv models give identical accuracies as the drugs with greater than 30% ICaV block would result in EAD suppression in both of these models. For the Datasets 3, 5, and 7, druginduced blocks of multiple ion channels are reported. However, very few drugs among these datasets are located in the region between the EAD risk decision surfaces for the OHR (blue surface) and OHRmv (yellow surface) models (i.e., the region in the parameter space that would result in a different prediction between the OHR and OHRmv models, **Figure 2A**). Hence, similar accuracies are observed for both of the models across all datasets. For the Dataset 7, Ranolazine (TdP−) was the only drug that was located on the negative side of the EAD risk decision surface for the OHRmv and to the positive side of the decision surface for the OHR, and hence predicted correctly by the OHRmv model but not by the OHR model. On the contrary for Dataset 5, Quinine (TdP+) ended up on the negative side of the EAD risk separating surface for the OHRmv and to the positive side of the EAD risk decision surface of the OHR model resulting in its incorrect prediction using the OHRmv model (**Figure 2A**).

#### 3.2. Binary TdP Risk Discrimination from Direct Features

Although the biophysical models can provide mechanistic insights underlying TdP genesis, the benefits of using biophysical models in terms of classification is unclear. Here, we wanted to examine the performance of the classifiers built on direct features using the proposed method. The predictive power of the TdP risk classifiers built on the direct features using the proposed method (MCB@EAD) is shown in **Table 4** (two-step classifier column). Classification scores on the direct features at EFTPC are reported for comparison (one-step classifier column). The predictive ability of the two-step classifier was comparable or better than those for the classifiers built on the various features in the original datasets and also better than those for the one-step classifier. Most datasets comprise in-vitro assay data for druginduced block of IKr, INa,fast, and ICaV (Datasets 1, 2, 4, and 6). Drug-induced blocks of additional channels were reported in three datasets (Datasets 3, 5, and 7). The classifiers built using the block of IKr and ICaV as inputs provided high TdP risk prediction scores (**Table 4**). Utilizing the block of INaL as an additional input feature improved the prediction for the two datasets (Dataset 3 and Dataset 7) by classifying correctly one more drug, Ranolazine, as TdP−. On the contrary, in Dataset 5, addition of the block of INaL to the features reduced the number of correctly classified drugs by one (classifying Ritonavir incorrectly as TdP−). Taking into account the block of additional ion channels (INa,fast for Datasets 1, 2, 4, 6 and INa,fast, IKs, Ito, IK<sup>1</sup> for Datasets 3, 5 ,7) did not provide any further improvement in the performance of the classifier for all datasets.

For visualization of our two-step approach we presented two-dimensional risk maps. Drug-induced block of the ICaV or the sum of ICaV and INaL blocks is plotted against the hERG ratio ( IC60,hERG EFPTCdrug ) for each drug in a two-dimensional risk map (**Figure 3**). The values of the hERG ratio (x-axis) and the block of ICaV (y-axis) that provide the best discrimination vary widely


TABLE 4 | Binary TdP classifier scores of one-step and two-step classification on the direct features for the eight datasets.

*The total number of drugs in the particular dataset are reported in the NDrugs column. Table also lists the feature used for classification in the original methods and corresponding scores if applicable. The last column shows a list of channel currents used to construct the classifiers. For comparision with the classification accuracy obtained with the direct features, we reported the highest accuracy obtained for the classifiers from the 13 derived features in isolation at different pacing rate/cell type in the bracket in One step and Two step classifier columns. \*The derived features were extracted from simulations of the drug-induced block of all the reported ion channel currents in the in-vitro assay datasets.*

across the datasets (**Figure 3**). Using the threshold of 22 and 100 for the block of ICaV and hERG ratio, respectively, resulted in the perfect classification for Dataset 1 (Mirams et al., 2011). However, for Dataset 2 the hERG ratio threshold of 200 and threshold for ICaV of 57 provided the best classification. Looking at the risk maps in **Figure 3** we can see that the thresholds that provide best classification accuracy vary across datasets resulting in variations in the obtained high risk zones across datasets. For datasets 3, 5, 7 where we also considered block of INaL as one of the input feature in addition to the block of ICaV the value on y-axis of the risk map were reported using Equation (5). A two-dimensional risk map for Dataset 5 for two alternate TdP definitions is shown in **Figure 4**. On the two-dimensional risk map with only ICaV block on the y-axis, we also highlight, using a blue rectangular outline, the separation between the region with EAD presence and absence observed in the in-silico simulation at varying ICaV blocks. For example, at critical hERG block simulations in the model at block of ICaV less than 30% would result in EADs. Block of ICaV by more than 30% results in suppression of the observed EADs. There is approximate correspondence between the EAD observance region in the in-silico model and the high torsadogenic region obtained from classifying the direct-features using machine learning.

# 3.3. Derived vs. Direct Features as Predictors for TdP Risk

We examine the performance of classifiers from various derived features extracted from the simulated action potential and calcium transient in predicting TdP risk. Drug-induced multichannel block was simulated in the OHR model for all the compounds in the merged dataset (Dataset 8) considering the block IKr and ICaV channels. Simulations were also carried out taking into account drug-induced block of all the channels with available IC<sup>50</sup> values. Taking into account the block of additional channels resulted in similar accuracies and are reported in the Supplemental Material. **Figure 5** shows the performance of the logistic-regression classifier to discriminate TdP+ and TdP− drugs (**Figures 5A,B**) and to predict drug-induced EADs (**Figures 5C,D**). The classifiers were built on 13 features extracted from the steady-state APs and Ca2<sup>+</sup> transients (for 3 cell types at 3 pacing rates). The derived features were extracted at either EFTPC of the drugs (**Figures 5A,C**) or at concentrations at which each drug would produce 60% hERG block (Cdrug = IC60,hERG) (**Figures 5B,D**). Among the various derived features obtained at Cdrugs = EFTPC, diastolic Ca2<sup>+</sup> levels provided the best discrimination score between the TdP+ and TdP− drugs (∼79% accuracy at 1 Hz in epi cell type, **Figure 5A**) in agreement with a

et al., 2017), (G) Dataset 7 (*IKr*, *ICaV* ) (Li et al., 2017), (H) Dataset 7 (*IKr*, *ICaV* , *INaL*) (Li et al., 2017), and (I) Dataset 8 (merged dataset). The regions in green are low risk regions and the regions in red are high risk areas. Red dots (•) indicate TdP+ drugs and green dots (•) indicate TdP− drugs. For comparsion purposes, we superimpose a blue rectangular outline that shows the separation between EAD+ and EAD− regions of parameter space. For binary classification the high and intermediate risk drugs in Dataset 7 were assigned TdP+ and the low risk drugs were assigned to TdP−.

previous report (Lancaster and Sobie, 2016). Classifier was also built using APD<sup>50</sup> and Diastolic Ca2<sup>+</sup> together as inputs (the combination that provided the best prediction in Lancaster and Sobie, 2016) but did not give an improved classification for the merged dataset. Several derived features performed well (>90% accuracy) for EAD risk prediction (**Figure 5**). However, at drug concentrations equal to IC60,hERG (Cdrug = IC60,hERG), each of the 13 features from the Ca2<sup>+</sup> transient and AP provided high classification scores (∼85% maximum) for TdP risk assessment (**Figure 5C**). The highest accuracy for each of the features was obtained at different pacing rates (0.5, 1, and 2 Hz) and for different cell types (endo, mid and epi). The maximum classification scores to discriminate the drugs that induced EAD in the model from the drugs that did not induce EADs was 100% (**Figure 5D**) for each of the features. Our results suggest that at fixed hERG block concentrations where trigger events such as EADs arise, several derived features obtained from the model including features from the Ca2<sup>+</sup> transient can provide good TdP risk prediction. These derived features also highly correlate with EADs (**Figure 5**). However, the derived features extracted from simulations of the drug-induced effects in ventricular myocyte model did not result in much improvement in TdP risk assessment over the classifiers built on the direct-features using the proposed method (**Table 4**). Moreover, combining the direct and derived features to build the TdP risk classifiers also did not improve the classification performance (results are not shown).

#### 3.4. Direct Features Perform Well to Allow Tertiary Risk Classification

Our results show that classifiers built on the direct features serve as excellent predictors of TdP risk of the drugs categorized into binary risk groups. However, a working committee under the CiPA initiative led by FDA has recently categorized 28 drugs into

tertiary risk categories (low, medium, and high risk compounds) (Colatsky et al., 2016; Fermini et al., 2016). Hence, we test the predictive capabilities of the classifier based on direct features to classify the drugs categorized into tertiary risk categories. **Figures 6A,B** show a two-dimensional risk map for the 12 drugs in Li et al. (2017). These drugs have been analyzed previously using modified OHR model that incorporate dynamic hERG channel interactions. The 12 drugs are a subset of the 28 drugs categorized into three risk categories (CP1, CP2, and CP3) under the CiPA initiative. As a first step, we developed a TdP risk map using only the block of ICaV channel. The hERG ratio threshold of 150 and the threshold of ICaV block of 45%, the values that provided best classification for the merged dataset, were utilized for classifying the low high and intermediate risk drugs from low risk drugs **Figure 6A**. Arbitrary value of hERG ratio and ICaV block of 25 and 15, respectively (a value greater than the maximum hERG ratio and maximum block of ICaV among the high risk drugs in Datasets 7 and 9) was utilized to separate high risk drugs from the low and intermediate risk drugs. Three of the four drugs in low risk (CP3) category were classified correctly. Ranolazine was the only misclassified drug. The boundaries of red zone were defined to include all high risk drugs and hence all the drugs from CP1 category were correctly classified. However, several drugs in intermediate risk were incorrectly classified. Next, we built regression classifier using as input metric the sum of block of ICaV, INaL channels and the degree of drug-trapping parameter which was shown to be essential to improve risk prediction of intermediate risk drugs in the original dataset. **Figure 6B** shows the risk map built using this metric. The threshold along the y-axis was obtained from the regression coefficients. The hERG ratio threshold of 25 and 150 were utilized as before. Including the degree of drug trapping characterized by open-bound/closed-bound ratio for the drugs at steady-state (Li et al., 2017) as one of the features in addition to the blocks of CaV and NaL channels, resulted in the perfect separation of the 12 drugs in 3 categories (**Figure 6B**).

We employed the same approach to test all of the 28 drugs (Fermini et al., 2016) categorized in CP1, CP2, and CP3 categories under the CiPA initiative. In-vitro assays for 12 of these 28 drugs were reported in Crumb et al. (2016) and analyzed in Li et al. (2017). To augment this dataset, we extract the IC<sup>50</sup> values for hERG and CaV blocks from Datasets 1, 2, 3, 5, 6, 7 resulting in characterization of 26 of the 28 drugs categorized under the CiPA initiative. Two drugs (Azimilide and Loratidine) were absent in all of the datasets analyzed here and hence were not taken into consideration. We used the mean value of the block if the drug was present in more than one

dataset. The final dataset of the 26 drugs is reported in the Supplemental Material. **Figure 6C** show the two-dimensional risk maps for the 26 drugs with hERG ratio on the x-axis and the block of CaV on the y-axis. The 45% ICaV block threshold and hERG ratio threshold of 150 yielded almost perfect binary classification (high and intermediate vs. low risk drugs) with only 2 (Ranolazine and Tamoxifen) drugs of the 8 from the CP3 category and one drug (Clozapine) of the 16 drugs from CP1 and CP2 cateogry (high and intermediate risk drugs) classifying incorrectly. However, no clear separation was observed amoung the drugs in CP1 and CP2 categories, with several drugs from CP2 category ending up in the high risk region. Considering additional features such as INaL and the degree of drug trapping (if either of the features were not available their value was set to zero) and utilizing the threshold obtained from training the Dataset 7 (**Figure 6B**) resulted in only 3 intermediate risk drugs (Clarithromycin, Domperidone, Droperidol) and 1 low risk drug (Tamoxifen) of the 26 drugs to be misclassified (**Figure 6D**). The classifier already performs well in spite of testing data from heterogeneous sources with some missing values. Further refinement of the method may be possible when a dataset is available with all 28 drugs characterized with a consistent methodology.

#### 3.5. Diverse Definition of Drugs Torsadogenicity Lead to Different Prediction Accuracies

Different binary definitions for the drug's torsadogenic risk have been used across the literature (Lancaster and Sobie, 2016; Ando et al., 2017; Wi´sniowska and Polak, 2017). **Tables 5**, **6** list the different classification accuracy scores obtained for four different binary TdP definitions (Datasets 5 and 8, respectively). Classifiers were constructed on the block of one or multiple-ion channels as inputs at critical hERG block concentrations (Cdrug = IC60,hERG). The various definitions not only resulted in variability of classification scores (**Tables 5**, **6**), but also changed the role of different ion channels in accurate TdP risk classification

dots (•) indicate intermediate risk drugs. Metric = % block CaV + % block NaL + degree of drug trapping.

TABLE 5 | Accuracy scores of TdP classifiers on the direct features for Dataset 5 under four different TdP definitions.


*Target1: TdP*+ = *CM1, CH1, R1, R2, R3, and FDA label QT prolongation and torsade warnings. Target 2: TdP*+ = *CM1 and CM2. Target 3: TdP*+ = *CM1. Target 4: TdP*+ = *CM1 and CM3. Row reporting the maximum accuracies obtained using the derived features is reported for comparision with the direct features.*

(**Table 5**). Using the block of ICaV currents provided the best accuracy scores under two of the four definitions (Target 1 and Target 2) for Dataset 5. Including the effects on additional TABLE 6 | Accuracy scores of TdP classifiers on the direct features for Dataset 8 under four different TdP definitions.


*Target1: TdP*+ = *CM1, CH1, R1, R2, R3, and FDA label QT prolongation and torsade warnings. Target 2: TdP*+ = *CM1 and CM2. Target 3: TdP*+ = *CM1. Target 4: TdP+ = CM1 and CM3. Row reporting the maximum accuracies obtained using the derived features is reported for comparision with the direct features.*

ion-channels did not improve classification scores for these two definitions. Taking into account the block of late sodium currents in addition to CaV channels, provided the best classification accuracy for remaining two of the four TdP definitions (Target 3 and 4) (**Table 5**).

Step2: Derived features

86 76 74 73

# 4. DISCUSSION

Evaluation of drug-induced alterations in multiple cardiac ionchannel currents to determine the drug's torsadogenic potential is currently under investigation through initiatives like CiPA (Comprehensive In-vitro Proarrhythmia Assay) (Sager et al., 2014; Fermini et al., 2016). We have developed a novel twostep method (MCB@EAD) for classification of drugs according to their torsadogenic risk. Using the proposed method, we examined the drug effects at fixed hERG block (i.e., 60% block) concentrations for all tested compounds. This approach allows to isolate the effects of hERG and non-hERG channels in the classification problem. The proximity of the drug's EFTPC to the concentration that results in the critical hERG block provides one of the metrics for determining the drug's TdP risk. For the drugs that induce this critical hERG block at concentrations below a set threshold, the drug-induced effects on non-hERG channels provide an additional metric to determine pro-arrhythmic risk independently of the drug's EFTPC. Our classifier shows improved or equivalent prediction to existing methods. However, one of the advantages compared to previous studies is that the direct and derived features based MCB@EAD classifiers were tested on several in-vitro assay datasets reported previously, as well as on a large composite dataset obtained by merging the different datasets together. One of the important findings of the study was that MCB@EAD TdP classifiers from the direct features provides excellent TdP risk prediction and performs identical to the TdP classifiers from the derived features, which are extracted from complex biophysical models. Although the derived features provided by the biophysical models did not improve the predictive capability for TdP risk assessment, the biophysical models helped determine the amount of block that generates EADs (i.e., the concentration at which the direct features are analyzed using the MCB@EAD classifier). The proposed method not only performs comparably or better than the previous classifiers (**Table 4**) across various in-vitro assay datasets published previously, but also highlights the link between direct and derived feature based classifiers. The results also show strong correlation between the drugs that generate EADs and the drugs with positive TdP risk.

#### 4.1. Ion-Channels Critical for TdP Risk Prediction

Although the role of multiple ion-channels have been suggested for improved TdP risk prediction, classifiers have been primarily built on the blocks of IKr, ICaV, and INa,peak currents (Mirams et al., 2011; Christophe, 2013, 2015; Kramer et al., 2013; Lancaster and Sobie, 2016). A recent assay reports the drug-induced effects on seven ion channels (Crumb et al., 2016) providing an opportunity to identify the ion channels that are important for pro-arrhythmic risk assessment. The results of our parametric simulations of EAD indicate a potential role of block of ICaV, INaL, and IKs currents, in addition to IKr, for determination of torsadogenic risk of the drugs (**Figure 2**). It should be noted that the EAD simulations results are highly dependent on the ventricular myocyte model. For example, block of late sodium current in the OHRmv plays a more prominent role in regulation of AP sensitivity to EADs as compared to the OHR model (**Figure 2A**). The IKs plays a much bigger role in Ten Tusscher and Panfilov model (Ten Tusscher and Panfilov, 2006) than OHR model in regulation of APD as shown in Mirams et al. (2014). The present datasets have limited examples of block of ICaV, INaL, and IKs currents in the same compounds. Moreover, among the non-hERG channels, the regulatory effect of ICaV block was the highest with the block of ICaV by only 30% resulting in EAD suppression at critical hERG current block (**Figure 2**). The classifiers constructed on the block of IKr and ICaL provided the best discrimination between torsadogenic and non-torsadogenic drugs for the majority of the datasets tested here, including the dataset where drug-induced effects on seven ion channels were reported (**Figure 2**, **Tables 4**, **5**). Our results suggest that among different channels, examination of block of ICaV and IKr might be the most critical for TdP risk prediction. Relative block of ICaV and IKr (among the three currents measured in the in-vitro assay) was shown to provide the best risk prediction, with no role of peak/fast sodium currents in improving the classification in Kramer et al. (2013).

Examination of late sodium block can be important for the drugs with low to moderate ICaV block as these drugs would be predicted TdP+ if only IKr and ICaV block are considered for risk prediction. Moderate to high block of INaL by these drugs can result in suppression of EADs (**Figure 2**) indicating lower TdP risk. Earlier datasets did not report values for INaL block. Dataset 5 reports the value of drug-induced block of seven ion-channels, including the block of INaL. Among the drugs with low to moderate ICaV in Dataset 5, only three drugs [Ranolazine(CM3), Toremifene(CM2) and Quinine(CM3)] have greater than 30% INaL block at critical hERG block concentrations. For the limited data with inconsistent risk categorization, taking into account the INaL block did not improve predictive power of the classifiers (**Tables 4**, **5**). A small improvement in TdP prediction was observed for Datasets 3 and 7 (Okada et al., 2015; Li et al., 2017) when considering drug-induced block of INaL as one of the input features by correctly classifying Ranolazine (the only drug with high late sodium block in absence of ICaV block) in both the datasets (**Table 4** and **Figure 3**). The limited data and inconclusive/minor improvement in torsadogenic risk classification make it difficult to ascertain the role of ion channels such as INaL and IKs in predicting TdP risk.

## 4.2. Predictive Power of Direct vs. Derived Features

In-silico biophysical models can be thought of as a complex nonlinear transfer function, which translates the drug-induced multichannel block effects at channel level (input) to alterations in APs and calcium transients at cellular/tissue levels (output). Several in-silico electrical biophysical models of human ventricular cell models have been published over the last decade (e.g.,Ten Tusscher and Panfilov, 2006; Grandi et al., 2010; O'Hara et al., 2011; Himeno et al., 2015). TdP risk classification on features extracted from the drug-induced responses in isolated cell (Mirams et al., 2011; Christophe, 2013, 2015; Lancaster and Sobie, 2016), tissue (Trenor et al., 2013; Kubo et al., 2017) or organ level (Okada et al., 2015) computational models can provide physiological/mechanistic insights. Moreover, in-silico models serve as an excellent tool for evaluation of drug-safety in diseased conditions (Trenor et al., 2013; Kubo et al., 2017). Our simulations in the OHRmv model under pathological conditions (enhanced late sodium currents) reveal that EAD can appear at significantly lower drug concentrations as only 30% hERG block was required to induce pause-induced EADs under pathological conditions compared to 60% hERG block under normal conditions. Moreover, the modulatory effects of nonhERG channels on EAD induction was also significantly different for simulations under pathological conditions (**Figure 2**). On the other hand, biophysical models show considerable differences in their formulations and can lead to different predictions based on the chosen model. Simulations of EAD generation show a significant difference between the surfaces separating EAD+ region from EAD− region, that are obtained from the OHR and OHRmv models (**Figure 2**). Recently, several efforts have been carried out for optimization of in-silico cardiac cell models for pro-arrhythmia risk assessment (Dutta et al., 2016; Mann et al., 2016; Li et al., 2017).

Statistical/machine learning classifiers that use measured invitro block of multiple cardiac channels (direct features) as their input (Kramer et al., 2013; Mistry et al., 2015) demonstrated comparable accuracy as compared to TdP risk classifiers built on derived features, questioning the need of additional complexity provided by the in-silico models. On the contrary, the study by Okada et al. suggested the need of highly detailed threedimensional cardiac models for pro-arrhythmic risk assessment and showed relatively low predictive ability using the direct features and also certain derived features from the in-silico lumped parameter (zero-dimensional) cellular models (Okada et al., 2015). Derived features from in-silico simulations that incorporate dynamic drug-hERG channel interactions were shown to improve prediction of TdP risk (Li et al., 2017). For all the datasets tested here, including the datasets in Okada et al. (2015) and Li et al. (2017), we showed that the classifiers built on the direct features performed equally or better than the previously developed classifiers on the derived features (**Table 4**). Our results show that for currently available in-vitro assay datasets simple models based on the direct features can provide similar accuarcy to more complex models based on derived features. It should be noted that our two-dimensional risk classifiers on the direct features also utilized insights gained from the computational models (the direct features are examined at critical hERG block concentrations where EAD can arise in the in-silico models). Our parametric simulation for EAD induction highlights one of the possible reasons for the insignificant improvement in predictive power of classifiers built on the derived features from the in-silico models. Although a nonlinear surface is obtained from the in-silico models separating the EAD+ and EAD− regions (**Figure 2**), a hyperplane

$$a \times b \\ \text{lock}\_{I\_{\text{CaV}}} + b \times b \\ \text{lock}\_{I\_{\text{NaL}}} + c \times b \\ \text{lock}\_{I\_{\text{Ks}}} + d = 0 \quad (6)$$

constructed using direct features can result in nearly identical separation, where a, b, c, and d are the parameters of the hyperplane and blockICaV , blockINaL , and blockIKs are the values of block of ICaV INaL, and IKs, respectively. Moreover, with most of the datasets comprising values for block of few channels (Mirams et al., 2011; Kramer et al., 2013) and the much higher incidence of drug-induced block of particular ion channels (INaL, ICaV, and IKr) even when drug-induced modulation of several channels are examined (Crumb et al., 2016), the result is a congregation of majority of the data in a small region of the plausible highdimensional risk space (e.g., see **Figure 2**). For example, the data in Mirams et al. (2011) and Kramer et al. (2013) would fall on a single edge of the 3D EAD space in **Figure 2** in the absence of values for drug-induced block on INaL and IKs in these datasets. This allows risk classification to be performed by a hyperplane with a single parameter, such as blockICaV . Here, we utilized an additional metric, i.e., the hERG ratio, to further improve the classification performance of the direct-feature based classifiers (**Figures 3**, **4**, **6**). For the limited data currently available, risk classification using simple statistical models built on the direct features as the one presented here may suffice.

#### 4.3. Diversity in the Proposed Derived Features

The classifiers built on derived features obtained from the insilico models are based on certain underlying physiological phenomenon (APD, increase in calcium levels, etc.). Hence, derived features are thought to allow better extrapolation to examine drug targets other than those in the training set. However, diverse derived features from the in-silico models have been suggested as possible candidate metrics. Several features from the biophysical models, such as APD50, APD90, calcium level peak, and CaD<sup>90</sup> provided the best classification depending on the selected in-silico model (Mirams et al., 2011). Other derived features (EADs, TDR, change in ICaV & INaL) extracted from the AP and calcium transient (Christophe, 2013, 2015; Li et al., 2017) have also been suggested as possible candidate metrics for TdP risk prediction. Rather than examining the individual features separately, a recent study performed a comprehensive feature selection among 331 metrics and determined that two metrics, APD<sup>50</sup> and diastolic Ca2<sup>+</sup> in the OHR model at 1 Hz pacing, provided the best discrimination between torsadogenic and non-torsadogenic drugs (Lancaster and Sobie, 2016). The overall diversity in reported plausible candidate metrics for TdP risk classification can be attributed to different simulation protocols, drug concentrations and biophysical models. We showed that several derived features obtained from the in-silico models may track together and provide equal predictive power for risk classification when examined independent of drug EFTPC (**Figure 5C**). Equal predictive ability of several features makes it difficult to determine the underlying causal mechanism. In addition, the identical performance of several derived features limits the extensibility of the classifier to untrained targets, as classification results depend on the specific set of features chosen to perform the classification. For example, examination of untrained ion-channel targets using a classifier with diastolic Ca2<sup>+</sup> level as the primary risk discriminating feature predicts a decrease in torsadogenic risk for increased Na<sup>+</sup> − Ca <sup>2</sup><sup>+</sup> currents (Lancaster and Sobie, 2016). On the contrary, TdP risk prediction under Na<sup>+</sup> − Ca2<sup>+</sup> modulation using a classifier with APD<sup>50</sup> or APD<sup>90</sup> as the primary discriminating feature would predict opposite effects, with decreased Na<sup>+</sup> − Ca2<sup>+</sup> exchanger current being associated with decreased TdP risk. Moreover, the derived features obtained from the highly complex biophysical models did not result in improved prediction over the classfiers built on the direct features using the proposed method.

#### 4.4. Limitations

One of the primary limitations is the quality of the datasets itself. The variability in the IC<sup>50</sup> values among the several datasets can be one of the reasons for the observation of different thresholds for the hERG ratio and ICaV block that resulted in the best discrimination between TdP+ and TdP− drugs (**Figure 3**). Quantification of the uncertainties in the in-vitro channel screening data and their effects on risk prediction are presented in Johnstone et al. (2016). Inconsistencies in risk definition presents another important challenge for torsadogenic risk assessment. Wi´sniowska and Polak (2017) reports a comprehensive list of compounds that have been inconsistently defined as TdP+ or TdP− in different studies to develop torsadogenic risk classifiers. The different categorizations can lead to different interpretations and accuracy scores for TdP risk determination (**Table 5**). Standardization of torsadogenicity definition, which would allow comparison of the performance of different classifiers/features, is required. Certain steps in this direction have been started. Based on a general consensus, a working group formed under CiPA initiative picked 28 compounds and categorized each into three groups (Colatsky et al., 2016; Fermini et al., 2016)

#### REFERENCES


for testing/training of the classifiers. In-silico simulations of dynamic drug-channel interactions might be essential to further improve the TdP risk assessment (Li et al., 2017). Inclusion of the drug-binding parameter, in addition to the amount of block of ion-channels, resulted in 100% prediction using our approach. Sufficient IKr block was assumed to be necessary for TdP generation in our method. The effects of non-hERG channels are thought to enhance or mitigate the torsadogenic effects of IKr block. The method resulted in excellent predictive performance across several datasets that report drug-induced block of various ion channels only. However, drug-induced enhancement of ion-channel currents such as INaL can result in increased TdP risk in the absence of hERG block (Lacerda et al., 2008; Yang et al., 2014). The method could be further extended to examine such effects when more data are available. The present work not only provides a new method for invitro ion-channel screening based TdP risk classification but also highlights several important issues in regards to the use of drug-induced multi-channel blockage for torsadogenic risk prediction.

#### AUTHOR CONTRIBUTIONS

JP, VG, and JR wrote the manuscript. JP, VG, and JR designed the research. JP and VG performed the simulations. JP, VG, and JR analyzed the data.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphar. 2017.00816/full#supplementary-material


Pharmacol. Therapeut. 129, 109–119. doi: 10.1016/j.pharmthera.2010. 08.008


combining a patch clamp and heart simulator. Sci. Adv. 1:e1400142. doi: 10.1126/sciadv.1400142


**Conflict of Interest Statement:** All authors are employees of IBM Research.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer EP and handling Editor declared their shared affiliation.

Copyright © 2017 Parikh, Gurev and Rice. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Synergistic Anti-arrhythmic Effects in Human Atria with Combined Use of Sodium Blockers and Acacetin

Haibo Ni 1, 2, 3, Dominic G. Whittaker <sup>1</sup> , Wei Wang<sup>1</sup> , Wayne R. Giles <sup>4</sup> , Sanjiv M. Narayan<sup>5</sup> and Henggui Zhang1, 2, 3, 6 \*

*<sup>1</sup> Biological Physics Group, University of Manchester, Manchester, United Kingdom, <sup>2</sup> Space Institute of Southern China, Shenzhen, China, <sup>3</sup> Key Laboratory of Medical Electrophysiology, Ministry of Education, Collaborative Innovation Center for Prevention and Treatment of Cardiovascular Disease/Institute of Cardiovascular Research, Southwest Medical University, Luzhou, China, <sup>4</sup> Faculties of Kinesiology and Medicine, University of Calgary, Calgary, AB, Canada, <sup>5</sup> Department of Medicine, Stanford University School of Medicine, Stanford, CA, United States, <sup>6</sup> School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China*

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Christopher Huang, University of Cambridge, United Kingdom Andrew G. Edwards, Simula Research Laboratory, Norway*

\*Correspondence: *Henggui Zhang henggui.zhang@manchester.ac.uk*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *31 July 2017* Accepted: *08 November 2017* Published: *23 November 2017*

#### Citation:

*Ni H, Whittaker DG, Wang W, Giles WR, Narayan SM and Zhang H (2017) Synergistic Anti-arrhythmic Effects in Human Atria with Combined Use of Sodium Blockers and Acacetin. Front. Physiol. 8:946. doi: 10.3389/fphys.2017.00946* Atrial fibrillation (AF) is the most common cardiac arrhythmia. Developing effective and safe anti-AF drugs remains an unmet challenge. Simultaneous block of both atrial-specific ultra-rapid delayed rectifier potassium (K+) current (IKur) and the Na<sup>+</sup> current (INa) has been hypothesized to be anti-AF, without inducing significant QT prolongation and ventricular side effects. However, the antiarrhythmic advantage of simultaneously blocking these two channels vs. individual block in the setting of AF-induced electrical remodeling remains to be documented. Furthermore, many IKur blockers such as acacetin and AVE0118, partially inhibit other K<sup>+</sup> currents in the atria. Whether this multi-K+-block produces greater anti-AF effects compared with selective IKur-block has not been fully understood. The aim of this study was to use computer models to (i) assess the impact of multi-K+-block as exhibited by many IKur blokers, and (ii) evaluate the antiarrhythmic effect of blocking IKur and INa, either alone or in combination, on atrial and ventricular electrical excitation and recovery in the setting of AF-induced electrical-remodeling. Contemporary mathematical models of human atrial and ventricular cells were modified to incorporate dose-dependent actions of acacetin (a multichannel blocker primarily inhibiting IKur while less potently blocking Ito, IKr, and IKs). Rate- and atrial-selective inhibition of INa was also incorporated into the models. These single myocyte models were then incorporated into multicellular two-dimensional (2D) and three-dimensional (3D) anatomical models of the human atria. As expected, application of IKur blocker produced pronounced action potential duration (APD) prolongation in atrial myocytes. Furthermore, combined multiple K+-channel block that mimicked the effects of acacetin exhibited synergistic APD prolongations. Synergistically anti-AF effects following inhibition of INa and combined IKur/K+-channels were also observed. The attainable maximal AF-selectivity of INa inhibition was greatly augmented by blocking IKur or multiple K+-currents in the atrial myocytes. This enhanced anti-arrhythmic effects of combined block of Na+- and K+-channels were also seen in 2D and 3D simulations; specially, there was an enhanced efficacy in terminating re-entrant excitation waves, exerting improved antiarrhythmic effects in the human atria as compared to a single-channel block. However, in the human ventricular myocytes and tissue, cellular repolarization and computed QT intervals were modestly affected in the presence of actions of acacetin and INa blockers (either alone or in combination). In conclusion, this study demonstrates synergistic antiarrhythmic benefits of combined block of IKur and INa, as well as those of INa and combined multi K+-current block of acacetin, without significant alterations of ventricular repolarization and QT intervals. This approach may be a valuable strategy for the treatment of AF.

Keywords: atrial-selective block, atrial fibrillation, sodium and potassium current block, multiscale simulation, synergistic antiarrhythmic effect

#### INTRODUCTION

Despite recent advances in the management of Atrial fibrillation (AF), the world's most common cardiac arrhythmia (Dobrev et al., 2012; Nattel and Dobrev, 2017), developing effective and safe antiarrhythmic drugs for treatment of AF remains challenging (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015). Frequently these antiarrhythmic agents promote ventricular arrhythmias (Dobrev et al., 2012; Woods and Olgin, 2014; Voigt and Dobrev, 2016) by prolonging cellular action potential durations (APDs). The associated QT-interval prolongation can lead to life-threatening consequences. Developing atrial-selective drugs is acknowledged to be a current strategy for the treatment of AF (Burashnikov et al., 2007).

Atrial and ventricular tissues show intrinsic regional differences in their cellular ion channel properties, thus suggesting a basis for developing atrial-selective drugs. For example, the atrial and ventricular fast sodium (Na+) channel currents (INa) exhibit different voltage-dependent inactivation properties, opening the opportunity for atrial-selective Na<sup>+</sup> channel blockade (Burashnikov et al., 2007; Antzelevitch and Burashnikov, 2009; Zygmunt et al., 2011). Previous simulation studies have demonstrated that by optimizing state-dependent Na+-channel blocking dynamics (i.e., drug-channel interaction parameters), atrial-selective block of INa could be achieved and that could maximize pharmaceutical effects on the atria while minimizing their proarrhythmic actions in the ventricles (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015).

Another tissue-specific difference between the atria and ventricles is that the ultra-rapid delayed rectifier potassium current (IKur, carried by the KV1.5 channel) contributes to repolarization in the atria but plays little role in the ventricles (Tamargo et al., 2009; Ravens and Wettwer, 2011). Recent studies suggest that atrial-selective blockade of IKur may be an effective pharmacological treatment of AF (Li et al., 2008; Pavri et al., 2012; Loose et al., 2014; Ford et al., 2016). Although the efficacy of IKur block in the treatment of AF remains controversial (Burashnikov and Antzelevitch, 2008), multiple IKur blockers have been developed (Tamargo et al., 2009; Loose et al., 2014; Wettwer and Terlau, 2014; Ford et al., 2016). Interestingly, these IKur blockers actually target multiple channels, and are known to inhibit other K<sup>+</sup> currents including Ito and IK,ACh in the atria (Burashnikov and Antzelevitch, 2008). Examples of such blockers include AVE0118 (Gögelein et al., 2004), AVE1231 (Wirth et al., 2007), AZD7009 (Persson et al., 2005), and acacetin (Li et al., 2008). Among these channel blockers, acacetin, a natural flavone initially isolated from a traditional Chinese medicine Xuelianhua, potently blocks IKur, Ito, and IK,ACh, and has a smaller potency in inhibiting IKr and IKs (Li et al., 2008), similar to AVE0118 (Gögelein et al., 2004; Haan et al., 2006). Acacetin is regarded as a promising atrial-selective agent for the treatment of AF (Li et al., 2008). However, the actions of acacetin on atrial electrophysiology, especially its effects following AF-induced electrical remodeling of atrial electrophysiological properties (Dobrev et al., 2012), remain to be elucidated. Furthermore, since most IKur blockers inhibit other K<sup>+</sup> channels, the question whether the "additional" inhibitive actions produce favorable antiarrhythmic effects has not been addressed thoroughly. A better understanding of these effects of modulating multiple ion channels on atrial excitation and recovery/repolarization may provide insights into evaluating and developing antiarrhythmic drugs.

Interestingly, simultaneous multiple-channel blocking of both depolarization and repolarization currents is attracting more attention since empirical observations suggest that such multichannel blockers generally mediate more effective antiarrhythmic effects (Kirchhoff et al., 2015; Reiffel et al., 2015; Hartmann et al., 2016). A recent numerical and experimental study on the canine heart (Aguilar et al., 2015) suggested that blocking K<sup>+</sup> currents enhanced the anti-arrhythmic effects and AF-selectivity of INa blockade. In their study, IKur block was modeled using a simple pore block scheme by reducing the conductance of the channel. As the kinetics of drug action plays an important role in the effects of IKur blockers (Scholz et al., 2013; Ellinwood et al., 2017), in simulating IKur block a state-dependent block model reproducing a realistic blocker is more favorable. Once again, the effects of combined INa and IKur block on the human atria, especially in the setting of AF-induced electrical remodeling which reduced IKur, remain to be elucidated. It is also unclear how multiple-channel blockade may affect QT interval.

In the present study, it was hypothesized that combined block of INa and K+-currents (predominantly IKur) could produce antiarrhythmic benefits compared with the application of either blocker alone in the setting of AF-induced electrical remodeling. We have tested the hypothesis with the following three aims: (i) to identify and illustrate the effects of the realistic IKur

blocker, acacetin, on atrial electrophysiology following AFrelated remodeling; (ii) to assess whether combined INa and IKur block produce synergistic antiarrhythmic effects; and (iii) to investigate the action of such drug combinations on ventricular electrophysiology.

#### METHODS

### Modeling Electrophysiology of the Human Heart

To simulate human atrial electrophysiology, an updated Colman et al. model for atrial electrophysiology (Colman et al., 2013, 2017) was used. For in silico study of effects of chronic AF- (cAF) induced electrophysiological remodeling on the atria, we incorporated the cAF model parameters from our previous study (Colman et al., 2013) into the updated atrial single cell model (for details please see Online Supplement Material 1.1).

To assess the effects of the anti-AF drugs on the human ventricles, simulations were performed to investigate the actions of the anti-AF drugs on the ventricular AP, INa and QT intervals in the electrograms. In these simulations, the mathematical model developed by O'Hara et al. (2011) was used to represent the ventricular electrophysiology. Additionally, the INa formulation in the model was replaced by the one in the Luo–Rudy model (Luo and Rudy, 1994), which enabled electrical excitation to propagate in the tissue model.

More detailed descriptions of the electrophysiological models of human atrial and ventricular cells are given in Online Supplementary Material 1.1.

# Modeling State-Dependent INa Block

As in previous studies (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015), INa block was simulated using a guarded receptor model with dynamical drug-channel interactions. This approach allows for investigations of the role of the specified parameters for selected INa blockers, and effects of combined IKur block on the atrial selectivity of Na+-channel block. The guarded receptor model considers the binding and unbinding kinetics of the drug to INa channels in a drug concentration-dependent manner. They can be described by first-order transition equations (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015). It was also assumed that the drug predominantly binds to the activated and/or inactivated states of INa. The blockade of INa is given by Aguilar-Shardonofsky et al. (2012) and Aguilar et al. (2015):

$$I\_{\rm Na} = \mathcal{g}\_{\rm Na} \left( 1 - B\_A - B\_I \right) m^3 hj \left( V\_m - E\_{\rm Na} \right) \tag{1}$$

$$\frac{dB\_A}{dt} = K\_A \left[ D\_{Na^+} \right] m^3 h j \left( 1 - B\_A - B\_I \right) - L\_A B\_A \tag{2}$$

$$\frac{dB\_I}{dt} = K\_I \left[ D\_{Na^+} \right] \left( 1 - h \right) \left( 1 - B\_A - B\_I \right) - L\_I B\_I \tag{3}$$

where gNa is the maximum conductance of INa; B<sup>A</sup> and B<sup>I</sup> are the fractional blockade of activation and inactivation channels; m is the activation gate state variable, h and j are the inactivation gate state variables; V<sup>m</sup> the transmembrane potential; ENa the reversal potential of Na+; KA, K<sup>I</sup> the binding constants and LA, L<sup>I</sup> the unbinding constants; [DNa<sup>+</sup> ] is the concentration of a Na+-blocker. As in previous studies (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015), a concentration of 60µM was utilized unless otherwise stated; this concentration was chosen based on previous experimental and modeling studies (Zhu et al., 2006; Moreno et al., 2011; Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015); a parameter set (K<sup>A</sup> = 100 ms−<sup>1</sup> · M−<sup>1</sup> , K<sup>I</sup> = 100 ms−<sup>1</sup> · M−<sup>1</sup> , L<sup>A</sup> = 1 ms−<sup>1</sup> , L<sup>I</sup> = 0.01 ms−<sup>1</sup> ) was first used to represent the kinetics of an INa-selective blocker.

In our investigations of the AF-selectivity of INa block following AF-remodeling, the binding and unbinding constants of the INa blockers were varied to evaluate the dependence of INa block on these parameters, and whether an atrial-selective anti-AF action could be achieved in cAF-remodeled myoctes. The AFselectivity of Na+-channel blockade was defined as the product of atrial-selectivity, rate-selectivity and block efficacy. With fractional block (B<sup>f</sup> ) by Na+-channel blockers being measured as the relative reduction in the peak of INa, the rate-selectivity was defined as the ratio of B<sup>f</sup> measured in an atrial myocyte paced at 6 Hz to that paced at 1 Hz (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015). Atrial-selectivity was used to determine the extent of atrial-ventricular difference in response to each drug. This was represented by the ratio of B<sup>f</sup> observed from an atrial myocyte to that of a ventricular cell both paced at 1 Hz. In this study, we defined block efficacy (E) as:

$$E = \frac{1.0}{1.0 + \left(\frac{0.5}{B\_{\text{f},6\text{Hz}}}\right)^4} \tag{4}$$

where Bf,6Hz is the fractional block of INa measured in an atrial cell paced at 6 Hz. Different from Aguilar et al. (2015), we introduced block efficacy to constrain the measure of AFselectivity when the fractional block observed in a ventricular cell paced was minimal (and could result in a great atrialselectivity), which otherwise could give a great value in AFselectivity regardless of a small Bf,6Hz.

To assess the dependence of the AF-selectivity of INa block on the drug action kinetics, the unbinding constants L<sup>A</sup> and L<sup>I</sup> were first varied over a parameter space from 10−<sup>5</sup> to 10<sup>0</sup> ms−<sup>1</sup> , while K<sup>A</sup> and K<sup>I</sup> were fixed (see Figure S6 of online Supplementary Materials for more details). The resultant unbinding constants were used in subsequent optimizations varying K<sup>A</sup> and K<sup>I</sup> . The parameter space was {1, 10, 100, 500, 2,500, 10,000} for K<sup>A</sup> and {1, 10, 100, 200, 500, 2,500} for K<sup>I</sup> . The parameter space fell into a likely range of INa blockers as summarized in Aguilar-Shardonofsky et al. (2012).

#### Modeling Effects of Acacetin on Atrial and Ventricular Electrophysiology

Acacetin was the chosen IKur blocker in the present study. To reveal the functional effects of (i) pure IKur block vs. (ii) the effects of combined K<sup>+</sup> currents block by acacetin on human atrial electrophysiology, the actions of acacetin were modeled by considering its effects on (a) IKur only, and (b) all the respective K<sup>+</sup> currents as detailed in **Table 1**. This approach allows for modeling the effects of the selective IKur block as well as uncovering the role of "additional" inhibitory effects of acacetin on other K<sup>+</sup> currents.

TABLE 1 | Concentration-dependent block of K+-currents by acacetin (Li et al., 2008; Wu et al., 2011).


#### Modeling Effect of Acacetin on IKur

Previous modeling studies have demonstrated the important role of the kinetic properties of drug actions in IKur block (Tsujimae et al., 2008; Almquist et al., 2010; Scholz et al., 2013). In addition, the pharmaceutical effects of acacetin on IKur are characterized by use- and rate-dependencies (Wu et al., 2011), which have also been observed in other IKur blockers (Pavri et al., 2012; Ford et al., 2016). Therefore, it was necessary to adopt a statedependent block model (Brennan et al., 2009) for simulating the blockade of IKur by acacetin. Similar to our approach for modeling INa block, the binding and unbinding kinetics of a drug was described by a first-order transition equation, in contrast to simulating IKur block by reducing its conductance in Aguilar et al. (2015). Experimental studies revealed that acacetin binds to both the open and closed gates of KV1.5 (Wu et al., 2011). Therefore, following the guarded receptor formulas given in Equations (1–3), the formulation of inactivation-state binding and unbinding kinetics in INa block was modified to simulate the closed-state block of IKur by acacetin. The guarded receptor model of IKur block by acacetin is given by:

$$I\_{\rm Kur} = \mathcal{g}\_{\rm Kur} \left(1 - B\_O - B\_C\right) ai \left(V\_m - E\_K\right) \tag{5}$$

$$\frac{dB\_O}{dt} = K\_O \exp\left(Z\_{KO}\frac{V\_m F}{RT}\right) \left[D\_{K^+}\right] ai \left(1 - B\_O - B\_c\right)$$

$$-L\_O \exp\left(-Z\_{LO}\frac{V\_m F}{RT}\right) B\_O \tag{6}$$

$$-L\_O \exp\left(-Z\_{LO}\frac{V\_m F}{RT}\right) B\_O \tag{6}$$

$$\frac{dB\_c}{dt} = K\_c \exp\left(Z\_{Kc}\frac{V\_m F}{RT}\right) [D\_{K^+}] \left(1 - a\right) i \left(1 - B\_O - B\_c\right)$$

$$-L\_c \exp\left(-Z\_{Lc}\frac{V\_m F}{RT}\right) B\_c \tag{7}$$

where gKur isthe conductance of IKur; B<sup>o</sup> and B<sup>C</sup> are the fractional block on open and closed state variables, respectively; a and i are the activation and inactivation gate variables; E<sup>K</sup> is the reversal potential of potassium; F, R, and T are the Faraday's constant, universal gas constant and temperature respectively. K<sup>O</sup> and K<sup>c</sup> are the binding constants; L<sup>O</sup> and L<sup>c</sup> are the unbinding constants; ZKO, ZLO, ZKc and ZLc are the drug charge parameters for the corresponding binding or unbinding processes; [DK<sup>+</sup> ] is the concentration of acacetin applied. The binding and unbinding parameters were obtained by fitting the model to the experimental data on the rate-dependent blockade of IKur by acacetin (Wu et al., 2011), as detailed in Online Supplementary Material 1.1.

**Figure 1** shows a simulated frequency-dependent block of IKur by acacetin, and this is compared to the experimental data (**Figures 1A,B**). As shown, repeating the voltage command (**Figure 1B**, insert) at 0.5 Hz resulted in an approximately 50% blockade in this current after application of 3µM acacetin. Increasing the voltage command rate to 4 Hz significantly increased the relative fractional block to approximately 63% (**Figure 1C**).

#### Modeling Effect of Acacetin on Ito, IKr, and IKs

In addition to inhibiting IKur in the atria, acacetin potently blocks both Ito and IK,ACh, and also modulates IKr and IKs, exhibiting multiple K+-current block. The parameters of Hill equations describing use-dependent inhibitions of these channels by acacetin are shown in **Table 1**. In the simulations, the effects of acacetin on these channels were modeled using a simple pore block model (Yuan et al., 2015). In the present study, we did not simulate the effects of acacetin on IK,ACh inhibitions as the role of autonomic regulation on AF is beyond the scope of the study.

#### Simulations of the Effects of Acacetin on Human Ventricle

The effects of acacetin on human ventricular APs are unknown, although experimental data demonstrated that acacetin at 30µM did not affect the heart rate and QT interval in isolated rabbit hearts (Li et al., 2008). In the present study, it was assumed that similar effects on the K<sup>+</sup> currents (Ito, IKr, IKs) in atrial myocytes could be extrapolated to the ventricular myocytes. We acknowledge that IKur is negligible in ventricles (Ravens and Wettwer, 2011), therefore in simulations of blocking IKur alone, the ventricular electrophysiology was not affected.

#### Tissue Models

The effects of acacetin and INa blockers on atrial and ventricular electrophysiology were further evaluated using tissue models. The monodomain equation (Clayton et al., 2011) was employed to simulate the excitation wave propagation in the myocardium. 1D models of human atrial strands were used to quantify the effects of channel blockers on atrial conduction velocity and APD restitution properties. Changes in ventricular depolarization and repolarization in response to these drugs were evaluated using a 1D model representing a transmural strand of ventricular tissue. In order to evaluate the antiarrhythmic effects of the channel blockers on re-entrant excitations in atria in the setting of cAF-induced remodeling, both idealized 2D models representing an isotropic slab of atrial tissue and an anatomically accurate 3D model of the human atria (Aslanidi et al., 2011; Colman et al., 2013, 2017; Whittaker et al., 2017) were employed to simulate the behavior of re-entrant excitations in atrial tissue. Pseudo-ECGs (pECGs) (Gima and Rudy, 2002; Baher et al., 2006) were computed as a measure of the excitation rates of intissue with sprial excitation waves. Detailed descriptions of these tissue models and pECGs are given in Online Supplementary Material 1.2, 1.3.

#### RESULTS

The updated Colman et al. human atrial model was first used to simulate effects cAF-induced remodeling on the

frequencies plotted against the pulse number of the voltage step. The simulated data (lines) were compared with experimental values (squares). The relative fraction was obtained by normalizing the end-step current measured from each pulse following application of acacetin to that of control. Experimental data were digitalized from Wu et al. (2011).

action potential (AP) and calcium transient (CaT). Details are presented in Online Supplementary Material 2.1. The resultant changes in APD, APD restitution and CaT following cAF-induced remodeling as compared to those under the normal condition showed good agreement with previous experimental (Bosch et al., 1999; Osaka et al., 2000; Workman et al., 2001; Dobrev and Ravens, 2003; Voigt et al., 2012) and simulation studies (Zhang et al., 2005; Grandi et al., 2011; Colman et al., 2013, 2017; Wilhelms et al., 2013).

# Effects of Application of Acacetin on Human Atrial Cells

To reveal the roles of inhibition of individual channels by acacetin in modulating cellular AP by acacetin, both the individual and combined block of Ito, IKr, IKur, and IKs by acacetin (3.2µM) in simulated SR at cycle length 1,000 ms without (normal) or with cAF-related electrical remodeling were simulated. **Figures 2A,B** illustrates the effects of individual and combined K+ channel block by acacetin on AP waveform. The alterations to APD relative to the control are summarized in **Figures 2C,D**.

In the absence of electrical remodeling, in normal myocytes at a cycle length of 1,000 ms, simulated IKs or IKr block by acacetin (3.2µM) presented no significant alterations to the atrial AP: although the atrial repolarization was delayed by 1.3 and 5.9 ms, respectively, the plateau phase was not affected, which is consistent with the minimal potency of acacetin on these channels (**Table 1**). Similar effects were also obtained from our simulated IKr and IKs block by the compound in the cAFremodeled atrial cells.

Selective block of Ito (alone) by acacetin elevated the atrial plateau potential in both normal and cAF-remodeled myocytes paced at 1 Hz, and this led to modest prolongations in APD<sup>30</sup> (by 6.4 and 3.6 ms for normal and AF-remodeling myocytes, respectively). The changes in APD<sup>90</sup> due to Ito block varied between the two conditions: under normal conditions the atrial APD<sup>90</sup> was shortened by 2.4 ms, whereas it was prolonged by 3.7 ms following cAF-remodeling at a stimulus rate of 1 Hz.

In contrast, blocking IKur alone by acacetin resulted in a pronounced alteration to the shape and duration of the AP in both normal and cAF-remodeled myocytes. The inhibition in IKur significantly elevated the plateau potential of atrial AP (by 7.1 and 5.7 mV in normal and cAF-remodeled myocytes, respectively), and this was accompanied by marked prolongations in APD<sup>30</sup> (by 105.9 and 23.6 ms in normal and cAF-remodeled myocytes, respectively). The prolongation in APD<sup>90</sup> induced by the IKur block was 9.8 ms for normal atrial cells, and was more pronounced (23.6 ms) in cAFremodeled myocytes, despite that IKur was down-regulated by cAF-remodeling.

We note that combined effects of acacetin (3.2µM) on multiple K+-currents produced greater alterations to the AP than those of any individual blocking effect. We have quantified effects produced by the combined block and compared it with the sum of the changes seen in each individual block. Synergistic effects were observed in the changes in APD90, represented by a further prolongation of 9.3 and 1.1 ms in APD<sup>90</sup> in normal and cAFremodeled myocytes, respectively. Additionally, the effects of IKur block dominated the AP-modulation by the compound, which is consistent with the high potency of acacetin on the channel (**Table 1**).

# Effects of Sodium Blocker and Acacetin on cAF-Remodeled Atrial Myocytes and Ventricular Cells

#### Effects on Single Myocyte AP and INa

Individual and combined effects of Na+-block (indicated by Bl·INa) and K+-block by acacetin (3.2µM) on human atrial electrophysiology after cAF-remodeling were simulated to assess any anti-AF benefits. Effects of acacetin (representing K+-block) were simulated in different settings: (i) IKur block alone (denoted by Bl·IKur) and (ii) combined block of all K+-currents in **Table 1** (denoted by Comb·Bl·IX). In addition, the effects of Na+- and K <sup>+</sup>- block on human ventricular myocytes were also studied to assess the atrial-selectivity of the block. The results are shown in **Figures 3A–C** and quantitative measurements are shown in **Figures 4A–C**.

For atrial myocytes paced at 1 Hz, Bl·IKur, and Comb·Bl·I<sup>X</sup> prolonged atrial APD (**Figure 4Ai** and as presented in Effects of Application of Acacetin on Human Atrial Cells) whilst their effects on peak INa were minimal (reducing peak INa by less than 0.3%). Bl·INa alone slightly reduced the peak INa by 1.63% without affecting the APD. The fractional inhibition in INa by INa-block was slightly increased by the addition of Bl·IKur or Comb·Bl·I<sup>X</sup> (**Figure 4Aii**). In the ventricles, the simulated application of acacetin induced a prolongation of 19.5 ms in APD<sup>90</sup> compared with that in control (drug-free) condition (**Figures 3B**, **4Ci**). Bl·INa alone showed a negligible inhibitory effect on the ventricular INa (by 0.42%), which was also not affected by combining Bl·INa and Comb·Bl·I<sup>X</sup> (**Figure 4Cii**).

In atrial myocytes paced at 6 Hz, AP alternans were observed under the drug-free condition (**Figure 3Ci**): the APD varied between 100.1 and 88.1 ms. In the presence of AP alternans, the changes in APD by the Na+- and K+- blockers were quantified by comparing the corresponding big APs at baseline and after drug actions. These values were selected based on the characteristics of AP (APD prolongations seen in the long AP, and reduced INa for the short AP) that may be anti-arrhythmic. The fractional reductions in peak INa were calculated from the INa associated with the shorter APs. The results showed that applying Bl·IKur or Comb·Bl·I<sup>X</sup> alone both abolished the AP alternans while prolonging the APD to 116.3 and 126.3 ms and reducing the peak INa by 5.9 and 20.1%, respectively. The application of Bl·INa alone produced a minor APD prolongation (3.5 ms) and a reduction of 16.2% in peak INa. Combining block of INa with Bl·IKur or Comb·Bl·I<sup>X</sup> promoted the genesis of AP alternans, resulting in substantial prolongations in the APD of the big APs (by 35.4 ms for Bl·IKur + Bl·INa, and 55.6 ms for Comb·Bl·I<sup>X</sup> + Bl·INa) and dramatic decreases in the peak INa (by 57.5% for Bl·IKur + Bl·INa and 88.2% for Comb·Bl·I<sup>X</sup> + Bl·INa) in the corresponding small APs. These results suggest that the combined block of Bl·INa and Comb·Bl·IX/Bl·IKur exhibited synergistic antiarrhythmic effects manifested by prolongation in APD and reduction in peak INa. However, an increased susceptibility to AP alternans was observed at a fast pacing rate of 6 Hz, which may be potentially proarrhythmic at fast heart rates.

#### Effects on Steady-State Restitutions of APD and Conduction Velocity

Steady-state APD restitutions of cAF-remodeled human atria were simulated at both the cellular and tissue levels. In single myocyte simulations (Figure S5 in Online Supplementary Material 2.2), APD was prolonged over the entire range of simulated basic cycle lengths (BCL) for Bl·IKur and Comb·Bl·I<sup>X</sup> as compared to the control (drug-free) conditions. The reduction in peak INa in Bl·INa was rate-dependent and significantly greater at fast pacing rates. K+-block alone (Bl·IKur or Comb·Bl·IX) slightly shifted the rate-dependence of peak INa to larger BCLs. In comparison to the effects of individual current block scenarios, synergistic reductions in peak INa were observed following combined blocks of Bl·INa with Bl·IKur or Comb·Bl·I<sup>X</sup> over a wide range of BCLs. As compared to the drug-free conditions, AP alternans were observed at greater BCLs after K+-block, and this was further increased by combined Na+- and K+-block (Figure S5 in Online Supplementary Material 2.2).

.

FIGURE 3 | Simulated AP and INa traces of cAF-remodeled atrial myocytes and ventricular cells in response to Na+- and K+- block regimens. (Ai) APs from

#### Effects of Combined Na+- and K <sup>+</sup>- Block on the AF-Selectivity of INa block

AF-selectivity of Na<sup>+</sup> blockers in cAF-remodeled hearts was examined by varying the drug binding and unbinding constants over wide parameters spaces to provide information concerning drug-Na+-channel interactions for various drug candidates. This was done by independently changing L<sup>A</sup> and L<sup>I</sup> for fixed {KA, KI} (Online Supplementary Material 2.3); and then varying K<sup>A</sup> and KI for fixed {LA, LI}. In this way we obtained the maximum AF-selectivity over the parameter space of drug binding and unbinding kinetics. Simulations with varied K<sup>A</sup> and K<sup>I</sup> were repeated for Bl·INa + Bl·IKur and Bl·INa + Comb·Bl·IX.

**Figures 6A–D** illustrates the block efficacy (defined in Equation 4), rate-selectivity, atrial-selectivity and the resultant AF-selectivity for Bl·INa alone and the combined block as a function of K<sup>A</sup> and K<sup>I</sup> . For Bl·INa alone, the block efficacy increased with increase of K<sup>I</sup> , whereas the rate-selectivity was reduced by increasing K<sup>A</sup> or K<sup>I</sup> . The AF-selectivity reached a maximum value of 9 at K<sup>A</sup> = 1 and K<sup>I</sup> = 500 ms−<sup>1</sup> · M−<sup>1</sup> . The combined blocks achieved significantly greater AF-selectivity than Bl·INa alone: the maximum attainable AF-selectivity was increased by nearly 6-fold for Bl·IKur + Bl·INa and more than 14-fold for Comb·Bl·I<sup>X</sup> + Bl·INa as compared to Bl·INa alone (**Figure 6C**). These dramatic increases were attributed to the significantly greater values in all metrics contributing to the AF-selectivity. The maximal block efficacy achieved by Bl·INa alone was 0.77, and was increased to 0.81 and 0.94 for Bl·IKur + Bl·INa and Comb·Bl·I<sup>X</sup> + Bl·INa, respectively. A more appreciable increase in the maximal rate-selectivity was observed by the combined blocks as compared to Bl·INa alone (8-fold for Bl·IKur + Bl·INa and nearly 10-fold for Comb·Bl·I<sup>X</sup> + Bl·INa). Additionally, the atrial-selectivity was also increased by the combined block, although to a lesser extent. Bl·IKur + Bl·INa exhibited a greater atrial-selectivity than that of Comb·Bl·I<sup>X</sup> + Bl·INa since Bl·IKur was assumed to have no effect on the ventricles.

Furthermore, these simulations revealed that the block efficacy, rate-selectivity and atrial-selectivity were strongly

dependent on the inactivation state binding rate K<sup>I</sup> . These measures were also dependent on the open-state binding kinetics KA, but to a much lesser extent. The block efficacy was mainly determined by K<sup>I</sup> : an increase in K<sup>I</sup> led to a significant increase in the block efficacy. In combined block, the maximal rate- and atrial-selectivity were observed for K<sup>A</sup> = K<sup>I</sup> = 1 ms−<sup>1</sup> · M−<sup>1</sup> and increases in K<sup>I</sup> resulted in substantial reductions in the rate- and atrial-selectivity. In Bl·INa alone, the parameter set K<sup>A</sup> = 1 ms−<sup>1</sup> · M−<sup>1</sup> , K<sup>I</sup> = 200 ms−<sup>1</sup> · M−<sup>1</sup> produced a maximal value in atrial-selectivity. Collectively, the optimal K<sup>I</sup> that maximized AF-selectivity was 200 ms−<sup>1</sup> · M−<sup>1</sup> for Bl·INa and Bl·IKur + Bl·INa, and smaller (100 ms−<sup>1</sup> · M−<sup>1</sup> ) for Comb·Bl·I<sup>X</sup> + Bl·INa. The optimal K<sup>A</sup> = 1 ms−<sup>1</sup> · M−<sup>1</sup> was seen for all conditions. Increasing K<sup>A</sup> consistently resulted in a smaller rate- and atrial-selectivity and therefore reduced AF-selectivity. These results suggest that the inactivation-state binding rate might be a more favorable targeting parameter than the open-state binding kinetics in optimizing AF-selectivity of Na+-blockers.

#### Effects of INa and IKur Block on Spiral Excitation Events in cAF-Remodeled Atria Two-Dimensional Simulations

Using the cross-shock protocol, spiral waves were initiated in a 2D model representing a tissue slab of cAF-remodeled human atria. For each condition, a 10-s episode of electrical activity was simulated. Representative snapshots of the re-entrant waves in control (drug-free) and following application of drugs are presented in **Figure 7A**. The trajectories of the tips of re-entrant rotors under these conditions were traced and are shown in **Figure 7B**. The number of rotors during the time course of wave evolution was also measured (**Figure 7C**). The simulated pseudo-ECGs, membrane potential traces extracted from a representative

myocyte and the corresponding fractional block of INa and IKur are detailed in Online Supplementary Material 2.4.

Under the control (drug-free) condition, a single rotor was formed at approximately t = 630 ms; this broke into two spiral waves at t = 830 ms. These two rotors were stably anchored with star-shaped tip trajectories at the bottom half of the slab and persisted throughout the rest of the simulated 10-s episode (**Figures 7Ai,Bi,C**). In simulating drug actions, each drug was applied at t = 2,500 ms. For Bl·INa the dual rotors progressively became unstable, and the tips of the spiral waves meandered out of the tissue at approximately t = 6,000 ms, leading to selftermination of the re-entrant waves (**Figures 7Aii,Bii,C**). The dual rotors persisted throughout the period of the simulation after applying Bl·IKur alone (**Figures 7Aiii,Biii,C**). For Bl·INa + Bl·IKur, the rotor at the bottom left corner of the slab became unstable and meandered out of the tissue at approximately t = 3,800 ms, whereas the trajectory of the second rotor was confined to a small tissue area until t = 7,000 ms and then gradually became chaotic, forming up to 3 transient rotors that self-terminated at t = 8,334 ms (**Figures 7Aiv,Biv,C**). A

tissue slab in drug-free condition or after applying the drugs. (A) Snapshots of simulated re-entrant excitation events; The time sequence (ms) is indicated at the top left corner of each screenshot. (B) Tip trajectories of re-entrant waves. (C) Temporal evolution of total number of rotors represented by the number of spiral wave tips in tissue. In both (A,B), (i) Drug-free (CTL) condition, (ii) Bl·INa alone, (iii) Bl·IKur alone, (iv) Combined Bl·INa and Bl·IKur, (v) Applying Comb·Bl·I<sup>X</sup> alone, and (vi) Combined Bl·INa and Comb·Bl·IX. Rate constants for INa block: *<sup>K</sup><sup>A</sup>* <sup>=</sup> 1 ms−<sup>1</sup> · M−<sup>1</sup> , *<sup>K</sup><sup>I</sup>* <sup>=</sup> 100 ms−<sup>1</sup> · M−<sup>1</sup> , *<sup>L</sup><sup>A</sup>* <sup>=</sup> 1 ms−<sup>1</sup> , *<sup>L</sup><sup>I</sup>* <sup>=</sup> 0.01 ms−<sup>1</sup> .

similar but more marked effect was seen in the simulations that addressed the aggregate effects of acacetin: the bottom left rotor quickly meandered out of the tissue at t = 3,510 ms whilst the tip trajectory of the other rotor became chaotic and terminated at t = 5,439 ms (**Figures 7Av,Bv,C**). We note that the combined Bl·INa and Comb·Bl·I<sup>X</sup> exerted the strongest potency in terminating re-entrant excitations in these simulations: the two rotors transiently turned unstable and chaotic and selfterminated at t = 3,555 ms, with up to 5 rotors during the excitation in the slab (**Figures 7Avi,Bvi,C**).

The anti-arrhythmic benefits of combined Na+- and K+ block were clearly revealed by additional simulations assuming the use of a different Na+-blocker (K<sup>A</sup> = 1 ms−<sup>1</sup> · M−<sup>1</sup> , K<sup>I</sup> = 200 ms−<sup>1</sup> · M−<sup>1</sup> , L<sup>A</sup> = 1 ms−<sup>1</sup> , L<sup>I</sup> = 0.01 ms−<sup>1</sup> ) and at a reduced dose (75%) of both Na+-blocker and acacetin. The life span of reentrant excitations was measured and shown in **Figure 8A**. Also, the pECG was computed and the segment from t = 3,000 ms to 500 ms before the termination of re-entries (or the end of the simulation if the rotor sustained) was analyzed using the Fast Fourier Transform to obtain the dominant frequency (DF) of the re-entrant excitations, which is illustrated in **Figure 8B**.

At the simulated doses of acacetin, applying Bl·IKur alone did not lead to termination of re-entrant waves within the duration of the simulation (7,500 ms after TDrug), whereas the rotors were terminated in the simulations for Comb·Bl·I<sup>X</sup> at both doses (**Figure 8Ai–iv**), thus demonstrating enhanced anti-AF benefits of combined K+-channel block. For the simulated Bl·INa alone, the Na+-blocker with K<sup>I</sup> = 100 ms−<sup>1</sup> · M−<sup>1</sup> led to termination of AF at the control dose (lifespan of 4,102 ms) but not at the reduced dose; increasing K<sup>I</sup> of the Na+-blocker to 200 ms−<sup>1</sup> ·M−<sup>1</sup> resulted in a reduced lifespan (1,305 and 1,459 ms for [DNa<sup>+</sup> ] = 60 and 45 µM, respectively). The lifespan for the combined Bl·INa + Comb·Bl·I<sup>X</sup> was consistently shorter than that of any individual applications of Bl·INa or Comb·Bl·I<sup>X</sup> alone in all cases. A similar augmented anti-arrhythmic effect (shown as shortened lifespan of re-entry) was also observed for the combined Bl·INa <sup>+</sup> Bl·IKur for [DNa<sup>+</sup> ] <sup>=</sup> <sup>45</sup> <sup>µ</sup>M and <sup>K</sup><sup>I</sup> <sup>=</sup> 200 ms−<sup>1</sup> · M−<sup>1</sup> (**Figure 8Aiv**) but not for the rest of the cases.

A consistent decrease in the DF was observed in the drugmodulated re-entrant excitations as compared to those in the drug-free condition (**Figure 8Bi–iv**). In the drug-free condition, the DF extracted from the pECG was 8.63 Hz, which is within the range of similar clinical data (Jarman et al., 2012). Applying Na+- or K+- block individually resulted in slowing of the rate of the rotors, and this was dependent on the concentrations and parameters of the blockers. For Bl·IKur the DF was 8.25 Hz

comparison. In the left column (i,iii) of (A,B), Bl·INa was simulated with *<sup>K</sup><sup>I</sup>* <sup>=</sup> 100 ms−<sup>1</sup> · M−<sup>1</sup> ; in the right column (ii,iv), *<sup>K</sup><sup>I</sup>* <sup>=</sup> 200 ms−<sup>1</sup> · M−<sup>1</sup> . In the top panels (i,ii) of (A,B), [*DK*<sup>+</sup> ] <sup>=</sup> 3.2µM, [*DNa*<sup>+</sup> ] <sup>=</sup> <sup>60</sup>µM; in the bottom panels (iii,iv), [*DK*<sup>+</sup> ] <sup>=</sup> 2.4µM, [*DNa*<sup>+</sup> ] <sup>=</sup> <sup>45</sup> <sup>µ</sup>M. In all panels, *<sup>K</sup><sup>A</sup>* <sup>=</sup> 1 ms−<sup>1</sup> · M−<sup>1</sup> , *<sup>L</sup><sup>A</sup>* <sup>=</sup> 1 ms−<sup>1</sup> , *<sup>L</sup><sup>I</sup>* <sup>=</sup> 0.01 ms−<sup>1</sup> .

with the control dose and 8.30 Hz for the reduced dose. In the simulations with Comb·Bl·IX, the DF was 6.63 Hz and was not affected by the 25% reduction in the dose of the compound. For Bl·INa alone the DF was 7.81 Hz and substantially smaller (6.24 Hz) for Na+-blockers of K<sup>I</sup> = 100 ms−<sup>1</sup> · M−<sup>1</sup> and K<sup>I</sup> = 200 ms−<sup>1</sup> · M−<sup>1</sup> , respectively. An enhanced deceleration of the rotors was observed for Bl·INa + Bl·IKur in all cases. The DF for simulations with Comb·Bl·I<sup>X</sup> + Bl·INa was not computed due to the short lifespan in these events.

#### 3D Simulations

The antiarrhythmic effects of acacetin and Na+-block on the reentrant waves in the cAF-remodeled atria were also evaluated using our 3D anatomical model of the human atria (Colman et al., 2013, 2017). A 10-s episode of sustained re-entrant excitation was first initiated in the cAF-remodeled atria in the drugfree condition; this produced the initial conditions of the 3D model for additional 10-s episode simulations. Next, the behavior of electrical waves of another 10-s episode simulation in the drug-free condition and after applying the selected blockers was analyzed and compared. **Figure 9A** shows snapshots of excitation wave evolution following the 10-s episode of re-entrant excitation events. pECGs computed from the excitation waves are shown in **Figure 9Bi–iv**. **Figures 9C,D** illustrates power spectrum analyses of the pECGs and a comparison of the lifespan of the electrical waves in the drug-free condition and after applying the drugs/blockers. In the drug-free condition, stable reentrant waves around the pulmonary veins and left atrium were observed; the power spectrum density (PSD) manifests a singlefocused peak around 8.16 Hz. Following applying Bl·INa, the reentrant waves became less organized and also decelerated. This was characterized by a smaller dominant frequency (6.58 Hz) and less focused PSD distribution; the excitation was not terminated. Following the application of Comb·Bl·IX, the re-entrant wave soon became unstable and eventually disappeared after t = 3,279 ms. Note that the peak PSD amplitude was much smaller and its distribution was much broader as compared to the drug-free condition. The combined drugs further destabilized the re-entrant waves and reduced the lifespan to approximately 1,120 ms.

# Simulated Effects of Acacetin and Na+-Current Blocker on the QT Interval

Further simulations were performed using a 1D ventricular transmural strand model to evaluate the changes in the waveform of electrograms in consequence of applying the drugs. A comparison of the computed electrogram waveforms are illustrated in **Figures 10A,B**, and the QT intervals are quantified in **Figure 10C**. Blocking small fractions of IKr, IKs and Ito in the human ventricles by acacetin slightly increased the QT interval by 21 ms. The electrograms were not noticeably affected by applications of the Na+-blocker with the simulated parameters. Results from both cases did not show dramatic QT prolongation, indicating no dramatic effects affecting ventricular repolarization process which might promote ventricular arrhythmias.

# DISCUSSION

Even decades after goal-directed work, successful development of effective and safe antiarrhythmic drugs for treating AF has not been accomplished and remains a major unmet clinical need. In a recent study on the canine heart, enhanced anti-arrhythmic effects and AF-selectivity of INa blockade by additional IKur block was demonstrated (Aguilar et al., 2015). Whether similar effects could be obtained in the human atria, especially following cAF-induced electrical remodeling which reduces IKur, remained unclear. How the combined Na<sup>+</sup> and K+-block modulates the QT interval also remained incompletely understood. In this study, the effects of IKur (combined with a modest block in Ito, IKr, and IKs as presented by acacetin, a compound shown to be effective in anti-AF treatment) and INa block (two potentially effective atrial-selective block on human atrial electrophysiology) were investigated in silico using multiscale models of the human atria and state-dependent block scheme. The simulation results demonstrate that both Na+-block and K+-block exhibited anti-arrhythmic effects in the atria following cAF-remodeling, despite reduced IKur by the remodeling. The present study highlighted that in addition to combined Na+- and K+-block, combined multi-K+-channels also exerted beneficial synergistic antiarrhythmic effects when compared with single channel block whilst having modest impact on ventricular repolarization (QT interval). This study suggests that multi-channel block (either combined Na+-K+-block, or combined multi-K+-block) may be a favorable strategy for the development of novel pharmaceutical therapies for AF.

# Effects of INa block

An atrial-ventricular difference in the properties of INa, especially in the voltage dependence of steady-state inactivation, has been reported (Li et al., 2002; Burashnikov et al., 2007; Chen et al., 2016; Fan et al., 2016; Caves et al., 2017). In these studies, the voltage dependent steady-state inactivation curves for INa were found to be negatively shifted (by 5–16 mV) in atrium as compared to the ventricular parameters. This difference gave rise to an on-going interest in developing an atrial-selective blocker of INa as a strategy in terminating AF (Burashnikov et al., 2007; Antzelevitch and Burashnikov, 2009; Zygmunt et al., 2011; Morotti et al., 2016; Caves et al., 2017). As was done in previous studies (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015), in this study, the kinetic parameters in drug actions of Na+ blockers were varied over wide parameter spaces to reveal AFselectivity of Na+-blockers in the ventricles and fibrillating atria. Our results demonstrated that in the presence of AF-remodeling, an atrial-selective block of INa could produce different effects between atrial and ventricular cells (**Figures 3**, **4**) and that the AF-selectivity could be maximized by optimizing the binding and unbinding rates of the Na+-blocker (**Figure 6**). Note also that, the fractional inhibition of INa by the Na+-blocker exhibited a substantial dependence on the rate of pacing (**Figures 3**, **4** and Online Supplementary Material 2.2), which was quantified using the rate-selectivity (**Figure 6**).

At the cellular level, Na+-block resulted in a significant inhibition in INa at fast pacing rates, but minor effects within

the range of normal heart rates in the atria (**Figures 5**, **6**). The antiarrhythmic effects of these changes were demonstrated in simulations of multicellular atrial tissue. In a 1D atrial strand model, applying Na+-block progressively enhanced the rateadaptations of Vmax and CV over a larger range of BCLs, whereas the atrial APD was not affected. At fast pacing rates, Vmax and CV were decreased significantly, suggesting reduced excitabilities of atrial myocytes (**Figure 5**). These results are in concordance with the recent study (Aguilar et al., 2015) where similar effects of Na+-block on the canine atria were demonstrated in silico and experimentally in coronary-perfused hearts.

In 2D tissue simulations, this Na+-block shortened the lifespan and caused slowing in the excitation rate of the spiral waves (**Figures 7**, **8**). In the 3D anatomical model, applying Na+-block alone produced antiarrhythmic effects by slowing the re-entrant excitations (**Figure 9**). Furthermore,

in our 1D model of transmural ventricular strand, the simulations suggested that the Na+-block had minimal impact on ventricular repolarization, as judged by modest QT interval prolongation. These results demonstrated that Na+-block could be beneficial in suppressing re-entrant activities in the cAF-remodeled atria, with modest impact on ventricular repolarization.

# Effects of K+-Current Block

K <sup>+</sup>-current blockers delay the repolarization phase of the AP and thus prolong atrial APD and refractory period. This can cause disruptions and eventually termination of the re-entrant circuits (Hancox et al., 2016). However, K+-channel blockers such as dofetilide and sotalol (which potently inhibit IKr) have a substantial risk of prolonging QT interval and promoting Torsades de pointes arrhythmias (Hondeghem and Snyders, 1990; Yap and Camm, 2003). In principle, blocking atrial-specific K+ channels may exert antiarrhythmic effects in the atria while minimizing potential risks of adverse effects in the ventricles. IKur is believed to be such an atrial-selective substrate for drug interventions, and effects of IKur block have been extensively studied (Burashnikov and Antzelevitch, 2008; Li et al., 2008; Tsujimae et al., 2008; Almquist et al., 2010; Pavri et al., 2012; Scholz et al., 2013; Loose et al., 2014; Ford et al., 2016). Interestingly, many existing IKur blockers potently block other K <sup>+</sup>-channels including Ito and IK,ACh (Gögelein et al., 2004; Wirth et al., 2007; Burashnikov and Antzelevitch, 2008; Li et al., 2008). The additional blockades of these channels may contribute to the antiarrhythmic effects of those drugs, which warrant further investigations.

In this study, acacetin, a compound initially isolated from the traditional Chinese medicine Xuelianhua, was selected as a representative IKur blocker. The effects of acacetin on atrial electrophysiology were evaluated in two ways: (a) the effects of acacetin blocking IKur only; and (b) the full actions of acacetin on the targeting channels (Ito, IKur, IKr, and IKs) (Li et al., 2008). This approach allowed for investigations into the effects of IKur block alone as well as the potential benefits of additional-but-modest inhibition of other K+-currents in the human atria.

#### Selective IKur Block

Blocking IKur with 3.2µM acacetin exerted APD prolongation (9.8 ms) under the baseline/normal conditions (**Figure 2**). Experimental data show that dependent on the baseline AP waveform the effect of IKur block on human atrial APD70−<sup>90</sup> under normal (SR) conditions can manifest as prolongation or shortening in the APD, (Workman et al., 2001; Wettwer et al., 2004; Schotten et al., 2007; Burashnikov and Antzelevitch, 2008; Loose et al., 2014). Additionally, the prolongation in APD by IKur block observed in the present study is similar to our previous paper (Colman et al., 2017) concerning the effects of genetically down-regulated IKur. Moreover, inhibiting IKur under normal conditions elevated the AP plateau potential and prolonged APD<sup>30</sup> (**Figure 2**). Both effects matched well with experimental studies (Workman et al., 2001; Wettwer et al., 2004; Schotten et al., 2007; Burashnikov and Antzelevitch, 2008; Loose et al., 2014) and our simulation study (Colman et al., 2017).

We note that in the cAF-remodeling cells, a more pronounced prolongation in APD (by 23.6 ms for 1 Hz and 16.2 ms at 6 Hz, **Figure 4**) was observed in the presence of 3.2µM acacetin, despite that this current was down-regulated by cAF-remodeling (Wagoner et al., 1997; Brandt et al., 2000; Christ et al., 2008). These results are in accordance with previous experimental results of blocking IKur with MK-0448 (Pavri et al., 2012; Loose et al., 2014). In addition, IKur block exhibited enhanced ratedependent adaptations in APD both at the cellular (Online Supplementary Material 2.2) and 1D strand models (**Figure 5**). Importantly, the CV restitution curve shifted toward higher BCLs, indicating that this tissue is less capable of conduction of atrial excitation waves at high rate while maintaining conduction of slow waves (**Figure 5**). In 2D tissue simulations, applying IKur block alone (3.2µM acacetin) destabilized the cores of rotors (i.e., potential organizing centers for AF), and slightly slowed their excitation rates, but failed to terminate them (**Figure 7**), suggesting a limited efficacy of terminating AF by IKur block alone. Similarly, a recent modeling study by Aguilar et al. (2017) suggested that the antiarrhythmic efficacy of IKur block was substantially decreased in the presence of AF-induced electrical remodeling. Also, the experimental study (Burashnikov and Antzelevitch, 2008) showed that block of IKur by 4-AP of small doses had limited efficacy in suppressing AF in canine atria. This may represent the fact that IKur is reduced at high frequencies (as discussed/suggested in Feng et al., 1998a; Burashnikov and Antzelevitch, 2008; Wu et al., 2011) and shown in **Figure 1**) as well as by cAF-induced remodeling (Wagoner et al., 1997; Brandt et al., 2000; Christ et al., 2008). In addition, IKur is primarily active during phase 2 of AP, and hence pure IKur block exerted a relatively greater prolongation in APD<sup>30</sup> than APD<sup>90</sup> (**Figure 3**), in contrast to other K+-block including dofetilide which mediates anti-AF effects by prolonging the terminal phase of the AP (Roukoz and Saliba, 2007).

In this study, IKur block was simulated using a state-dependent block model, which successfully reproduced the use- and ratedependent inhibition of acacetin (**Figure 1**). The rate-dependent block of IKur exerted a higher fractional inhibition in the current at faster pacing rates, which likely produces greater anti-AF effects in the presence of high-frequency excitations as seen during AF. Along with the previous modeling studies on investigating effects of IKur block (Almquist et al., 2010; Scholz et al., 2013; Ellinwood et al., 2017), this study demonstrated the importance of explicitly considering the kinetic properties of the block in computational efforts of understanding the consequences and underlying mechanisms of IKur block.

#### Effects of Combined K+-Current Block

The combined K+-block (as exhibited by acacetin and many other IKur blockers) resulted in synergistic APD prolongation as well as an increased efficacy in terminating re-entry in tissue as compared to the pure IKur block.

Note that at the single myocyte level, the combined actions of acacetin produced greater prolongation in atrial APD than the sum of changes due to drug-induced block of individual channel in normal and cAF-remodeled myocytes (**Figure 2**). Additionally, the combined K+-block increased the rateadditivity of APD as compared to the pure IKur block (Online Supplementary Material 2.2). This was also consistently observed in the 1D simulation (**Figure 5**). In the setting of pure IKur block, the elevated and prolonged plateau phase of the AP could promote the activation of IKr/IKs, which in return may accelerate the repolarization of AP-phase 3 (Colman et al., 2017). Therefore, additional inhibition in IKr by an identical fraction is expected to result in a greater APD prolongation than a pure IKur or IKr/IKs block.

In 2D simulations, the combined K+-block produced an enhanced efficacy in suppressing AF compared with the pure IKur block: promoting meandering of rotor tips (**Figure 7B**), shortening the lifespan of re-entries (**Figure 8A**) and slowing of spiral wave excitations (**Figure 8B**). Rotor meandering is one mechanism by which spiral waves may meet non-conducting boundaries to extinguish re-entry (Narayan et al., 2013; Pandit and Jalife, 2013; Rappel et al., 2015).

The effects of acacetin (3.2µM) on the ventricular AP and QT interval was assessed in a single cell model and 1D transmural strand model by assuming similar blockade effects of the compound on the human ventricles and atria. It was shown that following applying acacetin, the ventricular repolarization and QT interval was both preserved with slight prolongations around 21 ms (**Figure 10**). Our results are close to the previous experimental study (Li et al., 2008) showing that QT intervals were not prolonged by acacetin in isolated rabbit hearts and anesthetised dogs.

The synergistic effects demonstrated by the combined K+ blocks have implications on developing novel pharmaceutical anti-AF therapies. Given that Ito, IKr and IKs contribute to the repolarizations of ventricular APs, inhibitions in these channels may promote risks of side effects in the ventricles. In this regard, combined block of atrial-specific K<sup>+</sup> channels may be favorable. Recently, another two families of K+-channels that are dominantly expressed in the atria have been acknowledged: the small-conductance Ca2+-activated K<sup>+</sup> (SK) channels (ISK) (Qi et al., 2014), and the two-pore K<sup>+</sup> (K2P3.1) channel (ITASK−1) (Schmidt et al., 2015), further to the well-known constitutively active acetylcholine-activated K<sup>+</sup> current (IK,ACh). Combined block of these atrial-specific channels may exert greater and safer antiarrhythmic effects in the atria, warranting future investigations.

#### Synergistic Effects of Combined Na+- and K <sup>+</sup>- Block

The present study reveals novel and significant synergistic effects of combined block of Na+- and K+-currents (INa and pure-IKur/multi-K+-block) and demonstrates the additional synergistic anti-arrhythmic effects derived from the multi-K<sup>+</sup> channel block in cAF-remodeled atria.

In cAF-remodeled atria, combined Na+- and K+-block significantly increased the fractional INa inhibition and APD prolongation (**Figures 3**, **4**) and promoted pronounced AP alternans at 6 Hz, with complex effects in human AF (Narayan et al., 2011). In the simulations varying the blockade kinetics of INa block, the combined block dramatically augmented the attainable maximal AF-selectivity in consequence of enhanced atrial-selectivity and rate-selectivity as compared to the pure Na+-block (**Figure 6**).

In the 1D model of an atrial strand, combined Na<sup>+</sup> and K <sup>+</sup>-block produced synergistic reductions in Vmax and CV; the threshold of BCL allowing a 1:1 conduction was increased as compared to the control conditions (**Figure 5**). In simulated re-entrant waves in 2D and 3D atria, the combined Bl·INa + Comb·Bl·I<sup>X</sup> exhibited a greater efficacy in suppressing AF, with a decreased lifespan of rotors as compared to that by either individual block (**Figures 7**–**9**). Although the combined Bl·INa + Bl·IKur did not further reduce the lifespan of spiral waves as compared to the Bl·INa alone, the combination did lead to the extinction of one of the two rotors (**Figures 7Aiv,Biv**) and deceleration of re-entrant activations (**Figure 8B**). Follow-up simulations showed that consistent synergistic antiarrhythmic effects could be obtained with reduced doses of Na+- and K+ blockers.

The non-specific multi-channel blockade is increasingly recognized as a strategy for pharmaceutical therapy of AF both experimentally (Sicouri et al., 2010; Aguilar et al., 2015; Kirchhoff et al., 2015; Hartmann et al., 2016) and clinically (Koskinas et al., 2014; Reiffel et al., 2015). In a previous study (Aguilar et al., 2015), synergistic anti-arrhythmic effects were demonstrated both in silico and experimentally in healthy canine hearts. Additionally, the favorable synergistic antiarrhythmic effects have also been reported in combined block of ISK and INa in an experimental atrial-fibrillated guinea pig model (Kirchhoff et al., 2015). Also, the recent HARMONY trial (Reiffel et al., 2015) revealed synergistic AF-suppressing effects for combined use of ranolazine and dronedarone. While revealing the synergistic effects of combined Na+- and K+- block in cAF-remodeled human atria, this study supports and adds insights into the ongoing efforts in developing multi-channel block as a strategy for the treatment of AF.

#### Limitations and Future Work

In the absence of the required detailed experimental data, when simulating effects of acacetin on Ito, IKs and IKr, the dosedependence block of acacetin was assumed to be identical in both human atrial and ventricular cells. This assumption may warrant further investigations. In addition, the parameters of atrial Ito have been reported to be different from those of ventricular Ito in human (Amos et al., 1996). Previous studies reported that the IC<sup>50</sup> of 4-AP block of atrial Ito was one-third of that of ventricular Ito (Amos et al., 1996; Nattel et al., 2000). If a similar atrial-vs.-ventricular difference in the IC<sup>50</sup> of Ito and/or IKr/IKs could exist for acacetin, the effects of acacetin on the ventricular electrophysiology would be less significant than our simulations, which might result in to a smaller change in ventricular INa and APD for the combined block of Bl·INa and Comb·Bl·IX, and thus enhance the computed atrial-selectivity and AF-selectivity of the combined block. Given that applying acacetin in vivo did not prolong QT intervals in isolated rabbit hearts and anesthetised dogs (Li et al., 2008), any significant prolongation of the ventricular APD and QT interval is unlikely (**Figures 3B**, **4C**, **10**). Therefore, our assumption of no atrial-ventricular difference in the potency of acacetin on K+-currents may not affect our conclusions concerning the atrial-selectivity of combined Na+ and K+-block.

Additionally, in the absence of detailed experimental data for state-dependent block of Ito, IKr, and IKs by acacetin, the block of these channels was modeled using a single pore block model. The IC50 values (**Table 1**) were determined by fitting the concentration-response relation of the step current at 40 mV in previous experimental studies (Li et al., 2008; Wu et al., 2011). A recent study suggests that the IC50 values may be dependent on the voltage protocols applied, and this cannot be reflected by single pore models. In future studies, the pore block model for Ito, IKr, and IKs can be replaced by a state-dependent block model when such experimental data become available. Also, the present work did not attempt to model the effects of acacetin on IK,ACh, although the study shows the current is potently blocked by the compound. The 2D and 3D simulations of atrial tissue, while validated, may not fully capture the complexity of fibrosis-tissue interfaces which are seen in structurally remodeled atria and were not simulated in these monodomain experiments.

Thirdly, our simulation results showed a moderate QT prolongation of around 20 ms following applying both INa blocker and acacetin. While a QT prolongation of less than 5 ms does not raise a regulatory concern (Committee for Medicinal Products for Human Use, 2012), implications of QT prolongations between 5 and 20 ms remain inconclusive (Committee for Medicinal Products for Human Use, 2005). In the present study, though the extent of QT prolongation of 20 ms is far less than the threshold of discontinuation criteria of 60 ms as indicated in Committee for Medicinal Products for Human Use (2005), it would indeed raise a positive flag in thorough QT tests and necessitate extended safety assessment and intensive patient monitoring during late stages of trials (Committee for Medicinal Products for Human Use, 2012). On the other hand, the approach we used in accounting for the effects of acacetin on ventricular myocytes may result in upper bound of QT prolongation, since the potency of acacetin was assumed to be identical in atria and ventricles.

Fourthly, the threshold in BCL inducing AP alternans was increased by K+-block (**Figure 5**, Figure S5). However, AP alternans seen at slower pacing rates has been linked with occurrence of AF (Narayan et al., 2002, 2011). Therefore, the increased threshold in BCL developing AF by K+-block can be potentially proarrhythmic. The safety of K+-block and its proarrhythmic potential in the atria should be addressed in future studies.

Fifthly, there are limitations in the approaches used in simulating the INa blockers in single myocytes and tissue. Similar to previous studies (Aguilar-Shardonofsky et al., 2012; Aguilar et al., 2015), in our simulations, the drug action on INa was modeled through a state-dependent block assuming drugs binding to both activated and inactivated states of INa, and the gating variables of INa were modeled using an Hodgkin-Huxley scheme. The limitations in this approach outlined in Aguilar-Shardonofsky et al. (2012) therefore apply in the present study. The results of the use-dependent block may be affected by the models used (Aguilar-Shardonofsky et al., 2012). However, the previous study (Aguilar-Shardonofsky et al., 2012) compared this modeling scheme with simulations using a Markov model, showing qualitative agreement in major findings. Therefore, the major conclusions drawn from this study may not be affected by the selected modeling approach for INa and drug interactions. Furthermore, in optimizing the AFselectivity of the INa and K+-current blockers, the concentrations of Na<sup>+</sup> and K<sup>+</sup> blockers were fixed at 60 uM. This may potentially impose limitations in discomposing the role of the binding parameters in the modulatory effects of the blockers because of the very slow kinetics of the drug binding to its targeted channel at this high concentration. It warrants further studies by varying the concentration of blockers to simulate the optimized effects of the AF-selectivity of INa blocker. In tissue simulations, effects of drugs were modeled by increasing their doses homogeneously, simultaneously and instantaneously. The realistic actions of INa blockers in tissue, however, may be different. Also, in tissue simulations a homogenous cell model was used. As previous study (Feng et al., 1998b) showed atria are electrically heterogeneous, future work is needed to

assess how tissue heterogeneities affect the efficacy of atrialselective pharmaceutical interventions. Furthermore, the current simulations did not take the cardiac autonomic regulation into account in order to take into considerations of acacetin on IKACh. Future studies on interactions of atrial-selective anti-arrhythmic drug actions and autonomic systems may also render valuable findings.

It is important to acknowledge that administration of class Ic agents for Na+-block can cause cardiac arrhythmia and increased mortality (Echt et al., 1991). Further investigations are therefore warranted to assess the safety of the simulated Na+-block in the heart, especially in the ventricles.

# CONCLUSIONS

By using state-dependent drug block models and our mathematical models of the human atria, the antiarrhythmic effects of atrial selective Na+- and K+-blockers on the cAFremodeled atria were evaluated. The combined block of multiple K <sup>+</sup>-currents as well as simultaneous block of Na+- and K+ currents produced synergistic antiarrhythmic effects. Our results suggest that developing multi-channel (multiple K<sup>+</sup> currents and/or combined Na+- and K+-current) block is a potentially valuable strategy for the treatment of AF.

## REFERENCES


# AUTHOR CONTRIBUTIONS

HZ and HN conceived the study. HN designed experiments, developed and validated computational models, and performed numerical experiments. HN, DW, and WW analyzed data. HN, DW, WW, WG, SN, and HZ interpreted data and wrote the manuscript.

# FUNDING

This work was supported by grants from the British Heart Foundation FS/14/5/30533, EPSRC (UK) (EP/J00958X/1; EP/I029826/1), MC-IRSES CORDIS3D (317766), NSFC (61179009), Shenzhen Science and Technology Innovation Committee (JCYJ20151029173639477; JSGG20160229125049615). SN is supported by grants from the National Institutes of Health (R01 Hl83359).

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.00946/full#supplementary-material


London: EMEA. Available online at: http://www.ema.europa.eu/docs/en\_GB/ document\_library/Scientific\_guideline/2009/09/WC500002879.pdf


isolated heart model of atrial fibrillation. Heart Rhythm 12, 409–418. doi: 10.1016/j.hrthm.2014.12.010


and clinical studies. Circ. Arrhythm. Electrophysiol. 8, 1325–1333. doi: 10.1161/CIRCEP.115.002956


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Ni, Whittaker, Wang, Giles, Narayan and Zhang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Trigger vs. Substrate: Multi-Dimensional Modulation of QT-Prolongation Associated Arrhythmic Dynamics by a hERG Channel Activator

Michael A. Colman<sup>1</sup> \*, Erick A. Perez Alday <sup>2</sup> , Arun V. Holden<sup>1</sup> and Alan P. Benson<sup>1</sup>

*<sup>1</sup> School of Biomedical Sciences and Multidisciplinary Cardiovascular Research Centre, University of Leeds, Leeds, United Kingdom, <sup>2</sup> Division of Cardiovascular Medicine, Oregon Health and Science University, Portland, OR, United States*

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Sara Dutta, United States Food and Drug Administration, United States Kazuharu Furutani, Osaka University, Japan*

\*Correspondence:

*Michael A. Colman m.a.colman@leeds.ac.uk*

#### Specialty section:

*This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology*

Received: *02 August 2017* Accepted: *19 September 2017* Published: *04 October 2017*

#### Citation:

*Colman MA, Perez Alday EA, Holden AV and Benson AP (2017) Trigger vs. Substrate: Multi-Dimensional Modulation of QT-Prolongation Associated Arrhythmic Dynamics by a hERG Channel Activator. Front. Physiol. 8:757. doi: 10.3389/fphys.2017.00757* Background: Prolongation of the QT interval of the electrocardiogram (ECG), underlain by prolongation of the action potential duration (APD) at the cellular level, is linked to increased vulnerability to cardiac arrhythmia. Pharmacological management of arrhythmia associated with QT prolongation is typically achieved through attempting to restore APD to control ranges, reversing the enhanced vulnerability to Ca2+-dependent afterdepolarisations (arrhythmia triggers) and increased transmural dispersion of repolarisation (arrhythmia substrate) associated with APD prolongation. However, such pharmacological modulation has been demonstrated to have limited effectiveness. Understanding the integrative functional impact of pharmacological modulation requires simultaneous investigation of both the trigger and substrate.

Methods: We implemented a multi-scale (cell and tissue) *in silico* approach using a model of the human ventricular action potential, integrated with a model of stochastic 3D spatiotemporal Ca2<sup>+</sup> dynamics, and parameter modification to mimic prolonged QT conditions. We used these models to examine the efficacy of the hERG activator MC-II-157c in restoring APD to control ranges, examined its effects on arrhythmia triggers and substrates, and the interaction of these arrhythmia triggers and substrates.

Results: QT prolongation conditions promoted the development of spontaneous release events underlying afterdepolarisations during rapid pacing. MC-II-157c applied to prolonged QT conditions shortened the APD, inhibited the development of afterdepolarisations and reduced the probability of afterdepolarisations manifesting as triggered activity in single cells. In tissue, QT prolongation resulted in an increased transmural dispersion of repolarisation, which manifested as an increased vulnerable window for uni-directional conduction block. In some cases, MC-II-157c further increased the vulnerable window through its effects on *I*Na. The combination of stochastic release event modulation and transmural dispersion of repolarisation modulation by MC-II-157c resulted in an integrative behavior wherein the arrhythmia trigger is reduced but the arrhythmia substrate is increased, leading to variable and non-linear overall vulnerability to arrhythmia. Conclusion: The relative balance of reduced trigger and increased substrate underlies a multi-dimensional role of MC-II-157c in modulation of cardiac arrhythmia vulnerability associated with prolonged QT interval.

Keywords: QT interval, action potential duration, arrhythmia trigger, arrhythmia substrate, hERG activators, computational modeling

#### INTRODUCTION

Conditions in which the QT interval of the electrocardiogram (ECG) is prolonged, such as heart failure (Hart, 1994) and inherited or acquired long QT syndromes (LQTS) (Schwartz et al., 2012), are associated with an increased risk of ventricular arrhythmias (Tomaselli and Zipes, 2004; Moss and Kass, 2005). The prolonged QT interval reflects prolongation of the ventricular cellular action potential duration (APD), which can result in arrhythmias through an increase in cell-level arrhythmia triggers and/or modification of tissue-level arrhythmia substrates (Kalin et al., 2010; Benson et al., 2011a; Tse, 2016).

Cell-level triggers arise because delayed ventricular repolarisation modifies membrane and subcellular Ca2<sup>+</sup> handling (Clusin, 2003; Neme ˇ c et al., 2016), leading to either re-activation of the L-type Ca2<sup>+</sup> current and early afterdepolarisations (Lankipalli et al., 2005), or Ca2<sup>+</sup> overload of the sarcoplasmic reticulum (SR), causing spontaneous SR Ca2<sup>+</sup> release events and delayed-afterdepolarisations through activation of the forward-mode Na+-Ca2<sup>+</sup> exchange current (INaCa), which in turn can result in triggered activity if the delayed afterdepolarisation is of sufficient magnitude (Janse, 2004). Cardiomyocytes typically exhibit a threshold dependence of the occurrence of spontaneous release events as a function of SR Ca2<sup>+</sup> load, wherein the probability of a spontaneous release event rapidly rises from 0 to 1 within a critical region of SR Ca2<sup>+</sup> (Venetucci et al., 2007; Campos et al., 2015). Although originating at the cell level, triggers need to be coordinated at the tissue level in order to develop into arrhythmias: a critical compact region of tissue simultaneously exhibiting triggered behavior is required to initiate propagation of the trigger (Noble, 1972; Clayton et al., 2011; Bezekci et al., 2015; Campos et al., 2015).

An increase in the tissue-level substrates for arrhythmias (that is, the necessary conditions for triggered activity to propagate and develop into arrhythmias) arise because APD prolongation is rarely homogenous in and between the different regions of the ventricles (e.g., transmurally, or from base to apex) (Antzelevitch, 2005; Glukhov et al., 2010). This heterogeneous APD prolongation increases the spatial dispersion of repolarisation, potentially leading to regions of recovered (i.e., excitable) tissue partially bordered by still refractory (i.e., unexcitable) tissue. A propagating trigger event occurring in such a location can be partially blocked by the refractory tissue, leading to re-entrant arrhythmias (Pandit and Jalife, 2013). The spatiotemporal region where such partial conduction block could occur is termed the "vulnerable window" (VW) (Starmer et al., 1993; Shaw and Rudy, 1995; Benson et al., 2008, 2011a). It follows that heterogeneous APD prolongation increases not only the spatial dispersion of repolarisation, but also the VW, i.e., the arrhythmia substrate.

The interaction of triggers and substrates determines the initiation of arrhythmia: an arrhythmia cannot be initiated without both a suitably-sized and -timed trigger and the necessary substrate to allow that trigger to propagate in a reentrant manner (Kalin et al., 2010). Arrhythmias, therefore, are not cellular events, but tissue-level events.

Management of arrhythmias associated with QT prolongation can be achieved by attempting to restore the ventricular APD to control ranges (Nachimuthu et al., 2012), thus reversing the increases in arrhythmogenic triggers and substrates associated with APD prolongation. One such strategy is the use of human ether-a-go-go-related-gene channel (hERG) activators that enhance the repolarising rapid delayed rectifier K<sup>+</sup> current (IKr), thus reducing the APD (Grunnet et al., 2008; Wu and Sanguinetti, 2016). However, many anti-arrhythmic drugs have pro-arrhythmic effects (Kumar and Zimetbaum, 2013); such drugs can shorten the action potential and the QT interval (reducing arrhythmias associated with a prolonged QT interval), but they may have additional and unintended effects that increase (rather than reduce) the propensity for arrhythmias under certain conditions. For example, we have shown in a previous experimental and computational study that the hERG activator NS1643, one of the most effective and best characterized hERG activators (Hansen et al., 2006), successfully restores APD toward healthy durations and reduces arrhythmia triggers, but is associated with an increase in the VW, i.e., the substrate for arrhythmias, due to effects on the post-repolarisation refractory period (Peitersen et al., 2008). Furthermore, while low concentrations of NS1643 activates IKr and shortens APD, it has been shown that higher concentrations of NS1643 blocks (rather than activates) IKr (Bilet and Bauer, 2012).

The potentially pro-arrhythmic effects of hERG activators, such as NS1643 has prompted the search for novel hERG activators that do not display these effects. One recentlyidentified compound is MC-II-157c, an NS1643 analog. MC-II-157c activates IKr at low concentrations and, unlike NS1643, it continues to activate IKr at high concentrations; it may also block the sodium current (INa) (Guo et al., 2014). However, it remains unknown how the IKr activation and INa block seen with this new compound affect arrhythmia triggers and substrates, and importantly, how these (increased or decreased) triggers and substrates interact to induce arrhythmias (if at all).

Computational models provide powerful research tools to understand the intricacies of arrhythmia trigger and substrate interaction, as they allow us to modify parameters under precisely controlled conditions and quantify the resultant tissue-level arrhythmic behavior, and can predict how these arrhythmias will manifest in a clinical setting (e.g., changes to the ECG). We therefore used a computational approach to quantify the interaction of pharmacologically-modified arrhythmia trigger and substrate, using the novel hERG activator MC-II-157c as an example.

We wanted to quantify the modified triggers and substrate that result from MC-II-157c ion channel actions. To this end, we use detailed single cell and tissue level models to study the effect of QT prolongation and its modulation by MC-II-157c on: (i) APD heterogeneity in isolated cells; (ii) SR Ca2<sup>+</sup> loading and subsequent spontaneous SR Ca2<sup>+</sup> release events; (iii) the probability of spontaneous SR Ca2<sup>+</sup> release manifesting as triggered action potentials in single cell and ectopic activity in tissue; and (iv) the vulnerability to the initiation of re-entrant like conduction patterns.

#### METHODS

We implemented a multi-scale in silico approach to study the interactions between arrhythmia trigger and substrate in conditions associated with prolonged QT intervals, and their modulation by the hERG activator MC-II-157c.

# Isolated Cell Models – Intracellular Ca2<sup>+</sup> Handling

In order to simulate triggered and ectopic activity underlain by spontaneous Ca2<sup>+</sup> release events, a spatial model of intracellular Ca2<sup>+</sup> handling which explicitly accounts for stochastic state transitions and spatial coupling is required. We therefore implemented an efficient, idealized reduction of a previously developed and validated general model of spatio-temporal Ca2<sup>+</sup> handling with realistic structure (Colman et al., 2017), using a similar approach implemented by other groups (e.g., Restrepo et al., 2008). Briefly, 15 × 20 × 65 spatially-discrete individual calcium release units (CRUs) were modeled throughout the geometry of the cell (**Figure 1**). Each CRU comprises of five compartments with associated Ca2<sup>+</sup> concentrations: the intracellular spaces of the dyadic cleft space ([Ca2+]ds), subspace ([Ca2+]SS) and bulk-cytosolic space ([Ca2+]i), and the network and junctional SR ([Ca2+]nSR, ([Ca2+]jSR). The bulk cytosol, subspace and network SR are diffusively coupled to neighboring CRUs; the dyadic cleft space and junctional SR are not spatially coupled to neighbors. The fundamental model equations describing this system are:

$$\begin{aligned} \frac{\mathbf{d}[\text{Ca}^{2+}]\_{\text{i}}}{\text{dt}} &= \beta \left(\mathbf{D}\nabla^{2}[\text{Ca}^{2+}]\_{\text{i}} + \varphi\_{\text{i}} + (\upsilon\_{\text{SS}}/\upsilon\_{\text{i}})f\_{\text{SS}}\right) \\ \frac{\mathbf{d}[\text{Ca}^{2+}]\_{\text{SS}}}{\text{dt}} &= \mathbf{D}\nabla^{2}[\text{Ca}^{2+}]\_{\text{SS}} + \varphi\_{\text{SS}} - f\_{\text{SS}} + (\upsilon\_{\text{ds}}/\upsilon\_{\text{SS}})f\_{\text{ds}} \\ \frac{\mathbf{d}[\text{Ca}^{2+}]\_{\text{nSR}}}{\text{dt}} &= \beta\_{\text{nSR}} \left(\mathbf{D}\nabla^{2}[\text{Ca}^{2+}]\_{\text{nSR}} + \varphi\_{\text{nSR}} - \left(\upsilon\_{\text{j}\text{SR}}/\upsilon\_{\text{nSR}}\right)f\_{\text{j}\text{SR}}\right) \\ \frac{\mathbf{d}[\text{Ca}^{2+}]\_{\text{ds}}}{\text{dt}} &= \varphi\_{\text{ds}} - f\_{\text{ds}} \\ \frac{\mathbf{d}[\text{Ca}^{2+}]\_{\text{j}\_{\text{SR}}}}{\text{dt}} &= \varphi\_{\text{j}\text{SR}} - f\_{\text{j}\text{SR}} \end{aligned}$$

where transfer between compartments is given by:

$$\begin{array}{rcl} J\_{\rm SS} & = \left( \left[ \text{Ca}^{2+} \right]\_{\rm SS} - \left[ \text{Ca}^{2+} \right]\_{\rm i} \right) \text{\tiny\tau}\_{\rm SS}^{-1} \\ J\_{\rm ds} & = \left( \left[ \text{Ca}^{2+} \right]\_{\rm ds} - \left[ \text{Ca}^{2+} \right]\_{\rm SS} \right) \text{\tiny\tau}\_{\rm ds}^{-1} \\ J\_{\rm jSR} & = \left( \left[ \text{Ca}^{2+} \right]\_{\rm jSR} - \left[ \text{Ca}^{2+} \right]\_{\rm nSR} \right) \text{\tiny\tau}\_{\rm jSR}^{-1} \end{array}$$

where v<sup>x</sup> is the volume of compartment x, β<sup>x</sup> is an instantaneous buffering term, and ϕ<sup>x</sup> is the reaction term. Stochastic dynamics are modeled for the RyRs and LTCCs, which are part of the dyadic cleft space reaction term. All parameters and reaction terms are given in the Supplementary Material.

#### Isolated Cell Models - Action Potential Model

Ion currents were described by a simplified version of the O'Hara-Rudy dynamic (ORd) human ventricular cell model (O'Hara et al., 2011), wherein the major currents only (INa, IKr, IKs, IK1, Ito, INaK) were included, without the further details of phosphorylation included in the original study; Ca2<sup>+</sup> currents (ICaL, INaCa, ICap, ICab) are described by the Ca2<sup>+</sup> handling model. These simplifications were implemented to improve computational efficiency and for integration with the general stochastic Ca2<sup>+</sup> handling model described above. The model provides specific formulations to describe the heterogeneity in ionic currents of the transmural cell types (endocardial, midmyocardial, and epicardial) found in the left ventricular free wall of the human heart (see O'Hara et al., 2011) for details.

This integrated stochastic framework captures spontaneous Ca2<sup>+</sup> release events that could lead to triggered activity (see details in Simulating Spontaneous Release Events in Tissue Models below). Default model action potentials and cytosolic Ca2<sup>+</sup> transients, for the three transmural cell types of the simplified ORd model with stochastic Ca2<sup>+</sup> handling, are shown in **Figure 1B**. The updated cell model exhibits action potential and Ca2<sup>+</sup> transient properties similar to the original cell model and within the range of experimental data presented in the original study (O'Hara et al., 2011): APD = 272–360 ms and intracellular Ca2<sup>+</sup> transient magnitude of ∼0.6µM for the three cell-types during control pacing; note that the present study does not consider heterogeneity in the intracellular Ca2<sup>+</sup> handling system and thus the Ca2<sup>+</sup> transient is more homogeneous between the cell types than in the original study (see Limitations). The model is therefore considered suitable for the mechanistic study undertaken.

#### Prolonged QT and Pharmacological Modulation

We were interested in general cases of QT prolongation rather than modeling the kinetics of very specific conditions, while still making our results broadly applicable to clinical conditions, such as LQTS. We therefore simulated QT interval prolongation (i.e., prolongation of the ventricular APD) in one of three ways: (i) downregulation of the slow delayed rectifier K<sup>+</sup> current (IKs) maximal conductance by 50%, similar to LQTS1, which we term "prolonged QT variant a" (PQTa) in the remainder of the manuscript; (ii) downregulation of IKr maximal conductance by

50% (PQTb), similar to LQTS2; and (iii) upregulation of ICa,L maximal conductance by 50% (PQTc), similar to LQT8 (Bohnen et al., 2017).

Effects of 10µM of the hERG activator MC-II-157c on IKr were modeled by modifying the IKr formulation according to experimental data (Guo et al., 2014): maximal conductance was decreased by 12%, activation was shifted by −14 mV and inactivation by +14 mV, and deactivation kinetics were slowed 3.3-fold (note that, although the maximal conductance of IKr is reduced by MC-II-157c, its kinetic effects enhance the activity of the current; see The hERG Activator MC-II-157c Partially or Fully Reverses APD Prolongation Heterogeneously). Effects of MC-II-157c on blocking INa (which are not as well characterized as its effects on IKr; Guo et al., 2014) were simulated by reducing the maximal conductance of INa by 0, 40, and 80%.

# Tissue Models

We used a 20 mm 1D virtual tissue strand (Kléber and Rudy, 2004) for quantifying transmural propagation and vulnerability, with equal spatial distributions of endocardial, midmyocardial and epicardial cells. A 20 × 40 mm 2D tissue sheet (Clayton et al., 2011) was used for simulations examining propagation of triggered activity, with equal distributions of endocardial, midmyocardial and epicardial tissue in the x direction. For examining intramural propagation and ectopic activity in 3D, we used an anatomically detailed 3D ventricular wedge model, obtained by diffusion tensor MRI, and used equal proportions of endocardial, midmyocardial and epicardial tissue in the transmural direction (see Benson et al., 2007, 2011b; Walton et al., 2013 for details).

All tissues were isotropic, i.e., conduction velocity was set to be equal in all directions: We used an electrical diffusion coefficient of D = 0.048 mm2ms−<sup>1</sup> , to give a conduction time along the 1D strand (i.e., a transmural activation time) of 40 ms (cf. Glukhov et al., 2010), and a plane wave conduction velocity of 0.5 m.s−<sup>1</sup> in all tissues. The body surface potential was computed by placing the ventricular wedge model in a human torso mesh; the forward problem was solved by a boundary element method, as has been described in previous studies (Perez Alday et al., 2015, 2016, 2017). ECGs were derived from the body surface potential by selecting elements of the torso mesh which correspond to the ECG electrodes.

# Simulating Spontaneous Release Events in Tissue Models

Performing tissue level simulations using the fully detailed spatial Ca2<sup>+</sup> handling model to describe individual cells is computationally intractable due to the large number of equations that need to be solved in such situations. Furthermore, the focus of this study was not to dissect the mechanisms of spontaneous Ca2<sup>+</sup> release in single cell, but rather to understand the considerations determining the manifestation of sub-cellular Ca2<sup>+</sup> release as triggered action potentials and propagating electrical excitation in the presence of prolonged APD and its pharmacological modulation.

We therefore implemented a "non-spatial" simplification of the Ca2<sup>+</sup> handling model (described in Isolated Cell Models– Intracellular Ca2<sup>+</sup> Handling, above) for use in tissue-level simulations, to capture spontaneous Ca2<sup>+</sup> release events at significantly reduced computational cost and with complete controllability. The non-spatial model consists of a single CRU (with RyR and LTCC dynamics solved deterministically) with additional analytical functions which describe the RyR waveform associated with whole-cell spontaneous release events, derived from analysis of the fully detailed spatial cell model, similar to the approach used in Campos et al. (2015) and Colman et al. (2015). For a simple transientspike morphology (**Figure 2**) this function has the form: from functions describing their physiological distributions. The distributions describing initiation time of whole-cell spontaneous release events in the spatial cell model are typically skewed (**Figure 3Aa**) and well approximated by two sigmoidal functions, split around the cumulative probability of 0.25 (corresponding to a specific initiation time, ti\_sep; **Figure 3Ab**). The initiation time can therefore be determined by passing a random number into the inverse of the two sigmoidal functions:

$$t\_i = \begin{cases} -k\_{F1} \ln\left(\frac{0.5}{rand} - 1\right) + t\_{i\_{\rm{sp}}}, \text{ } rand < 0.25\\ -k\_{F2} \ln\left(\frac{1.5}{rand + 0.5} - 1\right) + t\_{i\_{\rm{sp}}}, \text{ } rand \ge 0.25 \end{cases}$$

$$N\_{\text{RyR\\_O}} = \frac{N\_{\text{RyR\\_peak}}}{\left(1 + e^{-\left(t - \left(t + 0.5t\_{\text{dip}}\right)\right)/\left(0.1689t\_{\text{dip}} + 0.00255\right)}\right)\left(1 + e^{-\left(t - \left(t + t\_{\text{dip}} + 0.5t\_{\text{delay}}\right)\right)/\left(0.1689t\_{\text{delay}} + 0.00255\right)}\right)}$$

where t<sup>i</sup> is the initiation time of the spontaneous release and tup, tdecay and NRyR\_peak describe the shape of the waveform and are all determined from the duration (**Figures 2**, **3** and described below). The function for the plateau-like waveform (corresponding to durations longer than 250 ms) is derived from the same parameters (note the peak time, tp, is ti+tup):

$$N\_{\rm RyR\\_O} = \frac{N\_{\rm RyR\\_plateau}}{\left(1 + e^{-\left(t - \left(t\_i + 17.5\right)\right)/5.946}\right)\left(1 + e^{\left(t - \left(t\_f - 17.5\right)\right)/5.946}\right)}$$

$$+\frac{N\_{\rm RyR\\_peak} - N\_{\rm RyR\\_plateau}}{\left(1 + e^{-\left(t - \left(t\_p - 17.5\right)\right)/5.946}\right)\left(1 + e^{\left(t - \left(t\_p + 17.5\right)\right)/5.946}\right)}$$

Thus, the waveform is completely described by the initiation time and the duration. The stochastic nature of spontaneous Ca2<sup>+</sup> release is captured by randomly selecting these parameters where the gradient parameters of the two sigmoidal functions (kF1, kF2) and the t<sup>i</sup> at the cumulative probability of 0.25, ti\_sep, completely control the resulting distribution. The duration, D, of the RyR waveform can be determined from distributions in an analogous manner:

$$D = \begin{cases} k\_{1\\_MD} \ln\left[1/\left(rand - 1\right)\right] + MD, \text{ } rand < 0.5\\ k\_{2\\_MD} \ln\left[1/\left(rand - 1\right)\right] + MD, \text{ } rand \ge 0.5 \end{cases}$$

where MD refers to the median and k1\_MD and k2\_MD are functions of the median (in conditions where longer waveforms are observed, the variability in waveform duration between simulations is larger; **Figure 3Ba–c**):

$$k\_{1\,MD} = 0.1366MD - 7.98$$

$$k\_{2\,MD} = 0.12MD - 3.265$$

Frontiers in Physiology | www.frontiersin.org

listed.

the spatial cell model. Parameters describing the shape of the waveform are labeled. (B) Analytical waveforms approximating those in (A) using the input parameters

FIGURE 3 | Derivation of the RyR waveform parameters. (A) Initiation time distributions: (a) is an example distribution produced by the spatial cell model; (b) is the cumulative frequency of the distribution (purple dots) and two sigmoidal functions (red and green lines) which approximate it–the distribution itself is shown for reference (blue shading); (c) cumulative frequencies of the three distributions used in this study (*t i* distribution widths of 350 ms–blue; 550 ms–red; 1,000 ms–purple), with the histogram corresponding to the red distribution shown for reference. (B) Duration distributions: (a) scatter-plot of the durations associated with multiple simulations under different conditions (colors), plotted against the median of each distribution, which is also shown as the red diamonds for reference; (b,c) correlation of the gradient parameters of sigmoidal functions describing the distribution either side of the median with the median value; (d) four duration distributions used in the present study (Median Duration = 150 ms–red; 200 ms–blue; 250 ms–purple; 300 ms–green). (C) Other parameters correlate with the duration–time to peak (*tup*, a) and the waveform peak (*NRyR\_peak* , b).

Thus, the distribution is entirely described by the median. Finally, tup and NRyR\_peak can be determined from the given duration (**Figure 3C**):

NRyR\_plateau = 31.09(0.01D) −7.39 +(rand − 0.5)(−5 × 10−4D\_0.0275) + 0.34

$$\begin{aligned} t\_{up} &= 24 + rand(D - 52) \\ N\_{\text{RyR\\_peak}} &= \begin{cases} MRYR - rand(159.59(D^{-1.327} - D^{-1.4})), \text{rand} < 0.5 \\ MRYR - (1 - rand)(159.59 \left( (D + 30)^{-1.15} + D^{-1.327} \right) + 0.08), \text{rand} \ge 0.5 \end{cases} \end{aligned}$$

Where MRYR refers to the median and is given by:

$$MRYR = 159.59 D^{-1.327} + 0.028$$

And if duration > 250 ms, it is also necessary to compute NRyR\_plateau:

These formulations therefore allow complete control over spontaneous release dynamics through just four parameters (kF1, kF2, ti\_sep, median duration). We fix ti\_sep in simulations such that only the width of the initiation time distribution (kF1, kF2) and the median of the duration distribution are varied: t<sup>i</sup> distribution widths of 350, 550, and 1,000 ms (**Figure 3Ac**) were used in tissue simulations; duration medians of 150, 200, 250, 300, and 350 ms (**Figure 3Bd**) were used in single-cell and tissue simulations. Derivation of these equations from the fully detailed spatial cell model ensures self-consistency and physiological validity of the resulting waveforms.

# Computational Aspects

Models were coded in C/C++ and run on a Linux desktop machine, or using the University of Leeds ARC2 High Performance Computing facilities. Equations for isolated cell models were solved using a forward Euler method with a time step of 1t = 0.05 ms; ion channel gating equations were solved using the Rush-Larsen scheme (Rush and Larsen, 1978). For tissue models, the monodomain equation was solved using a Forward Time Centred Space method: Space steps of 1x = 0.2 mm were used in the 1D strand, 1x = 1y = 0.2 mm in the 2D tissue, and 1x = 1y = 0.425 mm and 1z = 0.5 mm in the 3D wedge model (as defined by the diffusion tensor MRI dataset). Parallelisation was implemented with OpenMP. Cell APD was measured from the time the membrane potential crossed −80 mV during the upstroke of the action potential, to when the membrane potential crossed back over −80 mV during the repolarisation phase.

# RESULTS

#### The hERG Activator MC-II-157c Partially or Fully Reverses APD Prolongation Heterogeneously

The single cell model was paced at a cycle length of 1,000 ms for 100 beats under control (WT), PQT and PQT + MC-II-157c conditions to evaluate the efficacy of MC-II-157c on reversing PQT induced APD prolongation (**Figure 4**). **Figure 4A** shows effects on AP morphology of the PQTa, PQTb, and PQTc conditions in endocardial, midmyocardial, and epicardial cells, with WT action potentials shown as a reference. The PQTb condition (downregulation of IKr) has the largest effect on prolonging APD (from 360 to 649 ms in midmyocardial cells, an increase of 80%), due to the larger IKr conductance in human cells relative to IKs conductance, and its primary role in AP repolarisation. All three PQT conditions increase the transmural difference in APD (the difference between the longest and shortest APDs in the three cell types), from 88 ms in WT to 97, 279 and 122 ms with PQTa, PQTb, and PQTc, respectively.

**Figure 4B** shows how the hERG activator MC-II-157c reduces APD back towards control levels in all cell types and with all PQT conditions. The drug reduced APD back to control levels in PQTa (downregulation of IKs) due to the minimal effect this condition has on initially prolonging APD, but the largest decrease was seen with PQTb in midmyocardial cells, where APD was reduced from 649 to 540 ms, a reduction of 17% (**Figure 4C**). It should be noted, however, that MC-II-157c has transmurally heterogeneous effects; that is, the degree of APD reduction seen in the three different cell types is not identical, with the drug under PQTb conditions (for example) giving a 5% decrease in endocardial cells, 17% in midmyocardial cells and 4% in epicardial cells. Consequently, the maximal transmural difference in APD in PQTb reduces from 279 ms with the PQT condition alone to 184 ms with PQTb plus MC-II-157c, but does not reduce transmural difference in APD back down to WT levels (184 vs. 88 ms).

ECGs were computed for the different conditions using the 3D ventricular wedge model under normal pacing (BCL = 1,000 ms). QT-prolongation was observed for all three remodeling types (**Figure 4C**), with PQTb exhibiting the longest QT-interval, congruent with single cell results (QT = 310 ms in WT compared to 326, 418, and 329 ms in PQTa-c, respectively). MC-II-157c resulted in a delay in the QRS peak as well as earlier absolute repolarisation time and consequent shortening of the QT interval (QT = 309 ms, 403 and 310 ms in PQTa-c + MC-II-157c; **Figure 4C**); in PQTa and PQTc, MC-II-157c fully reverses QT prolongation.

The mechanism by which MC-II-157c shortens APD, despire reducing the maximal conductance of IKr, is illustrated in **Figure 5**: the shifts in the activation and inactivation curves and the slowing of deactivation kinetics result in an increased current during both voltage clamp and AP clamp experiments. These results are generally congruent with the original study of Guo et al. (2014), although the current traces do differ in morphology and extent of effect of MC-II-157c (see Limitations).

#### MC-II-157c has PQT-Type Dependent Effectiveness in Reversing SR Loading and Spontaneous Release Events

The vulnerability to the emergence of whole-cell spontaneous Ca2<sup>+</sup> release events (such as intracellular Ca2<sup>+</sup> waves, **Figure 6A**) is primarily controlled by the dynamics of the intracellular Ca2<sup>+</sup> handling system and the SR Ca2<sup>+</sup> load, wherein cells typically exhibit an SR load threshold above which the probability of spontaneous release events significantly increases (Wagner et al., 2015). The focus of this study is not on the mechanisms of spontaneous Ca2<sup>+</sup> release, and therefore investigation of Ca2<sup>+</sup> handling remodeling is beyond its scope. However, APD prolongation associated with PQT, and its subsequent reversal by MC-II-157c, may influence SR loading and consequently the vulnerability to the emergence of whole-cell spontaneous Ca2<sup>+</sup> release.

An SR-loading protocol was used to analyse this behavior, by pacing the spatial cell model at a rapid rate (cycle length of 400 ms). The maximal flux rate of intracellular uptake was increased, simulating the effect of sympathetic stimulation, in order to promote SR loading. An increase by a factor of two was chosen as this loaded the SR-Ca2<sup>+</sup> in the WT model to just above the spontaneous release threshold; the most suitable region to reveal the consequence of APD modulation on spontaneous activity.

The time series of SR-Ca2<sup>+</sup> in WT and the PQTc condition in isolated epicardial cells illustrates the effect on SR-Ca2<sup>+</sup> loading under rapid pacing and highlights that APD prolongation associated with PQT can promote loading (**Figure 6B**). The peak of the SR Ca2<sup>+</sup> concentration during this time provides a measure of SR Ca2<sup>+</sup> loading; these data are shown in **Figure 6C** for WT and all PQT conditions with and without MC-II-157c. The PQTa condition (downregulation of IKs) does not promote

with the application of MC-II-157c (black line), relative to the WT (purple line). MC-II-157c was modeled as *I*Kr modification + 40% *I*Na block. Any impact of *I*Na block on the upstroke velocity is not clear at this scale.

SR loading compared to WT (peak SR Ca2<sup>+</sup> load of 1.07 mM in WT and 1.06 mM in PQTa), but the PQTb (downregulation of IKr) and PQTc (upregulation of ICa,L) conditions do (peak SR Ca2<sup>+</sup> load of 1.106 and 1.13 mM, respectively), with PQTc having the largest effect due to the increase in the transmembrane Ca2<sup>+</sup> current in this condition. MC-II-157c reverses SR Ca2<sup>+</sup> loading in PQTb, reducing peak SR Ca2<sup>+</sup> load at periodic steady-state

to 1.05 mM, which is below WT levels. However, the drug has only a very small effect in PQTc (down to 1.108 mM) due to the minimal effect MC-II-157c has on APD in this condition, and the subsequently small change in the time course of ICa,L.

These relatively small changes in SR-Ca2<sup>+</sup> can manifest as significant differences in the vulnerability to spontaneous Ca2<sup>+</sup> release due to the non-linear threshold dependence on SR

Ca2<sup>+</sup> concentration (**Figures 6D,E**). The probability of wholecell spontaneous release events and the probability distributions describing the initiation time can be computed from a large set of simulations (N = 1,000 per condition). Example distributions are shown in **Figure 6E** for the WT and PQTc with and without MC-II-157c, highlighting that even the small change in SR Ca2<sup>+</sup> as a result of MC-II-157c significantly reduces the probability of spontaneous release (∼50% in PQTc with MC-II-157c compared to 98% in PQTc alone) as well as widening the distribution (although not fully reversed to WT). Due to the choice of loading parameters giving the WT close to threshold, no spontaneous release occurs for either PQTa or PQTb under the application of MC-II-157c as in these conditions threshold SR Ca2<sup>+</sup> is not reached.

## MC-II-157c Is Effective in Inhibiting DADs Turning into Triggered Activity

The effect of MC-II-157c on the probability of DADs manifesting as full triggered action potentials was investigated using the simplified, non-spatial model such that spontaneous release waveforms could be directly controlled. The initiation time was set to 1,000 ms and behavior of the cell models for WT, PQT and PQT + MC-II-157c was compared over multiple simulations (N = 1,000 per condition) for four different RyR waveform duration distributions (see details in Simulating Spontaneous Release Events in Tissue Models; the distribution determines the values of duration which can be selected from a random number input and thus the actual value of the duration will vary randomly within the 1,000 simulations according to the given distribution).

Examples of 100 simulations for WT and PQTb, with and without MC-II-157c, are shown in **Figure 7A**. In PQTb, more DADs turn into triggered activity compared to in WT (top two panels), while simulated application of MC-II-157c reduces the occurances of triggered activity (bottom two panels). These data are summarized for all conditions and two duration distributions (median 300 and 350 ms, see Simulating Spontaneous Release Events in Tissue Models) in **Figure 7B**, wherein the degree of block of INa associated with MC-II-157c is varied (0, 40, and 80% block). In all cases, the IKr modification reduces the probability of triggered activity (defined as the number of simulations in which triggered activity occurred as a proportion of the total), but the role of INa is less clear; blocking INa is important, but the degree of INa block has different effects depending on the condition. The mechanism of the drug's action is shown in **Figure 7C**: principally, an increase in repolarising IKr acts during the DAD to keep the cell's membrane potential below the threshold for triggered activity; reduced INa also pays a role (although not as great as that of IKr) in the drug's mechanism of action as it reduces excitability of the cell, again reducing the ease with which the cell's membrane potential can reach threshold.

# MC-II-157c Reduces Vulnerability to Ectopic Activity in Tissue

The vulnerability to the development of ectopic activity (i.e., propagation of triggered activity in all directions through the tissue) was assessed in a 2D homogeneous sheet to provide a medium for the synchronization of independent stochastic release events. Ten simulations were performed for each condition (WT and PQT variants ± MC-II-157c for the combinations of t<sup>i</sup> and duration median distributions; Epicardial cell model) wherein the tissue model was paced to steady state and then left quiescent for two simulation seconds within which time the spontaneous release occurs.

The occurrence of ectopic activity exhibits a largely "allor-nothing" response, where most conditions lead to either 0 or 100% of simulations resulting in a premature excitation

model of stochastic intracellular Ca2<sup>+</sup> handling, showing the Ca2<sup>+</sup> transient (upper) and snapshots of Ca2<sup>+</sup> concentration in the 3D cell volume (lower). The triangular makers in the upper panel indicate the timings of the snapshots in the lower panel. (B) Time-series of SR-Ca2<sup>+</sup> during the SR-loading protocol, shown for control (WT, purple) and PQTc (red). (C) Peak SR-Ca2<sup>+</sup> during the loading protocol for all conditions. (D) Examples of spontaneous release resulting from SR-loading for control (WT, purple), PQTc (red) and PQTc + MC-II-157c (orange). 100 simulations of each conditions are shown to indicate variation in spontaneous release. (E) Distributions of initiation time of spontaneous release events, corresponding to the same conditions shown in (D). The time is relative to the start of the simulation (3 beats, initial conditions of dynamic steady state) to align with (D). MC-II-157c was modeled as *I*Kr modification + 40% *I*Na block.

(**Table 1**). Ectopic activity was promoted by narrow distributions of initiation time (i.e., tight synchronization) and short RyR waveforms (i.e., large spontaneous Ca2<sup>+</sup> transients), and conversely inhibited by wide distributions of initiation time (i.e., lose synchronization) and long RyR waveforms (i.e., small spontaneous Ca2<sup>+</sup> transients). For example, no ectopic activity was observed for any condition with t<sup>i</sup> distribution widths of 1,000 ms or duration medians of 300 ms or longer, whereas a t<sup>i</sup> distribution width of 350 ms combined with median durations of 150 or 200 ms resulted in ectopic activity occurring in 100% of simulations (**Table 1**).

PQT variants were more susceptible to the development of ectopic activity in tissue than WT, congruent with the single-cell results (See MC-II-157c Is Effective in Inhibiting DADs Turning into Triggered Activity). Similarly in-line with single-cell results, MC-II-157c can inhibit ectopic activity (**Table 1**): for example, it reduces or entirely inhibits the occurrence of premature excitation in four conditions: PQTa with t<sup>i</sup> width of 550 ms and duration median 150 ms; PQTc with t<sup>i</sup> width of 550 ms and duration median 200 ms; PQTc with t<sup>i</sup> width of 550 ms and duration median 150 ms; and PQTc with t<sup>i</sup> width of 350 ms and duration median 250 ms. The effect of INa block is also congruent with single cell results: it contributes to the inhibition of ectopic activity, but to a smaller extent than IKr modification.

**Figure 8A** shows an example of synchronized triggered activity initiating in a region of the 2D tissue (shown by the clustered peaks the images), before this triggered activity spreads throughout the tissue (shown by the yellow region) as an ectopic propagation. When the same situation is simulated with

MC-II-157c (**Figure 8B**), triggered activity, and therefore ectopic propagation, is inhibited.

## MC-II-157c Increases the Vulnerable Window in Tissue

An S1-S2 pacing protocol was applied to the 1D strand model in order to compute the vulnerability window: S2 stimuli were applied across a range of time intervals, centered on one in every five cells of the 100 comprising the model, from the tenth to the 90th.

Examples of propagation applied during the repolarisation phase in 1D tissue simulations are shown in **Figure 9A**: if the triggered activity occurs early (at 311 ms in this example), the resultant excitation is surrounded by refractory tissue and the triggered activity dies out without propagating; If the triggered activity occurs slightly later (e.g., 316 ms) then refractory tissue is encountered at only one side of the triggered activity site and unidirectional block (or unidirectional propagation) occurs, in the retrograde direction (back toward the endocardium) in this example; If triggered activity occurs later than this (321 ms in this example) then all surrounding tissue has recovered and the triggered activity propagates in both directions along the strand (i.e., ectopic propagation, analogous to the situation shown in 2D tissue in **Figure 8A**). It is the unidirectional block situation (i.e., when the triggered activity occurs in the VW) that can lead to re-entrant arrhythmias if this situation occurred in 2D or 3D tissue. The VW identifies occurrences of trigger and substrate interaction that may lead to arrhythmias, and so quantifying the size VW is a convenient method to examine effects of disease conditions and drugs on trigger and substrate interaction. The baseline VWs for WT and the PQTa condition are mapped out in **Figure 9B**, as well as VWs in


*The number of simulations where a premature excitation was observed is shown for each condition (out of a total of 10). The compound MC-II-157c is denoted by a "C" with IKr modification alone and "CNa" with inclusion of 40% block of INa. Highlighted with red borders are the conditions in which MC-II-157c inhibits the development of ectopic activity.*

these two situations with simulated addition of MC-II-157c (IKr modification plus 50% INa block), as well as with only the MC-II-157c IKr modification. These VWs are quantified by length (over which they occur in the 1D strand) and area (length × temporal width). In both WT and PQTa conditions, the drug increases both the length and the area of the VW (for example, length increases from 9 to 16 mm in the PQTa condition, and area increases from 78 to 101 mm.ms). Again, the influence of INa is different depending on the condition: including the effects of INa (i.e., the full MC-II-157c simulations compared to the IKr only simulations) increases the length of tissue over which the VW occurs in all conditions (e.g., from 12 to 16 mm in

PQTa), but reduces the overall area of the VW (e.g., from 126 to 101 mm.ms).

#### DISCUSSION

We used a multi-scale computational modeling approach to examine the interactions between cardiac arrhythmia trigger and substrate in general conditions associated with prolonged QT intervals, and their modulation by the hERG activator and sodium channel blocker MC-II-157c. Although we examined the effects of pharmacological modification on trigger and substrate interaction using a specific hERG activator, and gained novel insights into how modification of the depolarising (INa) and repolarising (IKr) membrane ionic currents targeted by the drug affects arrhythmia triggers and substrates, our findings also provide general insight into the role of ion-currents in controlling triggers and substrate at multiple scales which, along with insight from other in silico studies [see (Dutta et al., 2016; Mann et al., 2016) for recent examples], may be applicable to other pharmacological compounds that modify membrane ionic currents as well as pro-arrhythmic electrical remodeling.

#### Key Findings

Our key findings are that: (i) Despite the hERG activator MC-II-157c reducing the maximal conductance of IKr by 12% compared to WT, the drug's modifications to IKr activation, inactivation and deactivation kinetics result in an overall increase in IKr during the action potential, and a concomitantly reduced APD under all PQT conditions in all transmural cell types; (ii) Although MC-II-157c acts on membrane ionic currents carrying K<sup>+</sup> and Na+, the drug has indirect effects on intracellular Ca2<sup>+</sup> handling, particularly SR Ca2<sup>+</sup> loading and related spontaneous SR Ca2<sup>+</sup> release events and subsequent DADs, through modulation of the AP; (iii) Increased IKr (through its repolarising effects) and reduced INa (by decreasing cell excitability) act to reduce the probability of a DAD reaching threshold and developing into triggered activity at both cellular and tissue scales; and (iv) Despite MC-II-157c reducing triggered activity at the cell level, the drug can increase both the spatial region of tissue over which a VW for unidirectional conduction block occurs, as well as the temporal width of the VW at all points along the tissue, and in doing so increases the total spatiotemporal size of the VW. These results highlight the complex considerations which underlie overall vulnerability to arrhythmia at multiple scales.

# Efficacy of MC-II-157c as an Anti-Arrhythmic Drug

At the isolated cell level, MC-II-157c reduces SR Ca2<sup>+</sup> loading, reduces the occurrences of spontaneous SR Ca2<sup>+</sup> release events, reduces DAD occurrences, and reduces the probability of a DAD developing into a triggered action potential. At the tissue level, the combination of these factors leads to a significantly reduced vulnerability to the development of ectopic beats; MC-II-157c reduces the probability of an ectopic beat development at given spontaneous release function distributions (i.e., synchronization degree) as well as inhibiting SR Ca2<sup>+</sup> loading and thus reducing synchronization (which, itself, reduces the probability of ectopic beats). In relation to the development of Ca2<sup>+</sup> induced triggers at single cell and tissue levels, therefore, our simulation results suggest that the drug has efficacy as an anti-arrhythmic.

However, even though arrhythmic triggered activity is reduced with the drug, the spatiotemporal area of the VW increased, and so the anti-arrhythmic effects of the reduced probability of an arrhythmia trigger occurring is opposed by the pro-arrhythmic effects of an increased arrhythmia substrate. This highlights the importance of examining the effects of pharmacological compounds on both the triggers and the substrates that underlie arrhythmia initiation: there is a delicate balance between increased/decreased trigger and increased/decreased substrate (i.e., trigger-substrate interaction) that determines whether any given trigger stimulus (e.g., a spontaneous SR Ca2<sup>+</sup> release event) will result in unidirectional propagation and, potentially, initiation of a reentrant arrhythmia. This is one potential reason that single cell studies showing efficacious effects of putative anti-arrhythmic drugs may not translate to the clinic.

The effects of MC-II-157c on the VW occur through two mechanisms due to the drug's action on both IKr and INa, both of which modify transmural dispersion of repolarisation. Activation of IKr causes heterogeneous changes to APD at the tissue level, the same mechanism as in our previous studies examining the effects of NS1643 (Peitersen et al., 2008). Block of INa results in slowed transmural conduction (Kléber and Rudy, 2004) and therefore delayed activation of epicardial (but not endocardial) tissue: this in turn modifies transmural dispersion of repolarisation, even though the change to APD is minimal with INa block. Block of INa also reduces excitability of the tissue, necessitating a larger trigger to initiate propagation, which also contributes to the change in the VW.

# Varying Effects of Sodium Current Block

The role of INa loss of function in arrhythmogenesis has been examined in detail previously (see Clancy et al., 2015 for a review); however, one intriguing finding from our cell and tissue simulations was the varying effects that different magnitudes of INa block had on trigger development and substrate size. At the cell level, the probability of triggered activity developing from DADs did not follow a simple monotonic change with increasing INa block in all cases. Take, for example, the 350 ms Ca2<sup>+</sup> release duration distribution results shown in the top panels of **Figure 7B**: In WT and the PQTb condition, INa block (in addition to the IKr modification) reduces the probability of DADs developing into triggered activity (relative to the IKr modification alone), with more block reducing this probability; that is to say, the greater the INa block, the more anti-arrhythmic (in terms of reducing triggered activity) the effects. However, in the PQTa condition, while 40% block of INa reduced the probability of triggered activity occurring, increasing block of the current to 80% slightly increased the probability of triggered activity; in this condition, a small amount of INa block has anti-arrhythmic effects, but increasing this small level of block is pro-arrhythmic. In the PQTc condition, INa block of any magnitude increased the probability of triggered activity (i.e., INa block is pro-arrhythmic), with the probability of triggered activity occurring increasing as INa block is increased. Similarly varied results were found for the 300 ms Ca2<sup>+</sup> release duration distribution (lower panels in **Figure 7B**), although the anti-/pro-arrhythmic effects did not necessarily match those seen with the 350 ms distribution.

One further note of caution with regards to INa block comes from our tissue-level VW results in **Figure 9B**. Quantification of the length of tissue over which the VW occurs shows that 50% INa block (compare the full MC-II-157c effects to the effects with the IKr modification alone) increases this length, potentially due to an increase in transmural dispersion of repolarisation with INa block; analyses of these results alone would conclude that INa block is pro-arrhythmic. However, despite the spatial width of the VW increasing, block of INa results in the total spatiotemporal area of the VW decreasing (again, compare the full MC-II-157c effects to the effects with the IKr modification alone), i.e., an anti-arrhythmic result, likely due to the reduced excitability that results from INa block reducing the likelihood that any triggered activity would propagate.

Our tissue-level findings therefore indicate that INa block per se is an effective antiarrhythmic strategy (as seen with class I antiarrhythmic drugs; Camm, 2012), but our cell-level findings highlight that the magnitude of INa determines cell (and by extension, tissue) electrophysiological consequences in a manner that is not intuitive. The mechanisms underlying these varying effects of INa block on arrhythmogenesis, particularly on DAD initiation and their development into triggered activity, remain to be elucidated.

# Modifying Abnormal Intracellular Calcium Handling through Membrane Current Modification

Although this study did not focus on the mechanisms of arrhythmia triggers (in that we prescribed SR Ca2<sup>+</sup> release events under certain conditions), one interesting finding did emerge in relation to arrhythmia triggers that can result from abnormal intracellular Ca2<sup>+</sup> handling: Modification of membrane ion channels carrying ions other than Ca2<sup>+</sup> (K<sup>+</sup> and Na<sup>+</sup> in this case) can have beneficial effects in terms of restoring abnormal intracellular Ca2<sup>+</sup> handling, through their actions in shortening APD. This was shown in **Figure 6**, where the increased SR Ca2<sup>+</sup> loading (and resultant spontaneous SR Ca2<sup>+</sup> release events) seen under PQT conditions was reversed by upregulating IKr and downregulating INa, which in turn shortened APD. This reduces the duration over which ICa,L is activated, reduces the amount of Ca2<sup>+</sup> crossing the cell membrane and entering the cell via that current, and thus reduces SR Ca2<sup>+</sup> load. Furthermore, the combined action of both of these current modifications reduced the probability of DADs manifesting as triggered action potentials in single cell as well as triggered action potentials manifesting as fully propagating ectopic beats at the tissue scale. Targeting cell membrane ion channels carrying ions other than Ca2<sup>+</sup> in order to restore abnormal intracellular Ca2<sup>+</sup> handling (as seen in heart failure, for example; Lou et al., 2012) may be beneficial in cases where up/downregulation of Ca2+-specific drug targets (ryanodine receptors or SERCA, for example) will alter the delicate homeostasis of an already-compromised system, yielding negative results (Ratner, 2015).

### Development of Arrhythmic Conduction Patterns

One-dimensional models (other than 1D rings; e.g., Vinet and Roberge, 1994) cannot simulate re-entrant activity, and so it is necessary to use 2D and 3D models to examine how unidirectional propagation develops into re-entry. Although the quantitative characteristics of the VW examined in 1D tissues may change in 2D and 3D depending on the spatial locations of cell types (e.g., "base-apex" as well as transmural distributions), based on our previous work we would expect the qualitative characteristics to remain similar (Benson et al., 2007, 2008, 2011a). We show examples of 2D and 3D modeling in **Figure 10**: In **Figure 10A**, a trigger occurring in the VW (resulting in unidirectional conduction block) develops into re-entry in a simple 2D model; In **Figure 10B**, a trigger occurring outside the VW develops into ectopic propagation (i.e., not re-entrant) in a detailed 3D model of a human left ventricular wall slab, which manifests as significant differences in the body surface potential activation maps (**Figure 10C**). The advantages of using detailed 3D models (in this case, where the geometry is obtained from diffusion tensor MRI) lie in their ability to reproduce the orthotropic conduction velocities resulting from complicated tissue architecture (i.e., fiber and sheet structure; Benson et al., 2007; Smaill et al., 2013) and the boundary and curvature effects that can modulate electrotonic coupling and propagation (Walton et al., 2013; Campos et al., 2015): these effects are crucial in understanding the complex and chaotic propagation patterns underlying cardiac arrhythmias. Nevertheless, the 1D models used in this study allow us to examine arrhythmia triggersubstrate interaction in a simple and methodological manner.

#### Limitations

In this study, a general model of intracellular Ca2<sup>+</sup> handling was integrated with a simplified formulation of a human ventricular AP model. Due to the general nature of the Ca2<sup>+</sup> handling model, details of heterogeneity in Ca2<sup>+</sup> handling were not included in order to avoid introducing artifacts. For this reason, and due to the multi-scale focus of the study, detailed investigation of the mechanisms of spontaneous release in single cell, and their regional dependencies, was not performed, and investigation was instead limited to the potential effect of MC-II-157c on reversing SR Ca2<sup>+</sup> loading. There are many possible mechanisms of spontaneous release associated with diseases linked to prolonged QT interval (e.g., hyper phosphorylation of the RyRs; upregulation of SERCA; detubulation) which were not considered in the present study. However, the aim of this study was to investigate the multiscale interaction between trigger and substrate, and the use of the simplified spontaneous release functions in single-cell and tissue simulations allowed this to be analyzed in a general manner and across a large range of conditions, independent of spontaneous release mechanism. In future, combining detailed single cell studies of the mechanisms of spontaneous release in disease conditions with tissue simulations of the same conditions would provide further mechanistic insight; a dynamic simplified spontaneous release model would furthermore allow the study of long-term interactions between trigger and substrate in tissue e.g., during re-entry.

The factors underlying the synchronization and propagation of ectopic activity are highly complex and it is therefore worth making explicit that our simplified approach (which does not consider, for example, heterogeneity in the distributions describing Ca2<sup>+</sup> release) is primarily suitable for interpretation of general trends only, rather than as a quantitative analysis of the efficacy of MC-II-157c in modulating Ca2<sup>+</sup> release dependent triggers; it is encouraging to note that our results are consistent with those of a previous study (Campos et al., 2015), with the emergence of premature excitation from independent stochastic events overcoming electrotonic load, and the steep, "all-ornothing" relationship observed in tissue. This steep relationship also likely accounts for the lack of effect of MC-II-157c on PQTb (the condition exhibiting the highest vulnerability to ectopic activity), wherein the distributions selected were not close enough to the threshold region to reveal an effect.

The relative contribution of IKr to repolarisation is different in different models of the human ventricular action potential (Mirams et al., 2014): for example, IKr contributes more repolarising current in the ORd model (O'Hara et al., 2011) than in the ten Tusscher & Panfilov model (ten Tusscher and Panfilov, 2006), despite both models being validated against experimental data. It is therefore possible that our results overestimate the effects of the hERG activator MC-II-157c, although the identified pro- and anti-arrhythmic mechanisms will still be relevant.

The limitations of using 1D and 2D simplifications of 3D cardiac tissue have been discussed in detail previously (Clayton et al., 2011). Here we only note that the 1D strand model of the left ventricular wall allows us to examine mechanisms underlying how arrhythmia triggers and substrates interact to initiate unidirectional propagation, without the added complicating effects that geometrical (shape) and architectural (fiber, sheet etc.) considerations would bring. Nevertheless, it is anticipated that these geometrical and architectural effects will play a role not only in the transition from unidirectional propagation to re-entry, but on the initiation of the unidirectional propagation itself through, for example, electrotonic effects (Benson et al., 2007; Walton et al., 2013). Similarly, our 2D and 3D tissues were isotropic, i.e., no fiber or sheet structure, and so any conclusions drawn from these simulations should be interpreted with this in mind. Elucidating the roles that tissue geometry and architecture play in

arrhythmogenesis (Smaill et al., 2013) is an important next step in fully understanding arrhythmia trigger and substrate interaction.

The spatial distributions of endocardial, midmyocardial, and epicardial cell types across the human ventricular wall has still not been confirmed: some studies suggest that midmyocardial cells are found predominantly in isolated regions of the subendocardium (Glukhov et al., 2010), while others suggest a continuous population of midmyocardial cells in the subepicardial region (Drouin et al., 1995); these distributions may be dependent on species, location in the ventricular wall, and disease state (Antzelevitch, 2010; Strom et al., 2010). Because of this uncertainty, we set the spatial distribution of the three cell types to be equal in the transmural direction, but the effects of the electrotonic interactions of different regions of cell types are likely to be qualitatively similar if these distributions are altered.

The simulated model of MC-II-157c reproduced qualitatively the key features of the effect of the compound on IKr (i.e., an increased activity during a depolarising pulse), but it is important to note that there were significant differences between the simulation and experimental data (**Figure 5**): firstly, the formulation of IKr implemented does not have a time-dependent inactivation, which is observed in the experimental trace; secondly, the simulated data exhibited a larger difference in the magnitude of the current during the depolarisation step between baseline and MC-II-157c than observed experimentally. A more detailed model of IKr in both basal and MC-II-157c conditions would be essential for future and more detailed analysis of the compound specifically.

Furthermore, recent work, (e.g., Li et al., 2017), has highlighted that simple modulation of Hodgkin-Huxley current formulations, as used to simulate IKr in the ORd model, may not sufficiently capture complex drug-channel interaction dynamics, and that more complex Markov model formulations may be necessary to simulate such dynamics. However, until a full experimental characterisation of the dynamics of MC-II-157c effects on IKr under a range of conditions is carried out, allowing a validated Markov model of drug-channel interactions to be developed, we make use of the available data (Guo et al., 2014) to modify the Hodgkin-Huxley formulation used in the ORd model. The effects of MC-II-157c on INa are not as well characterized as its effects on IKr (Guo et al., 2014). We simulated the drug's action on INa by a simple reduction in the maximal conductance of the current. It is possible, however, that MC-II-157c also modifies the current's kinetics (i.e., shifts to the current's activation and inactivation curves, and/or a change to the time constants associated with these processes) in a similar manner to the way in which the kinetics of IKr are modified. Thus, further experimental characterisation of the drug's effects on both IKr and INa are required.

# CONCLUSION

The relative balance of reduced trigger and increased substrate underlies a multi-dimensional role of MC-II-157c in modulation of arrhythmia vulnerability associated with prolonged QT interval. Our results highlight that studies examining the efficacy of putative anti-arrhythmic drugs need to assess the effects of the drug on both the triggers and the substrates involved in arrhythmogenesis, i.e., such studies should adopt a multiscale approach to examine both cell- and tissue-level effects.

# AUTHOR CONTRIBUTIONS

All authors conceived and designed the study; MC, EP, and AB carried out simulations, and acquired and analyzed data; all authors interpreted the data; MC and AB prepared the first draft of the manuscript text; MC and EP prepared the figures; all authors edited the manuscript; all authors approved the final version of the manuscript; all authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

#### FUNDING

Supported by a Medical Research Council Strategic Skills Fellowship to MC (MR/M014967/1) and a British Heart Foundation project grant to AB (PG/16/74/32374).

#### REFERENCES


#### ACKNOWLEDGMENTS

Parts of this work were undertaken on ARC2, part of the High Performance Computing facilities at the University of Leeds, UK.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fphys. 2017.00757/full#supplementary-material

reticulum and t-tubule reconstructions. PLOS Comput. Biol. 13:e1005714. doi: 10.1371/journal.pcbi.1005714


electrophysiology after global optimization to recapitulate clinical long QT phenotypes. J. Mol. Cell. Cardiol. 100, 25–34. doi: 10.1016/j.yjmcc.2016.09.011


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer KF and handling Editor declared their shared affiliation.

Copyright © 2017 Colman, Perez Alday, Holden and Benson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Simultaneous Quantification of Spatially Discordant Alternans in Voltage and Intracellular Calcium in Langendorff-Perfused Rabbit Hearts and Inconsistencies with Models of Cardiac Action Potentials and Ca Transients

#### Edited by:

Eleonora Grandi, University of California, Davis, United States

#### Reviewed by:

Daisuke Sato, University of California, Davis, United States Yohannes Castro Shiferaw, California State University, Northridge, United States

#### \*Correspondence:

Flavio H. Fenton flavio.fenton@physics.gatech.edu

†

These authors have contributed equally to this work.

#### Specialty section:

This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology

Received: 19 July 2017 Accepted: 05 October 2017 Published: 20 October 2017

#### Citation:

Uzelac I, Ji YC, Hornung D, Schröder-Scheteling J, Luther S, Gray RA, Cherry EM and Fenton FH (2017) Simultaneous Quantification of Spatially Discordant Alternans in Voltage and Intracellular Calcium in Langendorff-Perfused Rabbit Hearts and Inconsistencies with Models of Cardiac Action Potentials and Ca Transients. Front. Physiol. 8:819. doi: 10.3389/fphys.2017.00819 Ilija Uzelac1†, Yanyan C. Ji 1†, Daniel Hornung<sup>2</sup> , Johannes Schröder-Scheteling<sup>2</sup> , Stefan Luther <sup>2</sup> , Richard A. Gray <sup>3</sup> , Elizabeth M. Cherry <sup>4</sup> and Flavio H. Fenton<sup>1</sup> \*

<sup>1</sup> School of Physics, Georgia Institute of Technology, Atlanta, GA, United States, <sup>2</sup> Max Planck Institute for Dynamics and Self-Organization, Gottingen, Germany, <sup>3</sup> Center for Device and Radiological Health, Food and Drug Administration, Silver Spring, MD, United States, <sup>4</sup> School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, United States

Rationale: Discordant alternans, a phenomenon in which the action potential duration (APDs) and/or intracellular calcium transient durations (CaDs) in different spatial regions of cardiac tissue are out of phase, present a dynamical instability for complex spatial dispersion that can be associated with long-QT syndrome (LQTS) and the initiation of reentrant arrhythmias. Because the use of numerical simulations to investigate arrhythmic effects, such as acquired LQTS by drugs is beginning to be studied by the FDA, it is crucial to validate mathematical models that may be used during this process.

Objective: In this study, we characterized with high spatio-temporal resolution the development of discordant alternans patterns in transmembrane voltage (Vm) and intracellular calcium concentration ([Ca<sup>i</sup> ] +2 ) as a function of pacing period in rabbit hearts. Then we compared the dynamics to that of the latest state-of-the-art model for ventricular action potentials and calcium transients to better understand the underlying mechanisms of discordant alternans and compared the experimental data to the mathematical models representing V<sup>m</sup> and [Ca<sup>i</sup> ] <sup>+</sup><sup>2</sup> dynamics.

Methods and Results: We performed simultaneous dual optical mapping imaging of V<sup>m</sup> and [Ca<sup>i</sup> ] +2 in Langendorff-perfused rabbit hearts with higher spatial resolutions compared with previous studies. The rabbit hearts developed discordant alternans through decreased pacing period protocols and we quantified the presence of multiple nodal points along the direction of wave propagation, both in APD and CaD, and compared these findings with results from theoretical models. In experiments, the nodal lines of CaD alternans have a steeper slope than those of APD alternans, but not as steep as predicted by numerical simulations in rabbit models. We further quantified several additional discrepancies between models and experiments. Conclusions: Alternans in CaD have nodal lines that are about an order of magnitude steeper compared to those of APD alternans. Current action potential models lack the necessary coupling between voltage and calcium compared to experiments and fail to reproduce some key dynamics such as, voltage amplitude alternans, smooth development of calcium alternans in time, conduction velocity and the steepness of the nodal lines of APD and CaD.

Keywords: discordant alternans, calcium dynamics, voltage-calcium coupling, arrhythmia, optical mapping, long QT syndrome, cardiac cell modeling

# INTRODUCTION

Long-QT syndrome (LQTS), characterized by abnormal prolongation of the QT interval (Schwartz et al., 1993), is a result of delayed repolarizations in the heart and can increase the risk of life-threatening arrhythmias, with a mortality rate of 20% within the first year after first detection and up to 50% in the next 10 years for untreated patients (Schwartz, 1985). The known dangers of LQTS have resulted in guidelines by the FDA concerning the design and testing of any new drug and in the interpretation and analysis of these drugs in clinical trials (Food and Drug Administration, 2005). In addition, many currently available medications can be very dangerous to some patients with heart problems, as they are known to further prolong QT intervals as shown in the compendium maintained by the Sudden Arrhythmia Death Syndromes Foundation (sads.org). LQTS is usually accompanied by T-wave alternans (Zareba et al., 1994) where the duration of the T wave can vary from one beat to the next (Jayakrishnan and Krishnakumar, 2006). This long-short alternation in duration and in some cases amplitude has been shown to arise from a period-doubling bifurcation (Nolasco and Dahlen, 1968; Guevara et al., 1984) originating at the cellular level (Pastore et al., 1999). In space, alternans can lead to complex spatiotemporal patterns along the epicardium and endocardium (Gizzi et al., 2013) and eventually to conduction block and fibrillation (Fenton et al., 2002; Choi et al., 2007).

During fast pacing, alternate patterns of action potential duration (APD) in space can be classified as concordant alternans (CA), in which all the tissue responds with a long APD on one beat and with a short APD on the following beat with the sequence repeating, or discordant alternans (DA), in which one section of tissue responds with a long APD and another with a short APD on the same beat followed by the reverse on the next beat. During DA, the regions of long and short APDs that alternate out-of-phase are separated by nodes, which are regions where the APDs have the same values for successive beats and hence do not alternate (Qu et al., 2000; Watanabe et al., 2001).

To date, two main mechanisms for the development of discordant alternans have been proposed, one driven by voltage and another by calcium (Saitoh et al., 1988, 1989). The first mechanism identified (Nolasco and Dahlen, 1968) was purely voltage-driven (Guevara et al., 1984); in space it is coupled through the dynamical interaction between the APD restitution curve and the conduction velocity (CV) restitution curve. When tissue is paced rapidly, diastolic intervals are shorter, causing slower CV near the stimulating site while CV increases downstream along wavefront propagation, causing a large spatial dispersion in the APD that can lead to DA (Qu et al., 2000; Watanabe et al., 2001).

The other mechanism, calcium-driven, is considered more complex, with DA caused by instabilities in [Cai] +2 cycling that in turn impacts APD through [Cai] <sup>+</sup>2–V<sup>m</sup> coupling (Chudin et al., 1999; Sato et al., 2006). [Cai] <sup>+</sup>2–V<sup>m</sup> coupling depends on a dynamical balance between the influx through the L-type calcium current (ICaL) and extrusion through the Na-Ca exchanger current (INCX) (Weiss et al., 2006). If the effect of INCX dominates, positive [Cai] <sup>+</sup>2–V<sup>m</sup> coupling will occur, where a large [Cai] +2 causes prolonged APD by an enhanced calcium extrusion through INCX. Otherwise, when a large Ca transient reduces ICaL through increased calcium-dependent inactivation, APD will be shortened (Edwards and Blatter, 2014). Ca instability is another multifactorial process. The key components are the fractional Ca release from the sarcoplasmic reticulum (SR), which refers to the relation between the Ca released from the SR and the SR calcium load, and the cytosolic Ca sequestration, which refers to the efficiency of Ca removal from the cytosol through the reuptake to the SR and the extrusion through the Na-Ca exchanger (Weiss et al., 2011). In general, factors increasing fractional Ca release promote Ca alternans and factors increasing Ca sequestration reduce alternans (Edwards and Blatter, 2014). Many studies have attributed cardiac alternans to disturbances of [Cai] +2 signaling, with APD alternans considered a secondary consequence (Eisner et al., 2006; Clusin, 2008; Laurita and Rosenbaum, 2008; Myles et al., 2008; Kanaporis and Blatter, 2015).

Alternans was observed in cardiac tissue as early as 1872 (Traube, 1872), and some of the earliest mathematical models of cardiac action potentials were able to produce such phenomena (Noble, 1962; Beeler and Reuter, 1977). However, later generations of models often failed to produce alternans (DiFrancesco and Noble, 1985; Luo and Rudy, 1991, 1994; Faber and Rudy, 2000), with more detailed species-specific models for rabbit (Puglisi and Bers, 2001; Shannon et al., 2004), dog (Winslow et al., 1999) and human (Priebe and Beuckelmann, 1998; Iyer et al., 2004; ten Tusscher et al., 2004) ventricular action potentials among them. In time, other models have been specifically designed to account for alternans (Fox et al., 2002; Mahajan et al., 2008; O'Hara et al., 2011; Sato et al., 2013).

Recently the FDA's sponsored Cardiac Safety Research Consortium (Sager et al., 2014) proposed a new initiative, the Comprehensive in-Vitro Pro-arrhythmia Assay (CiPA), which specifies the use of mathematical models of cardiac action potentials in the aid of pro-arrhythmic drug risk assessments. Many recently developed ionic models are complex singlecell models with a large number of variables. There exists a large variability in dynamics between them as well as failures to reproduce key physiological features when they are tested in tissue (alternans, reentrant wave dynamics, dominant frequencies, etc.). The known differences between many cell and tissue models make it imperative to validate and verify models with experiments.

Toward this end, in this study, we performed dual opticalmapping recordings with high spatial and temporal resolution for [Cai] <sup>+</sup>2–V<sup>m</sup> during discordant alternans in Langendorffperfused rabbit hearts to better quantify the alternans mechanism as it relates to LQTS. We then used the data for validation and verification of the Sato et al. voltage-calcium rabbit cell model (Sato et al., 2013).

## MATERIALS AND METHODS

#### Heart Preparation

All experiments conform to the current Guide for Care and Use of Laboratory Animals published by the National Institutes of Health (NIH Publication No. 85–23, revised 1996), and approved by the Office of Research and Integrity Assurance at Georgia Tech. New Zealand white rabbits (2–3 kg, n = 8) were anesthetized with ketamine/xylazine/ace-promazine (17/9/0.9 mg/kg) and then injected with heparin (300 U/Kg). After 5 min, euthanasia was induced with 120 mg/kg pentobarbital. Hearts were then quickly removed via a left thoracotomy and perfused retrogradely via the aorta with cardioplegic solution (NaCl: 6.43 g/L, KCl: 1.19 g/L, NaHCO3: 0.84 g/L, MgCl·6H2O: 3.25 g/L, CaCl2: 0.13 g/L), gassed with 95% O<sup>2</sup> and 5% CO2. Then the hearts were immersed in a chamber kept at 37.0 ± 0.3◦C and perfused with Tyrode's solution (NaCl: 7.24 g/L, KCl: 0.30 g/L, NaHCO3: 2.02 g/L, NaH2PO4·H2O: 0.12 g/L, MgCl·6H2O: 0.14 g/L, dextrose: 0.99 g/L, CaCl2·2H2O: 0.29 g/L) gassed with 95% O<sup>2</sup> and 5% CO<sup>2</sup> at a pressure of about 60 mmHg maintained by a peristaltic pump. Motion was suppressed by using blebbistatin at a concentration of 3–5 mM (dissolved in DMSO at the ratio of 5 mg/mL). For imaging, the heart was stained with the voltagesensitive dye JPW-6003 (0.4 mg dissolved in 40µL of pure ethanol) and intracellular calcium-sensitive dye Rhod-2 (1 mg dissolved in 1 mL of DMSO).

#### Optical Mapping

The optical system was previously described (Fenton et al., 2009; Ji et al., 2017). Briefly, six high-power LEDs were used for excitation (LED Engin, San Jose CA). Three LEDs were used for V<sup>m</sup> imaging, coupled with OD4 650/20 nm excitation filters (Edmund Optics), and the other three were used for [Cai] +2 imaging, coupled with OD4 550/20 nm excitation filters. The operations and the intensity of the LEDs were controlled by custom-designed apparatus. Series of fluorescent images corresponding to [Cai] +2 and V<sup>m</sup> dynamics were obtained using the time-multiplexing method with a single camera (Photometric Evolve 128 EMCCD), with which the switching of the different excitation LEDs was synchronized. Fluorescence images from the anterior view (partial RV and LV) were obtained at spatial resolution of 128 × 128 pixels (full frame) at 500 fps digitized with a 16-bit dynamic range A/D.

# Stimulation Protocol

External bipolar stimuli (3–5 ms, strength twice diastolic threshold) were applied from the apex or the base using a downsweep pacing protocol with the pacing cycle length (PCL) starting from 400 ms. For each PCL, 150–200 stimuli were delivered to allow the system to reach steady state. The PCL was gradually shortened with decreasing steps once alternans started to appear until the occurrence of VF or wave block at any point along the wavefront propagation, usually between 150 and 130 ms. The programming sequence was coordinated with the internal camera trigger clock using an Arduino (Uno R3) so that each pacing stimulus was delivered at a known time point when the camera started to acquire a certain frame. This method allowed us to perform image stacking (Uzelac and Fenton, 2015) once steady state was reached and to detect APD and CaD variations with temporal resolution better than the 2 ms sampling rate of the camera. We found the ability to reach faster pacing rates without inducing fibrillation was highly correlated with uniform physiological temperature across the entire heart and with smaller PCL steps, especially when the PCL was less than 160 ms. To achieve stable and uniform temperature, the heart was submerged in heated Tyrode's solution and a thermometer calibrated to the precision of 0.01◦C (Thermo-Fisher) was used for temperature measurement. In case of VF, the heart was defibrillated via low-energy anti-fibrillation pacing (Fenton et al., 2009) or with cardioplegia and was allowed to recover for 30 min before performing subsequent downsweep pacing for comparison.

#### Data Analysis

As part of the experimental data processing, stacking (ensemble averaging) was used to obtain a high S/N ratio to avoid filtering the [Cai] <sup>+</sup>2–V<sup>m</sup> signals (Uzelac and Fenton, 2015), which degraded both spatial and temporal resolutions. For each pixel, we recorded at least 150 cycles for one pacing period, then we stacked (summed) the signals for even and odd beats, excluding the first 10 cycles at the start of each PCL to allow the heart to reach the steady state.

Alternans in voltage were quantified by measuring the action potential duration (APD) and the alternans in calcium by measuring calcium transient duration (CaD). When calculating the APD and CaD, the voltage and calcium signals were first normalized between 0 and 1 for each pixel. Then the APD was calculated using a threshold of 0.5, and the CaD was calculated using a threshold of 0.4.

#### Numerical Simulations

The Sato et al. (2013) model for rabbit ventricular cells in space was used under conditions similar to those of the rabbit experiments. Briefly, each cardiac cell of a one-dimensional cable of tissue is modeled by 75 sarcomeres connected through the diffusion of cytosolic calcium (Cai) and network sarcoplasmic reticulum (NSR) calcium. The diffusion strengths are 8 × 10−<sup>9</sup> cm<sup>2</sup> /ms and 4 × 10−<sup>10</sup> cm<sup>2</sup> /ms, respectively. Voltage in the 75 sarcomeres within one cell is considered to be the same due to the fast diffusion inside a cell. Each sarcomere consists of four compartments: cytosol, submembrane, NSR and junctional SR (JSR). The calcium fluctuation is model by the Langevin equation with a noise term depending on the number of SERCA pumps.

One-dimensional tissue is modeled by the cable equation:

$$\frac{\partial V}{\partial t} = -\frac{I\_{ion}}{C\_m} + D\_V \frac{\partial^2 V}{\partial x^2},\tag{1}$$

where C<sup>m</sup> is the membrane capacitance (1 µF/cm<sup>2</sup> ), D<sup>v</sup> is the voltage diffusion coefficient (10−<sup>3</sup> cm<sup>2</sup> /ms), and Iion is the total transmembrane current, which is the sum of all the ionic currents:

$$I\_{ion}^i = I\_{Na}^i + I\_K^i + \sum\_{j=1}^{M} \left( I\_{Ca}^{i,j} + I\_{NaCa}^{i,j} \right) \tag{2}$$

Here I i ion is the ionic current (Sato et al., 2013). Index i is the cell index in the 1D cable and index j is the index for the jth sarcomere in the ith cell. M is the total number of sarcomeres in one cell (i.e., 75 in our simulations). The cable equation is integrated using an operator splitting approach with 1x = 0.015 cm and 1t = 0.1 ms. The diffusion of calcium between cells is considered negligible.

Three different pacing protocols were used for the 1D simulations, with each using a stimulus current applied to the first five cells for a duration of 2 ms. In the first pacing protocol, we started by pacing with PCL = 600 ms until steady state was reached, then decreased the PCL to 300 ms and paced until steady state was reached. In the second pacing protocol, we initially assigned to the whole cable the steady state variables for the leftmost cell for PCL = 600 ms, then we gradually decreased the PCL to 300, 295, 290, 285, 280, 270, and 260 ms. For PCLs longer than 300 ms, we used the third pacing protocol, in which we used the steady state of PCL = 300 ms from the second protocol as the initial condition. When calculating APD, −80 mV (about 80% repolarization) was used as the threshold. When calculating CaD, the threshold was set to be between 10 and 20% of the repolarization, adjusted among different pacing cycle lengths to make sure both even and odd beats can be captured.

#### RESULTS

#### [Ca]i Alternans Develops at Longer PCLs than APD Alternans

The spatiotemporal dynamics of voltage and calcium in cardiac tissue depends on the pacing period. **Figure 1A** shows snapshots of voltage (upper two rows) and calcium (lower two rows) in a rabbit ventricle for a series of PCLs from 350 to 140 ms when stimulation was applied at the base of the heart (black arrow). Each column shows consecutive even and odd images during steady state 120 ms after stimulus application; all frame over two successive beats at steady state are shown in Supplementary Movie 1. **Figure 1B** shows the same situation but when the stimulus is applied to the apex, and Supplementary Movie 2 shows all frames over two successive beats at steady state for this case. In all rabbit experiments, Ca alternans clearly developed at longer PCLs than voltage alternans. As the tissue was paced more rapidly, inhomogeneity emerged in both voltage and calcium patterns with calcium displaying more spatial heterogeneity compared to voltage. **Figures 2A,B** shows the voltage and calcium signals, respectively, over time for one pixel indicated by a marker in **Figure 1** for all PCLs. As the PCL decreases, alternans was detected first in calcium amplitude (250 ± 10 ms), then in calcium duration (220 ± 15 ms), and finally in APD (200 ± 15 ms). The shortest PCLs can barely generate an excitation in calcium for the short beats (last two panels in **Figure 2B**), and alternans is more pronounced in both duration and amplitude for the calcium signal.

# Discordant Alternans Nodes Are More Pronounced in [Ca]i than in APD

**Figure 3A** shows the spatial dispersion of APD for successive beats at steady state. Several important features are worth noticing. At long PCLs (e.g., >250 ms), there is no difference between even and odd beats (no alternans), but there is an intrinsic smooth spatial dispersion of APDs in the range of 15 ms for each beat. As concordant alternans and then discordant alternans develop, the gradient of APD increases to around 30 ms as the PCL decreases. The distance between the locations of the longest and shortest APD decreases during DA, similar to what has been observed in canine hearts (Gizzi et al., 2013). During DA, the regions of long-short and short-long APD are separated by a collection of nodes (nodal lines) where the APD remains constant from beat to beat (shown as white lines in **Figure 3**), with more nodes forming as the PCL decreases. **Figure 3B** shows the CaD dispersion in tissue, similar to **Figure 3A**. However, during DA, the nodal lines are thicker and more pronounced compared to voltage nodal lines. **Figures 3C,D** shows plots similar to **Figures 3A,B** for the same preparation but with the pacing site located at the apex instead of the base. The progression from no alternans to CA and then to DA occurs at the same PCLs, but the spatial patterns are different. This difference of patterns depending on pacing site was observed in all 8 rabbit experiments as well as in previous studies using canine hearts (Gizzi et al., 2013).

Previous numerical studies of alternans (Qu et al., 2000; Watanabe et al., 2001; Fenton et al., 2002; Skardal et al., 2014) have used one-dimensional cables to quantify the spatial profiles of APDs, including the number of nodes present. In the same way, **Figure 4** displays the values of APD and CaD along a line across the heart's surface for two successive beats during alternans. As in **Figure 3**, it can be seen that there is no alternans for PCL >250 ms, then concordant alternans in voltage and calcium appears for PCLs between 200 and 180 ms. At 170 ms, there is CA in voltage but DA for calcium, and for PCL <170 ms DA is present for both voltage and calcium. We calculated in **Table 1** the steepness (slope) of the APD and CaD nodal lines for PCL between 160 and 146 ms corresponding to **Figures 4I–L** when the DA are most pronounced. Data was presented as mean ± s.d., averaged among the slopes at each node for even and odd

FIGURE 2 | Time traces of normalized voltage (A) and [Ca]i (B) signals from a single pixel marked in Figure 1A for the same PCLs.

beats for each pacing cycle length. It clearly shows that CaD nodal lines are about one order of magnitude steeper than APD nodal lines, indicating the diffusive connection among cells differs in voltage and calcium signals (Shiferaw and Karma, 2006; Gaeta et al., 2009), as the lack of diffusion in calcium leads to calcium profiles that are sharper in space compared to voltage.

## Experimental Alternans Features Smoother Spatial Profiles and Slower Alternans Amplitude Growth than Simulated Alternans

Simulation results using the Sato et al. model confirm that alternans appear as the PCL is decreased. However, the PCLs at which they appear are much longer compared to experiments. **Figures 5**, **6** show voltage and calcium alternans in a 1D cable 3 cm in length. **Figure 5** illustrates APD as a function of length in the left column for even and odd beats at PCLs of 400, 300, and 260 ms. The right column shows the voltage signal for the corresponding PCL for two cells, one near the left end and one near the right end of the cable, so that if it

but transitions between discordant alternans phases are sharper and nodes are more pronounced. (C,D) Spatial distributions as in (A,B) but for pacing from the apex.

PCLs as in Figure 3.

undergoes discordant alternans, the voltage signal of the two cells should be out of phase. **Figure 6** shows similar plots but for calcium. The left column indicates CaD over the cable for even and odd beats for the same PCLs as in **Figure 5**. The right column of **Figure 6** displays the calcium signal from two sarcomeres for corresponding PCLs, with the two sarcomeres chosen so that if there is discordant alternans in calcium, the two sarcomeres should be out of phase. Results for other PCLs (600, 500, 450, 350, 290, 280, and 270 ms) are presented in Supplementary Figure 1 for APD and Supplementary Figure 2 for CaD.

For large PCLs (>400 ms), there is no alternans in either voltage or calcium (Supplementary Figures 1A–C, 2A–C). When the PCL drops to 400 ms, concordant alternans appears (**Figures 5A**, **6A**). For PCLs 300 ms or below, discordant alternans occurs (**Figures 5C,D**, **6C,D** and Supplementary Figures 1E–G, 2E–G). In all these simulations, voltage and calcium alternans are "synchronized," such that if there is

TABLE 1 | Steepness of APD and CaD nodal lines.


no voltage alternans, there is no calcium alternans, and if there is discordant voltage alternans, there is discordant calcium alternans, with the exception of **Figures 5B**, **6B**. In **Figures 5B**, **6B**, where we used the second pacing protocol and the PCL is the same as **Figure 5C**, we obtained concordant voltage alternans, whereas the calcium alternans is discordant with multiple nodes. By using different initial conditions, it is possible to obtain completely different dynamics for the same PCL. The Sato et al. model is very sensitive to initial conditions due to the random fluctuation term in the SERCA pump, and in this respect, it is similar to experiments, where it has been shown that small changes in initial conditions can result in very different alternans patterns (Gizzi et al., 2013). In all the simulations presented in this paper, the random noise was generated using the same seed. We did not observe significant changes when we repeat the simulations with different seeds (data not shown).

One major difference between the experiments and the simulations is how sharp the calcium transition is between different alternans phases. In the experiments, both APD and CaD have relatively similar smooth transitions between the maximum and minimum values (**Figures 3**, **4**), with calcium showing only a slightly faster transition, whereas in simulations, CaD has a significantly sharper transition than APD (**Figures 5**, **6**). In addition, in experiments, as the PCL is decreased, CaD transitions from no alternans to concordant alternans and then to discordant alternans with the alternans amplitude increasing smoothly. In simulations, on the other hand, CaD changes drastically from no alternans to concordant alternans with an amplitude of 150 ms when the PCL decreases from 450 to 400 ms.

**Figure 7** shows a bifurcation diagram for APD (left) and CaD (right) as a function of PCL calculated at one point from the numerical simulation of the 1D cable (top) and experimental data (bottom) where the alternans has the largest amplitude. As the PCL is decreased from 600 to 260 ms in the numerical simulations, the bifurcation appears simultaneously for both voltage and intracellular calcium just above a CL of 400 ms (PCLc). The bifurcation amplitude for voltage grows at a rate of the square root away from the bifurcation point (∆APD ∼ (PCL − PCLc) 1/2 ) (Cherry and Fenton, 2008). The bifurcation amplitude in calcium experiences a sharp discontinuous jump (see Supplementary Figure 3 for the curve fitting). In contrast, the experimental bifurcations occur at much lower PCLs close to 250 ms, and the amplitude of alternans just beyond the bifurcation can be fit better into a linear function with a smoother growth than in the simulations.

# DISCUSSION

Patients with LQTS have a higher risk of cardiac arrhythmias due to augmentation of the T-wave and increased spatial dispersion. For many years now, detection of LQTS and Twave alternans in the ECG has been used as a quantitative tool for predicting dangerous spatial variations in dispersion, which are dynamically induced at the cellular level and can induce arrhythmias. Since 2005, the FDA has required that new drugs be tested for QT prolongation and development of T-wave alternans and recently an FDA-sponsored consortium proposed an initiative to use mathematical action potential models in the aid of drug risk assessment. If models are indeed to be used to investigate pro-arrhythmic and antiarrhythmic effects of drugs, they first need to be validated against experimental data in normal conditions. The main goal of this study is to create an in tissue experimental data set of simultaneous voltage and calcium optical mapping recordings from Langendorff-perfused rabbit hearts at high temporal and spatial resolution and in particular during alternans for use in validating the dynamics from numerical simulations from the most recent model of rabbit ventricular action potentials (Sato et al., 2013).

We found that alternans in voltage and calcium develops similarly in both experiments and simulations as the pacing cycle length is decreased; however, the model developed alternans much sooner at longer periods close to 420 ms compared to 240 ± 10 ms in experiments. Likewise, the minimum period of stimulation before conduction block developed earlier at 260 ms in the model vs. 140 ± 5 ms in the experiments. Also, it is important to notice that in experiments, as in the models, the magnitude in variations of the APD were much smaller than the variations in CaD during alternans. However, the magnitudes in alternans duration were about twice as large in the model as in the experiments, with maximum values of 55 ms for APD and 150 ms for CaD in the model vs. 25 ± 4 and 65 ± 5 ms, respectively, for the experiments.

More crucial differences arise from the larger differences in how alternans develops. In experiments, alternans in voltage develops gradually, appearing to be more consistent with a border-collision bifurcation (Cherry and Fenton, 2007, 2008; Zhao et al., 2008), where small changes in duration grow slowly and mostly linearly, whereas in the model alternans grows much faster, as with a pitchfork bifurcation (Cherry and Fenton, 2008). Furthermore, the model does not yield action potential amplitude (APA) alternans as observed in the experiments when the tissue is paced at very short pacing cycle lengths (see Supplementary Figure 4 for the APA bifurcation map from experiment), an important additional pro-arrhythmic mechanism recently described by Myles et al. (2011); Chen et al. (2017). On the other hand, while intracellular calcium does display amplitude alternans in both experiments and simulations, in experiments amplitude alternans develops slowly, while in the model a large difference in amplitude appears as soon as alternans develops and persists with a similar amplitude for all periods where alternans is present, as shown in **Figure 6**.

In regard to spatial distributions, in our experiments, we do not detect very sharp calcium duration transitions around nodal lines for most pacing cycle lengths; instead, we observe a smooth phase transition in both voltage and calcium, albeit with calcium appearing sharper, with more defined nodal lines than those in APD (**Figure 3** and **Table 1**). This is contrary to simulations where CaD alternans transition can happen within a cell. If the coupling between voltage and calcium is strong, calcium and voltage should have similar dynamics, i.e., the CaD alternans nodal line should follow that of the APD and vice versa. Therefore, we think the model, as it was published, lack necessary coupling between voltage and calcium. The resolution of our optical mapping is on the order of 200–250 microns; however, due to scattering (Bishop et al., 2007), the actual area may be smoothed to about a millimeter, which is still high enough to identify any possible sharp differences in heterogeneities between voltage and calcium. It is then possible that during pacing in tissue, calcium nodal lines still follow the smoother dynamics of voltage compared to when it is performed in single cell experiments (Gaeta et al., 2009).

#### Shortcomings of the Model

While the PCL at which alternans appears is much higher in the model than in the experiments by approximately 180 ms, this difference could be fixed with a simple re-scaling of some of the time constants of the model. Similarly, the difference between the minimum PCL for propagation (around 260 ms for the model compared to 140 ms for experiments) could also be fixed by modifications to the recovery and inactivation time constants of the sodium gating variables. Previous publication also showed that CaD alternans patterns can be smoothed by increasing voltage instability (and/or reducing Ca instability). However, there exist several other key physiological aspects that would require a more in-depth analysis and validation of the model's equations.

I. Type of bifurcation. The calcium dynamics should represent the fast nonlinear transition in the dynamical content of calcium in the sarcoplasmic reticulum (Díaz et al., 2004) that can result in a border-collision bifurcation with slow linear growth.


#### Limitations

The mechanical and electrical behaviors of the heart are strongly coupled through calcium signaling. Very few mathematical models incorporate both aspects (Ji et al., 2015) even though there exists a strong bi-directional coupling between them. We did not study the effect of alternans on contraction or vice versa in

#### REFERENCES


either experiments or simulations and we did not study the effect of temperature on calcium and voltage alternans. It has been shown that mammalian hearts can largely increase the magnitude of alternans when temperature is lowered (Pastore et al., 1999; Fenton et al., 2013; Filippi et al., 2014).

# DISCLOSURE

The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services.

# AUTHOR CONTRIBUTIONS

IU: experiment, data analysis and writing. YJ and EC: simulation and writing. DH, JS, SL, amd RG: experiment. FF: experiment, simulation and writing.

# FUNDING

AHA15POST25700285, NSF1341128, and CPS-1446312.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.00819/full#supplementary-material


formulation and experimental validation. PLoS Comput. Biol. 7:e1002061. doi: 10.1371/journal.pcbi.1002061


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer DS and handling Editor declared their shared affiliation, and the handling Editor states that the process met the standards of a fair and objective review.

Copyright © 2017 Uzelac, Ji, Hornung, Schröder-Scheteling, Luther, Gray, Cherry and Fenton. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics

Jaehee V. Shim<sup>1</sup> , Bryan Chun<sup>2</sup> , Johan G. C. van Hasselt <sup>1</sup> , Marc R. Birtwistle<sup>1</sup> , Jeffrey J. Saucerman<sup>2</sup> and Eric A. Sobie<sup>1</sup> \*

*<sup>1</sup> Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, United States, <sup>2</sup> Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, United States*

Tyrosine kinase inhibitors (TKIs) are highly potent cancer therapeutics that have been linked with serious cardiotoxicity, including left ventricular dysfunction, heart failure, and QT prolongation. TKI-induced cardiotoxicity is thought to result from interference with tyrosine kinase activity in cardiomyocytes, where these signaling pathways help to control critical processes such as survival signaling, energy homeostasis, and excitation–contraction coupling. However, mechanistic understanding is limited at present due to the complexities of tyrosine kinase signaling, and the wide range of targets inhibited by TKIs. Here, we review the use of TKIs in cancer and the cardiotoxicities that have been reported, discuss potential mechanisms underlying cardiotoxicity, and describe recent progress in achieving a more systematic understanding of cardiotoxicity via the use of mechanistic models. In particular, we argue that future advances are likely to be enabled by studies that combine large-scale experimental measurements with Quantitative Systems Pharmacology (QSP) models describing biological mechanisms and dynamics. As such approaches have proven extremely valuable for understanding and predicting other drug toxicities, it is likely that QSP modeling can be successfully applied to cardiotoxicity induced by TKIs. We conclude by discussing a potential strategy for integrating genome-wide expression measurements with models, illustrate initial advances in applying this approach to cardiotoxicity, and describe challenges that must be overcome to truly develop a mechanistic and systematic understanding of cardiotoxicity caused by TKIs.

Keywords: tyrosine kinase inhibitors, quantitative systems pharmacology, mathematical modeling, drug-induced adverse events

#### INTRODUCTION

Tyrosine kinase inhibitors (TKIs) constitute a class of cancer therapeutics, many of which are known to cause cardiotoxicity as a major adverse event. Reported cardiotoxicities include heart failure, cardiomyopathy, conduction abnormalities, QT prolongation, and myocardial injury. The most common toxicity is systolic dysfunction or cardiomyopathy, potentially leading to heart failure, which is most likely mediated through direct toxicity of cardiomyocytes (Albini et al., 2010; Eschenhagen et al., 2011; Force and Kolaja, 2011; Raschi and De Ponti, 2012; Ewer and Ewer, 2015).

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Daniel Andrew Beard, University of Michigan, United States Steven Alexander Niederer, King's College London, United Kingdom*

> \*Correspondence: *Eric A. Sobie eric.sobie@mssm.edu*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *29 June 2017* Accepted: *16 August 2017* Published: *08 September 2017*

#### Citation:

*Shim JV, Chun B, van Hasselt JGC, Birtwistle MR, Saucerman JJ and Sobie EA (2017) Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics. Front. Physiol. 8:651. doi: 10.3389/fphys.2017.00651*

**208**

Trastuzumab, an inhibitor of the HER2 receptor tyrosine kinase (Slamon et al., 2001; Piccart-Gebhart et al., 2005; Romond et al., 2005; Force et al., 2007) was both the first monoclonal antibody TKI given FDA approval (in 1998) and the first TKI reported to cause cardiotoxicity (Wu et al., 2016). Since the reports of trastuzumab-induced toxicity, several additional targeted cancer therapeutics have been classified as cardiotoxic, observations that have contributed to the emergence of a new research field, cardio-oncology (Albini et al., 2010; Bellinger et al., 2015).

Previous studies have shown that TKI-related cardiotoxicity, as seen with trastuzumab, is mostly due to the targeting of pathways that are shared between malignancies and cardiovascular cells (De Keulenaer et al., 2010; Bellinger et al., 2015). Investigations of these adverse events revealed that many of the tyrosine kinases targeted by TKIs serve critical roles in survival and maintenance of cardiomyocytes, leading to unintended on-target toxicity. At the same time, many TKIs inhibit multiple kinases simultaneously, which can cause off-target toxicity (Chen et al., 2008; Force and Kerkelä, 2008; Force and Kolaja, 2011).

Despite the risk of cardiotoxicity, TKIs are still one of the highly effective and favored cancer therapeutics on the market (Eschenhagen et al., 2011; Force and Kolaja, 2011). The success of drugs such as trastuzumab and imatinib, a small molecule inhibitor used to treat chronic myeloid leukemia (CML), has inspired the development of additional TKIs. As of April, 2015, 25 small molecule TKIs have entered the market (Shah and Morganroth, 2015), with many more under development (Bellinger et al., 2015). Given the booming research in the development of TKIs, it would be beneficial to develop a systematic strategy to: (1) evaluate and predict how new TKIs will affect signaling networks in cardiomyocytes; and (2) identify interventions that can reverse and/or mitigate any associated cardiotoxicity. These questions are well-suited to be addressed using a quantitative systems pharmacology (QSP) approach that combines large-scale measurements with mechanism-based mathematical modeling. The diversity of TKI targets and the complexity of cellular mechanisms responsible for cardiotoxicity mean that two drugs with similar targets may operate through different mechanisms, and the effects of two TKIs with different targets may converge on a common pathway. Untangling this type of complexity generally requires computational approaches that are based on biological mechanisms. Therefore, our aims in this Perspective are to review the progress that systems approaches have made in predicting TKI-induced cardiotoxicity and to offer suggestions for how mathematical modeling can be applied to elucidate mechanisms and predict potential adverse events caused by new drugs.

#### TYROSINE KINASE SIGNALING IN CANCER AND STRATEGIES UNDERLYING TKIs

The canonical roles of tyrosine kinases are found in mitogenesis and related processes such as differentiation, metabolism, and migration. Constitutive activation of tyrosine kinase (TK) signaling, via either gain-of-function (GOF) mutations or overexpression due to gene amplification, is found in about 70% of malignancies (Blume-Jensen and Hunter, 2001; Chen et al., 2008). Well-understood examples include overexpression of ERBB2 in HER2<sup>+</sup> breast cancer (Force et al., 2007) and the constitutively active oncogenic fusion protein BCR-ABL, which can cause CML (Force et al., 2007; Chen et al., 2008; Force and Kolaja, 2011). This dependency of tumor formation and proliferation on TK signaling led to the rise of TKIs as promising anti-cancer therapeutics.

Currently, there are two chemical classes of TKIs: (1) humanized monoclonal antibodies (mAbs) and (2) small molecule inhibitors (Force et al., 2007; Chen et al., 2008; Force and Kolaja, 2011). Small molecule TKIs can be further subcategorized based on whether they compete with ATP for the binding pocket or interact with other regions of the protein (Force and Kolaja, 2011). Additionally, TKIs are often identified by the intended target(s) or the target specificity (Force et al., 2007; Bellinger et al., 2015; Gharwan and Groninger, 2015). The most common target groups that are used to classify TKIs include EGFR/ERBB2 inhibitors, VEGFR inhibitors, ABL inhibitors, and multi-targeted drugs that are designed to inhibit at least two different target groups such as VEGFR and ABL (see **Table 1** for descriptions of the important cellular signaling proteins mentioned in the manuscript). **Figure 1A** shows the currentlyapproved TKIs, grouped by the published targets, and indicates how these classifications frequently overlap.

## REPORTED SERIOUS CARDIAC SIDE EFFECTS OF TKIs

The initial discovery of TKI-induced cardiotoxicity was made during the groundbreaking clinical trials of trastuzumab, the first such drug to be marketed (Seidman et al., 2002; De Keulenaer et al., 2010). However, estimated cardiotoxicities of 3–7% with trastuzumab alone and 25% when the drug was administered with an anthracycline (Slamon et al., 2001) were only determined during a post hoc analysis. Similar retrospective analyses have been performed to estimate that sunitinib causes left ventricular dysfunction with an incidence of 4–11% (Yeh and Bickford, 2009; Lenneman and Sawyer, 2016) and the VEGFR inhibitor bevacizumab induces either cardiomyopathy or heart failure in 1.5–3% of patients (Yeh and Bickford, 2009). These examples demonstrate the difficulties associated with identifying cardiotoxicity during drug development. Because clinical trials are primarily focused on evaluating efficacy, they often lack appropriate safety screening measures to identify side effects (Force et al., 2007).

Overall, of the 30 TKIs currently marketed for use in the United States, 26 list serious cardiac side effects as a "black box warning" in their prescription information (FDA and CDER, 2012; Boehringer Ingelheim International GmbH, 2014; Gharwan and Groninger, 2015). The cardiac related black box warnings of TKIs can be categorized into: cardiomyopathy, arrhythmia, myocardial infarction,



hypertension, and pericardial effusion, based on the specific potential adverse events listed in the package insert. In **Figure 1B**, which indicates both the adverse events and the target class for each TKI, we observe no obvious association between the intended primary target, and the reported cardiac risks.

#### MECHANISMS UNDERLYING CARDIOTOXICITY CAUSED BY TKIs

The initial discovery of TKI-induced cardiotoxicity was met with surprise due to the fact that cardiomyocytes are non-dividing and terminally differentiated (Force et al., 2007). Since TKs were mostly known for their role in proliferation and their association with cancer, these kinases were not expected to have any essential role in cardiomyocytes, and toxicity in heart was not anticipated (Chen et al., 2008; Bellinger et al., 2015). The discovery of TKIinduced cardiotoxicity, therefore, became a driving force for uncovering the roles of tyrosine kinases in heart. The research spurred by these adverse events has allowed us to appreciate that many of the pathways responsible for proliferation in malignant cells also play important roles in cardiomyocytes in: (1) survival signaling; (2) mitochondrial and sarcoplasmic reticulum (SR) homeostasis; and (3) electrical and contractile function.

#### Survival Signaling

The role of tyrosine kinases in cardiomyocyte survival signaling was first discovered through the on-target cardiotoxicity caused by trastuzumab. Before the cardiotoxicity reports, expression of trastuzumab's target, ERBB2, was reported to be low in cardiomyocytes, and this receptor's role was unknown (Bellinger et al., 2015). However, subsequent studies have discovered that ERBB2 plays an important role in maintaining cardiomyocyte health, evidenced by the spontaneous dilated cardiomyopathy that results from ERBB2 knockout (Crone et al., 2002; De Keulenaer et al., 2010). More specifically, ERBB2 in cardiomyocytes has been shown to serve as a co-receptor in a critical cardiomyocyte survival pathway initiated by neuregulin-1 (Mellor et al., 2011; Bellinger et al., 2015). Neuregulin-1, a paracrine factor secreted by cardiac endothelial cells, activates mitogenic pathways through ERBB2 heterodimer formation with other members of the EGFR family, ERBB3 or ERBB4 (Chen et al., 2008; De Keulenaer et al., 2010).

Similarly, another EGFR family member, ERBB1, has also been implicated in cardioprotection and myocyte survival (Mellor et al., 2011; Bellinger et al., 2015), including cardiomyocyte defenses against the deleterious consequences caused by excessive β-adrenergic receptor stimulation (Chen et al., 2008). This role was based on the finding that an ERBB1 inhibitor, erlotinib, exacerbates isoproterenol-induced myocardial injury (Chen et al., 2008). Erlotinib is associated with cardiotoxicity, including cardiac arrhythmia and myocardial infarction (Gharwan and Groninger, 2015). One of the downstream pathways common to signaling through ERBB1 and ERBB2 is the lipid kinase PI3K, which in turn activates the protein kinase Akt. The PI3K-Akt axis is critical in survival signaling, and dysregulation of this pathway has been shown to induce ischemic heart disease, hypertrophy, and heart failure (Reichelt et al., 2017).

Raf-1, which belongs to the Raf family of serine/threonine kinases, is another important component of pro-survival signaling that has been linked to both inherited heart disease (Dhandapany et al., 2014), and TKI-induced cardiotoxicity. Specifically, Raf-1 has been identified as a critical component of cardiotoxicity caused by sorafenib (Force et al., 2007; Chen et al., 2008), a multi-target TKI used to treat renal and liver cancers. The inhibition of Raf-1 by sorafenib is thought to block survival

signaling through the protein kinase ERK, and concurrently to disinhibit pro-apoptotic kinases. This dual action of prosurvival signaling inhibition and apoptotic signaling activation can culminate in cell death (Force et al., 2007).

# Sarcoplasmic Reticulum and Mitochondrial Homeostasis

In addition to pro-survival signaling, TKs are known to be closely linked to processes that maintain the health and function of cardiomyocytes through mitochondrial and SR homeostasis (Force and Kolaja, 2011). Mitochondria are responsible for matching the cellular supply of ATP with the energetic demand whereas the SR functions to both modulate the quantity of Ca2<sup>+</sup> released with each heartbeat and to control the processing of many critical proteins.

When TKI-induced toxicity involves mitochondrial or SR function, the processes seem to be closely linked. Specifically, mitochondrial dysfunction resulting from TKI treatment can lead to membrane permeabilization and the release of reactive oxidative species to the cytoplasm. This oxidative stress can in turn lead to SR dysfunction through both altered Ca2<sup>+</sup> release and the activation of signaling pathways that may ultimately lead to apoptosis (Groenendyk et al., 2010).

Cardiotoxicity caused by imatinib, a multi-targeted ABL inhibitor, has been proposed to follow this precise mechanism (Kerkelä et al., 2006; Force et al., 2007; Mellor et al., 2011). The on-target effect of imatinib has been linked to the disturbance of SR homeostasis via inhibition of an ABL isoform that is localized in the SR. This can eventually initiate apoptosis through JNK activation. Consistent with this hypothesis, postmortem histological examinations of patients treated with imatinib have revealed dilated SR structures, and experiments in isolated cardiomyocytes shown that imatinib can induce mitochondrial membrane potential collapse (Kerkelä et al., 2006).

Another example of interference with SR and mitochondrial homeostasis is cardiotoxicity caused by the multi-kinase inhibitor sunitinib. Sunitinib has been reported to cause ATP depletion in cardiomyocytes through an off-target effect involving AMPactivated protein kinase, or AMPK (Force et al., 2007). The unintentional inhibition of AMPK is thought to activate energyconsuming processes, including protein translation and lipid biosynthesis, which can deplete ATP. Given the tremendous energetic demands of the contracting cardiomyocyte, the improper activation of ATP-consuming processes can be highly toxic (Dyck and Lopaschuk, 2006; Zhang et al., 2008).

# Excitation and Contraction

TKI-induced cardiotoxicity can also manifest itself as altered excitation or contraction of cardiac myocytes. These detrimental effects can occur through: (1) direct or indirect modulation of cardiac ionic currents, resulting in pro-arrhythmic electrical activity (Chen et al., 2008; Ghatalia et al., 2015); or (2) structural remodeling that leads to altered myocyte contraction.

TKIs can induce electrophysiological abnormalities directly, via block of ion channels, or indirectly, by altered intracellular signaling that leads to a decrease in K<sup>+</sup> currents. Because K<sup>+</sup>

currents repolarize the cell membrane during action potentials, either direct or indirect reductions of K<sup>+</sup> currents can prolong electrocardiographic QT intervals and increase arrhythmia risk. TKIs that are known to block the most relevant K<sup>+</sup> channel (Kv11.1), encoded by the gene traditionally known as hERG (subsequently renamed KCNH2), include crizotinib, sunitinib, and nilotinib. These drugs have been shown to block the channel in vitro and to prolong action potentials in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) (Doherty et al., 2013). Indirect reductions in K<sup>+</sup> current may possibly be mediated by Src, a tyrosine kinase that can augment current carried by Kv11.1 (Schlichter et al., 2014). Thus, dasatinib and bosutinib, which are dual inhibitors of ABL and Src, can potentially cause reduced K<sup>+</sup> current and QT prolongation (Xu et al., 2009; Gharwan and Groninger, 2015).

Src may also be an important part of the mechanism by which TKIs can induce cellular structural remodeling and impaired contraction. In cardiomyocytes, Src is important for both the organization of sarcomeres and the formation of focal adhesions that connect adjacent cells (Kuramochi et al., 2006). In mice, genetic studies have shown that spontaneous cardiac chamber dilation and disorganization of myofibrils can result from knocking out any of several enzymes in the Src pathway (Peng et al., 2006). Thus, TKIs that inhibit Src may disrupt cardiac contraction by interfering with Src's role in maintaining myocyte structure.

## COMPLEXITIES OF TKI-INDUCED CARDIOTOXICITY AND THE NEED FOR A SYSTEMS APPROACH

From survival and homeostasis to contractile function, tyrosine kinases perform a wide variety of important roles in the health and function of cardiomyocytes. Although considerable progress has been made to decipher the roles of individual TKs, the breadth of the different mechanisms involved makes it difficult to draw general conclusions about TKI-induced cardiotoxicity. Moreover, even when some mechanistic details have been uncovered, our understanding is primarily qualitative, and biological mechanisms cannot usually be connected to factors such as dosing and the physiological characteristics of individual patients. Given the past success of TKIs as cancer therapeutics and the drive to develop additional TKIs, it would be beneficial to develop a systematic strategy to: (1) evaluate the potential cardiotoxicity of new TKIs; (2) predict the mostly likely mechanisms involved; and (3) suggest strategies for mitigating and/or reversing toxicity. Systems approaches that perform largescale measurements and quantitatively compare responses to multiple drugs are likely to be extremely useful for understanding the common and distinct features of cardiotoxicity caused by diverse TKIs.

A common approach in systems-level pharmacology studies is to utilize a cell based, high-throughput drug screening assay. Although cardiovascular pharmacology has traditionally not been well-suited for high throughput studies, the development of hiPSC-CMs has expanded the possibilities. For instance, a recent study described the development of a comprehensive assay that evaluated cellular effects of TKIs in hiPSC-CMs (Sharma et al., 2017). Using hiPSC lines from 13 individuals, the investigators examined how 21 FDA-approved small molecule TKIs affected cell viability, contractility, and gene expression. By integrating the results with literature-reported TKI serum levels in patients, the authors developed a novel cardiac safety index for TKIs (Sharma et al., 2017).

Although this study represents a significant milestone in that it integrates cutting edge technologies such as deep sequencing and high-throughput imaging, room for improvement nonetheless remains. Specifically, the experiments performed in this study represent snapshots of cell state after TKI treatment, and the data can therefore provide only limited insight into the dynamics of toxicity development. Moreover, experiments performed using individual drugs cannot predict how either a second drug or a circulating hormone (e.g., adrenaline, angiotensin) might either exacerbate or protect against cardiotoxicity. Although it is of course possible to expand the assay to treat cells with drug pairs and/or add relevant physiological stimuli, it is not clear a priori which additional perturbations might be informative or relevant. Finally, even when unambiguous results are seen in cellular highthroughput assays, the mechanistic details often remain hidden. It would therefore be helpful to couple such high-throughput measurements with integrative computational analyses that can potentially overcome these limitations.

#### MECHANISTIC MATHEMATICAL MODELING TO IMPROVE TOXICITY TESTING

One way to address the aforementioned limitations is to use mathematical models that mechanistically describe biological dynamics. When the processes simulated by these models overlap with toxicity mechanisms, the simulations can be used to generate testable predictions, to guide experimental studies, and ultimately to make decisions about new drugs based on a quantitative understanding of benefits and risks. In this context, models that describe biological mechanisms through differential equations are frequently referred to as QSP models (Leil and Bertz, 2014; Gadkar et al., 2016). Although precise definitions remain a matter of debate, QSP models are generally distinguished from both purely empirical, statistical approaches such as computing a risk score for a drug based on a series of measurements (Kramer et al., 2013; Mistry et al., 2015), and pharmacokinetic models that can predict the effects of dosing on cardiotoxicity (van Hasselt et al., 2012) but generally offer only limited mechanistic insight. Although QSP models have been exploited to understand cardiotoxicity caused by anthracyclines (de Oliveira et al., 2016), the application of QSP to TKI-induced cardiotoxicity is still in its early stages. Given the recent development of QSP modeling, it is instructive to consider examples in which mechanistic models have been successfully applied to the study of adverse events, in particular drug-induced liver injury (DILI) (Huang et al., 2013; Shoda et al., 2014; Yang et al., 2015), and drug-induced arrhythmias (Moreno et al., 2011; Sarkar and Sobie, 2011; Britton et al., 2013; Cummins et al., 2014; Grandi and Maleckar, 2016; Yang et al., 2016). Specifically, we emphasize how mechanistic models can be integrated with large in vitro data sets, as these studies may provide an important blueprint for future research on cardiotoxicity caused by kinase inhibitors.

An example of the success of QSP models for toxicity applications can be found in the development of DILIsym <sup>R</sup> , a mathematical model and software package used for predicting DILI. DILIsym <sup>R</sup> comprises multiple sub-models describing relevant biological processes involved in hepatotoxicity such as drug distribution in the liver, bile acid homeostasis, reactive metabolite generation and disposition, oxidative stress, immune responses, and the hepatocyte life cycle (Woodhead et al., 2017). The value of this approach was recently demonstrated in studies that examined differences in hepatotoxicity between acetaminophen and its less toxic isomer 3′ -hydroxyacetnilide. Although the former drug can cause toxicity across many species, the latter has been shown to cause DILI in humans and rats, but not in mice. Using the mechanistic DILIsym <sup>R</sup> model, a testable hypothesis was generated in which the amount of reactive metabolite produced from each isomer was identified as an important contributor to the observed species differences, and this prediction was confirmed experimentally in a later study (Kyriakides et al., 2016). In addition to the consortium that has developed the DILIsym <sup>R</sup> package, other groups have gained important insight into DILI through mathematical modeling (Smith et al., 2016; Blais et al., 2017; Thiel et al., 2017).

To understand and predict drug-induced arrhythmias, e.g., Torsades de Pointes (TdP), the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative is highly relevant. This effort, part of the FDA's Critical Path Initiative, aims to improve the accuracy and cost effectiveness of screening for TdP risk. Whereas current in vitro methods for predicting TdP risk focus almost exclusively on block of Kv11.1 (i.e., the hERG channel), an approach that is often inadequate, CiPA intends to both assess how drugs block multiple ion channels and to combine these measurements with recordings in hiPSC-CMs and mechanistic simulations (Sager et al., 2014; Fermini et al., 2016). A couple of recently-published studies highlight the value that is gained by utilizing QSP models. Lancaster and Sobie, for example, used models of human ventricular myocytes to simulate physiological changes caused by 67 unique drugs, some that are known to cause TdP, and others that are apparently safe. In addition to providing a classification model that was superior to Kv11.1 block alone, the simulations provided testable predictions about the most informative assays to perform in cellular experiments and the specific ion transport pathways that, when affected by a drug, may contribute to TdP risk (Lancaster and Sobie, 2016). More recently, Li et al. showed that incorporating the kinetics of Kv11.1 block into simulations provides superior identification of TdP risk than simply considering steady-state block measurements (i.e., an IC50-value), and the study suggested an experimental protocol for measuring drug block kinetics (Li et al., 2017).

The examples of both DILI and drug-induced TdP demonstrate the value that can be added when mechanistic modeling is used to address toxicity. The simulations can uncover the reasons for counterintuitive results, such as drugs that block Kv11.1 but are nonetheless safe (Kramer et al., 2013; Lancaster and Sobie, 2016; Li et al., 2017), or drugs that only cause hepatotoxicity in some species (Kyriakides et al., 2016; Smith et al., 2016; Blais et al., 2017; Thiel et al., 2017; Woodhead et al., 2017). The simulations can also suggest the prioritization of experiments that are most likely to provide additional insight.

# INITIAL EFFORTS TO USE QSP APPROACHES TO UNDERSTAND TKI-INDUCED CARDIOTOXICITY

TKI-induced cardiotoxicity is a problem that seems well-suited to a QSP approach because tyrosine kinase signaling encompasses large, complex networks with numerous feedback loops, and understanding how a drug alters TK cascades is therefore extremely complicated. Although mechanistic modeling to predict TKI-induced cardiotoxicity is much less well-developed than for DILI or TdP, efforts that may yield breakthroughs in the next few years are currently underway.

As noted above, an important recent study by Sharma et al. (2017) derived a "toxicity index" by examining effects of TKIs in hiPSC-CMs through several assays. Although the large-scale nature of this study justifies the "systems" label, and the toxicity index is a quantitative risk score, it's important to emphasize that QSP modeling, which can provide mechanistic insight and actionable predictions, is complementary to a high-throughput, data-driven strategy such as that used in this study (Sharma et al., 2017).

Another notable recent effort is a study by Shin et al. (2014). These investigators combined experimental measurements with simulations to uncover mechanisms by which high and sustained doses of the β-adrenergic receptor agonist isoproterenol could increase myocyte susceptibility to apoptosis (Shin et al., 2014). This study is an important example of how simulations often generate novel experimentally-testable predictions, and the work can potentially be extended to examine TKI-induced toxicity.

To fill current gaps in knowledge and obtain new mechanistic insight, the Drug Toxicity Signature Generation (DToxS) Center at Mount Sinai has initiated a large-scale project to advance cellular assays and computational approaches that can improve our understanding of TKI-induced cardiotoxicity. One aspect of this project involves employing QSP models that describe biological processes potentially involved in this cardiotoxicity. We outline here an approach by which whole transcriptome expression assays can be integrated with mechanistic models to classify drugs and generate novel, experimentally-testable predictions.

For this part of the analysis, the project has designed a standard experimental protocol (DtoxS—Drug Toxicity Signature Generation Center—SOP, https://martip03.u.hpc. mssm.edu/sop.php) that captures early effects of drugs, as reflected in gene expression changes. The experiments treat cultured cardiomyocyte-derived cells with potentially cardiotoxic TKIs as well as drugs from different classes that are presumably safe. After 48 h, mRNA is harvested, and sequencing is performed to quantify drug-induced changes in gene expression (compared with vehicle-treated controls). Data are released at the DToxS website and can be freely-downloaded (DtoxS—Drug Toxicity Signature Generation Center—Data

data obtained in a single cell line after treatment with 24 TKIs, and six non-TKIs (control drugs that are presumed to not cause cardiotoxicity). Each circle represents an individual drug, the line indicates the mean value for each group under basal activity (left), isoproterenol stimulation (middle), and endothelin-1 stimulation (right).

& Resources, https://martip03.u.hpc.mssm.edu/data.php). The pipeline for integrating these released data with mechanistic mathematical models is shown in **Figure 2**, top. Changes in mRNA levels in drug treated cells (**Figure 2A**) can be translated into parameter alterations in models that describe processes potentially relevant to the toxicity (**Figure 2B**), and simulations are then performed with these models. This workflow assumes that before overt toxicity is induced, drugs can alter the cellular state in relatively subtle ways. Mechanistic simulations may then allow one to predict how this drug-induced altered cellular state influences the response to various physiological stimuli.

For example, results shown here are obtained with a QSP model that describes signaling events relevant to cardiac hypertrophy through a system of 106 ordinary differential equations, each one describing activity of a signaling component (Ryall et al., 2012). This model was chosen for initial simulations because the progression to heart failure due to pathological remodeling often includes a transient induction of hypertrophy. In addition, many known TKI targets (e.g., ERBB2, Raf-1) and critical nodes in cardiac survival signaling (e.g., PI3K, Akt, and ERK) are included. Using this model, simulations were performed to predict how drug-induced network alterations affected 7 hypertrophy biomarkers (the model's "outputs"), under conditions meant to simulate a variety of physiological or pharmacological stimuli (e.g., stretch, angiotensin, EGF, phenylephrine). For instance, time courses in **Figure 2C** show simulated normalized levels of Brain Natriuretic Peptide (BNP) under six conditions: before and after isoproterenol stimulation, and in three groups of cells: untreated (control), nilotinib-treated, and dasatinib-treated. BNP is an appropriate output to consider because it is both measured in patients with hypertrophy and heart failure and has been shown to be relevant for drug-induced cardiotoxicity (Nousiainen et al., 2002; Sandri et al., 2005; Skovgaard et al., 2014).

These example simulation results, summarized in **Figure 2D**, suggest that nilotinib leads to increases in BNP, both before and after isoproterenol, whereas dasatinib may reduce the upregulation of BNP that isoproterenol normally causes. The hypertrophy index, a summary statistic, condenses results by summing drug-induced changes across seven biomarkers in response to different stimuli applied in the model. The hypertrophy index confirms the impression from the simulated time courses, namely a pro-hypertrophic response to nilotinib contrasted with a slight anti-hypertrophic response to dasatinib (**Figure 2E**).

By simulating responses to stimuli, using gene expression changes induced by all drugs, patterns begin to emerge. Specifically, in myocytes that are not exposed to a physiological stimulus, TKIs and non-TKIs cause similar changes in hypertrophy biomarkers (**Figure 2F**). However, simulations predict that when TKI-treated myocytes are also exposed to isoproterenol or endothelin-1, agonists that are used experimentally to induce hypertrophy (Ichikawa et al., 1996; Yamazaki et al., 1996; Shohet et al., 2004; Ryall et al., 2012), the pro-hypertrophic response is exaggerated compared with non-TKI-treated cells.

These preliminary simulation results indicate the potential strengths of combining large scale measurements with mechanism-based mathematical models. First the simulations do not simply describe existing data—they can predict how drug-treated cells will respond to an additional stimulus that has not yet been applied experimentally. These predictions can be subsequently tested. Second, the simulation approach does not merely generate qualitative predictions; because the quantitative models predict that some drugs and/or stimuli may cause large effects whereas others cause only minor effects, this provides a means to prioritize experimental tests and use resources efficiently. Third, when clear differences are observed, for instance between individual drugs or between drug classes, the simulations predict the mechanisms responsible for the differences.

# FUTURE DIRECTIONS

Although the preliminary simulation results shown here are encouraging, they also hint at the future research that must be performed to fully realize the potential of this approach. First, although the simulations predict how drug-induced changes in gene expression may influence both baseline signaling and cellular responses to stimuli, they do not describe direct inhibition of kinase activity by drugs, which is of course the more traditional and straightforward method for simulating drug effects. We excluded these effects from initial simulations because many TKI targets are not included in the model, but future work will expand the model by systematically adding drug targets based on published protein-protein interaction databases (Warde-Farley et al., 2010) and large-scale kinase inhibition assays (Anastassiadis et al., 2011; Davis et al., 2011). For such work, a promising way to expand the model will be to use largescale, data-driven network identification algorithms (Thiagarajan et al., 2017) that can provide an unbiased approach for identifying potential off-targets.

A second important extension of the work will be to simulate additional biological processes potentially involved in cardiotoxicity. For instance, cell death via apoptosis, which may be important in the development of toxicity caused by some TKIs, has been described mathematically by many previous models (Schleich and Lavrik, 2013; Shin et al., 2014). Once these are tuned to reflect apoptotic signaling in cardiac myocytes, the models can be integrated with the experimental gene expression data to generate novel predictions. Similarly, models describing mitochondrial function, including the production of reactive oxygen species (Aon and Cortassa, 2012; Bazil et al., 2016; Wacquier et al., 2016), and the coupling of electrical excitation, and contractile function (Rice et al., 2008; Tewari et al., 2016), are also likely to be relevant. Finally, once a number of QSP models, describing additional processes, have been added, further secondary analyses can be performed. These include sensitivity analysis to identify the most important nodes in each model (Sobie, 2009), systematic simulations to potential targets for toxicity mitigation or reversal, and effects of combination therapy.

# CONCLUSIONS

Here, we have discussed contemporary challenges in understanding TKI-induced cardiotoxicity and have illustrated how a QSP approach can be used to address unresolved questions and improve understanding. Previous successes of QSP in illuminating and predicting other forms of drug toxicity, including hepatotoxicity and drug-induced arrhythmia, demonstrate its potential utility for other drug toxicities. The initial results presented here show how mechanistic models can be integrated with "omics" measurements such as mRNA-seq, generating simulations that can suggest underlying mechanisms and help in prioritizing costly experiments. In the coming years, future work along these lines can be used to develop strategies to mitigate or reverse TKI-induced cardiotoxicity, thereby contributing to the development of therapeutic regimens that are both effective and safe.

# AUTHOR CONTRIBUTIONS

JVS and BC performed an extensive literature review and analysis of published clinical and experimental data. JVS performed simulations and analysis. JVS and ES wrote the initial draft of the manuscript. BC, JvH, MB, and JJS provided critical feedback and editorial suggestions.

# ACKNOWLEDGMENTS

This work was supported as a part of the National Institutes of Health (NIH) Common Fund's Library of Integrated Network-Based Cellular Signatures (LINCS) program through grants U54 HG008098 and U54 HL127624. Additional support has been provided by NIH grants and R01 HL137100 (to JJS) and U01 HL136297 (to ES), and National Science Foundation grant 1252854 to JJS.

# REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Shim, Chun, van Hasselt, Birtwistle, Saucerman and Sobie. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Proton Pump Inhibitors and Serum Magnesium Levels in Patients With Torsades de Pointes

Pietro E. Lazzerini <sup>1</sup> \*, Iacopo Bertolozzi <sup>2</sup> , Francesco Finizola<sup>1</sup> , Maurizio Acampa<sup>3</sup> , Mariarita Natale<sup>1</sup> , Francesca Vanni <sup>1</sup> , Rosella Fulceri <sup>4</sup> , Alessandra Gamberucci <sup>4</sup> , Marco Rossi 1,5, Beatrice Giabbani <sup>1</sup> , Michele Caselli <sup>1</sup> , Ilaria Lamberti <sup>1</sup> , Gabriele Cevenini <sup>6</sup> , Franco Laghi-Pasini 1† and Pier L. Capecchi 1†

*<sup>1</sup> Department of Medical Sciences, Surgery and Neurosciences, University of Siena, Siena, Italy, <sup>2</sup> Cardiology Intensive Therapy Unit, Department of Internal Medicine, Hospital of Carrara, Carrara, Italy, <sup>3</sup> Stroke Unit, University Hospital of Siena, Siena, Italy, <sup>4</sup> Department of Molecular and Developmental Medicine, University of Siena, Siena, Italy, <sup>5</sup> Centre of Pharmacovigilance, University Hospital of Siena, Siena, Italy, <sup>6</sup> Department of Medical Biotechnologies, University of Siena, Siena, Italy*

#### Edited by:

*Esther Pueyo, University of Zaragoza, Spain*

Reviewed by:

*Øyvind Bruserud, University of Bergen, Norway Domenico Criscuolo, Genovax S.r.l., Italy Stefano Giovagnoli, University of Perugia, Italy*

#### \*Correspondence:

*Pietro E. Lazzerini lazzerini7@unisi.it*

*†These authors have contributed equally to this work.*

#### Specialty section:

*This article was submitted to Pharmaceutical Medicine and Outcomes Research, a section of the journal Frontiers in Pharmacology*

Received: *08 October 2017* Accepted: *28 March 2018* Published: *20 April 2018*

#### Citation:

*Lazzerini PE, Bertolozzi I, Finizola F, Acampa M, Natale M, Vanni F, Fulceri R, Gamberucci A, Rossi M, Giabbani B, Caselli M, Lamberti I, Cevenini G, Laghi-Pasini F and Capecchi PL (2018) Proton Pump Inhibitors and Serum Magnesium Levels in Patients With Torsades de Pointes. Front. Pharmacol. 9:363. doi: 10.3389/fphar.2018.00363* Background: Torsades de pointes (TdP) is a life-threatening ventricular tachycardia occurring in long QT-syndrome patients. It usually develops when multiple QT-prolonging factors are concomitantly present, more frequently drugs and electrolyte imbalances. Since proton–pump inhibitors (PPIs)-associated hypomagnesemia is an increasingly recognized adverse event, PPIs were recently included in the list of drugs with conditional risk of TdP, despite only few cases of TdP in PPI users have been reported so far.

Objectives: Aim of the present study is to evaluate whether PPI-induced hypomagnesemia actually has a significant clinical impact on the risk of TdP in the general population.

Methods: Forty-eight unselected patients who experienced TdP were consecutively enrolled (2008-2017). Shortly after the first TdP episode, in those patients who did not receive magnesium sulfate and/or potassium or calcium replacement therapy, serum electrolytes were measured and their relationship with PPI usage analyzed.

Results: Many patients (28/48, 58%) were under current PPI treatment when TdP occurred. Among TdP patients in whom serum electrolyte determinations were obtained before replacement therapy (27/48), those taking PPIs had significantly lower serum magnesium levels than those who did not. Hypomagnesemia occurred in ∼40% of patients receiving PPIs (6/14), in all cases after an extended treatment (>2 weeks). In patients taking PPIs the mean QT-prolonging risk factor number was significantly higher than in those who did not, a difference which was mainly driven by lower magnesium levels.

Conclusions: In unselected TdP patients, PPI-induced hypomagnesemia was common and significantly contributed to their cumulative arrhythmic risk. By providing clinical support to current recommendations, our data confirm that more awareness is needed when a PPI is prescribed, specifically as regards the risk of life-threatening arrhythmias.

Keywords: proton-pump inhibitors, Torsades de pointes, serum magnesium levels, long-QT syndrome, sudden cardiac death

#### Lazzerini et al. PPI and Magnesium Levels in TdP

# INTRODUCTION

Torsades de pointes (TdP) is a life-threatening polymorphic ventricular tachycardia that can degenerate into ventricular fibrillation (VF) and cause sudden cardiac death (SCD) (Drew et al., 2010). It is characterized by a pattern of twisting points and occurs in patients with long QT syndrome (LQTS), both acquired and congenital. Indeed, in congenital-LQTS the more the heart rate-corrected QT interval (QTc) prolongs, the greater the TdP risk exponentially increases (i.e., 5–7% risk increase each 10 ms prolongation in QTc) until being significant for QTc>500 ms; such a value associated with a 2–3-fold higher risk for TdP (Drew et al., 2010).

Since a marked QTc prolongation is usually required for TdP development, in most cases the simultaneous presence of multiple QTc-prolonging factors synergistically operating in impairing ion channels responsible for the ventricular repolarization process is necessary. Congenital factors are included, mainly resulting from mutations affecting genes encoding for potassium or sodium channels, as well as acquired risk factors (Viskin, 1999; El-Sherif and Turitto, 2003; Drew et al., 2010; Itoh et al., 2016). Among the latter factors, electrolyte imbalances (i.e., hypokaliemia, hypocalcemia, hypomagnesemia) and QT-prolonging drugs blocking the hERG potassium channel are those most frequently implicated in TdP development. Other established causes of acquired LQTS and TdP include structural heart diseases, bradyarrhythmias, endocrine disorders, liver diseases, nervous system injuries, HIV infection, starvation, hypothermia and toxins (El-Sherif and Turitto, 2003; Drew et al., 2010). In addition, autoimmunity (Lazzerini et al., 2017d) (particularly anti-Ro/SSA antibodies) (Yue et al., 2015; Lazzerini et al., 2016) and systemic inflammation (Lazzerini et al., 2015, 2017a,b) in the recent years are being increasingly recognized as novel acquired QT-prolonging risk factors significantly impacting TdP risk in the general population.

Proton–pump inhibitors (PPIs) are the most effective therapeutic agents for acid related disorders (ARD), including peptic ulcer disease and gastroesophageal reflux disease (Strand et al., 2017). Moreover, such drugs are also used for the prevention of non-steroidal anti-inflammatory drug-induced gastric injury and as a part of Helicobacter pylori eradication regimens (Strand et al., 2017). As a result, PPIs currently represent the fifth best-selling drug in the market with millions of chronic users worldwide (Patterson Burdsall et al., 2013). During the last years, concern has been raised because of PPIs longterm overutilization. In fact, in the clinical practice PPIs are often prescribed in patients without a specific ARD, and such a habit is leading to significant cost expenditure and possible adverse events (Moayyedi and Leontiadis, 2012).

Hypomagnesemia is a potentially serious side effect of PPIs, that could account for ∼1% of all adverse events reported by drug users (Famularo et al., 2013; Luk et al., 2013). Although several data suggest an interference on intestinal magnesium absorption, the exact underlying mechanism is poorly understood (Famularo et al., 2013). In 2011 the US FDA warned that long-term use of PPI has the potential to reduce circulating magnesium levels, particularly in patients concomitantly receiving other drugs capable to cause magnesium depletion such as diuretics (2011) 1 . Accordingly, in 2016 the Arizona Center for Education and research on Therapeutics (AZCERT) included the PPIs omeprazole, esomeprazole, lansoprazole and pantoprazole in the list of drugs with conditional risk of TdP and to be avoided in patients with congenital LQTS (AZCERT, 2016), despite only few cases of QTc prolongation and TdP have been reported in patients with severe PPI-induced hypomagnesemia and/or taking a PPI concomitantly with drugs known to directly prolong QTc (Asajima et al., 2012; Bibawy et al., 2013; Hansen and Bruserud, 2016). As a result, it is now recommended that in patients taking a PPI for an extended period of time (>2 weeks) serum magnesium levels be monitored periodically, particularly if extended PPI therapy is used in association with drugs carrying a known risk of TdP (Asajima et al., 2012; 2016). Notably, a very recent longitudinal observational study performed in a large primary cohort of new users of acid suppression therapy followed for a median of 5.7 years, found a significant association between PPI use and risk of all-cause mortality. The risk was increased among those with no documented medical indications for PPI use and prolonged duration of use (Xie et al., 2017).

Regardless of official recommendations, available real-life information on this subject is relatively poor so far. The present study is specifically aimed at evaluating whether PPI-induced hypomagnesemia has a significant clinical impact on the risk of TdP in the general population. Thus, the actual usage of PPIs and its relationship with serum magnesium levels were analyzed in a cohort of TdP patients, prospectively and consecutively enrolled independent of ongoing therapies and concomitant diseases.

# PATIENTS AND METHODS

## Study Populations

Local Ethical Committee approved the study, and patients gave their oral and written informed consent in accordance with the Principles of the Declaration of Helsinki.

We prospectively enrolled (from January 2008 to May 2017) 48 consecutive hospitalized patients who presented with TdP, independent of ongoing therapies and concomitant diseases. Since the only inclusion criteria was the occurrence of TdP, all patients who came to our attention in that period of time were enrolled. No patients were excluded. Demographic, clinical and laboratory characteristics of study patients, as well as ongoing treatment with QTc-prolonging medications are provided in **Table 1**. In these patients, PPI usage was assessed, and a cutoff time of 2 weeks was used to define treatment duration as extended (>2 weeks) or not, according to current AZCERT recommendations to minimize the risk of TdP in patients treated with PPI (AZCERT, 2016).

# ECG Recordings

Diagnosis of TdP was based on the presence of at least one episode of polymorphic ventricular arrhythmia at a rate ranging

<sup>1</sup>FDA Drug Safety Communication: Low magnesium levels can be associated with long-term use of proton pump inhibitor drugs (PPIs). Available at www.fda.gov/ Drugs/DrugSafety/ucm245011.htm Accessed May 26 (2017).



*Except where indicated otherwise, data are expressed as mean* ± *standard deviation or median (range).*

*Appropriate serum potassium, calcium or magnesium measurements available in 45, 37, and 27 out of 48 patients, respectively; anti-Ro/SSA antibodies tested in 32 out of 48 patients.*

\**Diseases recognized to be a risk factor for QTc prolongation (Viskin, 1999; El-Sherif and Turitto, 2003; Drew et al., 2010).*

*† Increased C-reactive protein level (*>*0.5 mg/dl) with or without a definite inflammatory disease.* § *Including electrolyte imbalances, diseases, QTc-prolonging medications, anti-Ro/SSA positivity, and systemic inflammation (Viskin, 1999; El-Sherif and Turitto, 2003; Drew et al., 2010; Yue et al., 2015; Lazzerini et al., 2016, 2017b).*

from 160 to 240 beats/min, associated with QTc prolongation (Drew et al., 2010; **Figure 1**). The QT interval was manually measured on a standard 12-lead ECG, from the onset of the Q wave or the onset of the QRS complex to the end of the T wave, defined as the return to the T-P baseline. When present, prominent U waves (>1 mm) merging into T waves were included in QT measurement (Gupta et al., 2007). QTc, determined as the longest hand-measured QTc in any lead (Rautaharju et al., 2009) was corrected for heart rate by the Bazett formula (dividing the QT by the square root of the preceding R-R interval of each beat: QT/<sup>√</sup> RR) to yield the QTc value. QTc was measured from 3 non-consecutive beats (mean value) by a single investigator.

#### Laboratory Analysis

Shortly after the first TdP episode [no later than 24 h (median 6 h, range 1–22 h)], patients underwent a venous withdrawal to determine serum electrolyte levels, including potassium, sodium, calcium, and magnesium. Potassium and sodium were determined by indirect potentiometry (COBAS-6000 platform); values were expressed as mEq/L (reference values: potassium 3.5– 5.5; sodium 132–148). Calcium and magnesium were assayed by a colorimetric method (COBAS-6000 platform); values were expressed as mg/dl (reference values: calcium 8.0-11.0; magnesium 1.5–2.5).

Only determinations obtained before the administration of intravenous magnesium sulfate and/or replacement therapy with potassium or calcium were considered appropriate to be included in the study. As a result, serum potassium, calcium or magnesium measurements were available in 45, 37, and 27 out of 48 patients, respectively.

Other laboratory parameters included circulating levels of anti-Ro/SSA antibodies (see Supplementary Methods for more details) and C-reactive protein (CRP), as well as pH, bicarbonates and serum glucose.

#### Statistical Analysis

To compare TdP patients subgroups, the following parametric or non-parametric statistical analyses were respectively carried out: the two-tail Student's unpaired t-test, or the two-tail Mann-Whitney test to evaluate differences in quantitative variables; the Pearson or Spearman rank correlation-test to verify possible statistical association between quantitative variables; the twosided Fisher's exact test to evaluate statistical correlation between categorical variables. p < 0.05 were considered as significant. All statistical analyses were performed using GraphPad-InStat, version 3.06 for Windows 2000.

#### RESULTS

#### TdP Patients Characteristics

As detailed in **Table 1**, demographic, clinical and laboratory characteristics of our cohort were fully consistent with those expected in TdP patients based on established epidemiological data. In fact, the large majority of subjects were females (31/48, 65%) and older than 65 years (median age: ∼80 years). Moreover, many recognized QTc-prolonging risk factors of acquired origin

FIGURE 1 | Electrocardiographic findings of a patient with TdP and PPI-associated hypomagnesemia. ECG strip in sinus rhythm (A) and during TdP (B) from a patient who was under current and extended treatment with oral lansoprazole (15 mg/day), and had low magnesium levels (1.46 mg/dl) and a QTc of 670 ms. Red vertical lines and arrow in lead II show QT interval.

were identifiable, particularly an underlying cardiac disease (45/48, 83%, more frequently ventricular hypertrophy, dilated cardiomyopathy/heart failure and atrio-ventricular blocks), electrolyte imbalances (37/47, 79%) and QTc-prolonging medications (34/48, 71%). Hypokalemia occurred in 62% of patients (28/45), thereby representing the most common specific risk factor. Anti-Ro/SSA-52 kD antibodies were detected in 56% of the tested cases (18/32), although a history of autoimmune disease was present in two patients only (1 rheumatoid arthritis, 1 celiac disease). The majority of TdP patients (38/48, 79%) showed signs of systemic inflammation, as indicated by the increase in CRP levels (>0.5 mg/dl; median value 2.66 mg/dl). A definite inflammatory disease was present in 22/48 patients (46%), most commonly an acute infection (n = 15, particularly sepsis and pneumonia), but also chronic immune-mediated diseases (n = 5, including 3 chronic inflammatory arthritis), or acute aseptic inflammatory processes (n = 2). Among drugs, amiodarone was the most frequently administered (14/48, 29%). Notably, in almost all cases more than one known QTc-prolonging factor was simultaneously identifiable; on average ∼5. In addition, a significant proportion of patients (25/48, 52%) experienced an adverse short-term arrhythmic outcome, i.e., VF/cardiac arrest (CA), and/or underwent electric shock (TdP rapidly degenerated to VF/CA; out-of-hospital VF/CA followed with DC-shock, only later revealing a manifestation of TdP episodes; sustained TdP not responsive to medical therapy).

## Proton-Pump Inhibitors Usage in TdP Patients

In our cohort, a significant percentage of patients were under active treatment with PPI when TdP occurred (28/48, 58%). Many subjects (16/25, 64%) were taking a PPI for an extended period of time, i.e., >2 weeks. The most frequently administered PPI was pantoprazole, followed by lansoprazole, together accounting for ∼85% of the cases (24/28). Remaining patients (n = 4), were administered with omeprazole (n = 3), or esomeprazole (n = 1). In three patients under extended home PPI therapy, the molecule was changed during hospitalization, before TdP development (from oral lansoprazole or pantoprazole to intravenous pantoprazole in two cases; from oral omeprazole to oral pantoprazole in the other one). The commonest route of administration was the oral one, but in 6/28 cases (21%) where the PPI was being given intravenously at the time of TdP occurrence (**Table 2**). Notably, none of the intravenously-treated patients showed hypomagnesemia.

#### Serum Electrolytes Levels and Other TdP Risk Factors in Patients Taking or Not Taking Proton-Pump Inhibitors

Consistently with the findings obtained in the whole TdP population, a high prevalence of electrolyte imbalances (collectively ∼80%) was found in both patients taking (PPI+) or not taking PPI (PPI−). However, while the prevalence of hypokaliemia and hypocalcemia as well as serum potassium, calcium (and sodium) levels in the two groups were overalapping, circulating magnesium levels were significantly lower in PPI+ than in PPI− subjects (1.60 ± 0.21 vs. 1.84 ± 0.33 mg/dl, 1 = −0.24 mg/dl; p = 0.03) (**Figures 2**, **3**). Hypomagnesemia (<1.5 mg/dl) occurred 5-times more frequently in the PPI+ vs. PPIgroup (6/14, 43% vs. 1/13, 8%), although this difference did not reach statistical significance (p = 0.07) (**Table 3**). Notably, hypomagnesemia was found almost exclusively (6 out of 7 cases, TABLE 2 | Proton-pump inhibitors use in patients with Torsades de Pointes.


*Except where indicated otherwise, values are expressed as mean* ± *standard deviation.* \**Data missing in 3 out of 28 patients.*

*† At the moment of TdP occurrence.*

85%) in patients receiving PPI therapy; all cases of PPI-associated hypomagnesemia (n = 6) were observed in patients under extended PPI therapy (>2 weeks), involving all the 4 different PPIs used in the cohort (pantoprazole, n = 3; lansoprazole, n = 1; omeprazole, n = 1; esomeprazole, n = 1). Diuretics usage, which was not different in the PPI+ vs. PPI− group (**Table 3**), was not per se associated with significant magnesium changes in our cohort. In fact, by comparing patients taking (n = 16) and not taking diuretics (n = 11), neither serum magnesium levels (1.67 ± 0.31 vs. 1.78 ± 0.26 mg/dl; p = 0.32, two-tail unpaired t-test) nor the prevalence of hypomagnesemia (6/16, 37% vs. 1/11, 9%; p = 0.18, two-sided Fisher's exact test) were significantly different. Although these findings suggest that diuretics alone, differently to PPIs alone, were not sufficient to cause magnesium depletion, nevertheless diuretics may exacerbate PPI-associated magnesium reduction when administered in association. Indeed, in patients concomitantly receiving PPIs and diuretics (n = 9, vs. others n = 18) serum magnesium levels further decreased slightly (1.55 ± 0.21 vs. 1.80 ± 0.30 mg/dl, 1 = −0,25 mg/dl; p = 0.02, two-tail Mann-Whitney test), and the prevalence of hypomagnesemia increased, reaching statistical significance (5/9, 56% vs. 2/18, 11%; p = 0.02, two-sided Fisher's exact test). Despite a specific investigation, no any significant impact of other common causes of hypomagnesemia was found in our cohort of patients (see Supplementary Results for more details). Moreover, no significant correlation was present between magnesium levels and other continuous variables, particularly calcium (r = 0.33, p = 0.10; Pearson correlation-test) potassium (r = 0.10, p = 0.57; Pearson correlation-test), sodium (r = 0.11, p = 0.58; Spearman rank correlation-test) or CRP levels (r = −0.14, p = 0.46; Spearman rank correlation-test), or QTc duration (r = −0.19, p = 0.32; Pearson correlation-test).

As regards the other QTc-prolonging risk factors of acquired origin, individually considered, no significant differences in terms of concomitant diseases, both cardiac and extra.-cardiac, QTc prolonging medications use, anti-Ro/SSA positivity or presence of systemic inflammation were observed by comparing PPI+ vs. PPI− patients (**Table 3**). Nevertheless, when all these factors were considered together, also including electrolyte imbalances, the mean QTc-prolonging risk factor number per patient was significantly higher in the PPI+ than the PPI- group (5.8 ± 1.6 vs. 4.9 ± 1.4, 1: 0.9; p = 0.04). Notably, statistical significance of this difference was lost if hypomagnesemia, i.e., the only individual TdP risk factor discriminating the two groups, was selectively excluded by the total count (5.6 ± 1.5 vs. 4.9 ± 1.4, 1: 0.7; p = 0.07; **Table 3**). It is important to underline that for a number of patients, some data on QTprolonging risk factors were missing, particularly serum levels of potassium (available in 26/28 of PPI+ 19/20 of PPI− patients, respectively), calcium (27/28 of PPI+ and 18/20 of PPI− patients, respectively), magnesium (14/28 of PPI+ and 13/20 of PPI− patients, respectively), and anti-Ro/SSA positivity (18/28 of PPI+ and 14/20 of PPI− patients, respectively). Nevertheless, when we restricted the analysis to patients with full data only, i.e., 8 PPI+ and 10 PPI−, differences (1) in mean QTc-prolonging risk factor number per patient remained completely unchanged, both when all risk factors were considered (6.1 ± 1.7 vs. 5.2 ± 1.3, 1: 0.9) and when hypomagnesemia was excluded (5.8 ± 1.4 vs. 5.1 ± 1.3, 1: 0.7), thus indicating that the results were not influenced by missing data.

Conversely, PPI treatment did not seem to affect the shortterm outcome in our cohort of patients. In fact, the percentage of subjects experiencing VF/CA, and/or that underwent electric shock was not significantly different by comparing PPI+ vs. PPI− patients (15/28, 54% vs. 10/20, 50%) (**Table 3**).

Finally, in order to specifically address the question of whether magnesium levels are different between PPI+ patients who developed TdP vs. PPI+ patients who did not, 21 hospitalized patients matched for age, gender and concomitant diseases (Supplementary Table 1), but without QTc prolongation or history of TdP were prospectively enrolled as a control group (C). Similarly to that observed in TdP subjects, more than a half of control patients were under current treatment with PPIs (12/21, 57%), in most cases for an extended period of time (10/12, 83%) (Supplementary Table 2). Among these patients, hypomagnesemia was found in 2 patients (2/21, 9%), one treated and one untreated with PPIs. As shown in **Figure 4A**, circulating magnesium levels were significantly lower in TdP vs. controls (1.72 ± 0.30 vs. 1.91 ± 0.40 mg/dl; p = 0.0094). Such a difference significantly increased when the comparison was restricted to PPI-treated patients from the two groups (TdP/PPI+: 1.60 ± 0.21 vs. C/PPI+: 1.93 ± 0.48 mg/dl; p = 0.0007; **Figure 4B**), while serum magnesium levels were not different in PPI-untreated TdP vs. control patients (TdP/PPI−: 1.84 ± 0.33 vs. C/PPI−: 1.88 ± 0.30 mg/dl; p = 0.78, two-tail Student's unpaired t-test).

As a confirmation of the results on subgroups, we also evaluated the interaction between magnesemia and PPI treatment (PPI+/PPI−), by combining (multiplying) the two variables in the whole population (TdP vs. C). We found that sample differences between TdP and C in such interactioncorrected levels of magnesium were not longer statistically significant (p = 0.09, two-tail Mann-Whitney test).

#### DISCUSSION

The key findings of the present study are the following: a large proportion of patients (>50%) who developed TdP were under current treatment with a PPI; TdP patients taking PPIs had significantly lower serum magnesium levels with respect to TdP patients not taking PPIs; hypomagnesemia frequently occurred in patients receiving PPIs (∼40%, 6/14), in all cases after an extended period of time (>2 weeks) of administration; in subjects taking PPIs the mean QTc-prolonging risk factor number per patient was significantly higher than it was in those not taking PPIs, a difference which was mainly driven by lower magnesium levels.

Magnesium, representing the most abundant intracellular divalent cation, plays a key role in regulating potassium and calcium channels in the heart (Gupta et al., 2007). Experimental studies demonstrated that cytosolic magnesium promotes repolarization of myocardial cells via modulating effects on several potassium currents, including the rapid component of the delayed rectifier potassium current (IKr) and transient outward current (Ito) (Kelepouris et al., 1993; El-Sherif and Turitto, 2011). Moreover, magnesium markedly inhibits the L(long-lasting)-type calcium current (ICaL), possibly as a result of a direct block of the L-type-calcium channel pore by external magnesium or via modification of the activity of protein kinases or phosphoprotein phosphatases (Zhao et al., 2015). ICaL determines the plateau phase thereby critically contributing to action potential duration (APD) (Viskin, 1999; El-Sherif and Turitto, 2003). Moreover, ICaL is the main depolarizing current that generates early after depolarizations (EADs), in turn representing the primary

electrophysiological mechanism underlying TdP development (Viskin, 1999; El-Sherif and Turitto, 2003). This supports the fact that hypomagnesemia is a recognized risk factor for QTc prolongation and TdP (Viskin, 1999; El-Sherif and Turitto, 2003, 2011), as well as the clinical evidence that magnesium sulfate is very effective for the treatment of TdP thus being considered the standard of care for this arrhythmia (Drew et al., 2010).

Horizontal dotted line indicates the lower limit of reference values for sodium levels, i.e., 132 mEq/L.

PPI-induced hypomagnesemia, for the first time described in 2006, has been increasingly recognized in the last years as a potentially life-threatening adverse event whose actual incidence is probably largely underestimated (Famularo et al., 2013). Two recent systematic reviews and meta-analysis, each one including nine studies and over 100,000 patients, consistently found that PPI users have a ∼40–80% higher risk of developing hypomagnesemia when compared to non-users (Park et al., 2014; Cheungpasitporn et al., 2015).

PPI-associated hypomagnesemia occurs after extended treatments (>2 weeks, but in most cases > 1 year), is not clearly dose-related, and was reported with different PPIs, thus suggesting a class effect. Until PPI interruption, hypomagnesemia is refractory to oral or parenteral magnesium replacement irrespective of high-dose supplementation; when the PPI is stopped, serum magnesium levels returned to normal in less than 2 weeks (2011; Famularo et al., 2013). However, hypomagnesemia may recur after re-challenge with the same or a different PPI. In these patients, when prolonged antiacid treatment is needed, prescription of a H<sup>2</sup> histamine receptor-blocker (H2-blocker) may be an appropriate therapeutic alternative (Famularo et al., 2013). In fact, although mechanisms of PPI-induced hypomagnesemia are not clear, hypochlorhydria does not seem to be involved. Pathogenesis possibly includes both gastrointestinal and renal losses, via dysfunction of the Transient Receptor Potential Melastatin 6/7 (TRPM6/7) located in the intestine as well as in the distal convoluted tubule (Famularo et al., 2013). Accordingly, recent data suggest that carriers of TRPM6 polymorphisms are at increased risk (Hess et al., 2017).

To date only three reports of patients who developed TdP while they were taking a PPI (i.e., omeprazole, pantoprazole, or lansoprazole, respectively) (Asajima et al., 2012; Bibawy et al., 2013; Hansen and Bruserud, 2016) have been described in the literature, in two cases associated with hypomagnesemia (Bibawy et al., 2013; Hansen and Bruserud, 2016). The results of the present study suggest that the phenomenon is significantly more common than reported, being probably underestimated because in the clinical practice PPIs do not currently receive the due attention as a factor potentially contributing to QTc prolongation and TdP. Consistently with literature data (Famularo et al., 2013), PPI-associated hypomagnesemia seems to be a class effect which requires extended drug administration to occur. In fact, although in our TdP patients most subjects used pantoprazole, hypomagnesemia was found to be associated with all 4 PPIs included in the AZCERT list (AZCERT, 2016) (i.e., pantoprazole, omeprazole, esomeprazole, lansoprazole),



*Wherever not specified, data are expressed as mean*±*standard deviation. Appropriate serum potassium, calcium or magnesium measurements available in 45, 37, and 27 out of 48 patients, respectively; anti-Ro/SSA antibodies tested in 32 out of 48 patients. VF, ventricular fibrillation; CA, cardiac arrest; EcS, electric shock.*

\**Diseases recognized to be a risk factor for QTc prolongation (Viskin, 1999; El-Sherif and Turitto, 2003; Drew et al., 2010).*

*† Including electrolyte imbalances, diseases, QTc-prolonging medications, anti-Ro/SSA positivity, and systemic inflammation (Viskin, 1999; El-Sherif and Turitto, 2003; Drew et al., 2010; Yue et al., 2015; Lazzerini et al., 2016, 2017b).*

*Differences were evaluated by the two-tailed unpaired t-test, or the two-tailed Mann-Whitney test. Difference in categorical variables were evaluated by the two-sided Fisher's exact test.*

*Statistically significant p values are reported in bold.*

in all cases administered for an extended period of time (>2 weeks). Our data seem also to confirm that the risk of PPI-induced hypomagnesemia further increases when PPIs are co-administered with diuretics, probably as a result of an enhancement of the renal loss of magnesium. Conversely, although in PPI users hypomagnesemia has been reported to be often accompanied by hypocalcemia and hypokalaemia (Famularo et al., 2013), the prevalence of these electrolyte imbalances as well as serum calcium, potassium and sodium

controls. (A) Serum magnesium levels in all TdP patients (*n* = 27) vs. controls (C, *n* = 21), regardless of PPI therapy. Two-tail Mann-Whitney test, \*\**p* < 0.01. (B) Serum magnesium levels in TdP patients under PPI therapy (TdP/PPI+) (*n* = 14) vs. controls under PPI therapy (C/PPI+, *n* = 12). Two-tail Student's unpaired *t*-test, \*\*\**p* < 0.001. Horizontal dotted line indicates the lower limit of reference values for magnesium levels, i.e., 1.5 mg/dl.

levels were similar in PPI+ vs. PPI− TdP patients, thus indicating a rather selective effect of this class of drugs on magnesium levels.

Another important suggestion arising from the present study is that PPI-associated changes in magnesium levels have a relevant clinical impact by increasing the risk of developing TdP in these patients. In fact, PPI users showed a significantly higher mean total number of QTc-prolonging risk factors per patient when compared to non-users. Nevertheless, despite a comprehensive evaluation also taking into account recently recognized "non-classical" QT-prolonging factors, such as anti-Ro/SSA antibodies (Yue et al., 2015; Lazzerini et al., 2016, 2017d) and systemic inflammatory activation (Lazzerini et al., 2015, 2017a,b), serum magnesium levels represented the only specific TdP risk factor which was significantly different between the two groups. Accordingly, when hypomagnesemia was excluded from the total risk factor count, this difference was no longer statistically significant.

Notably, we also found that magnesium levels in TdP/PPI+ patients were significantly lower when compared to C/PPI+ matched for age, gender and concomitant diseases. It suggests that TdP may act as a "clustering factor" for those patients, among the general population, who are more susceptible to the magnesium-lowering effect of PPIs, possibly as a result of a genetic predisposition (Hess et al., 2017). This view, further supporting the role of PPI-induced hypomagnesemia as a risk factor for TdP, warrants specific investigation.

Although our data point to the conclusion that PPIs can increase the risk of TdP by inducing hypomagnesemia, the involvement of additional, possibly molecule-related mechanisms could not be ruled out. In particular, this may be the case of lansoprazole which has been recently associated to an increased risk of QTc prolongation and TdP when used in combination with ceftriaxone, via direct blocking effects of the drug association on the hERG potassium channel (Lorberbaum et al., 2016; Lazzerini et al., 2017c). Indeed, 2 patients in our cohort were under current treatment with lansoprazole + ceftriaxone when TdP occurred, in 1 case in the absence of hypomagnesemia. Notably, it has been demonstrated that also lansoprazole alone significantly inhibits hERG potassium channel and related current IKr (−14%), although to a lesser extent when compared to the drug combination (−58%) (Lorberbaum et al., 2016). This may help explain why serum magnesium level was normal in one out of three case reports of PPI-associated TdP, in which lansoprazole administration precipitated arrhythmia development in a patients under long-term treatment with a drug known to directly prolong QTc (disopyramide) (Asajima et al., 2012). Thus, it cannot be ruled out that also in our patients, particularly those without hypomagnesemia, lansoprazole (and possibly also the other PPIs involved, since to date no specific patch-clamp studies are available) could have contributed to promote TdP occurrence also via a direct electrophysiological interference.

Our data suggest a number of important recommendations to translate in the clinical practice. In particular, patients may experience TdP in the presence of hypomagnesemia while they were under active treatment with a PPI. Such patients may be required to stop PPI treatment as it could have significantly contributed to development and maintenance of the electrolyte imbalance. Since it is expected that PPI-induced hypomagnesemia is refractory to magnesium oral or parenteral supplementation despite high doses (Famularo et al., 2013), drug discontinuation is a key action to normalize serum magnesium levels and thereby reduce the associated risk of TdP recurrence. This measure may be of particular importance in patients concomitantly requiring diuretic therapy, given the role of this class of drugs in exacerbating magnesium depletion. Moreover, based on the evidence that PPI-induced hypomagnesemia may rapidly recur after re-challenge with the same or a different PPI (median time ∼2 weeks; Famularo et al., 2013), the alternative use of a H2-blocker may be appropriate in the case the patient needs prolonged antiacid treatment. Finally, since some data suggest that PPIs may also directly contribute to QTc prolongation via electrophysiological effects on the cardiomyocyte, it cannot be excluded that PPI discontinuation could be a useful therapeutic measure even in TdP patients without evidence of hypomagnesemia, particularly when the PPI involved is lansporazole and other known QT-prolonging drugs are concomitantly administered.

In conclusion, the present study demonstrates that PPIinduced hypomagnesemia is a more than expected common finding in unselected patients with TdP, significantly contributing to increase the cumulative risk of developing this life-threatening arrhythmia. Our real-life data provide important clinical evidence in support to AZCERT recommendations which cautiously already had warned about the potential role of PPI-induced hypomagnesemia in promoting TdP, despite only few cases were reported. Nevertheless, considering the relative small sample size as well as the main focus on magnesium levels, we did not perform any multivariate analysis on our population. Since this may represent a limitation of the study, larger sample studies are warranted to confirm our results. They should include non-TdP patients and/or younger populations, and could clarify whether PPIs significantly influence the QTc also regardless of hypomagnesemia.

In practice, more awareness is needed by the clinician when a PPI is prescribed since the safety profile of this class of drugs is probably not so neutral as commonly believed, specifically as regards the risk of life-threatening arrhythmias and SCD.

# AUTHOR CONTRIBUTIONS

PL: Conception and design of the work; PL, IB, FF, MA, MN, FV, BG, MC, and IL: Substantial contributions to the acquisition of data for the work; PL, RF, AG, MR, GC, FL-P, and PC: Substantial contributions to the analysis of data for the work; PL, RF, AG, MR, GC, FL-P, and PC: Substantial contributions to the interpretation of data for the work; PL and PC: Drafting the work; PL, RF, AG, MR, FL-P, and PC: Revising the draft of the work critically for important intellectual content; PL, IB, FF, MA, MN, FV, RF, AG, MR, BG, MC, IL, GC, FL-P, and PC: Final approval of the version to be published; PL, IB, FF, MA, MN, FV, RF, AG, MR, BG, MC, IL, GC, FL-P, and PC: Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

#### ACKNOWLEDGMENTS

This work has received funding from FAS-Salute ToRSADE project (FAS Salute 2014, Regione Toscana).

# SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphar. 2018.00363/full#supplementary-material

#### REFERENCES

(2011). In brief: PPI's and hypomagnesemia. Med. Lett. Drugs Ther. 53:25.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Lazzerini, Bertolozzi, Finizola, Acampa, Natale, Vanni, Fulceri, Gamberucci, Rossi, Giabbani, Caselli, Lamberti, Cevenini, Laghi-Pasini and Capecchi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Clinical Pharmacokinetics and Pharmacodynamics of Warfarin When Combined with Compound Danshen: A Case Study for Combined Treatment of Coronary Heart Diseases with Atrial Fibrillation

Chunxiao Lv<sup>1</sup> , Changxiao Liu<sup>2</sup> , Zhuhua Yao<sup>3</sup> , Xiumei Gao<sup>4</sup> , Lanjun Sun<sup>5</sup> , Jia Liu<sup>1</sup> , Haibo Song<sup>6</sup> , Ziqiang Li<sup>1</sup> , Xi Du<sup>1</sup> , Jinxia Sun<sup>1</sup> , Yanfen Li<sup>1</sup> , Kui Ye<sup>7</sup> , Ruihua Wang<sup>1</sup> and Yuhong Huang<sup>1</sup> \*

<sup>1</sup> Department of Clinical Pharmacology, Second Affiliated Hospital of Tianjin University of Traditional Chinese Medicine, Tianjin, China, <sup>2</sup> State Key Laboratory of Drug Delivery Technology and Pharmacokinetics, Tianjin Institute of Pharmaceutical Research, Tianjin, China, <sup>3</sup> Department of Cardiology, People's Hospital of Tianjin, Tianjin, China, <sup>4</sup> Engineering Research Center of Modern Chinese Medicine Discovery and Preparation Technique, Tianjin University of Traditional Chinese Medicine, Tianjin, China, <sup>5</sup> Department of Cardiology, Second Affiliated Hospital of Tianjin University of Traditional Chinese Medicine, Tianjin, China, <sup>6</sup> National Center for ADR Monitoring of China, Center for Drug Reevaluation of CFDA, Beijing, China, <sup>7</sup> Department of Vascular Surgery, Tianjin 4th Center Hospital, Tianjin, China

Warfarin is used as anticoagulant and Compound Danshen prescription (CDP) is able to promote blood circulation. The combination might produce a synergic effect for patients of coronary heart diseases (CHDs) with atrial fibrillation (AF). Whether the combination increases the bleeding risk of warfarin is unclear, so the effects of Compound Danshen dripping pill (CDDP) on the pharmacokinetics (PK) and pharmacodynamics (PD) profiles of warfarin was investigated in patients. The dose and blood concentrations of warfarin, the four indicators of blood coagulation, prothrombin time, activated partial thromboplatin time, thrombin time, fibrinogen, and international normalized ratio value were compared when with and without CDDP treatment. The population PK (PPK) and PPK-PD models were established to assess patient demographics, genetic polymorphisms and CDDP as covariates. And the Seattle Angina Questionnaire was used to evaluate clinical efficacy, and the bleeding risk of combination was analyzed. The results indicated that CDDP had little influence on PK and PD profiles of warfarin in most patients and the combination of CCDP and warfarin would be a promising alternative regime for CHD with AF patients. The study was registered on China Clinical Trial Registry with number ChiCTR-ONRC-13003523.

Keywords: warfarin, compound Danshen dripping pill, pharmacokinetics, pharmacodynamics, patients, coronary heart diseases, atrial fibrillation

#### Edited by:

Blanca Rodriguez, University of Oxford, United Kingdom

#### Reviewed by:

Domenico Criscuolo, Genovax S.r.l., Italy Robert L. Lins, Retired, Antwerpen, Belgium

> \*Correspondence: Yuhong Huang

hyh101@126.com

#### Specialty section:

This article was submitted to Pharmaceutical Medicine and Outcomes Research, a section of the journal Frontiers in Pharmacology

Received: 28 August 2017 Accepted: 31 October 2017 Published: 21 November 2017

#### Citation:

Lv C, Liu C, Yao Z, Gao X, Sun L, Liu J, Song H, Li Z, Du X, Sun J, Li Y, Ye K, Wang R and Huang Y (2017) The Clinical Pharmacokinetics and Pharmacodynamics of Warfarin When Combined with Compound Danshen: A Case Study for Combined Treatment of Coronary Heart Diseases with Atrial Fibrillation. Front. Pharmacol. 8:826. doi: 10.3389/fphar.2017.00826

# INTRODUCTION

fphar-08-00826 November 18, 2017 Time: 15:47 # 2

It was reported that about 10%∼15% patients in coronary heart diseases (CHDs) would be associated with atrial fibrillation (AF). Moreover, about 30% patients in AF would be associated with CHD (Jason et al., 2014). The main hazard of AF is thromboembolic complications. Anticoagulants may reduce the risk of death rate in AF patients by 38% (Alpesh, 2013), so about 70–80% patients with AF are suitable for long-term use of warfarin, which was initially used in humans in the early 1950s as vitamin K antagonist (Liu et al., 2014; Darcy et al., 2017).

It is more than 100 years history in China that Compound Danshen prescription (CDP) has being applied to treat CHD, which consists of Radix salvia miltiorrhizae, Radix notoginseng, and Borneolum (Xin et al., 2013). In order to get market approval in the United States, the Compound Danshen dripping pill (CDDP), one Chinese patent drug of CDP, had recently completed a multinational phase III clinical trial. Pre-clinical and clinical studies have suggested that CDDP may increase coronary flow-rate and superoxide dismutase activity, expand blood vessel, promote blood circulation, relieve blood stasis, improve microcirculation, and improve hemorheological property, as well as decrease myocardial oxygen consumption (Pei et al., 2004; Zheng et al., 2007).

Concurrent use of CDDP with warfarin may be a desirable combination that may produce a synergistic effect, to relieve the symptoms of CHD with AF by CDDP part and meanwhile to decrease the incidence of thromboembolic complication by warfarin. Warfarin treatment is difficult to handle due to its narrow therapeutic window with a large inter-individual variability in the dose-response relationship (Zeng et al., 2016). Both pharmacodynamic (PD) and pharmacokinetic (PK) factors may contribute to more than 10–20 fold inter-individual variability in dose requirement (Hamberg et al., 2007; Steven et al., 2011; Zeng et al., 2016). Whether the CDDP could have impact on the PK and/or PD characteristics of warfarin increasing the bleeding risk as a result, is not clear. It is necessary, therefore, to get the information about the interactions between CDDP and warfarin. Only one literature report has been retrieved to address the interactions between CDDP and warfarin in rats (Chu et al., 2011), but any information on such interactions in humans has not been reported.

We conducted the study to explore the potential effects of CDDP on the PK and PD of warfarin in patients. During two periods on and off CDDP, we collected the dose and blood concentration of warfarin, the four indicators of blood coagulation, international normalized ratio (INR) value, and to establish appropriate population pharmacokinetics (PPK) and population pharmacodynamics (PPD) models to assess patient demographics, genetic polymorphisms and CDDP as covariates to evaluate the interaction effects of CDDP on warfarin. The seattle angina questionnaire (SAQ) was used to evaluate the effect of warfarin combined with CDDP on CHD with AF patients. In addition, 2 years follow-up was done after the two periods to learn about the drug compliance, the incidence of bleeding and other important outcomes, such as myocardial infarction, severe arrhythmia, revascularization, death and so on. We hope the study could provide useful clinical information for patients of CHD with AF.

### MATERIALS AND METHODS

# Patients

The study was conducted in four hospitals in Tianjin from November 2013 to January 2016. Participants, suffered from CHD with AF, had been administrated warfarin with a long time. The study included two periods, in the first period patients took warfarin (Orion Corporation, Finland) at dose titration manner guided by INR values on the daily determined basis to guarantee the INR value maintained in the range of 2–3. When the INR value reached stable and maintained for successive 2 weeks on the fixed dose of warfarin, then the participants switched to the second period, in which, 10 dripping pills of CDDP (Tianjin Tasly Group Co., Ltd, China) were added orally to patients three times per day for at least 4 weeks. The dose of warfarin was re-adjusted according to the changed INR value, until the INR value was stable again and the dose of warfarin was retained for 2 weeks. Four blood samples (4<sup>∗</sup> 3 ml) were collected at the end of each period for warfarin concentration assay. The sampling time points were arranged at trough (before the administration of warfarin), at peak, two random times on elimination phase (before the next dose of warfarin). All the time points of blood sampling and warfarin dosing were recorded accurately.

This study was carried out in accordance with the recommendations of Ethics committees of the Second Affiliated Hospital of Tianjin University of TCM with written informed consent from (ICF) all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Ethics committees of the Second Affiliated Hospital of Tianjin University of TCM in August 2013.

#### Genotyping

The information of genes which affect the metabolism of warfarin was obtained by literatures (Lin G.G. et al., 2015; Zeng et al., 2016). In this study, genotyping of VKORC1, CYP2C9<sup>∗</sup> 3, CYP4F2, EPHX1, and PROC were detected. Genomic DNA was isolated from peripheral blood leukocytes using a Genomic DNA Purification kit. Individual single-nucleotide polymorphism (SNP) loci were amplified using the polymerase chain reaction, which provided a template for allele-specific primer extension. All genotyping were performed using the gene sequencing methods (Kumar et al., 2008; Jorgensen et al., 2009; Steven et al., 2011; Lin G.G. et al., 2015). The VKORC1 was classified by detection of 1173 C > T variant (rs9923231), the CYP2C9<sup>∗</sup> 3 was classified by detection of 1075 A > C variant (rs1057910), the CYP4F2 was classified by detection of C > T variant (rs2108622), the EPHX1 was classified by detection of G > A variant (rs2292566), the PROC was classified by detection of G > T variant (rs5936).

#### Lv et al. Effect of CDDP on Warfarin

#### Bioanalysis

fphar-08-00826 November 18, 2017 Time: 15:47 # 3

Plasma warfarin concentrations were determined using a highperformance liquid chromatography tandem mass spectrometry method. Good chromatographic separation was achieved on an Astec CHIROBIOTIC V column (250 mm × 4.6 mm i.d., particle size 5 µm) with acetonitrile-5 mm ammonium acetate with 0.1% acetic acid in water (30:70, v/v) as the mobile phase at a flow rate of 0.50 mL/min (Jin et al., 2012). The column effluent was analyzed using a mass spectrometer in multiple reactions monitoring (MRM) mode by AB Triple Quad 5500 system in positive mode. S-warfarin, R-warfarin, and Tolglybutamide (Internal standard, IS) were extracted from plasma samples by protein precipitation with acetonitrile. Calibration curves were linear with 50.00–2000 ng/ml for S-warfarin and R-warfarin. Both intra-day and inter-day precision and accuracy of S-warfarin and R-warfarin were well within acceptance criteria (15%). The mean absolute extraction recoveries of S-warfarin, R-warfarin, and IS from human plasma were all more than 60.00%. The validated method has been successfully applied to determine of S-warfarin and R-warfarin in human plasma. Then total warfarin was the sum of S-warfarin and R-warfarin.

#### Software

The population PK and PK-PD models were developed using a nonlinear mixed-effect modeling approached with the NONMEMTM (nonlinear mixed-effect modeling, version VII, level 2.0, ICON Development Solutions, Ellicott City, MD, United States). Goodness-of-fit diagnostic plots were prepared with R software (3.2.1, R-project. org). All models were run using the first-order conditional estimation method with interaction (FOCEI).

#### PK Model Development Structural Model

After inspection of the PK profiles, a one-compartment model with first-order absorption was adopted as the optimal base model for warfarin, R-warfarin, and S-warfarin. Structural PK model was fit to plasma concentrations, and typical values of absorption rate constant (Ka), apparent volume of distribution (V/F), and oral clearance (CL/F) were calculated (where F denotes bioavailability). In this study, each individual parameter was expressed approximately as a coefficient of variation to be a log-normal distribution with the mean of population parameters according to results of previous researches (Maria et al., 2003; Eunice et al., 2010; Mark et al., 2010; Juno et al., 2013).

$$P\_{i\dot{j}} = P\_{TV\,\dot{j}} \cdot \exp(\eta\_{i\dot{j}}) \tag{1}$$

Where Pij was the PK Parameters j for ith individual, PTVj was mean of predicted population of PK Parameters j, ηij was a between-subject random variable distributed normally. PK Parameters j was just about Ka, V/F, or CL/F.

The residual error model was assumed to be a mixed error model as following:

$$\mathcal{C}\_{Obs} = \mathcal{C}\_{Pred} \cdot (1 + \varepsilon\_1) + \varepsilon\_2 \tag{2}$$

Where CObs was the observed plasma concentration, CPred was the model prediction concentration. Both of multiplicative residual error (ε<sup>1</sup> ) and additive residual error (ε<sup>2</sup> ) were assumed as a normal distribution.

#### Covariate Models

These covariates were first explored graphically and each potential covariate individually added to the base model if graphical trends were shown. For the covariate models, stepwise of a forward inclusion step and a backward elimination step method was used. When a variable was considered for entering in the final model, it must reduce the objective function value (OFV) by more than 3.84 if p < 0.05 (5% significance level assuming a one degree of freedom, 1OFV > 3.84, df = 1; 1OFV > 5.99, df = 2; 1OFV > 7.81, df = 3). The variable that had the biggest impact on the OFV could enter first and subsequent variables added according to their impact on the OFV. The forward process described above was repeated again until no further covariates were incorporated into the model. Then, the backward elimination step was implementing. The variables were retained in the model if its removal caused an increase in OFV at least 6.63 if p < 0.05(1OFV > 6.63, df = 1). The relative contribution of each covariate to the goodness of fit was evaluated by deleting it from the full model. With these restrictive criteria, only covariates showing statistically significant and clinically relevant contributions were kept in the population PK (PPK) model.

In our research, the covariate of weight was described by allometric scaling equation:

$$P\_{i,j} = P\_{TV} \cdot (\frac{WT}{\overline{WT}})^{\theta\_2} \cdot \exp(\eta\_{i,j}) \tag{3}$$

Where Pi,<sup>j</sup> was the PPK parameters, PTV was a reference value of PPK parameters, WT was weight, WT was median of WT,θ<sup>2</sup> was effect value of WT to PPK parameter.

Other covariates (except weight) were divided into categorical covariates (gender, genotyping, administrated CDDP) and continuous covariates (age, BMI, ALT, AST, BUN, CRE, CRCL).

For the categorical covariates, the following equation was adopted:

$$\text{If}\\
(COV = l)\ P\_{i,j} = (P\_{TV} + \theta\_l) \cdot Exp(\eta\_{i,j}) \, l = 2, \ldots m \qquad (4)$$

Where COV was a categorical covariate which had m levels, θ<sup>l</sup> was adjusted value for PTV to Pi,<sup>j</sup> .

For categorical covariates, the linear models were employed:

$$P\_{i,j} = P\_{TV} \cdot (1 + (COV - \overline{COV}) \cdot \theta\_3) \cdot Exp(\eta\_{i,j}) \tag{5}$$

Where COV was continuous covariates, COV was median of continuous covariate, θ<sup>3</sup> was a coefficient for the effect of covariate to parameter.

#### PK–PD Model Development

The PK–PD model was developed only for S-warfarin, because S-warfarin is the main active ingredient, which is 3–5 times more potent than R-warfarin. According to the plot of relationship between INR and concentration of S-warfarin, the Emax model was selected as the PD model. For the covariate models, stepwise of forward and backward method was used as mentioned in PK model.

# Model Evaluation

fphar-08-00826 November 18, 2017 Time: 15:47 # 4

#### Model Diagnostics

The PK models for warfarin, R-warfarin, S-warfarin, and PK-PD model for S-warfarin was evaluated by the goodness of fit of these models using visual inspection of diagnostic scatter plots of the observed plasma concentrations (DV) versus mean population predicted plasma concentrations (PRED), DV versus individual predicted plasma concentrations (IPRED), conditional weighted residuals (CWRES) versus time, individual weighted residuals (IWRES) versus population predictions (PRED).

TABLE 1 | The demographic profile summary for subjects.


#### Model Validation

#### **Visual predictive check (VPC)**

A visual predictive check (VPC) was performed to evaluate the prediction of PK models for warfarin, R-warfarin, S-warfarin, and PK-PD model for S-warfarin. The VPC were conducted by comparing 1000 datasets simulated from the final parameters with the observed plasma concentrations. The 95% predicted intervals (PIs) obtained from the simulation were superimposed and compared with the observations.

#### **Bootstrap**

A nonparametric bootstrap analysis was used to assess the stability of the parameter estimates and to confirm the robustness of the models. The 1000 bootstrap sample datasets were re-sampled from random sampling with replacement from the original data using individual as sampling unit. Next, population parameters of final PK and PK-PD models for each dataset were estimated. Then, the median and 95% confidence intervals (CI) were constructed by obtaining the 2.5th and 97.5th smallest values out of 1000 parameters estimated from bootstrap sample datasets. Comparing with the mean and 95% CI, each estimated parameter derived from the mean and its standard error of the final parameters.

### SAQ and Follow-Up

The SAQ was applied to evaluate clinical symptoms of patients. The score of SAQ was collected after each period of clinical trial, and compared by paired t-test. In order to learn about more information about warfarin and CDDP administration, the follow-ups were done every 6 months and lasted for 2 years. The contents of follow-up included the length of taking the combination of warfarin and CDDP and some important and



main outcomes, such as bleeding, myocardial infarction, severe arrhythmia, revascularization, ACS, TIA, stroke, heart failure, death, and other conditions causing hospitalization.

#### RESULTS

#### Patients

Sixty-four patients were enrolled from four hospitals in Tianjin from November 2013 to January 2016. Fifty-nine patients completed the trial, among which 21 patients were female, and the mean age was 63 years (49–79 years). The demographic information of the patients was presented in **Table 1**. There were 404 samples and 600 INR values available for analysis from the 59 patients. About 41 patients completed the follow-up. The participant flow chart was shown in **Figure 1**.

#### Fixed Dose and Concentration of Warfarin

In the two periods, the fixed doses of warfarin were 3.39 ± 1.04 mg and 3.36 ± 0.92 mg (P = 0.691), respectively. The steady-state concentration in the two periods was 1.2225 ± 0.5329 mg kg−<sup>1</sup> and 1.1849 ± 0.4949 mg kg−<sup>1</sup> (P = 0.587) for warfarin, 0.8337 ± 0.3597 mg kg−<sup>1</sup> and 0.8128 ± 0.3132 mg kg−<sup>1</sup> (P = 0.650) for R- warfarin, 0.3887 ± 0.2253 mg kg−<sup>1</sup> and 0.3721 ± 0.2301 mg kg−<sup>1</sup> (P = 0.535) for S-warfarin. So, the fixed dose and the steady-state concentration of warfarin were no statistically different between warfarin alone and warfarin plus CDDP. The results were shown in **Table 2**.

# Four Indicators of Blood Coagulation and INR Value

The results were shown in **Table 3**. The four indicators of blood coagulation, prothrombin time (PT), activated partial thromboplatin time (APTT), thrombin time (TT), fibrinogen (FIB), and INR value between the two periods at the fixed warfarin dose had no statistical differences which was compared by paired t-test.

TABLE 3 | The INR value, four indicators of blood coagulation, and seattle angina questionnaire (SAQ) for patients in the first and second period.


TABLE 4 | The covariates of pharmacokinetics (PK) models for Warfarin, R-warfarin, and S-warfarin.


<sup>∗</sup>When CDDP was 0 represented the first period that patients was not administrated CDDP, and CDDP was 1 represented the second period that patients was administrated CDDP.

#### Structural Model for PK Models

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The PK profile of warfarin was in accordance with onecompartment model (Eunice et al., 2010; Steven et al., 2011) or two-compartment model (Jiang et al., 2006; Hamberg et al., 2007) based on literatures, including warfarin, S-warfarin, and R-warfarin. One-compartment and two-compartment models were both investigated for warfarin, S-warfarin and R-warfarin in this study. By comparing OFVs, goodness of fit to the models, as well as rational of parameters, one-compartment was chosen as the optimal ones for initial structure models for warfarin, S-warfarin, and R-warfarin.

#### Covariate Models for PK Models

Once the base structural models were established, potentially significant covariates were evaluated as described. The OFVs of structure models for warfarin, R-warfarin, and S-warfarin were –622.414, –897.240, and –1448.94. When the covariate of weight was on CL, OFV were –623.958, –898.783, and –1449.40 for warfarin, R-warfarin, and S-warfarin, respectively. When the covariate of weight was on V, OFV were –622.423, –897.335, and –1448.94 for warfarin, R-warfarin and S-warfarin, respectively. Comparing with structural models, these OFVs were not more than 3.84, so weight was not the significantly covariates for warfarin, R-warfarin, and S-warfarin.

For warfarin models, in the forward models, three covariates were brought in, PROC on CL, LU on CL, PROC on Ka, but in the backward models, LU on CL was eliminated. At last, the covariates of PROC on Cl and PROC on Ka were in the model. For R-warfarin models, PROC on Ka and PROC on CL were in the models, then PROC on CL was removed, so PROC on Ka was the significantly covariate. For S-warfarin model, the covariates PROC on Ka, CDDP on KA, CYP2C9<sup>∗</sup> 3 on CL, EPHX1 on V and VKORC1 on CL were in the forward models, then two covariates were rejected, PROC on Ka, CDDP on KA and CYP2C9<sup>∗</sup> 3 on CL were in the models as the significantly covariates. The detail information about the covariates for warfarin, R-warfarin, and S-warfarin were shown in **Table 4**.

## PK–PD Model

On the basis of the final PK model, individual estimates of S-warfarin concentrations were predicted and used in the development of PD model. Graphical analyses of the INR observations versus time for S-warfarin demonstrated the Emax model may be more suitable for PD model. So direct Emax models, as well as BIOPH Emax models were investigated in our research. The parameters of the two models were all within a reasonable range, but OFV of BIOPH Emax model decreased 16.35 compared with direct Emax model. Moreover, there was a considerable time delay between INR response and drug concentration. Therefore, BIOPH Emax model was at last considered as the PD model of S-warfarin.

Once the basic structural model was established, potentially significant covariates were evaluated. From the consequence of forward and backward method and the reasonable parameters, AST was finally brought on KE0 of PD model for S-warfarin. The detail information about covariates of PK-PD model for S-warfarin was shown in **Table 5**.

# Model Evaluation

#### Model Diagnostics

The model diagnostic plots were shown in **Figure 2**. **Figures 2A,B** demonstrated that all the data points distributed uniformly in both sides of line y = x. **Figures 2C,D** demonstrated that CWRES and IWRES distributed uniformly in both sides of line y = 0, and the absolute value were less than 4. So, these models adequately described the plasma concentrations, suggesting good fitness of the PK models for warfarin, R-warfarin, S-warfarin, and PK-PD model for S-warfarin.

#### Visual Predictive Check

The VPC plots were shown in **Figure 3**. Most of the observations were in the 95% PIs, so the fit of the models were acceptable in terms of visual or statistical biases for the prediction.

#### Bootstrap

The estimated parameters and 95% values from all bootstrap runs for the PK models of warfarin, R-warfarin, and PK-PD model of S-warfarin were given in **Table 6**. The data indicated that the parameter estimated in PK models and PK-PD model had little bias and the models were fairly robust.

#### The Results of SAQ and Follow-Up

The results of SAQ were shown in **Table 3**. The score of SAQ during trail were 19.71 ± 5.05 for the first period and



<sup>∗</sup>When CDDP was 0 represented the first period that patients was not administrated CDDP, and CDDP was 1 represented the second period that patients was administrated CDDP.

21.02 ± 5.07 for the second period. There was significant difference between two periods (P = 0.002). During 2 years of follow-up, the mean length of taking CDDP is 0.96 ± 0.80 years and 1.70 ± 0.83 years for warfarin. Severe arrhythmia occurred in one patient, revascularization in two patients, death in one patient, and 16 patients were hospitalized due to other conditions. The incidence of severe arrhythmia, revascularization, death, and hospitalization were 2.44% (1/41), 4.88% (2/41), 2.44% (1/41), and 39.02% (16/41).

#### DISCUSSION

In this study a total of 404 blood samples, instead of 472 as required by protocol (eight for each patient), were collected for warfarin assay. There were 600 INR values obtained in the study. Being serious in nature of the heart disease, the compliance of the enrolled patients in the study was relatively low. With the limited number of patients enrolled in this study, we use the principle of PPK algorithm with more detail information collected from the participants, as described in the Guidance for Industry PPK published by FDA which states "Since patients are studied in more detail in this design, the design requires fewer subjects, and the relationship of trough levels to patient characteristics can be evaluated with more precision". Similarly, in some other PPK-PPD studies (Hamberg et al., 2007; Parker et al., 2015; Agarwal et al., 2016; Pier et al., 2017), these numbers of subjects enrolled were comparable to our study.

These CHD patients with AF had been taking warfarin for a long period of time to decrease the risk of thromboembolic


TABLE

6 | The bootstrap results of PK models for warfarin, R-warfarin and PK-PD model for S-warfarin.

complications. The underlying conditions included hypertension (28.8%), diabetes (18.7%), and cerebral ischemic stroke (16.9%) in the study. Various medications were concomitantly used in the patients due to its complicated property of the disease. More frequently used drugs included β-blockers (39.0%), nitric esters (33.9%), statins (22.0%), diuretics (22.0%), cardiac glycosides (18.7%), calcium channel blockers (15.3%), and antidiabetic drugs (15.3%). Identification of the effect of CDDP on profiles of PK and PD of warfarin were established on a self-control design, maintaining all concomitant medications except warfarin from beginning to end of trial. The INR value, fixed warfarin doses and trough concentration of plasma warfarin had not significantly difference (P > 0.05) with or without CDDP. That suggested there is no drug-drug interaction between CDDP and warfarin in human, and CDDP did not affect anticoagulant mechanism of warfarin because CDDP did not interfere metabolic process of warfarin in human.

The PPK models for warfarin, S-warfarin and R-warfarin and PPD model for S-warfarin were developed with assessing patient demographics, genetic polymorphisms and CDDP as covariates. The PK behavior of warfarin, S-warfarin and R-warfarin was in accordance with one-compartment model or two-compartment model based on literatures (Jiang et al., 2006; Hamberg et al., 2007; Eunice et al., 2010; Steven et al., 2011). The Onecompartment models were more optimal and reasonable for warfarin, either S-warfarin or R-warfarin in our study. The consequence of CYP2C9<sup>∗</sup> 3 on CL of S-warfarin was identical to other researches (Chanan et al., 2016; Darcy et al., 2017), but the age, gender, weight had no significant effects on S-warfarin or R-warfarin which were inconsistent with some research (Hamberg et al., 2007; John et al., 2012; Lin R.F. et al., 2015). The gene of CYP4F2, PROC, VKOR, CYP2C9<sup>∗</sup> 3, and EPHX1 were investigated in this research. There was no precise conclusion about the effects of gene subtypes on PK and PD characteristics of warfarin due to limited distribution rate of each individual subtype, which was consistent with other literatures (Özer et al., 2011; Radka et al., 2015). The change of the fixed dose of warfarin in EPHXI gene subtype A/A is higher than the other gene types. Because only two patients with EPHX1 gene subtype A/A were enrolled, it is difficult to make the conclusion that CDDP affect the PK and PD characteristics of warfarin on this kind of patient.

The study result also suggested by PPK model and PPD model that there may be no influence of CDDP on PK and PD of warfarin in patients, although CDDP was as a covariate on Ka of S-warfarin. There had a great variation of Ka with a higher RSE (43.7%, 129.4%, 74.6% for PK models of warfarin, R- warfarin, and S- warfarin) meaning an incredible consequence

#### REFERENCES

Agarwal, N., McPherson, J. P., Bailey, H., Gupta, S., Werner, T. L., Reddy, G., et al. (2016). A phase I clinical trial of the effect of belinostat on the pharmacokinetics and pharmacodynamics of warfarin. Cancer Chemother. Pharmacol. 77, 299–308. doi: 10.1007/s00280-015- 2934-1

about absorption. The bioavailability of warfarin is more than 95% (Mark et al., 2010; Juno et al., 2013), some reports had applied 100% bioavailability when developing models (Maria et al., 2003; Hamberg et al., 2007; Steven et al., 2011). Moreover, there were few reports to evaluate the absorption of warfarin due to its high bioavailability.

The SAQ was applied to evaluate efficacy effect of the co-treatment of warfarin and CDDP in the patients of CHD with AF. It's showed that there was significant difference in the SAQ score with or without CDDP. It may indicate that CDDP can improve the life quality of CHD with AF patients when both INR and dose of warfarin are stable. During 2 years followup, many patients still took the combination for a long time, and there were no report about bleeding. So, the combination of CDDP with warfarin might relieve clinical symptoms and provide benefits for patients with CHD and AF. However, this was not a randomized clinical trial, some researches would be needed to further demonstrate the clinical efficacy.

# CONCLUSION

In summary, robust and stable PK-PD models have been successfully developed for evaluating the effect of CDDP on the PK and PD of warfarin. The results indicated that CDDP did not influence the INR stability and PK characteristic of warfarin when warfarin was administrated simultaneously with CDDP in most CHDs patients. Moreover, The SAQ and follow-up results showed the CDDP combined with warfarin might provide benefit in clinical practice for patients. This study would provide some useful information of the combined regimen of CDDP and warfarin for the treatment of CHDs with AF, but the result in Chinese genetic subtypes of EPHX1 and the clinical efficacy study need to be confirmed further.

# AUTHOR CONTRIBUTIONS

CLv and YH wrote the manuscript. CLiu, YH, XG, and HS designed the research. ZY, LS, XD, JS, YL, and KY performed research. CLv, JL, ZL, and RW analyzed data.

# ACKNOWLEDGMENTS

This study was supported by the Chinese National Natural Science Foundation (No. 81273936). We wish to thank all those who volunteered to participate in this study.

Chanan, S., Simcha, B., Mordechai, M., Meir, B., and Yoseph, C. (2016). Quantitative assessment of CYP2C9 genetic polymorphisms effect on the oral clearance of S-Warfarin in healthy subjects. Mol. Diagn. Ther. 21, 75–83. doi: 10.1007/s40291-016-0247-7

Alpesh, A. (2013). Oral anticoagulation to reduce risk of stroke in patients with atrial fibrillation: current and future therapies. Clin. Interv. Aging 8, 75–84. doi: 10.2147/CIA.S37818


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Lv, Liu, Yao, Gao, Sun, Liu, Song, Li, Du, Sun, Li, Ye, Wang and Huang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

fphar-08-00826 November 18, 2017 Time: 15:47 # 10

# Have the Findings from Clinical Risk Prediction and Trials Any Key Messages for Safety Pharmacology?

Jem D. Lane1, 2 and Andrew Tinker <sup>1</sup> \*

*<sup>1</sup> William Harvey Heart Centre, Barts and The London School of Medicine and Dentistry, London, United Kingdom, <sup>2</sup> Department of Cardiac Electrophysiology, Barts Heart Centre, St Bartholomew's Hospital, London, United Kingdom*

Anti-arrhythmic drugs are a mainstay in the management of symptoms related to arrhythmias, and are adjuncts in prevention and treatment of life-threatening ventricular arrhythmias. However, they also have the potential for pro-arrhythmia and thus the prediction of arrhythmia predisposition and drug response are critical issues. Clinical trials are the latter stages in the safety testing and efficacy process prior to market release, and as such serve as a critical safeguard. In this review, we look at some of the lessons to be learned from approaches to arrhythmia prediction in patients, clinical trials of drugs used in the treatment of arrhythmias, and the implications for the design of pre-clinical safety pharmacology testing.

#### Edited by:

*Stefano Morotti, University of California, Davis, United States*

#### Reviewed by:

*Hugo M. Vargas, Amgen, United States Najah Abi Gerges, AnaBios Corporation, Inc., United States*

> \*Correspondence: *Andrew Tinker a.tinker@qmul.ac.uk*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *26 June 2017* Accepted: *20 October 2017* Published: *06 November 2017*

#### Citation:

*Lane JD and Tinker A (2017) Have the Findings from Clinical Risk Prediction and Trials Any Key Messages for Safety Pharmacology? Front. Physiol. 8:890. doi: 10.3389/fphys.2017.00890* Keywords: arrhythmias, cardiac, torsades de pointes, anti-arrhythmia agents, cardiac ion channels, long QT

# INTRODUCTION

Cardiac arrhythmias range from the benign to the life-threatening. The former typically arise in patients with structurally and functionally normal hearts, while the latter more commonly arise in those with acquired or genetically-determined abnormalities in cardiac structure or cellular electrophysiology. The two modalities currently available to directly target arrhythmias with the aim of prevention and/or eradication are anti-arrhythmic drugs and catheter ablation. Pharmacotherapy has been around for over 100 years, with quinine one of the first to be used (Sneader, 2005), and ironically, one of the first to be associated with inducing arrhythmia (Schwartz et al., 2016). For the majority of agents in use today, efficacy was based on clinical observation rather than a priori understanding of molecular mechanisms. Anti-arrhythmic drugs have retained a key role in the therapy of heart rhythm disorders, despite the advent of ablation. However, their potential to cause harm through pro-arrhythmic effects has placed constraints on the use of many existing drugs, and restricted the release of new agents to the market. The "catch-22" facing such drugs is the requirement to alter cardiac electrophysiology enough, and under the right circumstances, so as to prevent or terminate arrhythmias. Yet at the same time, they must not do so too much or they risk triggering drug-induced arrhythmias. Thus, it would seem a fine balance has to be achieved. In fact, what is required is detailed knowledge of the mechanisms of the arrhythmia requiring treatment at the cellular, tissue and organ levels, and its vulnerable parameter(s) (Task Force of the Working Group on Arrhythmias of the European Society of Cardiology, 1991; Rosen and Janse, 2010). Even more problematic is that non-cardiac drugs sometimes developed for relatively benign conditions can lead to malignant ventricular arrhythmias (Bednar et al., 2002).

Estimates of the incidence of drug-induced arrhythmia require the patient to come to medical attention, and that the diagnosis be considered. The fact that many have concomitant structural

**239**

heart disease makes disentangling drug-induced from endogenous arrhythmia difficult. Partly because of this, attention is focused on torsade de pointes (TdP), which outside the setting of long QT syndrome (LQTS) is rare. TdP is also characteristic of non-cardiac drug-induced long QT in patients with normal hearts. With these considerations in mind, estimates have been made (Sarganas et al., 2014).

Safety pharmacology seeks to exclude drugs with a significant risk of pro-arrhythmia. The challenge is to set the threshold at the correct level, so as to allow safe drugs to continue through development and on to the market, and this is dependent on the methods employed in risk assessment. These methods are in the process of being modified, in light of advances in our understanding of cellular electrophysiology, and the models available. In this review, we focus on anti-arrhythmic drugs, and the role of clinical data in informing our approaches to assessment of their risks of pro-arrhythmia. We adhere to the Vaughan-Williams classification system in referring to drugs by class, acknowledging its limitations.

# KEY CONCEPTS IN CARDIAC SAFETY PHARMACOLOGY

# Ion Channels and Cellular Electrophysiology

Cardiomyocyte electrophysiology serves as the basis for understanding arrhythmia mechanisms, pharmacological anti-arrhythmic and pro-arrhythmic effects. The currents responsible for generating these action potentials differ in atrial and ventricular cardiomyocytes, and sinoatrial/atrioventricular nodal tissue, as well as within different regions of each chamber (Nerbonne and Kass, 2005; Grant, 2009; **Figure 1**).

Activation results in depolarization of the cellular membrane, which if of sufficient magnitude to attain threshold voltage, leads to generation of an action potential. This may then excite a neighboring cell via gap junctions. If the source current from one cell or group of cells is sufficient to depolarize the neighboring cells (the "sink"), propagation occurs. This cyclical process of transmembrane and intercellular ionic fluxes requires reversal of the activation process, and this is termed repolarization. Refractoriness is a distinct though closely linked concept to repolarization, and describes the state of a cell or tissue which is unexcitable, and unable to undergo depolarization.

#### Mechanisms of Ventricular Arrhythmias

Traditionally, at a cellular and tissue level these have been divided into disorders of impulse formation, disorders of conduction/propagation, or a combination of both (Zipes et al., 2005). With regards to tachyarrhythmias, the three most common mechanisms are abnormal automaticity, triggered activity and re-entry. The latter two are considered most relevant to ventricular arrhythmias. Triggered activity takes the form of either early (EADs) or delayed afterdepolarizations (DADs). EADs usually occur with delayed repolarization, which can cause "repolarization instability," rendering cells more susceptible to premature depolarization (Shah et al., 2005). The postulated mechanisms relate either to arrest of repolarization due to diminished outward K<sup>+</sup> currents, or abnormal Ca2<sup>+</sup> influx, either through L-type calcium channels or the Na+/Ca2<sup>+</sup> exchange pump (Pogwizd and Bers, 2004; Shah et al., 2005). They are best described as triggers for TdP in the setting of long QT syndrome (LQTS). DADs occur during phase 4 following completion of repolarization. They result from release of Ca2<sup>+</sup> from the sarcoplasmic reticulum, which raises intracellular Ca2<sup>+</sup> concentration ([Ca2+]i). The Na+/Ca2<sup>+</sup> exchanger extrudes this, with resultant import of Na<sup>+</sup> and a net inward current which causes premature depolarization (Nattel and Carlsson, 2006; **Figure 2**).

Re-entry refers to a circus movement of wavefront propagation, and wavelength is defined as the product of conduction velocity and effective refractory period (ERP), and as such, it represents the length (or volume) of tissue that is refractory to new impulses. For re-entry to occur, wavelength must be shorter than the re-entrant circuit path length. The difference between these is known as the "excitable gap" the zone of non-refractory tissue between the wavefront and wavetail. In theory therefore, prolonging wavelength beyond path length should be antiarrhythmic. Indeed, this is the mechanism of "Class III" anti-arrhythmics, though ironically, the discipline of safety pharmacology in relation to anti-arrhythmic drugs has arisen largely as a result of this effect. More complex iterations of re-entry have been proposed, incorporating functional refractoriness. In particular, the "leading circle model", and rotors are considered important in our attempts to understand complex arrhythmias such as torsade de pointes and ventricular fibrillation (**Figure 3**). "Substrate" is the term used to refer to abnormal myocardium that either produces triggered activity, or by virtue of fibrosis and/or altered cellular electrophysiology, aids the creation of a path suitable for re-entry, or fosters wave break and rotor formation.

### QTc

The QT interval on the electrocardiogram (ECG) reflects the time between depolarization and repolarization of the ventricles. This interval varies with heart rate, so that a correction must be made (QTc). Measurement of the QT interval and adjustment for heart rate (utilizing the R-R interval—the time between successive QRS complexes) are deemed two of the major challenges of electrocardiography (Rautaharju et al., 2009). Variousformulae are available, and while based on measurements from only 39 subjects, Bazett's correction is most commonly used (QTc <sup>=</sup> QT/<sup>√</sup> (R-R). The QT interval is relied upon as an easily accessed biomarker, reflecting repolarization. Its relevance is borne out by its prolongation in the LQTS, and its presaging TdP. Nevertheless, it has a number of shortcomings (Rautaharju et al., 2009; Sager et al., 2014).

#### Repolarization Reserve and Risk Modifiers

As with most rare but serious occurrences, a single factor is rarely sufficient on its own to lead to a ventricular arrhythmia. In the case of TdP in particular, this is due to repolarization reserve. This describes a degree of redundancy among repolarizing

FIGURE 2 | Schematic ECG, action potentials with afterdepolarizations, and onset of torsade de pointes. (A) normal QRS complex and T wave on an ECG. (B) action potential with early afterdepolarizations (EADs). (C) action potential with delayed afterdepolarization (DAD, \*). (D) ECG showing onset of TdP, with a sinus beat (S) followed by a ventricular premature beat (VPB, blue) which is triggered by an EAD.

currents, such that if one is reduced, others may compensate to a degree, maintaining action potential duration, and preventing EADs (Roden and Abraham, 2011). Nevertheless, reserve only protects up to a point, and when several factors act in concert, protection may be lost and arrhythmia may ensue. Ion channel polymorphisms with subclinical effects, impaired clearance of an ion channel-blocking drug, concurrent use of more than one drug, female sex (Makkar et al., 1993; Gaborit et al., 2010) and hormonal derangement (Lane et al., 2012) are just a few of the factors that may modify risk (**Figure 4**).

# DRUG-INDUCED ARRHYTHMIAS

Whilst the focus of safety pharmacology for anti-arrhythmics is the potential to induce ventricular tachyarrhythmias, it is worth considering other arrhythmias that may result. For example, a number of drugs have been shown to trigger atrial fibrillation (AF) (Strickberger et al., 1997; van der Hooft et al., 2004; Kaakeh et al., 2012). For example, there are good data for adenosine, dobutamine, theophyllines and acute alcohol excess precipitating AF (Strickberger et al., 1997; van der Hooft et al., 2004; Kaakeh et al., 2012). In the setting of reduced clearance or concomitant administration, atrioventricular (AV) nodal-blocking drugs such as betablockers and calcium channel antagonists may induce heart block.

Ventricular arrhythmias may occur as a result of therapy with Class I agents (Falk, 1989; The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, 1989; Tisdale and Miller, 2010), though this is exceedingly rarely seen in practice, likely as

FIGURE 3 | Types of re-entry. (A) Classical anatomical re-entry. The wavelength is the product of conduction velocity and refractory period (shown in red). The excitable gap is the section of the circuit which is unexcited, ahead of the wavefront. (B) Leading circle re-entry. The wavefront impinges on the wavetail such that there is no excitable gap. In addition, centripetal invasion creates a central region of functional refractoriness. (C) Rotor re-entry. The wavefront and wavetail meet at a phase singularity, which rotates around an unexcited core. The wavelength (distance between the wavefront and tail) varies according to distance from the phase singularity. Modified from Pandit and Jalife (2013).

a result of the restriction of use of these drugs to patients without evidence of QRS or QT prolongation on the ECG, and structurally normal hearts. Closer attention has been paid to drugs that prolong the QT interval due to the risk of precipitating TdP. Probably this largely stems from the fact there are more drugs that affect repolarizing K<sup>+</sup> currents than INa, so the incidence of arrhythmias is higher due to more widespread use. It may be that in addition, repolarizing currents have less reserve than does INa, and phase 3 of the action potential is as a result, more vulnerable.

At present, clinical practice relies largely on drug indication, ECG markers, indices of cardiac contractility, electrolyte levels and concurrent use of other medication with QT prolonging effects (Drew et al., 2010) to guide risk assessment. More accurate evidence-based scoring systems have been developed (discussed below). Of the ECG biomarkers available, QRS duration, QT interval, T wave morphology and non-sustained or sustained VT are the most easily assessed and clinically useful (Wellens et al., 2014). For example, there has been interesting work done looking at periodic oscillations in repolarization as measured using the T-wave. The authors found a low frequency oscillation <0.1 Hz associated with sympathetic activity but not heart rate variability or respiratory ventilation. It correlated strongly with outcomes after myocardial infarction (Rizas et al., 2014, 2017). However, it is complex to measure. In the absence of a more readily available and accessible measure of cardiac repolarization, the QT interval has retained its role as an important biomarker despite its many shortcomings (Hondeghem, 2006). However, even without the difficulties in measurement, reliance on this oversimplifies the assessment of drug-induced repolarization disturbance (Hondeghem, 2006).

# PRE-CLINICAL APPROACHES TO SCREENING

A major issue for industry is identifying cardiac risk for noncardiac drugs: there seems to be little interest in developing new antiarrhythmic agents for ventricular arrhythmia for the reasons discussed below. However, it is also important not to exaggerate potential toxicity and discard potentially useful agents. Until recently, screening for pro-arrhythmia was based on the International Conference on Harmonization non-clinical and clinical evaluation guidelines, S7B and E14, respectively (International Conference on Harmonsation of Technical Requirements for Registration of Pharmaceuticals for Human Use, 2005a,b). Essentially, these focused on measurement of the human ether-a-go-go related gene (hERG) channel current IKr, and the ECG parameter QTc, as means of identifying drugs with the potential to cause TdP. Heterologous expression systems and animal models have been central to pre-clinical screening, with guinea pig, rabbit, dog and monkey being the most utilized species (Friedrichs et al., 2005; Champeroux et al., 2015). And non-rodent models have demonstrated good correlation of in vivo QT measurements with those in humans (Vargas et al., 2015).

Whilst effective at excluding torsadogenic compounds from market release, proposals for a new screening paradigm have come about due to concerns about oversensitivity and low specificity for detecting pro-arrhythmic potential with the S7B/E14 guidelines, as well as a drive to reduce the number of animals involved in experiments (Lu et al., 2008; Sager et al., 2014; NC3Rs). In addition, improvements in understanding of ion channel physiology, species differences in both cardiac electrophysiology and pharmacokinetics (Haushalter et al., 2008), developments in computer modeling, and the advent of stem cell technology, have reached a stage where it is advantageous to try to incorporate them in the process. A new paradigm known as the Comprehensive in vitro Proarrhythmia Assay (CiPA) has therefore been proposed, and is supported by a number of national and international government and commercial bodies (CiPA project, 2000). CiPA recommends a move toward human-based approaches, with screening of multiple ion channels and computer modeling central to this. There is also the aspiration to use human induced pluripotent stem cell (iPSC) models. Overall there is a move away from the emphasis on IKr and the QT interval, due to recognition of the co-dependence and interplay of ionic currents, multichannel effects of drugs (Li et al., 2017), and the shortcomings of the QT interval and importance of other ECG parameters such as the PR and QRS intervals (Sager et al., 2014).

CiPA is still in the process of being validated (Cavero et al., 2016; Colatsky et al., 2016), and has not yet been accepted to supersede the S7B/E14 guidelines. The hope that iPSC derived cardiomyocytes can assume a confirmatory role within the framework, is ambitious and perhaps the least certain of CiPA's four components, given their relative novelty. There is a growing acceptance that these cells are immature compared to native adult myocytes and are more fetal in terms of their electrophysiology and other properties (Veerman et al., 2015; Rodriguez et al., 2016). The latter may be circumvented by use of human cardiac tissue, for example from organ donors (Page et al., 2016), though this is not without its own difficulties, chiefly the lack of availability in many countries. It may be worthwhile to calibrate findings in iPSC cardiomyocytes with those from human myocytes to validate measurements. Nevertheless, a reappraisal of existing guidelines' strengths and weaknesses, and attempts to enhance the accuracy of cardiac safety testing by making use of new techniques and improved understanding, is commendable. And importantly, the new paradigm is being systematically validated prior to implementation.

## CLINICAL TRIALS ON ANTIARRHYTHMIC DRUGS

Clinical trials have been of paramount importance in the field of safety pharmacology for anti-arrhythmics. Unexpected findings have brought about the widespread use of beta-blockers in heart failure, and the restricted use of many other drugs such as flecainide and sotalol. They enable assessment of hard endpoints rather than surrogates, and provide opportunities to test repolarization and activation reserve in vivo. The main stages in this development process are illustrated in **Figure 5**. An overview of two of the most important trials is provided, prior to looking at the evidence relating to a number of anti-arrhythmic drugs. Rather than provide an exhaustive account of clinical trials involving anti-arrhythmic drugs, we try to focus on randomized trials that have been instructive in terms of safety, or changed practice.

## Cardiac Arrhythmia Suppression Trial (CAST)

This landmark randomized controlled trial (RCT) was both disappointing and hugely influential. To investigate whether suppression of ventricular premature beats (VPBs) in patients following myocardial infarction (MI) reduced their risk of sudden death, patients were assigned to the Na<sup>+</sup> channel/INa blockers, encainide, flecainide, moricizine, or placebo (flecainide also has some hERG/IKr-blocking effects, but INa blockade is pharmacodynamically more important). A preliminary report

of the drug titration phase in 1989 revealed that despite their apparent suppression of VPBs, there was an excess of arrhythmic deaths in patients assigned to encainide or flecainide (The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, 1989). This was confirmed in the full report of 1498 patients assigned to these two drugs or placebo. An excess of both arrhythmic and non-arrhythmic cardiac deaths were seen (Echt et al., 1991). A few points are noteworthy regarding the study. Firstly, beta-blocker use was low by contemporary standards: between 20 and 30% across all groups. Calcium channel blocker use, primarily diltiazem, was high (47–53%), as was digitalis (16–24%). Secondly, mean baseline left ventricular ejection fraction (LVEF) was 39–40%. The second part of the study comparing moricizine to placebo is less widely discussed, but found similar results (The Cardiac Arrhythmia Suppression Trial II Investigators, 1992). The drug was withdrawn in 2007 (Structural Bioinformatics Group at Charité, 2000). The fallout has resulted in avoidance of flecainide (and other "Class IC" drugs) in patients with "structural heart disease"—particularly ischaemic heart disease with a history of MI, but extrapolated to essentially anyone with any abnormality in ventricular structure and function. The rationale for this has been questioned (Kramer and Josephson, 2010). In terms of possible mechanisms for the observed pro-arrhythmia, slowing of conduction velocity with resultant facilitation of re-entry has been posited (Ruskin, 1989), though late development of ischaemia and accumulation of high drug levels may also have contributed (Aliot et al., 2011).

# Survival with Oral d-Sotalol (SWORD) Trial

This RCT recruited a similar patient demographic to CAST: those with LVEF <40% and a history of MI (Waldo et al., 1996). The objective was to evaluate whether a phase 3 K<sup>+</sup> channel (hERG/IKr) blocker, d-sotalol, reduced all-cause mortality compared to placebo. The trial was stopped prematurely due to an increased risk of death in the d-sotalol group (5.0 vs. 3.1%, relative risk 1.65, p = 0.006) (Waldo et al., 1996). This was presumed to be primarily due to arrhythmias; unfortunately beyond the fact that the risk of death was higher in women, justification for this assumption could be challenged. In terms of possible mechanisms for arrhythmic death, beta-blocker use was again low pre-randomization (32–33%), and digoxin use was high (48–50%). Importantly though, patients were initiated on 100 mg twice daily of d-sotalol, and if tolerated with a QTc < 520 ms, the dose was increased to 200 mg twice daily. Then, if this dose was tolerated with a QTc < 560 ms, patients remained on this dose for the study's duration. Such QT prolongation is well-established as a risk for TdP (Makkar et al., 1993; Drew et al., 2010), and would be inconceivable in a modern trial.

# Amiodarone

Amiodarone interacts with multiple ion channels, resulting in reduced INa, IKr, IKs, ICaL, as well as antagonizing α- and βadrenoceptors and acetylcholine receptors (Zimetbaum, 2012; Darbar, 2014). It has been studied in a large number of randomized trials in the setting of AF or ventricular arrhythmias (Doval et al., 1994; Julian et al., 1997; Roy et al., 2000; Bardy et al., 2005; Singh et al., 2005; Connolly et al., 2006; Le Heuzey et al., 2010). Paradoxically it often prolongs the QT interval, yet has long been known to have a low incidence of TdP, possibly due to its actions on inward currents (Lazzara, 1989; Vorperian et al., 1997; Roden, 2004). There is a higher risk of bradycardic events nevertheless (Vorperian et al., 1997). More recently, a metaanalysis of over 8,000 patients in RCTs comparing amiodarone to placebo or control found amiodarone was associated with a reduction in sudden cardiac death, though not a significant reduction in overall mortality (Piccini et al., 2009). Notably, in the GESICA trial it was found to confer improved survival in the setting of heart failure (Doval et al., 1994). And in the European Myocardial Infarct Amiodarone Trial (EMIAT), it was demonstrated to reduce arrhythmic deaths by 35% in those with LVEF ≤ 40%, though had no effect on all-cause or cardiac mortality (Julian et al., 1997). The lack of benefit on overall mortality was supported by SCD-HeFT (Bardy et al., 2005). Thus, it is one of the few drugs considered safe for use in patients with a history of MI and reduced LV function.

#### Beta-Adrenoceptor Antagonists

This class of drugs exerts effects via antagonism of β1 and/or β2-adrenoceptor signaling. β1-adrenoceptors signal via the stimulatory G protein, Gs, and the cyclic adenosine monophosphate (cAMP) and protein kinase A (PKA) cascade. PKA increases ICaL, IKs and possibly INa (Brodde and Michel, 1999; Grant, 2009). β2-adrenoceptor signaling is more complex: it also couples to Gs, but can also be induced to couple to Gi, the inhibitory isoform (Xiao et al., 1995). This increases IKACh, and may negatively regulate ICaL (Nagata et al., 2000; Zuberi et al., 2010). β-adrenoceptor antagonists are the most studied anti-arrhythmics, due to their use for both supraventricular and ventricular arrhythmias, as well as heart failure and hypertension (Packer et al., 1996, 2002; MERIT-HF Study Group, 1999; The Cardiac Insufficiency Bisoprolol Study II, 1999; Pedersen et al., 2014; Katritsis et al., 2017). They have been demonstrated to reduce mortality in heart failure, including the risk of sudden cardiac death (Hjalmarson, 1997; MERIT-HF Study Group, 1999; The Cardiac Insufficiency Bisoprolol Study II, 1999; Packer et al., 2002). Risk of pro-arrhythmia is essentially limited to the small risk of AV conduction block, which in the absence of overdose, severe renal dysfunction or concomitant AV nodal-blocking drug use, occurs extremely rarely.

# Dofetilide

A "pure" IKr blocker, dofetilide was investigated in patients with severe LV impairment and heart failure as a treatment for AF in the DIAMOND-CHF study (Torp-Pedersen et al., 1999). It performed better than placebo in converting patients with AF to sinus rhythm, though the rate of conversion by 1 month was low (12% vs. 1%). Maintenance of sinus rhythm was also higher for the dofetilide group. It was shown to be associated with a reduced rate of hospitalization for worsening heart failure. However, there was a 3.3% rate of TdP in those treated with the drug. A subsequent trial (DIAMOND-MI) investigated use of the drug in patients with recent MI and LV dysfunction (Køber et al., 2000). Again, there was no effect on all-cause or cardiac mortality, nor on arrhythmic deaths. It showed some efficacy in restoring sinus rhythm in those with AF, but there was a TdP event rate of approximately 1%. Further trials, predominantly in AF and atrial flutter have confirmed its anti-arrhythmic efficacy, but also its pro-arrhythmic potential (Bianconi et al., 2000; Singh et al., 2000). Thus, dofetilide exhibits reasonable anti-arrhythmic efficacy, and does not appear to increase mortality, yet there is a significant risk of TdP such that its use requires close monitoring (Abraham et al., 2015; Schwartz et al., 2016). Therefore, whilst current guidelines indicate it can be used to treat atrial flutter acutely (Katritsis et al., 2017), alternative drug therapy and catheter ablation have rendered this largely obsolete, in Europe at least.

#### Dronedarone

This multichannel blocking drug is similar to amiodarone but with reduced extra-cardiac effects (Tadros et al., 2016). Despite a promising start in trials such as EURIDIS/ADONIS and ATHENA (Singh et al., 2007; Hohnloser et al., 2009), subsequent trials in patients with permanent AF and heart failure did not support its anti-arrhythmic potency, and moreover, it was associated with worsening of heart failure and increased mortality (Køber et al., 2008; Connolly et al., 2011). Nevertheless, there does not appear to be a significant pro-arrhythmic tendency, reinforcing the notion that drugs with multichannel effects and complex actions can still be safe, in this regard at least.

# ALTERNATIVE AND EVOLVING CLINICAL APPROACHES

The preceding discussion has shown that there is room for improvement in prediction of pro-arrhythmia. At the clinical level, strategies can broadly be divided into those focusing on the drugs, and those focusing on patient factors. Haverkamp et al addressed both in 2001 (Haverkamp et al., 2001). They identified many of the clinical risk factors still in use today, and came up with what is to our knowledge the first attempt to stratify drugs according to propensity to induce TdP. The list of drugs was limited, and the classification was not developed. Around the same time, the Georgetown University Center for Education and Research on Therapeutics (GUCERT) was awarded money to investigate the potential of drugs to induce TdP. Subsequently based in Arizona and renamed, AZCERT, a not-for-profit organization published lists of drugs known to be associated with, and causative of QT prolongation and TdP at www.qtdrugs.org. Currently the lists are available at www. crediblemeds.org. Brugadadrugs.org is a similar website set up by the University of Amsterdam Academic Medical Center, providing advice on drugs to avoid, and drugs with possible therapeutic use for patients with Brugada syndrome (University of Amsterdam Academic Medical Center, 2017).

Clinical risk factors for ventricular fibrillation (VF) were evaluated by Da Costa et al in 91 patients with pause-dependent TdP in the setting of QT prolongation. LVEF, presence of structural heart disease, and an index of QT dispersion were found to be significant predictors (Da Costa et al., 2000). And clinical scoring systems based on patient factors have been developed. For example, Tisdale et al utilized data from 900 patients to develop a scoring system to predict QTc prolongation, and then validated this in 300 additional patients (Tisdale et al., 2013). Female sex, diagnosis of MI, sepsis, LV dysfunction, administration of QT-prolonging drugs, use of loop diuretics, serum K<sup>+</sup> < 3.5 mEq/L and QT interval on admission >450 ms were identified as independent risk factors. The system had reasonable sensitivity and specificity. Although useful, it utilized a biomarker rather than a patient outcome as an endpoint. Such risk scores are likely to gain importance as electronic prescribing becomes more widespread, with automated alert systems also becoming more feasible (Haugaa et al., 2013).

The ultimate aim of precision medicine is to tailor treatment to the specific patient and the genetic make-up is likely to play a major role in determining this. There have been substantial efforts to understand the genomic architecture of the heritability of the QT interval in the general population. A variety of loci have been identified from genome wide association study (GWAS) findings (Arking et al., 2014). It was shown that one of the signals in the nitric oxide synthase 1 adaptor protein predicted predisposition to drug-induced long QT syndrome (Jamshidi et al., 2012). Furthermore, Strauss and colleagues created a "genetic QT" score, and investigated its ability to predict druginduced QTc prolongation, and TdP (Strauss et al., 2017). While it was a significant predictor of both, the predictive power was modest, leaving much of the variability unaccounted for.

## IMPLICATIONS FOR SAFETY PHARMACOLOGY

The literature on the use of antiarrhythmic drugs illustrates a number of important points.

## There Is No Universal Biomarker Predicting Risk

The QTc remains an important biomarker, though it is far from the only clinical marker of a drug's pro-arrhythmic risk. Clinical trials have demonstrated that amiodarone and betablockers remain two of the safest agents in terms of proarrhythmia. Their mechanisms are different, yet they both exert anti-arrhythmic effects, and cardiac contra-indications are few. Importantly, amiodarone confounds the predictive power of IKr and QTc screening, by virtue of its APD and QTprolonging effects, with minimal associated pro-arrhythmic risk. It highlights the oversensitivity of the S7B and E14 guidelines: had it not been in use already, one of the most effective and safe (in arrhythmia terms) drugs may have been excluded from the market. Amiodarone's cardiac safety, together with flecainide's and sotalol's pro-arrhythmogenicity, serve as the strongest reminders of the current importance of clinical trials and post-marketing surveillance in bringing to light unexpected, unpredicted and counterintuitive findings; of how predictions based on theory may not be borne out in practice. But where this is the case, there is an opportunity to learn.

#### Underlying Patient Pathology Is Important

The presence of pre-existing cardiac conditions such as LV impairment and ischaemic heart disease modulate risk of proarrhythmia, such that use of certain drugs, deemed safe in those with structurally normal hearts, is given careful consideration in patients with a history of these conditions. They, and other risk modifiers, such as female sex, diuretic use, hypokalaemia, and concomitant use of other QT-prolonging drugs, identified in clinical reports and risk models (Drew et al., 2010), must be included in in silico models (Wi´sniowska and Polak, 2016) if computer modeling and prediction is to fully realize its potential. Identification of drugs with significant risk of arrhythmia may enable us to gain insight into the reasons for this. For example, the list of drugs available at www.crediblemeds.org may have arisen due to similarities in the behavior of the drug molecules in their interaction with ion channels, or alternatively their pharmacokinetics. Ultimately, feedback such as this to preclinical models, and clinical trials' validation of these models will hopefully lead, via an iterative process, to greater confidence in the predictive powers of computer, animal and stem cell models (Carusi et al., 2012), with a greater burden of safety testing and prediction occurring in these, rather than in trials in humans. Those models that cannot predict with reasonable accuracy must be honed, or discarded. Increased pre-clinical predictive accuracy should allow more compounds to reach the clinical trial stage. This, together with post-marketing surveillance, will retain a key role in highlighting unexpected findings, due to our inability to completely account for human physiology, pathophysiology, pharmacokinetics, and pharmacodynamics, as well as interindividual variability in these factors, in any model.

### Ion Channels Remodel in Disease and Disease Specific Models May Be Necessary

Many of the experimental and computational approaches rely on the assessment of a compound against parameters or cells derived from healthy normal individuals. However, it is clear that the expression of ion channels significantly remodels in pathological states and this may account for proarrhythmia under such conditions. For example, in atrial fibrillation the expression of L-type calcium currents in the atria is reduced and this in itself generates a substrate for further atrial fibrillation (Wijffels et al., 1995; Gaspo et al., 1997; Yue et al., 1999). It is clear that ion channel remodeling also occurs in many other cardiac pathologies although is not so well defined (Nattel et al., 2007). On this background individual genetic differences are likely to modify the response (Munroe and Tinker, 2015). Thus, we may see the development of disease specific computational models and/or engineered cellular assay systems. In this regard the development of computational approaches to explore models with large numbers of varying parameters is likely to be valuable (Britton et al., 2013, 2017).

# AUTHOR CONTRIBUTIONS

Both authors have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

# ACKNOWLEDGMENTS

This work was supported by the British Heart Foundation (FS/12/11/29289 and RG/15/15/31742 and facilitated by the NIHR Biomedical Research Centre at Barts.

# REFERENCES


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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Lane and Tinker. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Humans Vary, So Cardiac Models Should Account for That Too!

#### Barbara Wisniowska ´ 1 , Zofia Tylutki <sup>1</sup> and Sebastian Polak 1, 2 \*

*<sup>1</sup> Pharmacoepidemiology and Pharmacoeconomics Unit, Faculty of Pharmacy, Jagiellonian University Medical College, Krakow, Poland, <sup>2</sup> Simcyp, Certara, Sheffield, United Kingdom*

The utilization of mathematical modeling and simulation in drug development encompasses multiple mathematical techniques and the location of a drug candidate in the development pipeline. Historically speaking they have been used to analyze experimental data (i.e., Hill equation) and clarify the involved physical and chemical processes (i.e., Fick laws and drug molecule diffusion). In recent years the advanced utilization of mathematical modeling has been an important part of the regulatory review process. Physiologically based pharmacokinetic (PBPK) models identify the need to conduct specific clinical studies, suggest specific study designs and propose appropriate labeling language. Their application allows the evaluation of the influence of intrinsic (e.g., age, gender, genetics, disease) and extrinsic [e.g., dosing schedule, drug-drug interactions (DDIs)] factors, alone or in combinations, on drug exposure and therefore provides accurate population assessment. A similar pathway has been taken for the assessment of drug safety with cardiac safety being one the most advanced examples. Mechanistic mathematical model-informed safety evaluation, with a focus on drug potential for causing arrhythmias, is now discussed as an element of the Comprehensive *in vitro* Proarrhythmia Assay. One of the pillars of this paradigm is the use of an *in silico* model of the adult human ventricular cardiomyocyte to integrate *in vitro* measured data. Existing examples (*in vitro—in vivo* extrapolation with the use of PBPK models) suggest that deterministic, epidemiological and clinical data based variability models can be merged with the mechanistic models describing human physiology. There are other methods available, based on the stochastic approach and on population of models generated by randomly assigning specific parameter values (ionic current conductance and kinetic) and further pruning. Both approaches are briefly characterized in this manuscript, in parallel with the drug-specific variability.

Keywords: variability, cardiac models, IVIVE, drug cardiac safety, modeling and simulation

#### INTRODUCTION

# Mechanistic Modeling and Simulation Approach in the Process of Drug Development in Light of the Recent Changes to FDA/EMA/PMDA Regulations

The mathematical modeling and simulation (M&S) approach has held its place in the drug development process since the very beginning. Having moved from academic curiosity to industrial practice the approach is used to both analyze the data and understand the physical mechanisms

#### Edited by:

*Stefano Morotti, University of California, Davis, United States*

#### Reviewed by:

*Eric A. Sobie, Icahn School of Medicine at Mount Sinai, United States Alfonso Bueno-Orovio, University of Oxford, United Kingdom*

> \*Correspondence: *Sebastian Polak spolak@cm-uj.krakow.pl*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *24 July 2017* Accepted: *30 August 2017* Published: *21 September 2017*

#### Citation:

*Wisniowska B, Tylutki Z and Polak S ´ (2017) Humans Vary, So Cardiac Models Should Account for That Too! Front. Physiol. 8:700. doi: 10.3389/fphys.2017.00700*

**250**

involved. Model-informed drug development (MIDD) is here to stay and it also has been recently indicated as one of the major areas of scientific priority by the regulators (Huang et al., 2013; Zineh et al., 2017). Initially, the outcome of pharmacometric analyses has impacted the decision making process of drug development (Miller et al., 2005; Lee et al., 2011). In recent years regulatory support for mechanistic physiological modeling has helped to bridge the gap between preclinical and clinical observations with respect to understanding biological systems (Rowland et al., 2015; Friedrich, 2016).

Special interest has been given to physiologically based pharmacokinetic (PBPK) modeling defined by WHO as "quantitative descriptions of the absorption, distribution, metabolism, and excretion (ADME) of chemicals in biota based on interrelationships among key physiological, biochemical and physicochemical determinants of these processes"<sup>1</sup> . A physiologically based pharmacokinetic approach is based on a combination of the physiology, environment, and drug specific information. These parameters are further utilized in the mechanistic models describing the pharmacokinetics (PK) and/or pharmacodynamics (PD) of a drug(s) of interest (Rostami-Hodjegan, 2012). This is not a new concept and it is suggested that the roots of PBPK models originate from the work of Teorell, published in 1937 (Teorell, 1937). Recent scientific advances and the development of models utilizing PBPK scaffolding are invaluable in the situation where clinical trials are extremely challenging or impossible. This includes specialized populations and situations of special interest such as pregnant woman and pediatric applications (Lu et al., 2012; Abduljalil et al., 2014). PBPK models are utilized for various applications throughout a drug's life cycle. Results of their simulations can be used to support the planning of specialized clinical studies, support dosing recommendations and the labeling of products (Zhao et al., 2011; Jones et al., 2015; Shepard et al., 2015; Wagner et al., 2015). The simulation results are used in lieu of conducting clinical studies or provide information that otherwise would have been missing in some specific situations (Jamei, 2016).

The use of PBPK modeling was included in the guidance documents for industry provided by the U.S. Food and Drug Administration (FDA), the European Medicines Agency (EMA) and the Ministry of Health Labor and Welfare (MHLW) of Japan. The latter, namely the draft of the drug interaction guideline for drug development and labeling recommendations published by the Japanese Ministry of Health, Labor and Welfare in 2014, suggested the PBPK application in the assessment of drugdrug interaction (DDI; Saito et al., 2014). Recent guidelines published by the FDA and EMA list several points in the drug development process where PBPK modeling may be applicable in order to support decisions in the premarketing, as well as at postmarketing, stage2,3. PBPK analyses are currently widely accepted and used not only as a research tool but also to support drug registration applications including investigational new drugs (INDs), new drug applications (NDAs), biologics license applications (BLAs), or abbreviated new drug applications (ANDAs; Sato et al., 2017). As of December 2016 there were 36 approved drugs, which provided PBPK M&S results, in the U.S. new drug application labeling procedure. In addition to PBPK, the Advisory Committee mentioned mechanistic safety modeling, particularly, risk prediction/assessment as a promising MIDD area<sup>4</sup> .

It is highly likely that the next application for PBPK models is in the area of precision dosing and personalized medicine (Hartmanshenn et al., 2016). This is achievable due to the specific structure of the physiologically-based models, where system description is clearly separated from the drug and external parameters (i.e., dosing schema). The biological parameters are described by large collections of anatomical and physiological data derived from literature or existing databases. For the assessment of inter- and to some degree intraindividual variability, virtual individuals, and virtual populations are randomly created (Jamei et al., 2009a).

### In Vitro—in Vivo Extrapolation (IVIVE) as an Approach

In vitro—in vivo extrapolation (IVIVE) as a phrase covers all techniques utilized for the prediction of human pharmacokinetics and pharmacodynamics based on the ADME information ADME in addition to drug activity and toxicity. It is crucial to mention that, in principle, the data comes from the in vitro studies, where various models and techniques are utilized. The main challenge is to translate the data, often heterogeneous, from the level of a "Petri dish" to the complex system of the human body. Therefore, what is needed are in vitro methods mimicking basic phenomena occurring in a human body at the cellular or subcellular level, and models describing the human body as a biological system. The latter describing models of human organs, tissues, or the whole body include the incorporation of the above mentioned PBPK systems. There are other approaches currently implemented, which combine and merge traditional compartmental models and various systems biology models, to describe biochemical and physiological phenomena (Sorger et al., 2011). It's worth adding that the addition of available human in vivo data enriches the model and can improve the degree of predictability (Tsamandouras et al., 2015). Practical utilization of the IVIVE concept, with the use of PBPK models and population data, covers various populations from healthy individuals up to the special populations (e.g., diseased—renal insufficiency, cirrhosis etc.) and pediatric populations (Sager et al., 2015).

Interestingly, conceptually similar approaches were independently introduced in the pharmacokinetics and pharmacodynamics area (Visser et al., 2014). The biophysically detailed models describing cell electrophysiology can be used for the in vitro—in vivo extrapolation, as proposed in the CiPA

<sup>1</sup>www.who.int/ipcs/methods/harmonization/areas/pbpk/en/

<sup>2</sup>www.ema.europa.eu/docs/en\_GB/document\_library/Scientific\_guideline/2016/ 07/WC500211315.pdf

<sup>3</sup>www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/ Guidances/UCM531207.pdf

<sup>4</sup>www.fda.gov/downloads/AdvisoryCommittees/CommitteesMeetingMaterials/ Drugs/AdvisoryCommitteeforPharmaceuticalScienceandClinicalPharmacology/ UCM544838.pdf

(Comprehensive in vitro Proarrhythmia Assay) initiative, as described below (O'Hara et al., 2011; Gintant et al., 2016). There is although one difference between the IVIVE/PBPK approach and the proposed IVIVE/safety approach. The latter, namely safety in vitro—in vivo extrapolation, has so far been done with the use of models describing cell electrophysiology without accounting for variability.

#### CiPA Initiative—What Does It Change, Where We Are, and What Is Potentially Lacking

Regardless of the opinion on the current changes—whether it is a logical consequence of the evolutionary changes or Copernican Revolution—we are witnessing a significant paradigm shift in the area of drug cardiac safety assessment. The recently proposed CiPA schema for the preclinical evaluation of proarrhythmic liabilities proposes to assess proarrhythmic risk based on in silico reconstructions of human ventricular electrical activity. A biophysically detailed model aims to analyze repolarization abnormalities such as EADs. The input information includes in vitro measured data on the drug concentration-dependent inhibition of multiple human cardiac currents (Colatsky et al., 2016; Gintant et al., 2016). The O'Hara-Rudy (ORd) model was chosen as the starting point for developing an in silico model with the ultimate aim of providing a system suitable for regulatory decision making (O'Hara et al., 2011). The model is being further developed by the addition of a more mechanistic description of drug-channel binding kinetics (Li et al., 2017). The model proposes to generate output allowing for the separation of the reference drugs into three distinct risk categories—low, intermediate and high risk. The validation is planned to be performed with the use of 28 (12) drugs as detailed in the report presented at the FDA Briefing Document Pharmaceutical Science and Clinical Pharmacology Advisory Committee Meeting March 15, 2017 Topic: Strategies, approaches, and challenges in modelinformed drug development (MIDD). According to the FDA's suggested strategy, estimation of the inter-individual variability in a drug's pharmacokinetics and pharmacodynamics is a key issue in recent drug development. PBPK modeling addresses this issue and so should mechanistic safety modeling. In PBPK, the variability in PK prediction is assured by specifying the population-dependent distribution of parameters' values and the covariation between these parameters (Jones et al., 2015). Regarding cardiac risk assessment, the variability is already observed at the stage of in vitro measurements, e.g., in drug effects on the ventricular ion currents or in the effects on human stem cell-derived cardiomyocytes (iPSC-CM) which differ in channel gene expression profiles and patterns of arrhythmic events after testing with the same model drug (Elkins et al., 2013; Blinova et al., 2017). The observational uncertainty together with other sources of uncertainty influence computational model inputs, and consequently, the confidence of the output, regardless of the electrophysiological model used (Johnstone et al., 2016; Mirams et al., 2016). The frequently used cardiac models do not account for physiological or experimental variation in their default parametrization (Davies et al., 2016). However, clinical observations leave no doubts that variability is important, and drug-independent factors may play a crucial role in triggering a drug cardiac effect. The analyses of case reports of QT interval prolongation and ventricular arrhythmia, associated with cisapride, revealed that often in the case of these adverse events the patients had more than one contraindication that predisposed them to arrhythmia. The drug was therefore withdrawn from the U.S. market in 2000 (Wysowski et al., 2001). The coincidence of multiple risk factors, both physiological and pathophysiological was also the case for TdP induction after the administration of certain drugs, e.g., erythromycin (Hancox et al., 2014), quetiapine (Hasnain et al., 2014), methadone (Vieweg et al., 2013b), and risperidone (Vieweg et al., 2013a). These are all exemplary drugs which are known to pose the risk of TdP according to the Credible Meds classification and are at the same time safely used if taken properly<sup>5</sup> . The observed variability in the PD response may come from the drug itself, since for some compounds the QTc interval prolongation is said to be dose or concentration-related (Krantz et al., 2003; Fanoe et al., 2009). However, even then the variation in individual QTc length cannot be explained solely by PK and factors that affect the ADME processes. There are examples illustrating the lack of correlation between electrophysiological changes and drug plasma concentrations (Wi´sniowska et al., 2016). Even in healthy subjects the observed QTc changes, following drug administration, may vary by about 80 ms (Jerling and Abdallah, 2005; Hulhoven et al., 2008) as age, sex, and race are said to affect cardiac electrophysiology (Macfarlane et al., 1994) not to mention observed circadian intra-subject variations (Molnar et al., 1996).

There are also special populations that should be considered when assessing drug triggered cardiac effects. First of all, the cardiac action potential is affected in patients with cardiac channelopathies associated with genetic mutations. One of the main congenital phenotypes is long QT syndrome (LQTS) which is prevalent in 1:3,000–1:5,000 in the general population (Goldenberg and Moss, 2008) manifesting with a QTc length of above 460 ms (Abriel and Zaklyazminskaya, 2013). The most frequent mutations that are responsible for congenital LQTS were found in genes that code for proteins in the potassium hERG channel (KCNQ1 and KCNH2) and the Nav1.5 sodium channel (SCN5A; Bohnen et al., 2016). The LQTS patients are said to be particularly vulnerable to drug-related arrhythmias (Goldenberg et al., 2008). Also, comorbidities were found to contribute to QTc-prolongation. The analysis conducted by Vandael et al. (2017) revealed strong evidence for ischemic cardiomyopathy, hypertension, arrhythmia, and thyroid disturbances to be risk factors contributing to QTc interval prolongation.

## Variability in Cardiac Models—Stochastic vs. Deterministic Approach

Mathematical models of cardiac cell electrophysiology have proved their value and now hold an established position in research and drug development (Amanfu and Saucerman, 2011; Davies et al., 2016). It all began with the work of Hodgkin and

<sup>5</sup>https://crediblemeds.org/

Huxley where they modeled the cell membrane as a capacitor with batteries and resistors and described its electrophysiological behavior (Hodgkin and Huxley, 1952). The following ordinary differential equation was established:

$$\frac{dV}{dt} = \frac{I\_{\text{ion}} - I\_{\text{stim}}}{C\_m},$$

where V is voltage, t is time, Iion is the sum of all transmembrane ionic currents, Istim is the externally applied stimulus current, and C<sup>m</sup> is cell capacitance of the membrane per unit surface area (Ten Tusscher and Panfilov, 2006). Beginning from the relatively simple Noble's model (Noble, 1962), cardiac electrophysiology models have evolved tremendously, and now include a detailed description on cardiac ion channels, pumps and transporters, as well as intracellular calcium handling (Noble, 2007; Fink et al., 2011). The models proved successful for studying cardiac physiology and understanding pathological changes (e.g., arrhythmias) associated with diseases over the last decades and currently they are used in the safety assessment of drugs (Mirams et al., 2012; Roberts et al., 2012; Davies et al., 2016; Gintant et al., 2016). To be a vital element of the safety-related decisions made through the various stages of drug development and in the clinic, the models have to ascertain credibility, i.e., properly reproduce the electrophysiology of a population and individual patients. The question arises asking if it is feasible to use a single traditional cardiac model with input parameters being the mean values, averaged across many subjects, and generating an output as a single value, thus presenting behavior a of "representative" cell. Until recently there wasn't much interest in the variability in the field of cardiac electrophysiology modeling. Several approaches have now been proposed, and implemented, to introduce variability into cardiac models and account for inter- and intra-patients differences. All of the approaches stem from the belief that the "average patient" does not exist and a traditional model cannot accurately explain the observed differences between patients.

#### Stochastic Approach

Physiological variability can be investigated and modeled by constructing populations of experimentally calibrated models. This approach has been introduced a while ago and is further developed by researchers from various organizations including, but not limited to, the Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York (Sobie, 2009; Sarkar et al., 2012), the Department of Computer Sciences at Oxford University (Britton et al., 2013; Sánchez et al., 2014; Muszkiewicz et al., 2016; Pueyo et al., 2016; Zhou et al., 2016), and other (Marder and Taylor, 2011). Variability in a model's behavior is accomplished by the multiplication of its parameter values by sampled scaling factors, which results in an ensemble of possible outputs instead of an average one. Once the baseline model (appropriate for the research question) is selected, the parameters of variation have to be chosen, and the ranges for parameter sampling need to be defined. Both depend on the study aim and the target population (e.g., healthy, diseased) to be investigated.

There are multiple approaches available for generating the population of models. For example, parameters and their ranges generate high-dimensional spaces from which their values are sampled using different sampling algorithms (e.g., the Latin Hypercube, Monte Carlo method) to generate an ensemble of variant models (Drovandi et al., 2016). The candidate models are simulated to mimic, for example, experimental settings regarding bath solution composition, voltage protocol, and pacing rate. The pool of models is pruned according to the boundaries for a range of permitted model outputs, defined by minimal and maximal values observed in the experiment. Such calibration yields the experimentally-calibrated populations of models presenting electrophysiological behavior that reproduce the results of experiments which can be further analyzed for the parameters underlying the observed response variability (Britton et al., 2013). The model could also be employed to assess a range of responses across the population under certain conditions, e.g., diseased, or reflecting drug application (Muszkiewicz et al., 2016).

The other approach is based on parameter sensitivity analysis techniques which can be applied to generate quantitative predictions based on considering behaviors within a population of models (Romero et al., 2009). In the single parameter scanning one can increase or decrease the parameter of interest, run simulation and save the simulation results. Such procedure can be performed for multiple parameters, with the use of various techniques and the outcome is expressed in a quantitative manner. Sobie and colleagues have also utilized more complex procedures and varied all parameters at once (Sarkar and Sobie, 2010, 2011). Assuming that the endpoint of interest is dichotomous in nature (i.e., EAD occurence) Morotti and Grandi proposed technique based on the multivariate logistic regression analysis, allowing for sensitivity analysis and investigating factors influencing the endpoint occurrence at the same time (Morotti and Grandi, 2016).

The methodology applied to experimentally-calibrated populations of models can be regarded as the refinement and extension of the sensitivity analysis method and populations of models constructed without a calibration step. In the latter two, values of single or multiple parameters are varied in a predefined range, while allowable values of model outputs are not constrained with experimental data thus may not be representative for certain subject groups. All of these models offer valuable insights into sources of variability and the pathological background of different heart conditions. Moreover, they allow the assessment of not only the average drug effect on cardiac electrophysiology, but also allow the screening of drug effects across a certain population. They, however, cannot be employed to evaluate the risk of an individual patient who is to be treated with a certain drug. This is because most variability sources considered by the model (e.g., ion channels conductance, gating kinetics, densities, resting membrane potential, membrane potential, upstroke velocity) are factors whose values cannot be determined for the particular patient. Another problem is the requirement to define the cut off threshold for nonphysiological simulation results, since such a decision is always arbitrary.

# Deterministic Approach

The other approach is based on the observation and description of the biological parameters characterizing the system of interest, in this case the human organism. Data describing demographic, genetic, anatomical, and physiological factors are collected and analyzed to describe the distribution of the parameter in a population and allow constructing its virtual counterpart instead of an average patient. Also some of those factors can be correlated with the parameters of a cardiomyocyte model, e.g., age and the cardiomyocyte volume and area (Polak et al., 2012). The main data sources remain the published scientific reports and clinical databases (ICRP, 2002; Valentin, 2003). This approach allows for differentiation between different populations; both healthy (e.g., considering ethnicity) and diseased (e.g., obese, renally impaired, diabetic), or of special interest (e.g., pregnant women, pediatric population; Jamei et al., 2009b). Equations describing the distribution of the system parameters for the PBPK model are derived from the distributions of data based on real populations and patients. Additionally, such an approach takes into account the dynamic changes observed with the parameter of choice (e.g., circadian changes of heart rate). An application includes the ontogeny description and age dependent variation of the chosen parameters (Salem et al., 2013). What is also of importance is the option to define the inter-correlation between various parameters. A virtual population can be generated from values and formulae describing demographic, anatomical, and physiological variables using a correlated Monte Carlo approach which protects from the non-physiological combinations of the model parameters (e.g., kidney size and liver size). This allows the prediction of variability before the clinical study phase, in contrast to a statistical approach (e.g., population PK analysis), which requires prior clinical data to characterize variability. Additionally it allows for the clear separation of information on the system (i.e., human body) from that of the drug (e.g., physicochemical characteristics), and the environment (e.g., dose, concomitant drugs).

It is obvious that the model prediction will depend on the quality of the gathered data, correctness of the analysis, and appropriateness of the conclusions drawn from the distribution of the parameters. Therefore, the criteria of inclusion and exclusion for the reports and papers (in addition to certain values) have to be defined prior to the commencement of the data collection process. The same applies to the statistical analysis, and all methods and tools.

There are multiple biological parameters influencing the ECG and its behavior. From a biological perspective, factors influencing cardiac electrophysiology can be classified into one of three key groups: (i) demography; (ii) anatomy, and/or physiology; and (iii) genetics. Examples of the most important parameters are listed below:


(iii) Genetics—common polymorphisms and mutations at the level of ion channels/pumps/exchangers

For some of the above mentioned parameters statistical models describing their distribution in the population were developed based on the available data. This includes relationship between age, human left ventricle cardiomyocyte volume, and electric capacitance (Polak et al., 2012), left ventricular heart wall thickness (Fijorek et al., 2014a), or plasma ions concentration (Fijorek et al., 2014b). The latter, namely plasma ions concentration, together with the heart rate follow the circadian variability (Massin et al., 2000; Sennels et al., 2012). Such time of the day dependent variation influences the ECG and the parameters including QT (Karjalainen et al., 1994). Therefore, models describing the diurnal variability of such crucial parameters are also being developed and utilized (Fijorek et al., 2013a,b). They are also included in the virtual population generators, which build the virtual individuals being exposed to the drug in the in silico conditions (Mishra et al., 2014; Wi´sniowska and Polak, 2016). The main limitation of this method is the limited amount of data available for the model building and information relating to the inter-correlation between parameters.

It is undisputable that sources of variability identified and already incorporated into in silico models cannot explain the whole observable inter- and intra-individual variability. The question is if it is already sufficient to provide reliable predictions.

## Drugs-Specific Variability

In the model-based drug safety assessment, apart from systemdependent variability, there is also another source of variability (or rather uncertainty) introduced into the model. The effects caused by exposure to a drug are modeled as concentrationdependent changes of ion currents known to be affected by the drug. The drug-channel interaction is quantified experimentally by constructing a Hill plot characterized by IC50 and the Hill coefficient value. There is no standardized protocol for drugtriggered ion channel block measurement, however multiple cell models and voltage protocols are accepted. This results in significant discrepancies between IC50 values reported for a given compound (amiodarone: 0.015–38.3 microM; cisapride: 0.0051–1.6 microM; dofetilide 0.003–25 microM; E4031: 0.001– 15.8 microM; moxifloxacin: 0.93–398.1 microM; propafenone: 0.085–123 microM; to give just a few examples)<sup>6</sup> . Additional, uncertainty introduced into in silico models comes from uncertainty in the Hill coefficients of reported concentrationinhibition curves, especially when ion channel blocking potency for a compound is estimated by high-throughput screening methods (Elkins et al., 2013). Moreover, even the well-controlled experiments, carefully conducted in the same experimental settings, generate different results. This can be due to the measurement errors, intrinsic- and extrinsic-variability between samples. The subjective selection of IC50 values, which are taken as inputs into in silico models, may lead to misleading results. Drug-specific uncertainty is an undesirable type of variability,

<sup>6</sup>www.tox-database.net

however infeasible to eliminate. The use of averaged values has been proposed to minimize drug-specific bias (Elkins et al., 2013). The question remains how, if possible, average results produced with different methods and experimental settings.

The situation is even more complex when the aim is to model a response to a drug in a realistic population where other drugrelated factors like concomitant medicines, compliance, food and alcohol consumption have to be accounted for since all these factors can substantially influence the response.

#### CONCLUSIONS

Drug pro-arrhythmic potency is a function of the intrinsic characteristics of the chemical structure and external parameters associated with the drug. The latter, namely external parameters, includes system-dependent and environment-dependent items. Therefore, to properly predict and assess the potential risk all significant elements should be considered. Translation of the in vitro data to an in vivo situation, e.g., to optimize clinical trials, requires such an approach. There are at least two ways to describe the population specific variability, as described above, and these elements should be accounted for in the in silico based cardiac safety assessment. On the other hand, the choice of an assessment method depends on the actual stage of the drug development cycle. In the early stages, including discovery phase such complexity is not necessary, but as the compound advances along the development process, the assessment should be more detailed and comprehensive.

It is worth noting that the diseased population would probably require even more parameters, and the variability would be larger, as compared against healthy individuals. This is because of the interrelation of parameters directly (e.g., cell volume and capacitance), and indirectly (e.g., thyroid-related diseases and fluid-electrolyte balance disruption) influence the heart cells

#### REFERENCES


electrophysiology. Examples of the above-mentioned parameters and their analysis clude hypertrophic cardiomyopathy (HCM) of various character (Polak and Fijorek, 2012). It is worth noting that stochastic approach, based on the virtually simulated population of models can be used to identify ionic mechanisms driving electrophysiological abnormalities not only in HCM, but also atrial fibrillation, and other diseases, accounting for of the disease specific variability (Liberos et al., 2016; Passini et al., 2016). Modeling and simulation approach can be also utilized to analyze the influence of genetic modifications at the level of ionic channels on the cardiac myocytes electrophysiology (Glinka and Polak, 2013). This includes the recently published example of the population of models optimized to recapitulate clinical long QT phenotypes (Mann et al., 2016). The detailed discussion of this element, namely the disease related variability is out of the current manuscript scope. There is however clear gap in all current approaches, namely comprehensive, or to be precise as comprehensive as possible—parametrization of the disease of choice, including all known parameters. This would allowed to simulate population of virtual individuals closely mimicking those met in the clinical settings. The models usage could be than extended from the drugs' safety assessment to the drugs therapy optimization.

## AUTHOR CONTRIBUTIONS

BW, ZT, and SP equally contributed to the conception of paper, drafting the manuscript and approved its final version.

#### ACKNOWLEDGMENTS

Authors would like to thank Dr. Ruth Clayton for professional proof-reading and editorial support.

initiative - update on progress. J. Pharmacol. Toxicol. Methods 81, 15–20. doi: 10.1016/j.vascn.2016.06.002


and their application to cardiac electrophysiology simulations at individual level. Comput. Math. Methods Med. 2013:429037. doi: 10.1155/2013/ 429037


comprehensive overview of clinical trials. BMC Pharmacol. Toxicol. 17:12. doi: 10.1186/s40360-016-0053-1


#### **Conflict of Interest Statement:** SP is a Simcyp (part of Certara) employee.

The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Wi´sniowska, Tylutki and Polak. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Human In Silico Drug Trials Demonstrate Higher Accuracy than Animal Models in Predicting Clinical Pro-Arrhythmic Cardiotoxicity

Elisa Passini <sup>1</sup> \*, Oliver J. Britton<sup>1</sup> , Hua Rong Lu<sup>2</sup> , Jutta Rohrbacher <sup>2</sup> , An N. Hermans <sup>2</sup> , David J. Gallacher <sup>2</sup> , Robert J. H. Greig<sup>3</sup> , Alfonso Bueno-Orovio<sup>1</sup> and Blanca Rodriguez <sup>1</sup>

<sup>1</sup> Computational Cardiovascular Science Group, Department of Computer Science, University of Oxford, Oxford, United Kingdom, <sup>2</sup> Global Safety, Pharmacology, Discovery Sciences, Janssen Research and Development, Janssen Pharmaceutica NV, Beerse, Belgium, <sup>3</sup> Oxford Computer Consultants Ltd., Oxford, United Kingdom

#### Edited by:

Ovidiu Constantin Baltatu, Anhembi Morumbi University, Brazil

#### Reviewed by:

David Christini, Weill Cornell Medical College, United States Simone Brogi, University of Siena, Italy

> \*Correspondence: Elisa Passini elisa.passini@cs.ox.ac.uk

#### Specialty section:

This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology

Received: 01 July 2017 Accepted: 23 August 2017 Published: 12 September 2017

#### Citation:

Passini E, Britton OJ, Lu HR, Rohrbacher J, Hermans AN, Gallacher DJ, Greig RJH, Bueno-Orovio A and Rodriguez B (2017) Human In Silico Drug Trials Demonstrate Higher Accuracy than Animal Models in Predicting Clinical Pro-Arrhythmic Cardiotoxicity. Front. Physiol. 8:668. doi: 10.3389/fphys.2017.00668 Early prediction of cardiotoxicity is critical for drug development. Current animal models raise ethical and translational questions, and have limited accuracy in clinical risk prediction. Human-based computer models constitute a fast, cheap and potentially effective alternative to experimental assays, also facilitating translation to human. Key challenges include consideration of inter-cellular variability in drug responses and integration of computational and experimental methods in safety pharmacology. Our aim is to evaluate the ability of in silico drug trials in populations of human action potential (AP) models to predict clinical risk of drug-induced arrhythmias based on ion channel information, and to compare simulation results against experimental assays commonly used for drug testing. A control population of 1,213 human ventricular AP models in agreement with experimental recordings was constructed. In silico drug trials were performed for 62 reference compounds at multiple concentrations, using pore-block drug models (IC50/Hill coefficient). Drug-induced changes in AP biomarkers were quantified, together with occurrence of repolarization/depolarization abnormalities. Simulation results were used to predict clinical risk based on reports of Torsade de Pointes arrhythmias, and further evaluated in a subset of compounds through comparison with electrocardiograms from rabbit wedge preparations and Ca2+-transient recordings in human induced pluripotent stem cell-derived cardiomyocytes (hiPS-CMs). Drug-induced changes in silico vary in magnitude depending on the specific ionic profile of each model in the population, thus allowing to identify cell sub-populations at higher risk of developing abnormal AP phenotypes. Models with low repolarization reserve (increased Ca2+/late Na<sup>+</sup> currents and Na+/Ca2+-exchanger, reduced Na+/K+ pump) are highly vulnerable to drug-induced repolarization abnormalities, while those with reduced inward current density (fast/late Na<sup>+</sup> and Ca2<sup>+</sup> currents) exhibit high susceptibility to depolarization abnormalities. Repolarization abnormalities in silico predict clinical risk for all compounds with 89% accuracy. Drug-induced changes in biomarkers are in overall agreement across different assays: in silico AP duration changes reflect the ones observed in rabbit QT interval and hiPS-CMs Ca2+-transient, and simulated upstroke velocity captures variations in rabbit QRS complex. Our results demonstrate that human in silico drug trials constitute a powerful methodology for prediction of clinical pro-arrhythmic cardiotoxicity, ready for integration in the existing drug safety assessment pipelines.

Keywords: in silico drug trials, drug safety, drug cardiotoxicity, Torsade de Pointes, computer models, human ventricular action potential

#### INTRODUCTION

Cardiotoxicity is one of the main causes of withdrawal during drug development, and identifying at early stages drugs that may cause adverse effects in specific human sub-populations is still a major challenge (Stevens and Baker, 2009; Laverty et al., 2011). Adverse effects can potentially lead to lethal arrhythmias, and are therefore a major cause of concern.

Before clinical testing, drugs undergo a thorough pipeline of preclinical testing, including identification of drug effects on cardiac ion channels (and particularly hERG), as well as in a variety of animal experiments (Leishman et al., 2012; Vargas et al., 2015). Animal models are good for predicting QT interval prolongation (Vargas et al., 2015), and some of them, including rabbit wedge preparations, rabbit isolated hearts and the in vivo atrioventricular block dog, have shown sensitive predictions of drug-induced Torsade de Pointes (TdP) (Valentin et al., 2004; Liu et al., 2006; Sugiyama, 2008). However, most of these studies only consider a small set of drugs. In fact, independent assessment against a larger number of compound (in the order of magnitude of those tested in silico in this contribution) highlight a prediction accuracy of 75% (Lawrence et al., 2008).

More recently, in silico and in vitro tests are considered as potentially important human-based tools for safety pharmacology evaluation, through the use of computational multiscale human modeling and human stem cell-derived cardiomyocytes (Bass et al., 2015; Rodriguez et al., 2016). Their profile has also been raised by the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative promoted by the pharmaceutical industries, the United States Food and Drug Administration (FDA), the Health and Environmental Sciences Institute and the Cardiac Safety Research Consortium (Sager et al., 2014; Colatsky et al., 2016).

The widespread translation of in silico modeling from academia to industrial and regulatory settings requires increasing the credibility of the models, understanding of their predictive power through comparison with existing experimental methods, and facilitating their uptake through the provision of software that can reduce the technical barriers of in silico methods for non-specialist users.

The aim of this study is to evaluate the ability of in silico drug trials using human ventricular model populations to predict the risk of drug-induced adverse cardiac events, based on ion channel information, and to identify ionic profiles underlying a higher risk of repolarization abnormalities. In silico drug trials were run for a large set of reference compounds with cardiac effects, and simulation results were analyzed to extract several biomarkers of drug pro-arrhythmic cardiotoxicity and compared against clinical reports of TdP arrhythmias. Because in silico drug trials are likely to be embedded in existing safety pharmacology pipelines and thus combined with experimental methodologies, it is important to evaluate their consistency with experimental recordings. Therefore, the outputs of the in silico drug trials for a sub-set of 15 reference compounds with varied modes of action were compared against the well-established electrocardiogram (ECG) recordings from isolated rabbit wedge preparations Lu et al. (2016) as well as the more recently considered technique of Ca2+-transient (CT) recordings from human induced pluripotent stem cell-derived cardiomyocytes (hiPS-CMs) (Lu et al., 2015; Zeng et al., 2016), even if with still controversial advantages (Abi-Gerges et al., 2017).

#### MATERIALS AND METHODS

#### Control Population of Human Ventricular Action Potential (AP) Models

All the in silico drug trials presented in this study were performed in a population of 1,213 human ventricular control models, built using the O'Hara-Rudy dynamic (ORd) model (O'Hara et al., 2011) as baseline and the methodology described by Britton et al. (2013) and further discussed by Muszkiewicz et al. (2016). The ORd human ventricular AP model was chosen for this study because of: (i) the large number of human ventricular experimental data obtained from more than 140 hearts used in its construction and evaluation; (ii) its ability to reproduce and probe pro-arrhythmic mechanisms, including repolarization abnormalities and APD alternans, as shown in multiple studies and reviewed by Britton et al. (2017); (iii) its choice within the CiPA initiative (Sager et al., 2014; Colatsky et al., 2016).

Ionic conductances were sampled in the [0–200]% range of the baseline model values, to include both healthy and potentially abnormal ionic current profiles (with low/high ion channel densities corresponding to loss/gain-of-function of specific ionic

**Abbreviations:** AP, Action potential; APDXX, Action potential duration at XX% of repolarization; CiPA, Comprehensive in vitro Proarrhythmia Assay; CT, Ca2+-transient; CTBR, Ca2+-transient beat rate; CTDXX, Ca2+-transient duration at XX% of the initial base value; DA, Depolarization abnormalities; dV/dtMAX, Maximum upstroke velocity; EADs, Early after-depolarizations; EFTPCmax, Maximal effective therapeutic free concentration; GX, I<sup>X</sup> conductance; h, Hill coefficient; hiPS-CMs, Human induced pluripotent stem cell-derived cardiomyocytes; IC50, Concentration for 50% channel inhibition; ICaL, L-type Ca2<sup>+</sup> current; IK1, Inward rectifier K<sup>+</sup> current; IKr, Rapid delayed rectifier K<sup>+</sup> current; IKs, Slow delayed rectifier K<sup>+</sup> current; INa, Fast Na<sup>+</sup> current; INaK, Na+- K <sup>+</sup> pump current; INaL, Late Na<sup>+</sup> current; INCX, Na+-Ca2<sup>+</sup> exchanger current; Ito, Transient outward K<sup>+</sup> current; ORd, O'Hara-Rudy dynamic human ventricular model; RA, Repolarization abnormalities; RMP, Resting membrane potential; TdP, Torsade de Pointes; Tri90−40, AP triangulation; Vm, Membrane potential; Vpeak, Peak voltage.

Passini et al. Human In Silico Drug Trials

channels due to e.g., genetic mutations), but still with a healthylooking AP. These are important as they have been implicated in increased pro-arrhythmic risk (Sanguinetti and Tristani-Firouzi, 2006; Itoh et al., 2016; Wang et al., 2016). Nine ionic conductances were considered: fast and late Na<sup>+</sup> current (GNa and GNaL respectively), transient outward K<sup>+</sup> current (Gto), rapid and slow delayed rectifier K<sup>+</sup> current (GKr and GKs), inward rectified K<sup>+</sup> current (GK1), Na+-Ca2<sup>+</sup> exchanger (GNCX), Na+- K <sup>+</sup> pump (GNaK), and the L-type Ca2<sup>+</sup> current (GCaL).

Only the AP models exhibiting a phenotype in agreement with human experimental data from undiseased hearts (Britton et al., 2017) were selected for the control population, which consists of 1,213 models. A more detailed description of the control population used in this study is included in the Supplementary Material, together with the experimental AP biomarker ranges used for the calibration process (Table S1) and the scaling factors of the ionic conductances for the 1,213 models (Table S2).

#### In silico Drug Assay Design

A total of 62 reference compounds were considered in this study. The list includes antiarrhythmic drugs in Classes I, III, and IV, as well as other drugs used for different purposes but with known effects on cardiac ion channels. Most of these drugs have a multichannel action, which makes prediction and interpretation of cardiotoxicity challenging. Drugs were selected to include all the ones in Kramer et al. (2013), as well as 15 compounds widely used as reference compounds, which were characterized in more depth both in simulations and experiments and are listed in **Table 1**.

Each drug was assigned to a TdP risk category, based on the classification by CredibleMeds <sup>R</sup> (Woosley and Romer, 1999), available on www.crediblemeds.org (as of July 2017): 1 (high risk), the drug prolongs the QT interval and is clearly associated with a known TdP risk, even when taken as recommended; 2 (possible risk), the drug prolongs the QT interval, but there is a lack of evidence of TdP risk when taken as recommended; 3 (conditional risk), the drug is associated with TdP but only under certain circumstances, e.g., excessive dose or interaction with other drugs; NC (not classified), the drug was reviewed by CredibleMeds <sup>R</sup> but the evidence available was not enough to assign it to any of the previous categories, and therefore no action was taken. Of the 62 compounds, 24 are classified as high risk and 13 as potential/conditional risk, for a total of 37 drugs associated with TdP risk. Verapamil (classified as NC) and the remaining 24 compounds (not listed) are considered as TdP category 0 (no TdP risk) for the purpose of this study.

Drug effects were simulated using a simple pore-block model consistent with data available for drug/ion channel interactions, consisting of IC<sup>50</sup> and Hill coefficient (h) for each drug/ion channel. Up to 7 ion channels were considered for this study: fast Na<sup>+</sup> current (INa), rapid/slow delayed rectified K<sup>+</sup> current (IKr/IKs), transient outward K<sup>+</sup> current (Ito), L-type Ca2<sup>+</sup> current (ICaL), inward rectifier K<sup>+</sup> current (IK1), and late Na<sup>+</sup> current (INaL). The experimental IC<sup>50</sup> and h used for the drug assays were collected mainly from three different sources: (i) our internal database, measured with either manual or automated patch-clamp techniques (when the IC<sup>50</sup> concentration was not TABLE 1 | List of the 15 compounds considered for in silico drug assays comparison against in vitro hiPS-CMs and ex vivo rabbit wedge preparations, including a short description and the clinical TdP Risk category based on CredibleMeds® (Woosley and Romer, 1999).


Risk categories from CredibleMeds® (Woosley and Romer, 1999): 1, high TdP risk; 3, conditional TdP risk; 0, no TdP risk (drugs not included in the CredibleMeds® database).

reached in the experiments, an estimate was computed from the percentage of block at the maximum tested concentration, with h equal to 1); (ii) (Kramer et al., 2013), data acquired with automated patch-clamp; (iii) (Crumb et al., 2016), data acquired with manual patch-clamp.

For the compounds that were included in more than one of these datasets, multiple inhibitory profiles were considered to investigate the impact of variability in drug characterization. Each IC<sup>50</sup> and h set was simulated separately, resulting in 87 different drug trials: each trial is referred to with the name of the compound together with a roman numeral, to differentiate multiple entries (e.g., Bepridil I, Bepridil II, Bepridil III).

Multiple concentrations were investigated for each compound, chosen to match those used in the experimental drug assays, as well as to explore different multiples of the maximal effective free therapeutic concentration (EFTPCmax), up to 100-fold. The EFTPCmax values were taken from literature, mainly from Kramer et al. (2013) or Crumb et al. (2016). When multiple values were found for the same compound, the higher one was considered for simulations.

The full list of compounds, together with the IC50, Hill coefficient and the EFTPCmax used for in silico drug trials is provided in Table S3.

#### Simulations and Simulated Data Analysis

All the simulations presented in this study were conducted using Virtual Assay (v.1.3.640 © 2014 Oxford University Innovation Ltd. Oxford, UK), a user-friendly C++ based software package with a graphical user interface for in silico drug assays, to facilitate its use by non-experts in computational modeling, and available upon request. Virtual Assay uses the ordinary differential equation solver CVODE, part of the open-source Sundials suite (Hindmarsh et al., 2005; Serban and Hindmarsh, 2005), implementing time adaptive Backward Differentiation Formulas with relative and absolute tolerance equal to 1e-5 and 1e-7, respectively. Our results could therefore be replicated using other software products, as Matlab (Mathworks Inc. Natwick, MA, USA) or Chaste (Pitt-Francis et al., 2008). As an example, a comparison of simulations obtained with Virtual Assay and with the Matlab solver ode15s (Shampine and Reichelt, 1997) is shown in the Supplemental Material, Figure S2. Simulation results were analyzed both in Virtual Assay and in Matlab.

Following drug application, all models were stimulated at 1 Hz for 150 beats, and the last AP trace in each simulation was analyzed. AP biomarkers were extracted, including: AP duration at 40, 50, and 90% of repolarization (APD40, APD50, APD90); APD<sup>90</sup> dispersion, defined as the difference between the maximum and minimum value of APD<sup>90</sup> in the population (1APD90), AP triangulation, defined as the difference between APD<sup>90</sup> and APD<sup>40</sup> (Tri90−40); maximum upstroke velocity (dV/dtMAX); peak voltage (Vpeak); resting membrane potential (RMP), computed as in Britton et al. (2017). Drug-induced changes in those biomarkers are presented as percentage change in median with drug, compared to control (no drug).

All AP traces were automatically checked for repolarization and depolarization abnormalities (RA and DA, respectively). RA were defined as the presence of a positive derivative of the membrane potential (Vm) 150 ms after the AP peak (representative of early after-depolarizations, EADs), or when the membrane potential did not reach the resting condition following an AP upstroke (V<sup>m</sup> > −40 mV) by the end of the beat. DA were defined as AP traces in which the upstroke phase was compromised, i.e., when the max upstroke V<sup>m</sup> was lower than 0 mV, or when the time needed to reach 0 mV was longer than 100 ms.

Drugs were classified as risky when RA occurred in the population of models at different concentrations, based on: true positives (drug with reports of TdP risk classified as risky); true negatives (drug with no reports of TdP risk classified as safe), false positives (drug with no reports of TdP risk, classified as risky); false negatives (drugs with reports of TdP risk, classified as safe). The performances of the classification were evaluated based on: sensitivity, defined as the number of true positives divided by the sum of true positives and false negatives; specificity, defined the number of true negatives divided by the sum of the true negatives and false positives; accuracy, defined as the sum of true positives and true negatives divided by the total number of drugs. Classification results based on RA were compared against the ones obtained for APD prolongation at 10x EFTPCmax. APD<sup>90</sup> prolongation threshold to define risk was fixed to 6%, considering the correspondence between QTc and APD90, and the current guidelines suggesting QTc prolongation >20 ms (which correspond to 5.7% for a normal QT of 350 ms) as a definite risk factor for TdP (Salvi et al., 2010). Results for the population of models were also compared against the same results obtained with the single ORd model.

A scoring system was developed by integrating RA occurrence at multiple concentrations. The fraction of models developing RA was multiplied by a factor inversely related to the drug concentration at which those RA occur (e.g., 1/100 for RA occurring at 100x EFTPCmax). Contributions from all the different concentrations were added together, and the total score was normalized, according to the following formula (where nRA<sup>i</sup> is the number of models showing RA at the tested concentration i, w<sup>i</sup> = EFTPCmax / i is the weight inversely related to the tested concentration i, and nmod is the total number of models in the population).

$$TdP\ score = \frac{\sum\_{i} (\nu\_i \star nRA\_i)}{n\_{mod} \star \sum\_{i} (\nu\_i)} \tag{1}$$

The TdP score thus obtained varies between 0 and 1, where 0 corresponds to a drug with no RA, and 1 to a drug which develops 100% of RA at every concentration. By using the proposed score, RA are considered more severe when occurring at low concentrations and/or affecting a high fraction of the population of models.

#### Experimental Drug Assays

In silico results were compared with properties computed from ECGs in rabbit wedge preparations and CT recordings from hiPS-CMs. Experimental data were acquired for the 15 compounds listed in **Table 1** at multiple concentrations, as described below.

Recordings of ECGs from left ventricular rabbit wedge preparations have been previously described and partly published in Lu et al. (2016). The biomarkers extracted include QRS complex and QT interval duration, defined as the time from the onset of the QRS complex to the point at which the final downslope of the T wave crossed the isoelectric line.

CT recordings from hiPS-CMs (Cor 4U) were acquired as part of this study on pre-plated preparations from Axiogenesis (Cologne, Germany). Full method details are included in the Supplementary Material. Quantified biomarkers included CT beat rate (CTBR) and duration at 90% of the initial base value (CTD90), known to be correlated with APD (Gauthier et al., 2012; Spencer et al., 2014), similarly to other studies (Lu et al., 2015; Zeng et al., 2016).

All experimental results are presented as median percentage changes with respect to the baseline. Drug-induced changes in experimental values need to be compared against the effect measured without drugs, i.e., with vehicle, defining cut-off values. In the rabbit wedge, the changes measured with the vehicle were always quite small: <5% for QT and <3% for QRS. On the other hand, in CT assays using hiPS-CMs, the lower and upper limit were 19% and 24% of the baseline, with 95% confidence interval (n = 222 vehicle controls). Therefore, only CTD<sup>90</sup> prolongations >25% were considered relevant for this assay. In silico, no biomarker changes are observed when the drug effect is not included, since the models are paced until steady state: therefore, the cut-off value is equal to 0%. Statistical analysis was performed with the Wilcoxon-Mann-Whitney Test by using R Project for Statistical Computing, and p < 0.05 was considered as significant. Very small p-values (e.g., p < 1e-6) were obtained in all simulation results due to the high number of models considered, and therefore we focus on the magnitude of the differences observed (White et al., 2014).

#### RESULTS

## In silico Drug Assays: Drug-Induced Changes in Action Potential (AP) Biomarkers

In silico drug trials for a total of 62 reference compounds were performed in the control population of 1,213 human ventricular AP control models, based on the ORd model (O'Hara et al., 2011) and constructed as described in Methods. Before drug application, all the models exhibit a healthy-looking AP phenotype, in agreement with human experimental recordings from un-diseased hearts (Figure S1A). When including drug effect for concentration up to 100-fold the EFTPCmax, each model responds in a different way, depending on its underlying ionic properties. We first evaluated drug-induced changes in the AP biomarkers.

**Figure 1** shows APD<sup>90</sup> and dV/dtMAX distributions from the in silico population for 5 compounds (Dofetilide I, Flecainide I, Nimodipine, Ranolazine I, and Verapamil II) at multiple concentrations. Extended results for additional compounds, including all AP biomarkers, are shown in Figures S3–S31.

Most drugs (all except Nimodipine and Nisoldipine) result in APD prolongation at 40, 50, and 90% of repolarization, as well as increased AP triangulation (Tri90−40), mainly as a result of hERG channel block (e.g., **Figure 1**, left column and A–C in Figures S3–S31). For 30x EFTPCmax dose, Flecainide III, Bepridil I, and Dofetilide III showed the largest APD<sup>90</sup> prolongations (+180%, +175%, and +157%, respectively).

APD prolongation caused by BaCl<sup>2</sup> (mainly due to IK1 block) is stronger in APD<sup>90</sup> compared to APD<sup>40</sup> and APD<sup>50</sup> (Figures S3A–C). As a secondary effect of IK1 block, BaCl<sup>2</sup> leads to a decrease in RMP (Figure S3H), which also exhibits larger variability, while for all the other compounds it remains almost constant (H in Figures S3–S31).

Consistent with their expected mode of action, class I anti-arrhythmic drugs (Procainamide, Lidocaine, Mexiletine, Phenytoin, Flecainide) as well as other drugs affecting Na<sup>+</sup> channels as secondary effect (e.g., Bepridil) show a strong decrease of upstroke velocity (e.g., **Figures 1D,H**), together with a decrease of Vpeak (F, G in Figures S3–S31).

Verapamil II represents an interesting example of the combined block of IKr and ICaL (**Figure 1I**). For low concentrations (0.01–0.1 µM) the Ca2<sup>+</sup> block is predominant, and APD<sup>90</sup> is slightly decreased (−1 and −4% respectively), whereas IKr block compensates its effects for higher concentrations (>0.5 µM), resulting in a clear APD prolongation (e.g., +38% for 1 µM). Verapamil II also leads to slower AP upstroke for high concentrations (**Figure 1J**).

Results obtained using the baseline ORd model (**Figure 1** and Figures S3–S31, black diamonds) are in overall agreement with the range of AP biomarkers in the population of human models. This is with the exception of cases in which the baseline ORd yields abnormal APs for high doses of certain drugs (e.g., Dofetilide I 0.1 and 0.2 µM, **Figures 1A,B**). In those cases, the human population of models still allows exploration of the full concentration range for each compound.

#### In silico Characterization of Drug-Induced Phenotypic Variability

Drug action resulted in an increase in the phenotypic variability yielded by the human ventricular population, as illustrated in **Figure 2** for Moxifloxacin III (**Figure 2A**) and Dofetilide I (**Figure 2B**), mainly blocking IKr, and for Flecainide I (**Figure 2C**), inhibiting both IKr and INa. Following drug application, some models in the in silico population display normal but prolonged APs (gray traces) while a fraction develop repolarization abnormalities (RA, pink traces). Due to its strong effect on INa, Flecainide I (**Figure 2C**) also cause an overall reduction of dV/dtMAX, visible in the upstroke phase of the AP, and depolarization abnormalities (DA, green traces) in specific models.

Quantitative analysis of the underlying ionic mechanisms reveals consistency on the mechanisms underlying RA and DA across different drugs and concentrations. Models displaying RA are characterized by low GKr, and GNaK, and high GCaL and GNCX, i.e., a reduced repolarization reserve (**Figures 2D–F**, pink vs. gray boxplots). Low GKs also plays a role when a larger fraction of the population displays RA (**Figures 2D,E**). Models displaying DA are characterized mainly by low GNa/GCaL/GNaL, i.e. the net inward current in the initial phase of the AP is reduced (**Figure 2F**, green vs. gray boxplots).

## Repolarization Abnormalities Occurrence Predicts TdP Risk

We hypothesized that occurrence of RA following drug application in the human population would be predictive of in vivo TdP, given the potential mechanistic link between them (El-sherif et al., 1990; Dutta et al., 2016). In silico drug trial predictions were evaluated against clinical reports of TdP using the TdP risk categories provided by CredibleMeds <sup>R</sup> (Woosley and Romer, 1999) and further described in Methods. When multiple inhibitory profiles were simulated for the same compound, the worse scenario was considered, i.e., the higher occurrence of RA, and the larger APD<sup>90</sup> prolongation.

**Figure 3** shows the classification results for the 49 compounds with either high or no TdP risk (**Figure 3A**), and for the full set of 62 compounds (**Figure 3B**) based on RA occurrence up to 100x EFTPCmax and APD<sup>90</sup> prolongation >6% at 10x EFTPCmax for both the population of models (top row), and the single ORd model (bottom row). Accuracy reached 96% for the classification of high vs. no TdP risk compounds using the RA-based classification with the in silico population of models, compared to 80% based on APD prolongation (**Figure 3A**). Using the single ORd model, the higher accuracy was 76% and was obtained using APD prolongation as biomarker.

When including also compounds with possible/conditional risk (**Figure 3B**), accuracy with the RA-based classification for the in silico population was 89%, compared to 81% based on APD

FIGURE 1 | Explanatory examples of in silico drug trial results in a population of human computational models, showing drug-induced changes on APD90 and dV/dtMAX (left and right column, respectively) for 5 compounds (Dofetilide I, Flecainide I, Nimodipine, Ranolazine I and Verapamil II). Results are presented as boxplots of AP biomarkers for the population of human ventricular models at increasing concentrations (A–J). Results for the single ORd model are shown as black diamonds. On each box, the central mark is the median of the population, box limits are the 25 and 75th percentiles, and whiskers extend to the most extreme data points not considered outliers, plotted individually as separate crosses. Extended results for the selected 15 reference compounds, including all the AP biomarkers, are available in the Supplementary Material, Figures S3–S31.

FIGURE 2 | Explanatory examples of variability in drug response in the in silico population of human AP models, with the underlying ionic mechanisms. Representative AP traces of different drug-induced AP phenotypes are shown on the left side for Moxifloxacin III (A), Dofetilide I (B), and Flecainide I (C) at selected concentrations. Models with a normal AP are shown in gray, while models displaying RA and DA are shown in pink and green, respectively. In each panel, the baseline ORd model is highlighted in black. The distribution of ionic conductances for the different AP phenotypes is shown on the right side (D–F), by using boxplots of the corresponding scaling factors, and with the same color code. For each conductance, the values shown (between 0 and 2) represent the scaling factors of the models in the population compared to the baseline ORd model, which had all the scaling factors equal to 1. Boxplots description as in Figure 1.

FIGURE 3 | In silico prediction of in vivo TdP risk for the 49 compounds belonging to TdP risk category 0 and 1 (A) and for all the 62 tested compounds (B). In each panel, predictions based on the occurrence of RA in any of the model at 1x, 10x, 30x, and 100x EFTPCmax (1st column) are compared against predictions based on APD90 prolongation >6% at 10x EFTPCmax (2nd column). Results obtained using the population of models (top half) are compared against the ones for the baseline ORd model (bottom half). High sensitivity/specificity/accuracy (>80%) are highlighted in bold.

prolongation (48 and 77% based on RA and APD prolongation, respectively, for the single ORd model).

In summary, all drugs with high TdP risk (category 1) were correctly identified as risky with the RA-based classification in the in silico population, and only 5 drugs with possible/conditional TdP risk (category 2 and 3) resulted as false negatives: Clozapine, Dasatinib, Paroxetine, Saquinavir, Voriconazole. It is worth noting that drugs with possible/conditional TdP risk lack evidence of pro-arrhythmic risk when taken as recommended: TdP reports are usually related to excessive dose or interaction with other drugs.

Overall, classification based on APD prolongation exhibited high sensitivity, but low specificity. Indeed, many compounds prolong APD without being associated with TdP risk, e.g., Verapamil, thus resulting in false positives. On the contrary, false positives are rare in the RA-based classification (Lidocaine and Mexiletine), and they only develop RA at the maximum tested concentration (100x EFTPCmax). Indeed, both Lidocaine and Mexiletine are Class Ib anti-arrhythmic drugs, which have been associated with cardiotoxicity in case of overdose (Denaro and Benowitz, 1989).

RA-based classification is dependent on the maximum tested concentration: a higher concentration is more likely to provoke RA in the in silico population, thus increasing sensitivity but possibly decreasing specificity, since even safe drugs might lead to RA at very high doses. We reported here the classification results obtained for concentrations up to 100x EFTPCmax, and a comparison between results for 30x and 100x EFTPCmax is included in the Supplementary Material (Figure S32).

#### A New Scoring System to Evaluate In vivo Risk of Drug-Induced TdP

**Figure 4** shows all the tested compounds classified using the TdP score computed from the in silico drug trials using the fraction of models displaying RA at each tested concentration, as described in Methods. The TdP score varies from 0 to 1, and is higher when RA occur at low concentrations and/or affecting a high fraction of the population of models.

The distribution of compounds in the safe zone (TdP equal to 0, left side) and risky zone (TdP > 0, right side) reflects the classification results summarized in the confusion matrix with the higher (89%) accuracy (**Figure 3**). All safe compounds (no reported TdP risk, green dots) have a TdP score equal to 0, except Lidocaine and Mexiletine. All compounds with known risk of TdP (TdP risk category 1, red dots) have a positive score, and tend to be distributed toward the right end of the plot. Most of the compounds with possible or conditional

TdP risk (TdP risk category 2 or 3, orange and yellow dots, respectively) have a positive score, except Clozapine, Dasatinib, Paroxetine, Saquinavir, Voriconazole. The TdP score is also dependent on the maximum considered concentrations. Again, higher concentrations lead to an increase in sensitivity while decreasing specificity. A comparison between the TdP scores computed up to 30x and 100x EFTPCmax is included in the Supplementary Material (Figure S33).

#### In silico Drug Assays are in Agreement with Rabbit Wedge and hiPs-CM Experimental Recordings

In silico drug trials are likely to be used as an additional tool for drug safety assessment in combination with experimental methods. It is therefore important to evaluate the consistency between in silico results and experimental data. Thus, simulation results for the 15 reference compounds with varied actions on ion channels (**Table 1**) were compared against recordings obtained using rabbit wedge and hiPS-CM preparations, as two techniques considered in safety pharmacology. In **Figure 5**, changes in QT interval duration in rabbit wedge, CTD<sup>90</sup> in hiPS-CMs and in silico APD<sup>90</sup> (from red to green, left side) were compared to evaluate drug-induced changes in repolarization. Changes in QRS complex duration in rabbit wedge and in silico dV/dtMAX were quantified to evaluate drug effects on depolarization (**Figure 5**, from purple to blue, right side). Negative variations in dV/dtMAX are considered as positive changes in depolarization time (opposite sign), to facilitate the comparison.

Drug-induced effects on biomarkers are in overall agreement for all three methodologies. **Figure 5** presents consistent increase/decrease of QT, CTD<sup>90</sup> and APD90, as well as consistency between positive changes in QRS and reduction of dV/dtMAX. Variations are generally larger in the in silico APD<sup>90</sup> than in QT interval in rabbit wedge, indicating higher sensitivity of the in silico assay, and the wider range of ionic scenarios evaluated in the virtual population than in the limited number of experiments.

For Verapamil at 0.1 µM, small changes were observed in both QT interval in rabbit wedge and simulated APD, whereas CTD<sup>90</sup> in hiPS-CMs was reduced. Such a reduction in CTD<sup>90</sup> in the hiPS-CMs is also accompanied by a significant increase in beating rate (CTBR +61%), which does not occur in silico and in the rabbit wedge experiments as these are paced externally.

For Lidocaine and Mexiletine, their main effect is fast INa block, which results in a decreased dV/dtMAX in the in silico models, and a wider QRS complex in the rabbit wedge ECG. Furthermore, both in vitro CTD<sup>90</sup> and in silico APD<sup>90</sup> are prolonged, whereas QT interval decreases slightly (Lidocaine) or remains unchanged (Mexiletine) in rabbit wedge, suggesting that in vitro CT and in silico AP are more prone to display prolongation for non-selective Class I anti-arrhythmic drugs. It is worth noticing that the AP prolongation in silico is reduced when inhibition of the INaL current is taken into account in

#### FIGURE 5 | Continued

Qualitative and quantitative comparison of in silico drug trial results in the population of human ventricular AP models against ECG from rabbit wedge preparations and Ca2<sup>+</sup> transient recordings from hiPS-CMs, for 15 reference compounds. On the left side (from red to green) are shown the drug-induced changes in the biomarkers related to the repolarization phase: QT interval in rabbit wedge, CTD90 in hiPS-CMs and APD90 in silico. On the right side (from purple to blue) are shown the drug-induced changes in the biomarkers related to the depolarization phase: QRS interval from rabbit wedge and dV/dtMAX in silico. For each assay, colors are scaled to span from the 15th to the 85th percentiles of the % changes observed in the biomarkers when considering drug effects, compared to no drug, and with respect to the cut-off values (3 and 5% for rabbit wedge QRS and QT, 25% for hiPS-CMs CTD90, and 0% for in silico APD90 and dV/dtMAX). To facilitate comparison, negative variations in dV/dtMAX were considered as positive changes in the depolarization time, and vice versa. When multiple combinations of IC50 and h were tested in simulation for the same compound, the corresponding in silico result sections consist of multiple sub-columns. Statistically significant changes in experiments have been highlighted in bold.

the simulations, corresponding to Lidocaine II and Mexiletine II (APD<sup>90</sup> +84% vs. +68%, Mexiletine I vs. Mexiletine II, 100 µM). The tendency for prolongation under Na<sup>+</sup> block of in silico AP and hiPS-CMs CT is confirmed also for another class I antiarrhythmic drug (Phenytoin), which causes negligible changes in both CTD<sup>90</sup> and in silico APD90, and a decrease in QT interval in rabbit wedge.

Bepridil constitutes a good example of multichannel block, intended to block ICaL, but also affecting IKr and INa. In the rabbit wedge, the QT interval is relatively prolonged at low concentrations (0.3–1 µM), compared to more selective Ca2<sup>+</sup> blockers (e.g., Nimodipine and Nisoldipine), and it goes back to normal (+4%) at 10 µM. Both hiPS-CMs CT and in silico AP are prolonged in a dose-dependent manner, confirming once again the higher sensitive to IKr block of these techniques.

Interestingly, BaCl<sup>2</sup> effects are of smaller magnitude in hiPS-CMs compared to rabbit wedge preparation and in silico models: relevant CTD<sup>90</sup> prolongation was detected only at 100 µM (+47%), while up to 10 µM (more than 2-fold BaCl<sup>2</sup> IC<sup>50</sup> for IK1) the drug-induced effects on CT were negligible. This may be due to differences in IK<sup>1</sup> expression between the cell types considered (Liang et al., 2013; Kim et al., 2015).

In silico results for compounds with multiple sets of IC<sup>50</sup> and h are in overall agreement with each other, even if the magnitude of drug-induced changes may vary. As an example, the decrease in dV/dtMAX for the three variations of Flecainide is almost the same at 10 µM (−64, −61, and −68%, respectively), while for lower concentrations the differences between the three inhibition profiles are more noticeable (e.g., −25, −7, and 0% at 1 µM, respectively).

# DISCUSSION

In silico human electrophysiology drug trials using a population of human AP models were conducted for 62 compounds with varied electrophysiological profiles to evaluate their ability to predict clinical pro-arrhythmic risk and their consistency with electrophysiological recordings currently considered in safety assessment.

The main findings of this simulation study are:

1. RA occurrence in populations of human models proves to be more predictive of clinical TdP risk than APD prolongation and standard biomarkers obtained with the single ORd model. Accuracy of 96% and specificity of 92% was obtained in the classification of high risk vs. safe drugs, compared to 80 and 64%, based on APD prolongation. 100% sensitivity was achieved considering RA in the population compared to 17% with the single ORd model.


Our results support the potential of RA in the in silico human population as a good predictor of clinical TdP risk, with sensitivity, specificity and accuracy higher or comparable to the ones obtained through animal studies (Valentin et al., 2009). RA-based classification for all 62 compounds reached 89% of accuracy, compared to 75% obtained for 64 compounds in rabbit isolated Langendorff heart model (Lawrence et al., 2006; Valentin et al., 2009). The in vivo atrioventricular block dog model showed sensitive predictions of drug-induced TdP, but in a limited set of 13 compounds (Sugiyama, 2008). Animal studies accuracy is higher when predicting QT prolongation rather that in vivo TdP risk: 85 and 79% for 19 compounds based on QT prolongation in in vivo dog studies and hERG assays, respectively (Valentin et al., 2009; Wallis, 2010); 90% accuracy for 40 compounds based on non-rodent QT prolongation (Vargas et al., 2015). However, "it is generally known that the sensitivity and the specificity of the QT interval prolongation as a surrogate marker of TdP is rather poor: only in 46% of the cases the TQT study results were concordant with the TdP risk classification, and 89% of drugs prolonging QT interval in thorough QT studies were approved by the FDA" (Wi´sniowska et al., in press). This is confirmed in our study by the fact that RA-based predictions in the population of human models have higher accuracy compared to the ones based on APD prolongation, due to a higher specificity (92 vs. 64% for 62 compounds).

Our methodology also offers mechanistic insights into subpopulations at higher risk, which is a key advantage with respect to previous in silico and in vitro studies (Kramer et al., 2013; Lancaster and Sobie, 2016). We identify human in silico cardiomyocytes with high propensity to develop RA as those with low INaK/IKs/IKr and high INCX/ICaL. The ionic profile is consistent with ionic remodeling in cardiac specific diseases such as heart failure (Carmeliet, 1999; Coppini et al., 2013; Coronel et al., 2013), suggesting disease modeling as crucial when investigating cardiotoxicity in response to drug action (Walmsley et al., 2013; Gomez et al., 2014; Elshrif et al., 2015; Dutta et al., 2016; Passini et al., 2016).

The range of concentrations considered for drug trials plays an important role in risk prediction. Expanding the concentration up to 100x EFTPCmax allows to account for possible overdose, but most importantly for inter-subject variability in protein binding and metabolism, which can lead to important different in blood concentrations in patients taking the same drug dose, or even hormones which might change the effect of the drug on ion channels (Shuba et al., 2001). As an example, Amiodarone is a very controversial drug, considered safe by most clinicians but at the same time known to be associated with TdP risk (Jurado Román et al., 2012), and indeed belonging to TdP risk category 1. Amiodarone is almost completely bound to plasma proteins: reported values in literature range from 95.6% (Lalloz et al., 1984; Latini et al., 1984) to 99.98% (Veronese et al., 1988). In addition, absorption following oral administration is erratic and unpredictable (Latini et al., 1984). This can lead to EFTPCmax variation of more than 100-fold, with a big impact on druginduced ion channels block.

An additional consideration about in silico trials concerns variability of recorded IC<sup>50</sup> values. We show one possible way to consider this variability, by evaluating its implications in the in silico human population. In most cases, results obtained with different IC<sup>50</sup> values were in overall agreement, thus building confidence in the answer provided. Should these results disagree, leading to contrasting scenarios, new ion channel recordings and experiments might be required for further drug characterization and refined in silico predictions. This may incorporate for example more detailed models of ion channel structure, based on the most recent crystallographic studies on human ion channels (Sun and MacKinnon, 2017; Wang and MacKinnon, 2017). Other in silico tools are also available at the ion channel level, to evaluate potential drug effects on the hERG channel, using ligand-based (Durdagi et al., 2011; Braga et al., 2015; Chemi et al., 2017) or receptor-based (Brindisi et al., 2014; Dempsey et al., 2014) approaches.

Indeed, in silico results are strictly dependent on the quality and consistency of the data used as inputs, which include ion channel assays costing time and money. In silico trials are a cheap complement to experimental methods following ion channel screening, which for some channels is already routine (hERG).

When fully integrated in the early stages of drug development, in silico methods provide predictions to partly replace animal experiments, thus reducing the corresponding costs. Therefore, in silico drug trials are likely to play soon a major role in drug development, identifying drug cardiotoxicity in the pre-clinical phase, thus improving the quality of new candidate drugs and reducing drug failure at later stages.

Our results are obtained using experimentally-calibrated population of human models for in silico drug trials. The wide range of conductances considered includes extreme up- or downregulation of ion channels, which can be linked to specific mutations or diseased conditions known to be pro-arrhythmic (Sanguinetti and Tristani-Firouzi, 2006; Itoh et al., 2016; Wang et al., 2016). Previous studies have also considered aspects of population variability for gender and age, mostly by changing cell volume and area (rather than ionic conductances) using a commercial software (Polak et al., 2012). The same software was also recently used to investigate potential drug-induced arrhythmias for 12 drugs (Abbasi et al., 2017). In that study, variability was taken into account by using different AP models (Ten Tusscher, 2003; Ten Tusscher and Panfilov, 2006; O'Hara et al., 2011) and different cell types (endo-, epi-, and midmyocardium). However, their results were presented only for a single model (mid-) since it was the one most prone to develop drug-induced APD prolongation and EADs.

Our results also demonstrate consistency between humanbased in silico simulations and recordings obtained from experimental models traditionally used in safety pharmacology, including rabbit wedge ECGs (Lu et al., 2016) and hiPS-CMs CT recordings. Previous in silico studies have focused on predictions of QT prolongation in human (Mirams et al., 2014; Lancaster and Sobie, 2016) and animal models (Bottino et al., 2006; Davies et al., 2012; Beattie et al., 2013). Evaluating the in silico results against experimental data is important as in silico tools are likely to be used in combination with experimental recordings for validation and identification of potential unknown effects. Importantly, our results also identifies discrepancies between in silico results and experimental and clinical data, when considering compounds with strong multichannel action, leading to large AP prolongation in silico and only a moderate increase of rabbit wedge QT. The potential causes of such discrepancies include: (i) differences in the balance of inward/outward currents in human adult cardiomyocytes as represented in silico with respect to rabbit wedge preparations, which may lead to higher sensitivity to hERG block. Indeed, it has been shown that APD prolongation due to IKr block is more pronounced in human, compared to rabbit (Bányász et al., 2011; O'Hara and Rudy, 2012); (ii) the fact that in silico results in our study are focused on single cell electrophysiology, as opposed to tissue (rabbit wedge) or whole heart, where coupling and other mechanisms may act to modulate AP duration, as supported by the fact that both in silico APD and hiPS-CMs CTD show larger prolongation compared to rabbit QT; (iii) the IC<sup>50</sup> values were often estimated based on current blocks measured at low drug concentrations, while simulations explored much higher ones. This can therefore lead to an overestimation of current blocks, producing a larger AP increase than expected. Further work could address these important factors.

To conclude, this study demonstrates that in silico drug trials in populations of human cardiomyocyte models constitute a powerful methodology to predict clinical risk of arrhythmias based on ion channel information. This study also highlights ionic profiles that have a higher risk of developing drug-induced abnormalities. This methodology is therefore ready for its integration into the existing pipeline for drug cardiotoxicity assessment, and contribute to the reduction of animal experiments in the near future.

#### AUTHOR CONTRIBUTIONS

All the authors conceived and designed the study; EP performed the in silico drug assays, analyzed the data, prepared the figures and drafted the manuscript; HL, JR, and AH performed experimental drug assays; RG, OB, and EP developed the software; EP, OB, AB, and BR interpreted the results; all the authors edited and revised the manuscript.

#### REFERENCES


#### FUNDING

EP, OB, AB, and BR are supported by BR's Wellcome Trust Senior Research Fellowship in Basic Biomedical Sciences (100246/Z/12/Z), an Engineering and Physical Sciences Research Council Impact Acceleration Award (EP/K503769/1), the CompBioMed project (European Commission grant agreement No 675451), the NC3Rs Infrastructure for Impact award (NC/P001076/1) and Project Grant (NC/P00122X/1), the Oxford British Heart Foundation Centre of Research Excellence (RE/08/004/23915, RE/13/1/30181) and the TransQST project (Innovative Medicines Initiative 2 Joint Undertaking under grant agreement No 116030, receiving support from the European Union's Horizon 2020 research and innovation programme and EFPIA).

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fphys. 2017.00668/full#supplementary-material

explains intersubject variability in cardiac cellular electrophysiology. Proc. Natl. Acad. Sci. U.S.A. 110, E2098–E2105. doi: 10.1073/pnas.1304382110


cellular electrophysiological remodeling: a population-based simulation study. PLoS ONE 8:e56359. doi: 10.1371/journal.pone.0056359


**Conflict of Interest Statement:** HL, JR, AH, and DG are employees of Janssen Pharmaceutica NV. RG is an employee of Oxford Computer Consultants, Oxford, UK.

The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Passini, Britton, Lu, Rohrbacher, Hermans, Gallacher, Greig, Bueno-Orovio and Rodriguez. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Quantitative Comparison of Effects of Dofetilide, Sotalol, Quinidine, and Verapamil between Human Ex vivo Trabeculae and In silico Ventricular Models Incorporating Inter-Individual Action Potential Variability

Oliver J. Britton<sup>1</sup> \*, Najah Abi-Gerges <sup>2</sup> , Guy Page<sup>2</sup> , Andre Ghetti <sup>2</sup> , Paul E. Miller <sup>2</sup> and Blanca Rodriguez <sup>1</sup>

*<sup>1</sup> Department of Computer Science, University of Oxford, Oxford, United Kingdom, <sup>2</sup> AnaBios Corporation, San Diego, CA, United States*

#### Edited by:

*Zhilin Qu, University of California, Los Angeles, United States*

#### Reviewed by:

*Trine Krogh-Madsen, Weill Cornell Medical College, United States Eric A. Sobie, Icahn School of Medicine at Mount Sinai, United States*

\*Correspondence:

*Oliver J. Britton oliver.britton@cs.ox.ac.uk*

#### Specialty section:

*This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology*

Received: *02 June 2017* Accepted: *02 August 2017* Published: *18 August 2017*

#### Citation:

*Britton OJ, Abi-Gerges N, Page G, Ghetti A, Miller PE and Rodriguez B (2017) Quantitative Comparison of Effects of Dofetilide, Sotalol, Quinidine, and Verapamil between Human Ex vivo Trabeculae and In silico Ventricular Models Incorporating Inter-Individual Action Potential Variability. Front. Physiol. 8:597. doi: 10.3389/fphys.2017.00597* Background: *In silico* modeling could soon become a mainstream method of pro-arrhythmic risk assessment in drug development. However, a lack of human-specific data and appropriate modeling techniques has previously prevented quantitative comparison of drug effects between *in silico* models and recordings from human cardiac preparations. Here, we directly compare changes in repolarization biomarkers caused by dofetilide, dl-sotalol, quinidine, and verapamil, between *in silico* populations of human ventricular cell models and *ex vivo* human ventricular trabeculae.

Methods and Results: *Ex vivo* recordings from human ventricular trabeculae in control conditions were used to develop populations of *in silico* human ventricular cell models that integrated intra- and inter-individual variability in action potential (AP) biomarker values. Models were based on the O'Hara-Rudy ventricular cardiomyocyte model, but integrated experimental AP variability through variation in underlying ionic conductances. Changes to AP duration, triangulation and early after-depolarization occurrence from application of the four drugs at multiple concentrations and pacing frequencies were compared between simulations and experiments. To assess the impact of variability in IC50 measurements, and the effects of including state-dependent drug binding dynamics, each drug simulation was repeated with two different IC50 datasets, and with both the original O'Hara-Rudy hERG model and a recently published state-dependent model of hERG and hERG block. For the selective hERG blockers dofetilide and sotalol, simulation predictions of AP prolongation and repolarization abnormality occurrence showed overall good agreement with experiments. However, for multichannel blockers quinidine and verapamil, simulations were not in agreement with experiments across all IC50 datasets and IKr block models tested. Quinidine simulations resulted in overprolonged APs and high incidence of repolarization abnormalities, which were not observed in experiments. Verapamil simulations showed substantial AP prolongation while experiments showed mild AP shortening.

**274**

Conclusions: Results for dofetilide and sotalol show good agreement between experiments and simulations for selective compounds, however lack of agreement from simulations of quinidine and verapamil suggest further work is needed to understand the more complex electrophysiological effects of these multichannel blocking drugs.

Keywords: safety pharmacology, dofetilide, sotalol, quinidine, verapamil, cardiac modeling

# INTRODUCTION

Cardiotoxicity is a major cause of attrition during drug development (Piccini et al., 2009). The current difficulty of predicting cardiotoxic effects of new drug candidates plays a major role in the termination of drug development programmes (Cook et al., 2014). Currently, the pro-arrhythmic potential of a candidate drug is assessed preclinically using a combination of an in vitro hERG channel assay and in vivo animal cardiovascular studies (Anon, 2005a), followed by a Thorough QT study an ECG-based study of cardiac repolarization in the later stages of drug development (Anon, 2005b; Wi´sniowska et al., 2017). While this strategy has been effective in preventing approval and marketing of new drugs with strongly proarrhythmic potential (Ewart et al., 2014; Vargas et al., 2015), QT prolongation alone is an imperfect marker for fatal proarrhythmic effects (Shah, 2005) and can result in ending development of safe drugs (Stockbridge et al., 2013; Polak et al., 2015).

The Comprehensive in vitro Pro-Arrhythmia Assay (CiPA), a public-private collaboration with the aim of updating the existing cardiac safety testing paradigm, has been proposed to improve the assessment of new drug candidates' pro-arrhythmic risk (Sager et al., 2014). CiPA will consist of multiple components including an ion channel screen of seven channels, combined with an in silico modeling component that will model the effect of new drugs on a human ventricular action potential (AP) using data from the ion channel screens (Colatsky et al., 2016; Fermini et al., 2016). Therefore, in silico modeling is likely to soon become part of mainstream pro-arrhythmic risk assessment in drug development (Rodriguez et al., 2016; Li et al., 2017; Windley et al., 2017).

Recently, several modeling methodologies have been developed to address simulating the effects of different sources of variability and the effect this has on the response of cardiomyocytes to drugs. In particular, methodologies have been developed to integrate the large amount of inter-individual variability present in electrophysiological recording, which is hypothesized to contribute to inter-individual variability of drug response, with traditional cardiac modeling that uses a single model representative of average cardiomyocyte behavior (Sarkar and Sobie, 2010; Davies et al., 2012; Britton et al., 2013; Sadrieh et al., 2013; Groenendaal et al., 2015). Methods are also under development to probabilistically quantify the high levels of uncertainty in measured drug IC50 values (Mirams et al., 2014; Johnstone et al., 2016).

However, the lack of human-specific data and appropriate modeling techniques have prevented assessment of the degree to which in silico models can predict potentially pro-arrhythmic drug-induced changes to the cardiac AP, including change to quantitative biomarkers such as action potential duration (APD) and triangulation (Hondeghem et al., 2001), and the occurrence of qualitative phenomena such as early after-depolarizations (EADs) (Qu et al., 2013). The ability to predict these cellular biomarkers of pro-arrhythmic risk underpins the use of in silico modeling to predict pro-arrhythmic risk for new drugs.

In this study, we systematically and quantitatively compare drug-induced changes in repolarization biomarkers predicted by human ventricular cell models against changes observed from AP recordings of human ventricular trabeculae (Page et al., 2016). We investigate four drugs commonly used as reference drugs, three of which are torsadogenic: dofetilide; dl-sotalol; and quinidine, and verapamil, which is a non-torsadogenic drug. Both the average drug response and the variability in drug response are compared against experiments using populations of models (Britton et al., 2013, 2017; Muszkiewicz et al., 2016) to mimic observed inter- and intra-heart variability in AP biomarkers through variability in underlying ion channel densities. The O'Hara-Rudy (ORd) ventricular cell model (O'Hara et al., 2011), which has been selected by a consensus of in silico modelers for use in CiPA's in silico assay (Colatsky et al., 2016; Fermini et al., 2016), is used as the baseline model forthe populations of models. Multiple recent datasets measuring drug block using both standard IC50-based approaches (Kramer et al., 2013; Crumb et al., 2016) and state- and voltagedependent models of hERG block (Li et al., 2017) are used to obtain simulation results from a variety of drug block models. We identify areas of qualitative and quantitative agreement and disagreement between simulations and this specific set of experiments and discuss strategies for interpreting the results of in silico drug response predictions.

We find that quinidine and verapamil produce substantial disagreement between experiments and simulations across multiple concentrations, IC50 datasets, and hERG block models, while dofetilide and sotalol have generally good agreement between experiments and simulations in both degree of AP prolongation and development of repolarization abnormalities.

# METHODS

# Experimental Data Acquisition

Microelectrode AP recordings from stimulated ex vivo human ventricular trabeculae at 1 and 2 Hz were obtained as described in detail in Page et al. (2016). Briefly, undiseased donor hearts were obtained from organ donors in the United States with legal consent. Trabeculae were dissected from the inner endocardial wall of the ventricle and used for microelectrode recording at ∼37◦C. Each trabecula was paced under control conditions to establish a baseline for that trabecula for each frequency, and then three increasing concentrations of drug were applied. For each step of this protocol, trabeculae were paced at both 1 and 2 Hz. For this study, we used the baseline control recordings and recordings from the two higher concentrations of each drug, as at the lowest concentration of each drug the effect of the drug was small compared to experimental variability. In addition, only data from left ventricular trabeculae were used, to remove electrophysiological differences between left and right ventricles as a source of variability. All donor hearts used in this study included recordings from at least three left ventricular trabeculae. Examples of AP traces used in this study are shown in Figure S1 in the Supplementary Material.

### Baseline Human Ventricular Cell Model

The ORd model (O'Hara et al., 2011) of the human ventricular cardiomyocyte was used as the baseline model for our investigations, as it is particularly well-suited for studying human ventricular repolarization; is one of the most recent, widely used and extensively tested models of the human ventricular cardiomyocyte using experimental recordings from over 140 human hearts; and has been identified as the model to be used in the in silico component of CiPA (Colatsky et al., 2016; Fermini et al., 2016).

Models were paced at 1 and 2 Hz using a biphasic stimulus protocol to approximate the electrotonic effects of tissue coupling (Livshitz and Rudy, 2009). Model code is available in the Supplementary Material and includes the modification proposed by Passini et al. (2016) of the INaF inactivation gate to improve upstroke robustness over different conductance profiles.

### Simulating Experimental Variability in AP Biomarkers through Variability in Ionic Conductances Using Populations of Models

Based on the ORd model and using the methodology described in Britton et al. (2013) and Britton et al. (2017), we first created an initial pool of 20,000 candidate models by varying 11 ionic conductances for the following currents: INaF, INaL, ICaL, Ito, IKr, IKs, IK1, INCX, INaK, IRyR, and ISERCA, with resulting differences in baseline electrophysiological properties and responses to drug application. Each conductance was randomly selected using Latin Hypercube Sampling (McKay et al., 1979) across a range of 0.25–1.75 times the baseline value of that conductance in the original ORd model. This range was selected for two reasons. Firstly, this range allows substantial conductance variability while disallowing extremely low conductance values, which would only be expected to occur under pathological conditions. This reflects the undiseased nature of the human hearts used in this study. Secondly, the range allows up to sevenfold variation in conductances, in line with the range of conductance variability reported from studies of neurons (Schulz et al., 2006). This is an approximation as equivalent measurements for cardiomyocytes have not yet been reported, although variability in the conductances of individual currents in cardiomyocytes are known to be highly variable (Qi et al., 2008; Xiao et al., 2008) and affected by a wide range of external factors including circadian rhythms, hormones and pacing rate (Qi et al., 2008; Jeyaraj et al., 2012; Odening and Koren, 2014). Finally, conductances were independently sampled as no evidence of covariation has been reported. Should advances in experimental methods allow for a better characterization of ionic conductances in intact tissue, these assumptions can be reviewed.

As different hearts were used in different experiments of drug block, we created populations of models based on the AP biomarker ranges for each individual heart. Due to the limited number of trabeculae available for each heart, biomarker ranges were calculated as the minimum and maximum values of each biomarker observed across all trabeculae from that heart at a particular pacing frequency. Ranges were calculated for both 1 and 2 Hz pacing in control conditions. Five AP biomarkers were used for filtering: APD10 (APD at 10% of repolarization); APD30; APD90; triangulation (APD90– APD30); and the maximum negative (repolarization) gradient of membrane potential with respect to time. These biomarkers were selected to focus on accurate representation of the variability during repolarization, without using a large number of biomarkers. The biomarker ranges for some hearts were narrow, and using larger numbers of biomarkers resulted in fewer models being found that were within range for all biomarkers. There was therefore a trade-off between the number of models in each of the final populations and the number of biomarkers that each model in a population was guaranteed to be within the experimental range for.

For each heart, the biomarker ranges calculated from trabeculae from that heart were used to select from the pool of 20,000 candidate models only those models which had all biomarkers within the ranges calculated for that heart, for both pacing frequencies. These models formed a population of models for the heart, where all models in the population had different conductance parameters, representing different possible ionic profiles that all produced AP biomarkers that were consistent with the observed variability between preparations from that heart. The populations of models therefore allow evaluation of predictions of the variability of response to drug application, not just the average response, and allow consideration of a wide range of ionic scenarios. The information content from action potential measurements such as those typically recorded in human-based studies is insufficient to identify the specific conductances of a cardiomyocyte. We therefore chose to analyse a wide range of ionic scenarios that are consistent with experimental recordings. This allows testing the hypothesis that variability in ionic conductances is critical for the comparison of experiments and simulations of drug block.

#### Biomarker Calculation

Biomarkers were calculated from the final pacing cycle of each simulation, and from the mean of a sequence of 30 pacing cycles from each experimental recording. In simulations, EADs were classified as depolarizations that occurred more than 100 ms after the beginning of a pacing cycle with a voltage gradient >0.01 mV/ms. For recordings, EADs were classified as any abnormal depolarizations during phases 2 or 3 of an AP, after the upstroke completed but before normal repolarization was complete.

#### Simulations

Simulations were performed using the CVODE adaptive timestep ODE solver (Hindmarsh et al., 2005) implemented within the CHASTE software package (Pitt-Francis et al., 2008). Data analysis was carried out using Python scripts.

## Simulation of Drug Effects–Simple Pore Block Model

Drug effects were first simulated using a simple pore block model using IC50 and Hill coefficient data. The blocked fraction of a current I was calculated as:

$$B = \frac{1}{1 + \left(\frac{C}{IC50}\right)^h},$$

where B is the fraction of I that is blocked by a compound, C is the concentration of the compound, and IC50 and h are the measured IC50 and Hill coefficient of the compound against that current, respectively. B was calculated for each simulation, and the conductance of each affected current was multiplied by the unblocked fraction (1 − B) to simulate block.

IC50 values have substantial uncertainty attached to them, and there is considerable variability between studies reporting IC50s of the same compounds. We chose to use and compare IC50 values from two recent studies, by Crumb et al. (2016), which assessed six ion channels (hERG—IKr, KvLQT1/mink— IKs, Kv4.3–Ito, Kir2.1–IK1, Nav1.5—INaF and INaL, and Cav1.2— ICaL), and by Kramer et al. (2013), which assessed 3 (hERG— IKr, Nav1.5—INaF, and Cav1.2—ICaL). We simulated two separate datasets to indicate whether variability in IC50 values and number of channels assessed substantially altered simulation results.

For each simulation of drug block, only models from the populations that corresponded to hearts that had been used for experiments with that drug were simulated. For each drug, simulations were performed at 1 and 2 Hz, for two different concentrations an order of magnitude apart. The fractional blocks of ionic currents calculated for each drug, concentration, and dataset are listed in Table S1 in the Supplementary Material.

# Simulation of Drug Effects–Dynamic hERG Block Model

To capture possible changes to effective hERG block caused by the binding kinetics of the drugs used in this study, we also performed repeats of each drug simulation with the ORd model's formulation of IKr replaced with the state-based model of IKr and IKr block developed by Li et al. (2017). Unlike the simplepore block model, this model of hERG block integrates data on drug-specific binding timescales and degrees of trapping, as well as the steady-state concentration dependence of channel block. Briefly, this model uses a state-transition modeling approach with six unbound states (two closed; two closed and inactivated; one open; and one open and inactivated) and three drug-bound states (open and bound; closed and bound; and inactivated, open and bound). Therefore, transient binding and unbinding of drugs during the AP can be simulated, and a trapping parameter determines the degree to which each drug can prevent a bound open channel from closing. Each drug simulation was repeated using this state-based hERG and hERG block model by replacing the ORd model's IKr formulation and simple pore block model of IKr block. In simulations for drugs with multichannel block, the previous drug blocks calculated from the Crumb and Kramer datasets were used for non-IKr currents. Changes to model biomarkers in control conditions caused by replacing the IKr model are summarized in Table S2 in the Supplementary Material.

## Statistics

Intra-individual, inter-individual and total variability in biomarker values was assessed using coefficients of variation (CV). Effects on AP biomarkers of drug application were assessed using change relative to control conditions. Drug response data from experiments and simulations are visualized using boxplots. The central box indicates the central quartiles and median of the data. Boxplot whiskers extend to the farthest data point less than two times the interquartile range from the median.

# RESULTS

## Inter-Heart APD Biomarker Variability is of Similar Magnitude to Intra-Heart Variability

**Figure 1** displays the mean APD30, APD50, and APD90 values recorded for each trabecula from the baseline control period of each experiment, for 1 and 2 Hz pacing, grouped by donor heart. Variability between trabeculae from the same heart (intraindividual variability) and between the means of different hearts (inter-individual variability) is quantified in **Table 1**. CVs for intra- and inter-individual variability were of similar magnitude– neither source of variability made a dominant contribution to total biomarker variability.

## Development of the Populations of Models in Control Conditions

**Figure 2** shows the biomarker distributions for the full experimental dataset and the models accepted for nine standard AP biomarkers, including the five biomarkers used for calibration. 860 models were accepted in total across all populations. Model biomarkers show good overlap with the range and shape of the experimental biomarker distribution for seven of the biomarkers, with the two exceptions being resting membrane potential (RMP) and action potential amplitude (APA). RMP is more variable between experiments than between models, which may be due to experimental fluctuations, particularly in extracellular K+, that are not modeled in this study. APA (the difference between RMP and peak membrane potential) has similar variability between models and experiments, but the distribution mean is shifted ∼ +20 mV in the model distribution relative to experiments.

The accepted models were in range with experimental biomarkers at both frequencies for 14/16 hearts (model APs for each population are shown in **Figure 3**). The majority of hearts had substantial variability between trabeculae (**Figure 1**) but for two hearts, the biomarker ranges between experiments

were very narrow and none of the 20,000 tested models were within range, simultaneously, for the five tested biomarkers at both 1 and 2 Hz pacing frequencies. The 860 accepted models provided acceptable coverage of the biomarker space for the purpose of our study, which was to allow comparison of drug response between experiments and simulations (rather than to construct a population for every heart).

**Figure 4** shows the overlap between experimental and model biomarkers for models accepted into all of the populations for APD90 and triangulation, two biomarkers of pro-arrhythmic risk that were also used to calibrate the populations. There is generally good coverage of the experimentally-observed range of biomarkers, potentially highlighting the ability of the ORd model and variability in ionic conductances to account for variability in human electrophysiological measurements, although for the most outlying combinations of biomarkers there were no candidate models that were in range for all five biomarkers at both pacing frequencies simultaneously. This highlights the fact that in spite of the large conductance variability imposed, simulations did not yield the most outlying combinations of

#### TABLE 1 | Total, intra- and inter-heart variability.


*Intra-individual variability was defined as the mean of CVs that were each calculated using biomarker values from an individual heart. Inter-individual variability was defined as the CV calculated from the mean biomarker values from each heart. Total variability was defined as the CV calculated from biomarker values from all trabeculae.*

biomarker values observed in experiments. Therefore, this type of quantitative comparison also allows identification of potential limitations of the ORd model in capturing outlying behaviors from experiments through variability in conductances, which may require sources of variability beyond ion channel densities to account for the variability in experimental recordings.

## Comparison of Experimental and Simulated Drug Application for Dofetilide, Sotalol, Quinidine, and Verapamil Using Multiple Ic50 Datasets and Ikr Models

Using data from studies by Kramer et al. (2013) and Crumb et al. (2016), we simulated application of four reference drugs, three that have high risk torsadogenic classifications (quinidine, dofetilide, dl-sotalol) and one that is classified as low risk, but has a significant hERG IC50 (verapamil).

Quinidine and verapamil, in addition to both being multichannel blocking compounds, are also known to have "untrapped" hERG binding dynamics, which means when bound to hERG they block the channel from closing and so can unbind at polarized membrane potentials (Zhang et al., 1999; Tsujimae et al., 2004; Windley et al., 2017). Depending on the timescales of channel binding and unbinding, this can result in reduced effective block. Due to the potential effects of these binding dynamics, which are not incorporated in the simple pore block model of drug action, we hypothesized that inclusion of these binding dynamics would improve agreement of quinidine and verapamil simulations with experiments, and that not accounting for these effects could result in overestimating the effects of hERG block, as demonstrated in a simulation study by Di Veroli et al. (2014). Therefore, we additionally evaluated the effects of replacing the ORd model's original IKr model with the recently developed state-based dynamic IKr model from Li et al. (2017), which includes state- and voltage-dependent drug binding and includes parameterized models for the four drugs used in this study.

**Figures 5**–**8** show the changes to repolarization biomarkers APD90 and triangulation under application of each drug for all models in the relevant populations of models for that drug (the populations that were calibrated using data from the hearts that were used in experiments with that drug), and for the original baseline ORd model, compared to experimental results recorded from trabeculae. Figures also indicate models and trabeculae that developed EADs and other repolarization abnormalities (e.g., repolarization failure) under drug application. Biomarker and repolarization abnormality data is additionally summarized in the Supplementary Material (Tables S3–S5).

As expected, there were substantial differences between drugs in the levels of qualitative and quantitative agreement between experiments and simulations. We therefore break down the agreement in changes to APD90, triangulation, and occurrence of EADs between experiments and populations of models using each of the IC50 datasets and IKr models, for each individual drugs used in this study.

#### Dofetilide

Dofetilide is a potent and selective IKr blocker that prolongs the QT interval and is classified as a high-risk compound for druginduced torsade de pointes (TdP). Qualitatively, application to human trabeculae caused substantial concentrationdependent APD90 and triangulation increase (**Figure 5**) at both concentrations tested (0.01 and 0.1 µM, Free Therapeutic Concentration (FTC) = 0.002 µM), which was captured by the populations of models and the baseline ORd model using all datasets. EADs occurred in trabeculae from 2/3 tested hearts at 0.1 µM, but did not occur at 0.01 µM. Simulations with the Crumb dataset and the dynamic hERG model both reproduced this behavior at 1 Hz (4/26 models developed repolarization abnormalities in both sets of simulations at 0.1 µM, 0/26 models at 0.01 µM), but no repolarization abnormalities were detected at either concentration using the Kramer dataset, or in any simulation at 2 Hz pacing. The baseline ORd model only developed EADs at 0.1 µM using the Crumb dataset.

Quantitatively, for 0.1 µM dofetilide, APD90 and triangulation changes (1APD and 1Triangulation) from all datasets were consistent with experiments at 1 Hz pacing, with the distributions of experiments and models overlapping, but not for 2 Hz, where experimental AP prolongation was >1 Hz, unlike all other drugs and concentration studied. In this case, experiments showed prolongation beyond the cycle length. This skipping behavior was not reproduced in any simulations, as the stimulus current was always sufficient to initiate a new AP, while in experiments the stimulus could cause a transient depolarization. Therefore, it is possible that at 2 Hz AP prolongation was >1 Hz due to the additional inward current provided during repolarization by the stimulus.

At the lower dofetilide concentration (0.01 µM), the two IC50 datasets gave substantially different results to each other, neither of which overlapped with the experimental range at 1 Hz. Simulations using the Crumb dataset overpredicted the experimental results, with much higher 1APD and 1Triangulation, and level of variability, than that observed experimentally. In contrast, use of the Kramer dataset underpredicted APD and triangulation increases and variability. However, the dynamic hERG model produced 1APD and 1Triangulation distributions between these two datasets, which did overlap with the experimental range at both pacing frequencies.

*n* = 89) and from all populations of models (blue, *n* = 860) under control conditions 1 Hz pacing.

Overall, simulations captured the effects of dofetilide—substantial AP prolongation along with incidence of repolarization abnormalities at the higher tested concentration. The comparison with experiments was reasonable for all three sets of simulations at 1 Hz, although no simulations captured the skipping behavior observed at 2 Hz. This could possibly be due to mismatch between experimental and simulated stimulus current strengths. Use of the dynamic hERG model produced the best overall agreement with experiments, as it had overlap with experimental 1APD90 and 1Triangulation ranges for three out of four concentration and frequency combinations (excepting 0.1 µM at 2 Hz), and showed occurrence of repolarization abnormalities.

#### Sotalol

Like dofetilide, dl-sotalol is a selective IKr blocker, although it also has beta-adrenergic receptor blocking effects in vivo. Sotalol is torsadogenic and prolongs the QT interval. In the Kramer dataset it was also measured as causing non-negligible block of Cav 1.2 (ICaL); however this was not replicated in the Crumb dataset. Application of sotalol caused concentration-dependent APD and triangulation increase in experiments at both tested

concentrations (10 and 100 µM, FTC = 14.7 µM), which was captured by all simulations (**Figure 6**). EADs did not occur at either concentration in any experiments, and this was also reflected in all simulations, as no model developed repolarization abnormalities.

At 100 µM, all sets of simulations displayed overlap with experiments for APD90 increase, although simulations with the Kramer dataset under-predicted the amount of triangulation and APD increase. Overall, results using the dynamic IKr model were similar to those using the default IKr model, but for both IC50 datasets use of the dynamic model caused a small increase in APD and triangulation which improved agreement with experiments. For 10 µM, all simulation datasets were fully within the experimental range for both biomarkers, however this was partly because experimental results for 10 µM sotalol displayed much higher variability than simulations. In contrast, for dofetilide, variability at the lower concentration—0.01 µM was of similar magnitude for experiment and simulations, and less than the variability of the higher concentration—0.1 µM. One potential reason for this is the relatively low IKr block predicted for 10 µM Sotalol (12.6% from Crumb et al. 14.7% from Kramer et al.) results in a low dispersion of APD prolongation, lower than the intrinsic experimental variability that would be present without drug application, which then dominates the total experimental variability but is not present in simulations.

Overall, sotalol simulations have relatively good agreement with experiments, due to the absence of repolarization abnormalities in all experiments and simulations, and the overlap between simulation and experimental ranges for APD90 and triangulation. The main disagreement between experiments and simulations is that the wide variability observed in both

biomarkers at 10 µM in the experiments is uniformly not replicated across all simulations.

#### Quinidine

drug-induced pro-arrhythmic risk.

Quinidine is a multichannel blocker, with significant IC50s found for all 3 channels measured in Kramer et al. (Nav1.5/INaF, hERG/IKr, Cav1.2/ICaL) and 3/7 of the channels measured by Crumb et al. (hERG/IKr, KvLQT1/IKs, and Kv4.3/Ito). Crumb et al. also detected block for Nav 1.5 and Cav 1.2 however an IC50 was not reached for these channels during experiments and so was not calculated.

Experimentally, quinidine caused a moderate increase in APD90 and triangulation (**Figure 7**) at the higher applied concentration (10 µM, FTC = 3.2 µM), and no substantial change at the lower concentration (1 µM) for both 1 and 2 Hz pacing. In addition, no EADs were observed in any experiments. However, 10 µM quinidine had the highest predicted level of hERG block out of all drugs and concentrations tested in this study for both sets of IC50s; the Crumb and Kramer hERG IC50s predicted 95% and 97% IKr block respectively for 10 µM quinidine (Table S1). In the simulations of quinidine's effects, the Kramer IC50s for quinidine (which measured IC50s for INaF, ICaL and IKr) resulted in higher APD and triangulation increases at both concentrations than were observed experimentally, and EADs were observed in 15/501 models at 10 µM (and none at 1 µM). For the Crumb dataset, in which IC50s were found for IKs, Ito, and IKr, EADs and other repolarization abnormalities (e.g., repolarization failure) occurred in a large majority of models (421/501) at 10 µM, and for 1/501 models at 1 µM at 1 Hz pacing. The ORd baseline model also developed complete repolarization failure using the Crumb IC50s for 10 µM quinidine. Results for 2 Hz pacing for both sets of IC50s were similar except that no model using the Kramer IC50s developed repolarization abnormalities (Table S5). For 10 µM quinidine, the 1APD90 and 1Triangulation values using the Crumb dataset were highly variable; however these values, particularly from models showing APD shortening, were due to abnormal APs with repolarization abnormalities, rather than due to shortening of normal APs. At 1 µM, the Crumb dataset, like the Kramer dataset, generated much higher levels of APD90 and triangulation increase than seen experimentally.

Quinidine both binds and unbinds rapidly from the hERG channel (Tsujimae et al., 2004; Li et al., 2017; Windley et al., 2017). Therefore, depending on the balance between the timescales of these two processes, there was the possibility that modeling state-dependent block of quinidine would reduce effective AP prolongation. However, results using the dynamic IKr model with the other measured IC50s produced similar levels of AP prolongation and EAD prevalence compared to the default ORd IKr model.

Overall, simulations of quinidine predicted far greater APD and triangulation increase (for both Crumb and Kramer datasets and both IKr block models) than seen in these experiments, and both datasets predicted occurrence of repolarization abnormalities that were also not observed in any trabeculae. The Kramer dataset, which included IC50s for both Nav 1.5 and Cav 1.2 as inward currents, and only hERG as an outward current, still predicted far higher AP prolongation than experiments. Quinidine appears to be a particularly challenging drug to model, which could be due to the wide range of both inward and outward ionic currents that it blocks, and our study identifies that additional experiments are required for its detailed characterization.

#### Verapamil

Verapamil blocks both hERG and Cav 1.2 (ICaL). Despite blocking hERG, it is non-torsadogenic and is known to have only a small effect on APD and on the QT interval (Johannesen et al., 2014; Vicente et al., 2015) which has been hypothesized to be due to its hERG binding kinetics (Zhang et al., 1999; Di Veroli et al., 2014) and/or counteracting effects of ICaL block.

Recordings obtained with verapamil applied at 0.1 and 1 µM (FTC = 0.081 µM) showed minor APD shortening of similar magnitude at both concentrations (**Figure 8**), while in all sets of simulations most models produced concentrationdependent APD and triangulation increase, in qualitative disagreement with experiments. A minority of models developed AP shortening, predominantly in 2 Hz simulations. For simulations at the lower concentration (0.1 µM) this was due to drug-induced shortening of normal APs, in line with experimental results. However for simulations at the higher concentration (1 µM) shortening was caused by AP prolongation beyond the duration of the pacing cycle. For these models, the APD was longer than the pacing cycle and

response is shown for (left to right): human ventricular trabeculae, populations of models using drug effects calculated using data from Crumb et al. from Kramer et al. and from use of the hERG model by Li et al. As Crumb and Kramer datasets both measured only hERG IC50s for dofetilide, unlike the other tested compounds, there is only one result from use of the dynamic model. Dots indicate results from individual trabeculae and models, crosses show the result from the baseline ORd model. Red symbols indicate simulations and experiments where repolarization abnormalities occurred.

so repolarization was incomplete during the next stimulus. This lead to a reduced upstroke and shortened APD on the subsequent pacing cycle. This behavior was not observed in experiments. However, simulations and experiments were in agreement for repolarization abnormality occurrence: no repolarization abnormalities were detected in any experiments or simulations.

Quantitatively, both Crumb and Kramer datasets generated similar distributions of APD and triangulation increase to each other, suggesting that uncertainty in IC50 values is less likely to be the source of the mismatch with experiments for verapamil. Instead, the simple pore drug model and IC50 data used in this study may not be sufficient to approximate the electrophysiological effects of verapamil due to its binding kinetics, and/or the balance of L-type calcium and hERG currents in the ORd model may not be accurate.

Verapamil can unbind from hERG channels at voltages close to typical cardiac resting membrane potentials (Zhang et al., 1999; Windley et al., 2017), although the timescale is relatively slow (time constant of recovery ∼100 s at −80 mV). This type of "untrapped" behavior has been shown in simulation studies (Di Veroli et al., 2014) to potentially reduce AP prolongation due to hERG block relative to a "trapped" hERG blocker (e.g.,

FIGURE 6 | Sotalol. Changes to APD90 and triangulation relative to control from application of 10 and 100 µM sotalol during 1 and 2 Hz pacing. In each panel, response is shown for (left to right): human ventricular trabeculae, populations of models using drug effects calculated using data from Crumb et al. from Crumb et al. with IKr replaced by the Li et al. IKr model; from Kramer et al. and from Kramer et al. with IKr replaced by the Li et al. IKr model. Dots indicate results from individual trabeculae and models, crosses show the result from the baseline ORd model.

dofetilide). Therefore, this was an important drug to simulate with the dynamic hERG model, as neglect of its unbinding dynamics could potentially cause a substantial overestimation of AP prolongation.

However, **Figure 8** shows that use of the dynamic hERG model did not substantially alter predictions of APD prolongation compared to the simple-pore block model using only IC50 data. For example, for the Crumb dataset, mean 1APD90 at 1 µM, 1 Hz pacing was 148 ± 32 ms for populations using the ORd IKr model, 198 ± 43 ms with the dynamic IKr model, while for the Kramer dataset in the same conditions, with the ORd IKr model 1APD90 was 195 ± 40 ms, and 194 ± 43 ms with the dynamic IKr model. Therefore, across all models simulated, use of a drug block model of IKr

that included data on binding rates and trapping behavior did not improve the agreement of simulated APD prolongation with experimental results (experimental 1APD90 in this case was −15 ± 30 ms).

Overall, no set of simulations was consistent with the minor AP shortening caused by verapamil in experiments, as all sets of simulations instead showed AP prolongation. However, all simulations were consistent with the observed lack of repolarization abnormalities.

## Comparison of Drug Block Datasets and Modeling Methodologies

In this study we simulated two different IC50 datasets and two different models of IKr and IKr block, each combination of

with IKr replaced by the Li et al. IKr model; from Kramer et al.; and from Kramer et al. with IKr replaced by the Li et al. IKr model. Dots indicate results from individual trabeculae and models, crosses show the result from the baseline ORd model. Red symbols indicate simulations and experiments where repolarization abnormalities occurred.

which produced a different simulated response to each drug. In addition we performed simulations with both populations of experimentally-calibrated models, and the baseline ORd model. **Figure 9** summarizes the differences between simulation predictions and experimental results for the mean and standard deviation of 1APD90 and 1Triangulation, separated by drug, drug block dataset, and modeling methodology. **Figure 9** shows results for dofetilide and sotalol only as for quinidine and verapamil, all drug block datasets have the same qualitative mismatch with experiments. This makes a quantitative comparison redundant—all simulations can be thought of as being equally mismatched for these drugs.

We see from this comparison that the overall best drug block dataset for predicting 1APD90 and 1Triangulation tested in this study is the dynamic IKr and IKr block model by Li et al. using the IC50s from Crumb et al. for non-hERG channels. In particular, the dynamic IKr model is consistently better than the default ORd IKr model using both Crumb and Kramer IC50s in all tested cases for both dofetilide and sotalol. Comparisons between the ORd baseline model and average of the populations of models are

FIGURE 8 | Verapamil. Changes to APD90 and triangulation relative to control from application of 0.1 and 1 µM verapamil during 1 and 2 Hz pacing. In each panel, response is shown for (left to right): human ventricular trabeculae, populations of models using drug effects calculated using data from Crumb et al.; from Crumb et al. with IKr replaced by the Li et al. IKr model; from Kramer et al. and from Kramer et al. with IKr replaced by the Li et al. IKr model. Dots indicate results from individual trabeculae and models, crosses show the result from the baseline ORd model.

inconclusive: the baseline ORd model is closer to experiments for dofetilide, while the average of the populations of models is closer for sotalol. However, only the populations of models and not the baseline ORd model can provide predictions on variability of drug response.

# DISCUSSION

#### Main Findings

In this study, changes in repolarization biomarkers and EAD occurrence caused by application of dofetilide, sotalol, quinidine, and verapamil were compared between in silico simulations using populations of human ventricular models and ex vivo human ventricular trabeculae. The four reference drugs examined in this study all blocked hERG but included both selective and multichannel blockers, as well as drugs in high and low TdP risk categories. Experimental data therefore spanned a wide range of effects from high APD prolongation with widespread EAD occurrence (dofetilide) to mild APD shortening with no EADs (verapamil). In silico populations of models were calibrated to reflect experimentally-observed AP variability between trabeculae from the same donor heart in control conditions, through variation in underlying ionic conductances. These populations were used to simulate the effects of each drug at multiple pacing rates and concentrations using IC50 data from two recent studies (Kramer et al., 2013; Crumb et al., 2016), and with both the ORd model's original model of hERG, and a recently developed state-dependent dynamic model of hERG

FIGURE 9 | Summary of average difference in mean and standard deviation between experiment and simulation for 1APD90 and 1Triangulation. Absolute differences in mean (top) and standard deviation (bottom) between experiments and simulations for 1APD90 and 1Triangulation are shown for dofetilide (left) and sotalol (right), for each drug block dataset. Differences in mean are shown for both the mean of the populations of models (dark blue) and the single biomarker value produced by the ORd baseline model (light blue), while differences in standard deviation can only be shown for the populations of models. Values for each drug block dataset are averaged across all concentrations and frequencies used in this study. Results for dofetilide show only one block dataset for the dynamic hERG model as neither Crumb nor Kramer IC50 datasets contained non-hERG IC50s for dofetilide (for sotalol, Kramer et al. measured an IC50 for Cav 1.2).

and hERG block (Li et al., 2017) that integrates additional drugspecific data on hERG binding rates and trapping to model state-dependent block.

The main findings of this study were:


#### Explanations for Qualitative Mismatch of APD Changes but Consistency in Lack of EADs Caused by Verapamil

Ex vivo (**Figure 8**) and in vivo recordings (Johannesen et al., 2014; Vicente et al., 2015) show that verapamil causes minor QT and APD shortening or no effect. However, voltage clamp studies have consistently reported substantial hERG block in the concentration range tested in this study (Kramer et al., 2013; Crumb et al., 2016; Li et al., 2017). There are two main hypotheses in the literature regarding the lack of APD prolongation from verapamil despite this measured hERG block. The first hypothesis is that block of ICaL by verapamil counteracts the AP prolonging effects of IKr block as both inward and outward currents are reduced, which produces the observed minor shortening of APD. However, the effects of IKr block alone are substantial and variable (e.g., **Figures 5**, **6**). Therefore, it seems that this mechanism would require fine tuning of the ratios of ICaL and IKr block, as well as the baseline cellular conductances GKr and GCaL, to consistently allow ICaL block to cancel out the effects of IKr block alone, which multiple voltage clamp studies predict to be substantial at the concentrations tested. For example, for 1 µM verapamil both Crumb and Kramer datasets predict greater IKr block (68 and 77% respectively) than for 100 µM sotalol, the effects of which can be seen in **Figure 6**. It therefore seems unlikely that block of ICaL could be a sufficient mechanism to precisely cancel out the AP prolongation from hERG block. However, verapamil's ICaL block could be one of several contributing factors that collectively limit the AP prolongation from its IKr block, and experimental and in silico studies indicate it is the main mechanism preventing the occurrence of EADs under verapamil application.

The second hypothesis for verapamil's effects on APD is that IKr block from verapamil is overestimated by dose-response curve models parameterized from voltage clamp experiments that do not measure its hERG binding dynamics. Data from Zhang et al. (1999) show that verapamil is an untrapped hERG blocker–when bound it reduces the probability of the hERG channel closing, increasing the probability of verapamil unbinding at voltages close to the resting membrane potential. This contrasts with other hERG blockers, such as dofetilide, that do not prevent the channel from closing and therefore remain bound when the membrane is polarized. Therefore, IC50s measured from voltage clamp studies that do not account for this may overestimate the level of IKr block, and therefore the level of AP prolongation, caused by verapamil under normal pacing conditions. A simulation study by Di Veroli et al. (2014) suggests that verapamil's increased unbinding from hERG relative to compounds such as dofetilide could result in reduced AP prolongation during normal pacing, depending on binding timescales. However, use of the dynamic hERG model incorporating verapamil's untrapped dynamics did not substantially lower AP prolongation. Therefore, the mechanism(s) that limit the impact of verapamil's measured IKr block are currently unclear.

## Mismatch in APD Prolongation and EAD Occurrence for Quinidine

Experimentally, quinidine causes QT and AP prolongation (Nademanee et al., 1990; Vicente et al., 2015), and is classified as a high risk torsadogenic drug. These features were qualitatively replicated in simulations (**Figure 7**); however the degree of AP prolongation was overestimated by simulations compared to ex vivo results. Additionally, while no EADs were recorded from any trabeculae under quinidine application, repolarization abnormalities occurred for the majority of models when using the IC50s from Crumb et al. in which only potassium channel IC50s were able to be calculated for quinidine, as recorded blocks of INa and ICaL at the maximally tested concentration were too low to estimate IC50s, and in a small minority of models when using the IC50s from Kramer et al. which included block of ICaL which is known to suppress EAD formation.

We can suggest four possible hypotheses for why simulations overestimated quinidine-induced AP prolongation. Firstly, as quinidine significantly blocks a particularly large number of channels, the compound effects of measurement uncertainty across multiple channels could result in a substantial total uncertainty when all channel blocks are integrated into an action potential model. Estimates of the hERG IC50 for the same drug across different studies have been shown to vary by an order of magnitude (Polak et al., 2009), and for a multichannel blocker like quinidine, this measurement uncertainty will be compounded over multiple ion channels. The second hypothesis is that the IKr current in the ORd model could have too large an influence on APD relative to other currents. However, the results for dofetilide and sotalol (**Figures 5**, **6**) show that over a range of different conductance profiles the ORd model provides good agreement with experiments for selective block of IKr across multiple compounds, which provides confidence that the strength of IKr relative to other currents is reasonable. Thirdly, inward currents acting during repolarization, particularly ICaL, may be too weak in the ORd model, so that block of these currents produces too little reduction in APD prolongation when combined with IKr block. This could be tested in future studies by comparing simulations to experiments with more selective calcium channel blockers. If APD shortening in experiments is found to be substantially larger than in simulations using the ORd model, this would support this hypothesis. Finally, quinidine is known to be an untrapped hERG blocker (Tsujimae et al., 2004), so simple-pore block models may overestimate the degree of hERG block. However, quinidine binds rapidly to hERG channels (Windley et al., 2017), which would limit the effects of transient unbinding, and simulations with the dynamic hERG model did not show substantial differences to using only IC50 data (**Figure 7**). Therefore, the causes of mismatch between experiment and simulations for quinidine in our study require further investigation and could include a range of contributing factors.

#### Limitations

This study investigated the response of models derived from a single baseline model, the ORd model, although with two different models of IKr and a wide range of different conductance profiles, to mimic biological variability in ion channel densities. Other sources of variability that are known to influence the electrophysiological phenotype, such as alterations in channel structure to change gating dynamics, are not included in this study. Other human ventricular models (e.g., ten Tusscher and Panfilov, 2006; Grandi et al., 2010) also have different balances of ionic currents and therefore produce different results in simulations and have different strengths and weaknesses. In particular, we found that across a wide range of conductances the ORd model could not reproduce the range of action potential amplitudes observed in this dataset, which were in the range of 87–119 mV (**Figure 2**). It is possible that the discrepancy in action potential amplitude could impact repolarization and ideally a modification to the model could be found to rectify this issue, but we have not yet found an appropriate modification. However, the ORd model was chosen as the baseline model for this study due to its integration of human-specific voltageclamp and current-clamp recordings from human ventricular cardiomyocytes, and its current relevance forin silico drug testing due to being selected as the model of choice for the in silico section of CiPA (Fermini et al., 2016).

To incorporate inter- and intra-heart variability into simulation predictions, we chose to use the population of models methodology. However, other methodologies for integrating biological variability into cardiac modeling have been developed and could have been used, including multivariate partial regression analysis (Sobie, 2009; Sarkar and Sobie, 2010; Sadrieh et al., 2013) and particularly cell-specific modeling (Davies et al., 2012; Groenendaal et al., 2015). Each of these methodologies has particular strengths, e.g., partial least squares regression analysis can constrain model parameters and identify relationships between many model parameters and outputs simultaneously without the need for additional experimental data while cell-specific modeling can estimate best-fit parameter sets for recordings from specific cells, and can take advantage of information from dynamically rich pacing protocols (Groenendaal et al., 2015). The advantage of using cell-specific modeling in this study would have been the ability to find a unique model that agreed with the experimental recordings for each trabecula. However, the likelihood of each model accurately representing conductances of the associated preparation would be low as experimental recordings typically recorded from human preparations, such as those available here, would not contain enough information to constrain each model. These techniques are still under investigation.

Instead, we decided populations of models were a good choice of methodology for the purposes of this study. Although populations of models do not reconstruct the conductances of a particular preparation, they can find models with a wide range of ionic profiles that are all consistent with experimental biomarkers. This is ideal for simulating drug effects, as a wide range of possible responses, including outliers, can be evaluated. If the response to a simulated drug is different to experimental results across all or most models, as with quinidine and verapamil, this can then suggest that the mismatch is due to other causes, such as the model of drug block, or nonconductance sources of variability, rather than the specific set(s) of conductances in one or a few models. In addition, all current methods for incorporating experimental variability rely on the equations of an underlying baseline cell model such as the ORd model. Regardless of which model is chosen, there will likely be experimentally observed combination of AP biomarkers across different pacing protocols that cannot be simultaneously reproduced by a model with any set of conductances, due to the structure of the model equations. Therefore, no matter which methodology is used it may not be possible for all experimental observations to be reproduced in simulations with a single set of underlying model equations. Our study yields important quantitative information on the ability of the ORd model with variations in ionic conductance and current knowledge on drug action to reproduce experimental recordings.

The simple pore block model of drug action assumes that channel block is independent of the state of each ion channel. For many drugs this is an effective approximation; however for others, incorporating state-dependent block and binding information could be necessary to explain mismatches between simulations and experiments. Therefore, we also evaluated the state-dependent hERG block model by Li et al. (2017). Use of this model did not result in substantial changes in simulation results compared to the ORd baseline hERG model, however only one parameterization of this block model was available for each drug. Given the substantial uncertainty in measurements of IC50 values it is likely there is also substantial uncertainty in the drug block parameters measured for the Li et al. model. Replications of the type of voltage clamp studies used to parameterize these drug block models would be necessary to determine the level of uncertainty in hERG binding and trapping parameters, combined with further simulation studies to understand the effects this uncertainty has when propagated to AP-level models.

#### Future Work

The identification of mismatches between experiments and simulations is vital for continued improvement of in silico cardiac models and for identifying areas where our understanding of electrophysiological mechanisms of drug action is inconsistent with experimental data. We hope this study will motivate combined experimental and simulation studies that can explain the causes of the mismatches for quinidine and verapamil, and in doing so allow iterative modification and improvement of the ORd model and other cardiac cell models. This iterative improvement has been an important part of cardiac electrophysiology from the beginning of the field (Noble, 2011).

Future studies could also build on this work by analyzing a wider range of drugs, particularly other multichannel blockers, and selective blockers of channels other than hERG. This would provide a more thorough understanding of agreement and disagreement across a broad range of ion channel blocking compounds, providing confidence where selective block showed

#### REFERENCES


good agreement between simulations and experiments (e.g., as for dofetilide and sotalol in this study) and identifying areas for model modification where there is significant mismatch. In particular, it will be important to investigate whether the results for quinidine and verapamil are representative of other multichannel blockers that block hERG, or are outliers due to unique features of these two drugs. If the former, then it is likely the ORd model will need modification, if the latter, then the mismatch may be due to an incomplete understanding of the mechanisms of verapamil and quinidine block.

#### ETHICS STATEMENT

All human tissues used for this study were obtained by legal consent from organ donors in the United States.

#### AUTHOR CONTRIBUTIONS

Conceived and designed study: OB, NA, BR. Acquired experimental recordings: NA, GP, AG, PM. Performed simulations and analyzed data: OB. Drafted manuscript: OB, NA, BR. All authors contributed to critical revision of the manuscript and approved the final version to be published.

#### FUNDING

The authors would like to acknowledge funding from an EPSRC Impact Acceleration Account (EP/K503769/1), an NC3Rs Project Grant (NC/P00122X/1), an NC3Rs Infrastructure for Impact Award (NC/P001076/1) and a Wellcome Trust Senior Research Fellowship in Basic Biomedical Science (100246/Z/12/Z).

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fphys. 2017.00597/full#supplementary-material


J. Pharmacol. Toxicol. Methods 81, 183–195. doi: 10.1016/j.vascn.2016. 05.016


**Conflict of Interest Statement:** OB and BR authors declare no conflicts of interest. NA, GP, AG and PM are employees of AnaBios Corporation.

Copyright © 2017 Britton, Abi-Gerges, Page, Ghetti, Miller and Rodriguez. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology

Chon Lok Lei <sup>1</sup> , Ken Wang<sup>2</sup> , Michael Clerx <sup>1</sup> , Ross H. Johnstone<sup>1</sup> , Maria P. Hortigon-Vinagre<sup>3</sup> , Victor Zamora<sup>3</sup> , Andrew Allan<sup>3</sup> , Godfrey L. Smith<sup>3</sup> , David J. Gavaghan<sup>1</sup> , Gary R. Mirams <sup>4</sup> and Liudmila Polonchuk <sup>2</sup> \*

*<sup>1</sup> Computational Biology, Department of Computer Science, University of Oxford, Oxford, United Kingdom, <sup>2</sup> Roche Pharma Research and Early Development, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland, <sup>3</sup> Clyde Biosciences, BioCity Scotland, Newhouse, United Kingdom, <sup>4</sup> Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom*

#### Edited by:

*Eleonora Grandi, University of California, Davis, United States*

#### Reviewed by:

*Axel Loewe, Karlsruhe Institute of Technology, Germany Jordi Heijman, Maastricht University, Netherlands Divya Charlotte Kernik, University of California, Davis, United States*

\*Correspondence:

*Liudmila Polonchuk liudmila.polonchuk@roche.com*

#### Specialty section:

*This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology*

Received: *31 August 2017* Accepted: *17 November 2017* Published: *12 December 2017*

#### Citation:

*Lei CL, Wang K, Clerx M, Johnstone RH, Hortigon-Vinagre MP, Zamora V, Allan A, Smith GL, Gavaghan DJ, Mirams GR and Polonchuk L (2017) Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology. Front. Physiol. 8:986. doi: 10.3389/fphys.2017.00986* Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.

Keywords: cardiomyocytes, stem cell derived, electrophysiology, mathematical model, pharmacology, variability, computational model

# 1. INTRODUCTION

Induced pluripotent stem cells (iPSCs) can be generated by harvesting fully differentiated and mature somatic cells from donors and reprogramming them to the pluripotent state (Takahashi et al., 2007; Yu et al., 2007). From this state, similarly to embryonic stem cells (ESCs), iPSCs can be differentiated into cell types used for drug screening, disease modeling, cell therapy, and testing of personalized treatments (Robinton and Daley, 2012; Shi et al., 2017). But unlike ESCs, iPSCs are harvested from mature donors, which greatly increases their availability, can provide patientspecific cells, and avoids ethical issues associated with the use of embryonic cells (Holm, 2008). Compared to animal ex-vivo cell models, iPSCs avoid issues of inter-species differences in protein expression and cellular physiology (Houser et al., 2012; Milani-Nejad and Janssen, 2014).

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different applications. These iPSC-CMs share some important characteristics with adult CMs: In terms of gene expression, iPSC-CMs show a pattern that is consistent with adult CMs (Kattman et al., 2011; Burridge et al., 2014; Bedada et al., 2016). Functionally, iPSC-CMs display most major types of ion current seen in adult CMs, including the fast inward sodium current (INa), the transient outward potassium current (Ito), the Land T-type calcium currents (ICaL and ICaT), the rapid and slowly activating delayed rectifier potassium currents (IKr and IKs), and the hyperpolarization-activated pacemaker current (If ) (Ma et al., 2011; Liang et al., 2013; Knollmann, 2013). In addition, iPSC-CMs can be created with genetic mutations that are presented in inherited cardiovascular diseases such as long QT syndrome (Moretti et al., 2010; Itzhaki et al., 2011; Yazawa et al., 2011; Egashira et al., 2012; Terrenoire et al., 2013), catecholaminergic polymorphic ventricular tachycardia (Fatima et al., 2011; Itzhaki et al., 2012; Jung et al., 2012; Kujala et al., 2012), and arrhythmogenic right ventricular cardiomyopathy (Ma et al., 2013). Using iPSC-CMs to investigate these mutations can provide crucial insights into cellular arrhythmia mechanisms and the genotype-phenotype correlation of cardiovascular diseases.

In drug screening and discovery, iPSC-CMs can be used to evaluate proarrhythmic risk. Here, iPSC-CMs can be used as in vitro models that closely resemble human physiology and patient-specific conditions (Ebert et al., 2012; Mathur et al., 2015; Avior et al., 2016). Recently, such in vitro studies have become more important for drug evaluation (Friedrichs et al., 2005; Pugsley, 2005; Lindgren et al., 2008; Giorgi et al., 2010) and the use of iPSC-CMs in drug safety pipelines has been proposed by the Food and Drug Administration (FDA)-led "Comprehensive in vitro Proarrhythmia Assay" (CiPA) initiative (Sager et al., 2014; Ando et al., 2017). As part of CiPA it is intended that iPSC-CMs act as a check on mathematical model predictions of pro-arrhythmic risk.

However, some care needs to be taken when interpreting the results of experiments on iPSC-CMs, as many differences between iPSC-CMs and adult CMs still exist. For example, iPSC-CMs have a smaller average cell size (Polak and Fijorek, 2012), lack T-tubules (Lieu et al., 2009) and have lower contractile force (Rodriguez et al., 2014). Their calcium handling machinery is underdeveloped, including changes to calcium-induced calcium release, buffering in the sarcoplasmic reticulum and recycling of calcium by SERCA (Sedan and Binah, 2011; Blazeski et al., 2012), although this is still under debate (Hwang et al., 2015). The expression levels of some ion channel genes also show some important differences. Unlike adult CMs, iPSC-CMs have little IK1 current (van den Heuvel et al., 2014), and a prominent I<sup>f</sup> current (Knollmann, 2013; Keung et al., 2014). These different current characteristics of iPSC-CMs give rise to a relatively positive diastolic potential and slower upstroke velocity compared with adult CMs. The need to further understand these sub-cellular differences, to translate findings in iPSC-CMs to adult myocytes, and to understand how they relate to cell and tissue-level effects, has driven researchers to develop computational models of iPSC-CMs (Paci et al., 2013,

Each iPSC-CM cell line is developed from a donor with a particular genetic background, using a specific set of protocols from differentiation to maturation. Besides the differences in iPSC-CM and adult-CM electrophysiology, differences between iPSC-CM cell lines have also been shown (Okano et al., 2013; Priori et al., 2013; Moran et al., 2014; Du et al., 2015). Cell-tocell variability of ion current characteristics within a single line of iPSC-CMs was also observed (López-Redondo et al., 2016) which, as in adult CMs, can have strong implications for our understanding of cell electrophysiology and prediction of drug effects (Mirams et al., 2016).

To use and trust iPSC-CMs as an in vitro model for drug screening and disease modeling, it is crucial to evaluate the differences between cell lines and the intra-cell line variability, and to understand how these differences impact experimental outcomes (Karakikes et al., 2015; Del Álamo et al., 2016). Computational modeling can be used to understand and to quantify this intra- and inter-cell line variability, and to gain mechanistic insights into iPSC-CM electrophysiology.

But how detailed does such modeling work need to be? Can a model based on one cell line be used to make inferences about another? How much, and what type of experimental data is needed to tailor a model to a new cell type, or even an individual cell?

In this exploratory study, we compared electrophysiological characteristics of the Cor.4U iPSC-CM cell line (Axiogenesis AG, Germany) to a model by Paci et al. (2013), based on the Ma et al. (2011) studies of an iPSC-CM cell line from Cellular Dynamics International (CDI), iCell. First, we measured the maximum conductances of sodium, calcium and lumped outward currents in individual Cor.4U cells, and by comparing this to model predictions we attempted to infer the maximum conductances of the individual ionic currents. We focused on the maximum conductances of INa, ICaL, IKs, INaCa. These maximum conductances were then used to tailor the Paci et al. (2013) model to create cellspecific models of 22 different Cor.4U cells. Using these tailored models to simulate APs, we found a variety of AP waveforms exhibiting a high level of variability similar to that found in real iPSC-CMs. We then optically measured action potential durations (APDs) in iPSC-CM cultures under both control and drug-applied conditions, and found that—in most cases—tailored models predicted the resulting changes better than the original model. This suggests that the ion current composition differs between cell lines, and highlights the need to tailor in silico models to different cell lines to interpret drug-induced alterations to their electrophysiology. Our results also show that even a relatively simple approach, in which only the maximum conductances are considered with limited experimental data, can already provide useful information in this regard, but that more intricate methods will be needed to characterize differences in outward currents between iPSC-CM cell lines.

### 2. METHODS

#### 2.1. Current Measurements in Cor.4U Cells

Sodium, calcium, and lumped outward currents were measured in Cor.4U cells in the whole-cell patch clamp configuration using the Nanion SyncroPatch 96 platform (Nanion Technologies GmbH, Germany). Sodium and lumped outward currents were measured using an intracellular solution containing (in mM) 50 KCl, 60 KF, 10 NaCl, 10 HEPES, and 20 EGTA (pH: 7.2), and a bath solution containing (in mM) 150 NaCl, 4 KCl, 1 MgCl2, 1.2 CaCl2, 10 HEPES, and 5 glucose (pH: 7.4). Calcium current recordings were made using an intracellular solution containing (in mM) 50 CsCl, 60 CsF, 10 TEA-Cl (a potassium current blocker), 5 HEPES, 10 EGTA, 4 Na2-ATP, 0.1 Na-GTP, and 0.1 cAMP (pH: 7.2) and a bath solution containing (in mM) 130 NMDG, 10 BaCl2, 4 CsCl2, 1 MgCl2, 2 CaCl2, 10 HEPES, and 5 glucose (pH: 7.4). All currents were recorded at room temperature.

For the sodium current measurements, cells were held at −80 mV and then stepped to potentials ranging from −60 to 60 mV with 10 mV increments, before returning to the holding potential. The step duration was 20 ms and the interval between steps was 5 s. The calcium current experiments used a similar protocol, but with 200 ms steps from −40 to 40 mV. Outward current was measured with 500 ms steps from −40 to 50 mV, with a 10 s interval between steps. All three protocols are shown in Supplementary Figure S1.

For the outward current experiments, we fitted directly to the experimental current traces (see section 2.5), and so leak correction was applied using Ileak = V/Rleak where Rleak was the leak resistance estimated at the holding potential. Capacitance artifacts were filtered out by omitting the first 10 ms after each change in potential (see e.g., Ogden and Stanfield, 1994).

#### 2.2. Patch Clamp AP Measurements in iPSC-CMs

Action potentials in iCell iPSC-CMs (CDI, USA) plated on coverslips were measured in whole-cell patch clamp configuration using a HEKA amplifier (EPC 10 USB Triple, HEKA Elektronik, Germany). Recordings were made using a pipette solution containing (in mM) 10 NaCl, 125 KCl, 1 MgCl2, 10 HEPES, 0.1 Na3GTP, 5 Mg-ATP, 5 EGTA (pH 7.2) and a bath solution containing (in mM) 150 NaCl, 4 KCl, 1.2 CaCl2, 1 MgCl2, 10 HEPES (pH 7.4). Cells were stimulated at a frequency of 1.0 Hz, for at least 50 cycles before recording.

#### 2.3. Optical Mapping AP Measurements in Cor.4U Cultures

Action potentials were recorded from Cor.4U cultures with optical mapping using the CellOPTIQ electrophysiology platform (Clyde Biosciences Ltd). Cells were incubated in serumfree media at 35 ± 2 ◦C, and transiently loaded with voltage sensitive fluorescent dye di-4-ANEPPS (20µL of stock solution 27 mM in ethanol; University of Connecticut Health Center). The loaded dye was then excited with a peak wavelength 470 nm LED, and the emitted fluorescence from the Cor.4U iPSC-CMs was recorded at a sample frequency of 10 kHz. Measurements were performed before and after addition of Dofetilide, Quinidine, Sotalol and Verapamil at the concentrations shown in **Table 1**. Paracetamol was applied as a negative control.

A semi-automatic data analysis method based in Wang et al. (2015) was employed to normalize the data. In short, heuristics were used to form an initial estimate of the start and end time of the AP. The region just before the estimated upstroke was used to determine Vnormalized = 0, while the 95th percentile of the data during the (estimated) AP was used as Vnormalized = 1. We then calculated the final APD<sup>90</sup> and APD<sup>50</sup> from this normalized signal.

#### 2.4. Simulated Experiments

Simulations of the patch clamp protocols were carried out using the model by Paci et al. (2013). Initial intracellular and extracellular ion concentrations were set to the values used in the experiments. For the INa, ICaL, and Ioutward voltage clamp experiments, concentrations were clamped (corresponding to the buffering effects of the pipette), but for AP simulations concentrations were allowed to vary following model equations. The temperature parameter in the model, which affects reversal potentials as well as ICaL permeability and IKr, INaK, and INaCa kinetics, was set to 25◦C (298 K) to match the experimental temperature. Simulations were run using Myokit (Clerx et al., 2016), with CVODE (Hindmarsh et al., 2005) set to the default tolerance settings of abs\_tol = 10 <sup>−</sup><sup>6</sup> and rel\_tol = 10 <sup>−</sup><sup>4</sup> . Model code was imported from a CellML (Cuellar et al., 2003) file downloaded from the Physiome model repository (Yu et al., 2011). Numerical integration was carried out using NumPy/SciPy (Jones et al., 2001). All codes and data are freely available from https://gitlab.com/MichaelClerx/tailoredipsc-models.

#### 2.5. Estimating Maximum Conductances of Individual Ion Currents

The maximum conductance of INa was estimated by scaling the INa conductance in the Paci model to match the peak current recorded experimentally with the sodium protocol (n = 35 cells), based on the assumption that the peak current is composed of INa alone. We tested this assumption by running a simulated experiment, where we observed that INa alone would reach 1.01× the initial inward deflection after each voltage step. So the peak is almost entirely due to sodium and only decreased slightly by the presence of other currents. Similarly, the recordings made with the calcium protocol (n = 25 cells) were used to directly infer the maximum conductance of ICaL.

To estimate the conductances of the remaining major currents, we used the recordings made with the outward-current protocol (n = 22 cells). Using the iPSC model by Paci et al. (2013) we simulated the response to this protocol of INa, ICaL, IK1, IKr, IKs, Ito, I<sup>f</sup> , and INaCa (see Supplementary Figure S2). We then tried to find a weighted sum of these simulated currents that could replicate the measured signal. This was done by minimizing the sum of square errors between measured and simulated current during the voltage steps, using the optimization method CMA-ES (Hansen, 2006). The procedure


TABLE 1 | Summary of the applied reference drugs which are a variety of multi-channel blockers, including the IC50 values for the corresponding ion channels, and the applied drug concentration (*x*).

*The IC50 data are from <sup>a</sup> , Obejero-Paz et al. (2015); b , Po et al. (1999); c , Mirams et al. (2011); and <sup>d</sup> , Kramer et al. (2013).*

was repeated for each of the 22 measured cells, resulting in a unique set of scaling factors per cell.

While this protocol was intended to find values for only the outward currents (such as IKr, IKs, and Ito) we chose to vary the inward currents INa and ICaL in the optimization to reduce the risk that any inward currents in the signal would erroneously be attributed to the outward currents (see e.g., Sarkar and Sobie, 2010). Note that we do not use these fitted INa and ICaL conductances because we fit these from other dedicated experiments; they were included here just to yield more accurate outward current fits. After finding that the most prominent outward currents were IKs and INaCa (see section 3.2), we ran a second optimization with only IKs and INaCa: little change was observed, but we expect that fitting outward currents together with INa and ICaL is likely to yield slightly more accurate results.

Convergence of the optimization results was verified by repeating the process 10 times, using different random seeds for each run. We found that the L<sup>2</sup> norm of the difference between the first and repeated scaling factor vectors was smaller than 10 <sup>−</sup><sup>5</sup> for all 10 random starting points. To further verify the identifiability of the problem, we performed the same analysis on synthetic data (with synthetic noise), and were able to successfully infer the conductance scaling factors (see Supplementary Figure S4 and Supplementary Table S1). We note that this analysis assumes the kinetics of the currents have low model discrepancy, i.e., reflect the kinetics of the real currents well.

Finally, to quantify the contribution of each current to the total outward current, we defined a contribution score c<sup>i</sup> for each current I<sup>i</sup> as:

$$c\_i = \frac{|I\_{\text{final},i}|}{\sum\_j |I\_{\text{final},j}|} \tag{1}$$

where Ifinal,<sup>i</sup> was defined as the current measured at the end of the final step of the outward-current protocol. This measure simply gives us a sense of the proportion of outward current that is contributed by each individual component during the end of the 50 mV step, but it is not used in tailoring the models.

#### 2.6. Predicting the Shape of the AP

Next, the estimated maximum conductances were used to tailor the Paci et al. (2013) model to individual cells from the Cor.4U cell line. A total of 22 model variants were parameterized, corresponding to the 22 cells for which the outward current was measured. Since we found many currents were not discernible in the recorded outward current (see **Table 2**), we only applied the cell-specific scaling factors for IKs and INaCa. All tailored models used the same INa and ICaL scaling factors, found in the inward current experiments which were measured in different cells and hence any covariance could not be accounted for. The remaining currents were left unchanged, as they are necessary for other cellular behavior, such as homeostasis, even though they might not contribute strongly to the recorded outward current. Note that we have used only linear scaling of the conductances, and the current kinetics of the original currents were not altered. Finally, Na+, K+, and Ca2<sup>+</sup> evolve in time according to the Paci et al. (2013) model, to mimic the intact cell conditions of our optical mapping experiments.

These tailored models were then used to simulate baseline APs, as well as APs with drug perturbation. The effects of drugs on ion current maximum conductances were modeled using the Hill equation (Hill, 1910; Weiss, 1997).

$$f(\mathbf{x}) = \frac{1}{1 + (\mathbf{x}/\text{IC50})^h} \tag{2}$$

where x denotes the concentration of the applied drug, IC50 is the inhibitory concentration 50% value, h is the Hill coefficient, and f(x) is a scaling factor for the maximum conductance that varies from 0 (full block) to 1 (no block).

For each cell and each drug, a model was created where the maximum conductances of the ion currents were scaled according to Equation (2) using the IC50 values from **Table 1** and a Hill coefficient of 1.0. For comparison, the same scaling factors were applied to an original model with the untailored conductance values from Paci et al. (2013).

In our optical mapping experiments, cells formed a spontaneously-beating and electrotonically-coupled monolayer. However, in this preparation not all cells beat at their spontaneous rates. Most cells will fire an AP when triggered by an activation wave from their neighbors rather than spontaneously, and a relatively small region of (by definition) faster spontaneously-beating cells sets the pacing rate for the entire monolayer. Therefore, to mimic this effect, we paced the cells at the mean rates observed in the optical mapping experiments, for a given compound, to account for any AP rate dependency. We used the cycle lengths of 1.375 s for Dofetilide,


TABLE 2 | The scaling factors (*s*) and the relative contribution (*c*) of individual ion currents to the measured outward current in Cor.4U cells (n = 22).

*Values lower than 10* <sup>−</sup>*<sup>10</sup> are shown as dashes (—). The scaling factors are taken with respect to the maximum conductance found in the original Paci et al. (2013) model. Ito values were lower than 10* <sup>−</sup>*<sup>10</sup> for all cells. Because of the many low values for Ito, IKr, IK1, and I<sup>f</sup> , only the values for INaCa and IKs were used to create the tailored models.*

1.176 s for Quinidine, 0.933 s for Sotalol, 0.905 s for Verapamil and 1.0 s for Paracetamol and all other experiments. To allow direct comparison with the optical mapping data, the simulated AP was normalized using the same algorithm (see section 2.3).

# 3. RESULTS

# 3.1. INa and ICaL in Cor.4U Cells

**Figure 1** shows the peak current-voltage relationships for INa and ICaL, measured in Cor.4U cells. The mean peak current in 35 cells (INa) and 25 cells (ICaL) is plotted, as are the 25th and 75th percentiles. Compared to the prediction of the original Paci et al. (2013) model (created from iCell iPSC-CM data), the experimental data show a lower amplitude of both currents in Cor.4U cells. We had to scale by a factor 0.69 to match the mean peak INa, and 0.80 to match the mean peak ICaL recordings. The simulated INa peaked at the same potential as the experimental data, suggesting the activation kinetics of INa in iCell and Cor.4U cell lines are similar. The simulated ICaL kinetics followed the Paci et al. (2013) model, and were left-shifted relative to experimental data. Further experiments established that this shift was due to a right-shift in the experimental IV curve due to Ba2<sup>+</sup> being present in the ICaL voltage clamp experiment bath solution (see Supplementary Figure S3), hence we do not adjust the kinetic terms and tailor only the maximum conductance.

# 3.2. The Outward Protocol Strongly Elicits IKs

**Figure 2** (left panel) shows the current measured with the outward-current protocol in a single Cor.4U cell. To analyse the composition of this current, we simulated the same protocol, and looked for a sum of scaled transmembrane currents from the Paci et al. (2013) model that gave a similar result (see section 2.5). We repeated this process for each of the 22 cells with measured outward current, and obtained the scaling factors s for each cell and current shown in **Table 2**. Note that the scaling factors s are relative to the original Paci et al. (2013) model. In many cases, the optimization routine indicated that the kinetic profile of certain currents was not discernible in the measured outward current. This is indicated in the table with a dash (—) for any scaling factor smaller than 10 -10. After seeing these results, as a comparison, we also tried fitting by varying only IKs and INaCa (and using the scaling factors for INa and ICaL determined previously), and the results are similar (see Supplementary Table S2).

For most cells, we found that the measured responses differed greatly, in both the shape and size of the currents, from the original model predictions (see Supplementary Figure S4), leading to a poor quality of fit (see Supplementary Figure S5). As a result, the best reconstructions of the simulated current relied almost entirely on a greatly amplified IKs current, along with strong INaCa, while other currents such as IKr and I<sup>f</sup> were notably absent. Based on this, we might assume that IKs and

FIGURE 1 | Current-voltage relationship for INa (left) and ICaL (right). The red lines represent the mean peak current measured experimentally in 35 (INa) and 25 cells (ICaL), and the shaded areas show the 25th and 75th percentiles of the experimental data. The peak-current voltage relation simulated with the unaltered Paci et al. (2013) model for the same protocol is shown in blue. The orange lines show the simulated results after scaling to match the maximum current.

examples of fits are shown in Supplementary Figure S5.

INaCa are more strongly expressed in Cor.4U cells than in the iCell cells the Paci et al. (2013) model was based on. As an initial verification of these findings, we repeated some outward current measurements in the presence of Chromanol (an IKs blocker), see Supplementary Figure S6 for an example where IKs is indeed significant. The near-zero contributions of other currents (e.g., IKr) does not imply that these currents are completely absent in Cor.4U cells, but instead suggests that the currents as simulated from the model could not be found in our recordings using the specified patch clamp protocol. This is a strong hint that changes to the kinetics of the currents will be required to accurately simulate the ion currents in Cor.4U cells at this temperature using the model by Paci et al. (2013). Such a mismatch in kinetics would also explain the large remaining errors between measurements and fit seen in Supplementary Figure S5, causing other currents, such as IKr, to be fitted as absent. This is discussed further in section 4.4.

### 3.3. Tailored Models

We then created tailored models by modifying the original Paci et al. (2013) model in two ways: First, we scaled the maximum conductances of INa and ICaL by a factor 0.69 and 0.8 respectively, to match the averaged data from the inward current experiments. We then further modified this model to create 22 tailored models based on the 22 cells in which outward current was measured, by applying the IKs and INaCa scaling factors from **Table 2**.

# 3.4. Variability in Ioutward Predicts Variability in AP

Significant variability in the outward currents was observed among the Cor.4U cells. This can be seen from the scaling factors in **Table 2**, but it is also evident when directly inspecting the currents measured from different cells (see Supplementary Figure S5) or when looking at peak Ioutward (see Supplementary Figure S7).

**Figure 3** (left panel) shows APs simulated with the tailored models. A wide variety of APs could be seen, with some models showing a spike-and-dome waveform, some showing a more triangular waveform, and with a varying slope in resting potential (leading to different degrees of auto-excitation). Some models also show beat-to-beat alternans, or fail to completely depolarize. The corresponding contribution of the major currents throughout the APs are also shown in Supplementary Figure S8.

Recordings of APs in single iPSC-CMs show a similar variety of AP waveforms. **Figure 2** (right panel) shows APs measured in 7 different iCell iPSC-CMs. Again, various waveform morphologies (roughly corresponding to atrial, ventricular and sinoatrial node APs) and differing levels of auto-excitability can be distinguished. Whilst these recordings are for a different cell line than our tailored models, the inter-cell variability in channel expression within a batch of iPSC-CMs has not been observed to be markedly different between cell lines (see e.g., the relative size of the "error bars" in Figure 2 of Blinova et al., 2017).

# 3.5. Tailored Models Improve Predictions of APD

**Figure 4** (left panel) shows the median of all simulated traces as shown in **Figure 3**, along with the 25th and 75th percentiles. The optically recorded APs from the Cor.4U cells were plotted on the same graph (the median shown as black line and the 25th and 75th percentiles shown as gray shading). Due to the increased outward current, the tailored models exhibit a shorter APD than the original model, that matches the measured APDs more closely in the early and late repolarization phase. A histogram of APDs in measured and simulated cells is shown in **Figure 4** (right panel), with the blue line representing the result from the original model. A similar histogram for APD<sup>50</sup> is shown in Supplementary Figure S9.

# 3.6. Tailored Models Can Give Better Prediction of Drug Block Effects

**Figure 5** shows the dose-response curves of the APD<sup>90</sup> of four drugs, measured experimentally and simulated using the original and tailored models. Equivalent results using the of the APD<sup>50</sup> are shown in Supplementary Figure S9. Results for the control drug paracetamol are shown in Supplementary Figure S10. For all four drugs tested, although not fitting the experimental data exactly, the tailored models match the measured data more closely than the original model. For Dofetilide in particular, the tailored models show a realistically smaller increase in APD than the original model, which shows alternans and then repolarization failure at higher drug concentrations. For Quinidine, although the tailored models do not fit better at the highest concentration, we improve the predictions at lower concentrations.

Predictions made with the adult-CM model by O'Hara et al. (2011) are shown for comparison. Note how the adult CM model predicts APD prolongation with Verapamil, whereas both the tailored and original iPSC-CM models accurately predict the shortening that is observed in iPSC-CM optical mapping. Such qualitative differences highlight the need for models specific to iPSC-CMs to interpret experimental findings in these cells.

# 4. DISCUSSION

Pre-clinical studies with iPSC-CMs can be used to evaluate proarrhythmic risk of compounds at the early drug discovery and development phase for compound optimization, and these experimental results can directly contribute to the design of safe

cell-specific Cor.4U models exhibit a variety of AP waveforms. Right: Experimentally measured APs in seven individual iCell iPSC-CMs also show significant variability.

measurements, but the distribution is centred appropriately.

first-in-human doses. Ideally, for reliable risk identification and translation, the electrophysiology of iPSC-CMs should accurately reflect that of adult cardiomyocytes. Yet the characteristics of iPSC-CMs are influenced by donor genetic background as well as differentiation and maturation protocols, and so differences between iPSC-CM cell lines may be expected, as well as differences from adult CMs. Mathematical models of the cellular AP can be used to gain mechanistic insight into such differences and to build a quantitative translational framework between iPSC-CMs and human adult CMs.

In this study we compared novel measurements in Cor.4U iPSC-CMs with predictions from a model based on the iCell cells. We found a decrease in INa and ICaL current densities, but a large increase in IKs and more modest increases in INaCa. Using the simple method of scaling maximum conductances without altering ion current kinetics—we created models tailored to individual iPSC-CMs. The obtained fits were not optimal, which suggests that the ion current kinetics in the iCellcell based model by Paci et al. (2013) do not closely match those in Cor.4U cells. However, like real iPSC-CMs, these tailored models show differences in AP from cell to cell, with AP waveforms broadly similar to ventricular, atrial and sinoatrial-node APs. The predicted single-cell APD<sup>90</sup> was shorter in tailored models than in the original model, and showed a better match with optical mapping measurements in electrotonically-coupled iPSC-CM cultures. The effects of Dofetilide, Quinidine, Sotalol and Verapamil on APD were simulated, and again the tailored models provided a closer fit. These results show that there are important electrophysiological differences between iPSC-CM cell lines, but that relatively simple adjustments to computational iPSC-CM models can already partially accommodate them. This has important implications for the suggested drug-screening workflows: one should really combine both iPSC-CM measurements and computational modeling of iPSC-CM for better interpretation of the iPSC-CM data in terms of its variability and translational power.

## 4.1. Cell-Line Differences in Ion Current Densities

We obtained maximum conductance values for the inward currents INa and ICaL that are lower than suggested by the Paci et al. (2013) model based on iCell cells, while IKs and INaCa were increased in most Cor.4U cells. The slight reduction in ICaL and increase in IKs suggests a decrease in APD. This was borne out by the AP simulations, and was consistent with our optical mapping measurements which showed shorter APDs compared to the AP simulated by the original Paci model. Our simulations displayed a similar degree of AP variability to the experimental iPSC recordings, but larger variability than the optical mapping measurements. Both findings are consistent given that electrotonic coupling of cells (present in the optical mapping experiments) reduces variability.

A potential explanation of the large IKs current is suggested by Lei et al. (2017). It shows that both the KCNQ1 and KCNE1 (subunits of the channel carrying IKs) were present in our Cor.4U cells, however, KCNE1 was not as well expressed in iCells. The difference in KCNE1 expression could lead to the observed larger IKs currents in the Cor.4U cells compared to iCells, and hence a shorter APD and less prolongation under IKr blockers, which is in agreement with Blinova et al. (2017). Our observation is supported by Silva and Rudy (2005) who found that native IKs (from channels comprised of both KCNQ1 and KCNE1) activates more than with KCNQ1 only.

FIGURE 5 | Dose-response curves of the APD90 for four drugs: Dofetilide, Quinidine, Sotalol, and Verapamil. The individual optical mapping measurements are shown as black dots, with the median shown as a dotted black line. Predicted responses from the original model are shown in blue, and the tailored model predictions are shown in orange (solid line is median and shaded region indicates 25th–75th percentiles. Models (tailored or original) that exhibited strong alternans (i.e., where only every second AP showed a spike-and-dome morphology) were omitted from the figure. Because this caused the number of predictions in the tailored model distribution to vary, the minimum and maximum number of predictions per drug is shown as *n* = *minimum* − *maximum*. At higher concentrations, Dofetilide block causes repolarization failure in both the original model and the O'Hara model.

# 4.2. Cell-to-Cell Differences in iPSC-CMs

iPSC cardiomyocytes, from the same donor and differentiated/matured in the same way, can display vastly different AP waveforms, reminiscent of those of ventricular, atrial, and sinoatrial-node cells. Our tailored models, created by varying the maximum conductances of INaCa and IKs, showed a similar model-to-model (cell-to-cell) variety in style of generated APs. This shows that variation in genetic expression, which correlates directly with maximum conductance (Schulz et al., 2006), could be enough to explain the different AP waveforms observed in iPSC-CMs. However, it does not preclude other explanations, and it is possible the APs could take on a more distinct shape if differences in ion channel kinetics were also included. As discussed in a recent white paper, the inclusion of cell-cell variability, as well as variability between cell lines is an important research area (Johnstone et al., 2016).

# 4.3. Predictions of Drug Action

The sharp increase in IKs seen in our Cor.4U tailored models suggests Cor.4U cells have a stronger reliance on IKs as a repolarizing force, and will therefore be less likely to show AP prolongation when treated with IKr blocking drugs (see, e.g., the Figure 5 of Blinova et al., 2017, which shows, for 8 out of 12 drugs with comparable concentrations and prolongation in iCells, the Cor.4U cells have a smaller APD prolongation than the iCells). Consistent with this suggestion, simulations of treatment with the potent IKr blocker Dofetilide showed only a modest increase in APD at concentrations that caused the iCell-cell based model to display excessive AP prolongation resulting in alternans. Treatment with Quinidine, a less potent IKr blocker, showed similar results. The modest APD increase predicted by the tailored models underestimated the APD prolongation observed in the data, suggesting the role of IKr as a repolarizing force was underestimated in these models. More refined experiments will

need to be conducted to separate the outward currents and to better estimate IKr conductance. Application of Verapamil, which blocks ICaL as well as IKr, had a smaller effect in our tailored models than in the original model, which is consistent with the lowered levels of IKr and ICaL.

The strong IKs-reliance we observed may be problematic when using these iPSC-CMs as models for ventricular myocytes, where IKs only plays a major part when other repolarizing currents are blocked or in the presence of sympathetic stimulation (Jost et al., 2005).

#### 4.4. Limitations and Future Work

This study showed the need to build cell-line or even cellspecific models for iPSC-CMs, and this work serves as a pilot attempt for such an approach. However, a refined study with additional experiments will be needed to improve the tailored models further.

As might be expected, the ion current profiles during voltage steps could not be recreated well using this approach. It is likely that ion channel kinetics also vary between cell lines due to (e.g.,) differences in subunit expression (Lei et al., 2017), although this could also be partly due to the difference of temperature, and that the model we used does not accurately capture the kinetics of ion currents in Cor.4U cells. Channel kinetics play an important role in the contribution of a current to the different phases of the AP. Modifying the kinetic parameters which characterize the voltage-current relationship for the activation, inactivation, deactivation, etc. of a channel could change both the current and the AP, and would influence responses to drugs. Varying the kinetic parameters would also alter the conductances we estimated by fitting the outward current. Further tailoring the models to include refitted kinetic parameters may lead to further improvements in predictive power. However, since models of ion channel kinetics contain many parameters, specifically designed experiments (e.g., with channel blockers and/or specialized voltage protocols) will be required to refine these tailored models.

The method of fitting multiple currents to a single experimental recording is a highly useful approach, as it reduces the number of experiments needed to tailor a model. However, due to the limitation of experiments being performed in different cells, we were not able to examine the covariance between the inward and outward currents. Also, since it depends on the number of current conductances to be fitted and the experimental data (e.g., the quality of the data and the actual current shape), one may run into problems of practical identifiability if one tries to refit kinetic parameters here (e.g., multiple combinations of conductance and kinetic parameters that can provide an equally good fit, as in Fink and Noble, 2009). Additional experimental data with refined experimental designs will be needed to identify all parameters; for example, to perform experiments with channel blockers to isolate the contribution of particular currents, or to iteratively refine the models using a dynamic clamp approach (Devenyi et al., 2017).

Variability/noise on drug-ion channel interaction parameters (IC50s) from different labs or repeats of experiments will also impact our simulation predictions. A probabilistic uncertainty quantification framework using the techniques proposed in Elkins et al. (2013), Johnstone et al. (2017) could be used in future to address this.

Our Cor.4U-tailored predictions of both baseline AP and drug responses matched the optical mapping data more closely than the un-tailored model. However, these optical mapping data were gathered from cultures of spontaneously beating electrotonically coupled cells, while our simulations are of paced single iPSC-CMs. Another avenue for future work would be to combine (a representative distribution of) tailored cell-specific models into heterogeneous tissue models (Bowler et al., 2016).

#### 4.5. Implications for Drug Testing

iPSC-CMs have gained significant popularity as an in vitro model for drug screening and, as one pillar of the CiPA strategy, are anticipated to become a routine part of the cardiac safety pipeline. It is therefore critical to understand how to interpret the iPSC-CM data variability (intra- and intercell line variability) and to translate these data to the adult human situation. Mathematical models are a promising tool to integrate data, gain mechanistic insights and perform this translation.

Our results show that differences between iPSC-CM cell lines can be analyzed and understood using tailored computational models. Furthermore, even models based on relatively simple methods (e.g., scaling maximum conductances) and a limited set of measurements (two inward current and one outward current experiments) can lead to improved predictions of baseline and drug-blocked electrophysiology parameters.

# 5. CONCLUSIONS

Using a combination of novel experiments and computational work, we have shown that Cor.4U cells display different ion current densities than the previously characterized model, which is based on iCell data. This included an increased reliance on IKs for repolarization with an accompanying decreased reliance on IKr. Incorporating these effects in cell-specific models of iPSC-CMs correctly predicted that this would lead to a shortening of the baseline APD and a reduced reaction to IKr-blocking drugs. These predictions were confirmed in optical mapping experiments with reference drugs, although further refinements to these methods are clearly needed. We conclude that tailoring models to specific cell lines—even with imperfect information will be a valuable tool for understanding the electrophysiology of iPSC-CMs and the actions of ion channel-blocking drugs.

# AUTHOR CONTRIBUTIONS

Conception—KW, DG, GM, LP; design—KW, DG, GM, LP; data collection—KW, RJ, MH-V, VZ, AA, GS, LP; analysis and interpretation—CL, KW, MC, RJ, DG, GM, LP; writing and review—CL, KW, MC, DG, GM, LP.

#### FUNDING

CL acknowledges support from the Clarendon Scholarship Fund, the Engineering and Physical Sciences Research Council (EPSRC) and the Medical Research Council (MRC) (Grant Number EP/L016044/1). KW was supported by a Roche Post-doctoral Fellowship. MC and DG acknowledge support from BBSRC grant BB/P010008/1. This work was supported by the Wellcome Trust [grant number 101222/Z/13/Z]: GM gratefully acknowledges support from a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society.

#### REFERENCES


#### ACKNOWLEDGMENTS

We thank Drs. Adrian Roth, Franz Schuler, Thierry Lavé, and Thomas Singer (F. Hoffmann-La Roche AG) for their scientific and managerial support.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.00986/full#supplementary-material


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cardiomyocytes: electrophysiological properties of action potentials and ionic currents. Am. J. Physiol. Heart Circ. Physiol. 301, H2006–H2017. doi: 10.1152/ajpheart.00694.2011


pluripotent stem cell-derived cardiomyocytes with arrays of microposts. J. Biomech. Eng. 136:051005. doi: 10.1115/1.4027145


optical mapping. Am. J. Physiol. Heart Circ. Physiol. 308, H1112–H1125. doi: 10.1152/ajpheart.00556.2014


**Conflict of Interest Statement:** LP and KW were employed by company F. Hoffmann—La Roche. MH-V, VZ, AA, and GS were employed by Clyde Biosciences.

The reviewer DK and handling Editor declared their shared affiliation, and the handling Editor states that the process met the standards of a fair and objective review.

The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Lei, Wang, Clerx, Johnstone, Hortigon-Vinagre, Zamora, Allan, Smith, Gavaghan, Mirams and Polonchuk. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Structural Immaturity of Human iPSC-Derived Cardiomyocytes: In Silico Investigation of Effects on Function and Disease Modeling

Jussi T. Koivumäki <sup>1</sup> , Nikolay Naumenko<sup>1</sup> , Tomi Tuomainen<sup>1</sup> , Jouni Takalo2,3 , Minna Oksanen<sup>1</sup> , Katja A. Puttonen<sup>1</sup> , Šárka Lehtonen<sup>1</sup> , Johanna Kuusisto<sup>4</sup> , Markku Laakso<sup>4</sup> , Jari Koistinaho<sup>1</sup> and Pasi Tavi <sup>1</sup> \*

<sup>1</sup> A.I. Virtanen Institute for Molecular Sciences, University of Eastern Finland, Kuopio, Finland, <sup>2</sup> Department of Biomedical Science, University of Sheffield, Sheffield, United Kingdom, <sup>3</sup> Biophysics, Department of Physics, University of Oulu, Oulu, Finland, <sup>4</sup> Institute of Clinical Medicine, Internal Medicine, University of Eastern Finland, Kuopio University Hospital, Kuopio, Finland

#### Edited by:

John Jeremy Rice, IBM, United States

#### Reviewed by:

Yael Yaniv, Technion – Israel Institute of Technology, Israel Divya Charlotte Kernik, University of California, Davis, United States Joshua Mayourian, Icahn School of Medicine at Mount Sinai, United States

> \*Correspondence: Pasi Tavi pasi.tavi@uef.fi

#### Specialty section:

This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology

Received: 10 October 2017 Accepted: 23 January 2018 Published: 07 February 2018

#### Citation:

Koivumäki JT, Naumenko N, Tuomainen T, Takalo J, Oksanen M, Puttonen KA, Lehtonen Š, Kuusisto J, Laakso M, Koistinaho J and Tavi P (2018) Structural Immaturity of Human iPSC-Derived Cardiomyocytes: In Silico Investigation of Effects on Function and Disease Modeling. Front. Physiol. 9:80. doi: 10.3389/fphys.2018.00080 Background: Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) have emerged as a promising experimental tool for translational heart research and drug development. However, their usability as a human adult cardiomyocyte model is limited by their functional immaturity. Our aim is to analyse quantitatively those characteristics and how they differ from adult CMs.

Methods and Results: We have developed a novel in silico model with all essential functional electrophysiology and calcium handling features of hiPSC-CMs. Importantly, the virtual cell recapitulates the immature intracellular ion dynamics that are characteristic for hiPSC-CMs, as quantified based our in vitro imaging data. The strong "calcium clock" is a source for a dual function of excitation-contraction coupling in hiPSC-CMs: action potential and calcium transient morphology vary substantially depending on the activation sequence of underlying ionic currents and fluxes that is altered in spontaneous vs. paced mode. Furthermore, parallel simulations with hiPSC-CM and adult cardiomyocyte models demonstrate the central differences. Results indicate that hiPSC-CMs translate poorly the disease specific phenotypes of Brugada syndrome, long QT Syndrome and catecholaminergic polymorphic ventricular tachycardia, showing less robustness and greater tendency for arrhythmic events than adult CMs. Based on a comparative sensitivity analysis, hiPSC-CMs share some features with adult CMs, but are still functionally closer to prenatal CMs than adult CMs. A database analysis of 3000 hiPSC-CM model variants suggests that hiPSC-CMs recapitulate poorly fundamental physiological properties of adult CMs. Single modifications do not appear to solve this problem, which is mostly contributed by the immaturity of intracellular calcium handling.

Conclusion: Our data indicates that translation of findings from hiPSC-CMs to human disease should be made with great caution. Furthermore, we established a mathematical platform that can be used to improve the translation from hiPSC-CMs to human, and to quantitatively evaluate hiPSC-CMs development toward more general and valuable model for human cardiac diseases.

Keywords: human induced pluripotent stem cell-derived cardiomyocytes, excitation-contraction coupling, arrhythmias, repolarization, computational modeling

# INTRODUCTION

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) have emerged as promising tools for cardiac research. In theory, hiPSC-CMs provide an accessible source of human cardiomyocytes without ethical and practical concerns that entail the use of human cardiac tissue or cells. From the experimental point of view hiPSC-CMs also solve the problems related with inter-species comparisons, thus enhancing the translation between basic research and clinical science. Moreover, since hiPSC-CMs retain the genetic identity of the individual donor, they enable generation of patient- and diseasespecific cells that can be employed in procedures of personalized medicine. While hiPSC-CMs have become useful and popular cellular models to study mechanisms of human cardiac diseases (Blazeski et al., 2012; Iglesias-García et al., 2013; Eschenhagen et al., 2015) and for drug screening (Zeevi-Levin et al., 2012; Engle and Puppala, 2013), increasing attention has been paid to the question how similar they are compared with the adult human cardiomyocytes (Knollmann, 2013; Hwang et al., 2015; Kane and Terracciano, 2015).

Initially, justification for using hiPSC-CMs as a model for human cardiomyocytes came from the notion that they express most of the basic components underlying excitation-contraction coupling, membrane voltage regulation and even signaling cascades of cardiac myocytes (Ivashchenko et al., 2013; Karakikes et al., 2015). Furthermore, hiPSC-CMs have ion currents for depolarization (INa, ICaL, I<sup>f</sup> ) and repolarization (Ito, IKr, IKs, IK1) of the membrane, which together produce, in subpopulations of hiPSC-CMs, action potential (AP) waveforms resembling that of human cardiomyocytes (Karakikes et al., 2015). hiPSC-CMs also express the central components of cardiac excitationcontraction (E-C) coupling, including L-type calcium channels and sodium-calcium exchangers (NCXs) (Ma et al., 2011; Yazawa et al., 2011; Zhang X.-H. et al., 2013; Uzun et al., 2016), as well as structures and proteins for sarcoplasmic reticulum (SR) calcium release and uptake (Germanguz et al., 2011; Itzhaki et al., 2011; Lee et al., 2011; Zhang X.-H. et al., 2013; Kim et al., 2015). However, the environment where all these components operate and interact differs substantially from the native or mature one. That is, compared to adult cardiomyocytes, hiPSC-CMs are much smaller and instead of having a rectangular shape they can also be round or polygonal (Hwang et al., 2015). Furthermore, iPSC-CMs lack a regular ultrastructure (Gherghiceanu et al., 2011; Itzhaki et al., 2011) and T-tubule network (Li et al., 2013; Kane et al., 2015). This results in poor co-localization of calcium channels and ryanodine receptors (RyRs) as well as non-uniform distribution of calcium release (Gherghiceanu et al., 2011; Rao et al., 2013). Therefore, in hiPSC-CMs the upstroke and decline rates of the whole-cell Ca2<sup>+</sup> signals are substantially slower than in adult cardiomyocytes (Lee et al., 2011; Hwang et al., 2015). The emerging function has characteristics not shared with adult cardiomyocytes such as spontaneous beating, depolarized diastolic membrane potential, flat action potential duration restitution, slow Ca2<sup>+</sup> signals and negative force-frequency relationship (Kane et al., 2015; Karakikes et al., 2015).

To evaluate quantitatively the translational potential of hiPSC-CMs, we constructed a mathematical model recapitulating their common in vitro features. Previous mathematical hiPSC-CM models focused mainly on the action potential morphology and sarcolemmal ion currents (Zhang H. et al., 2012; Paci et al., 2015). However, for a side-by-side comparison with detailed models of adult cardiomyocytes a more comprehensive hiPSC-CM model is required. One central feature to be included into such a model is a realistic representation of calcium dynamics, as well as cell-type-specific interplay between Ca2<sup>+</sup> signals and membrane voltage. Employing the novel in silico hiPSC-CM model in standard simulations, sensitivity analysis and construction of a screenable database enabled us to (1) study the physiological properties of hiPSC-CM, (2) probe the biological relevance of the phenotypic variability of hiPSC-CMs reported in vitro, (3) compare properties side-by-side to human adult ventricular (Grandi et al., 2010) and atrial (Grandi et al., 2011) myocytes as well as to embryonic cardiomyocytes (Korhonen et al., 2010), and (4) explore to what extent different heart diseases can be recapitulated in hiPSC-CMs.

# RESULTS

## Structural and Functional Characteristics of hiPSC Cardiomyocytes

The structural immaturity affects calcium-induced calcium release (CICR) and limits the maximum cycle frequency by posing a substantial delay of about 50–90 ms between the central and peripheral calcium signals (Lee et al., 2011; Zhang G. Q. et al., 2013). While RyR and SERCA (SR Ca2<sup>+</sup> ATPase) proteins are distributed throughout the cytosol (Ivashchenko et al., 2013) the bulk of the SR is located in the perinuclear region (**Figure 1A** and Supplementary Figure 1), with some extensions of SR throughout the cytosol (Itzhaki et al., 2011; Zhang X.-H. et al., 2013). In embryonic cardiomyocytes, with similar structures, the whole cell calcium transients are triggered from the perinuclear SR (Rapila et al., 2008) and the calcium propagation in the cytosol is boosted with local Ca2<sup>+</sup> releases from SR extensions (Korhonen et al., 2010). According to our 2-D calcium diffusion measurements (**Figure 1B**) the speed of Ca2<sup>+</sup> propagation in hiPSC-CMs (**Figure 1C**) is very similar to that of embryonic mouse myocytes both in vitro (Korhonen et al., 2010) and also when modeled in silico (Korhonen et al., 2010) (**Figure 1D**). Instead of pure diffusion, CICR underlies the "fire–diffusion–fire" propagation of the Ca2<sup>+</sup> wave inside hiPSC-CMs.

Although hiPSC-CMs express a functional pacemaker current (If ), the density of the current is not sufficient on its own for spontaneous action potential (AP) generation (Kim et al., 2015). Spontaneous activation of hiPSC-CMs thus relies on interaction between the "Ca2<sup>+</sup> clock" and the "membrane clock," similar sinoatrial node cells (SANCs) (Maltsev and Lakatta, 2013). Indeed, stabilization (Kim et al., 2015) or inhibition (Kim et al., 2015; Zhang et al., 2015) of RyRs, as well as SERCA inhibition (Zhang et al., 2015) all reduce or abolish spontaneous activity in hiPSC-CMs. This suggests that automaticity depends on spontaneous Ca2<sup>+</sup> release from SR initiated by activity of both

FIGURE 1 | Calcium handling characteristics of hiPSC-CMs. (A) Representative confocal image from a hiPSC-CM immunostained with SERCA2a antibody and line plots illustrating the localization of the stain in the cells. (B) Recording of calcium diffusion in hiPSC-CM; from left to right: fluorescence reference image (orange line: line-scan place), photograph of the experimental setup (yellow arrow—patch pipette), line-scan recording obtained during injection of 1µM Ca2<sup>+</sup> solution from patch pipette, and line-scan profile at two different position (blue arrow—near the injection place, red—near central SR). (C) The time-to-target plots for average in vitro (mean ± SEM, n = 10) and in silico data are very similar to previously published mouse embryonic ventricular myocyte data from Korhonen et al. (2010). (D) Schematic presentation of the in silico hiPSC-CM model components and geometry, for the acronyms and detailed description of the model components, please see Methods section. Ca2<sup>+</sup> concentrations in the central sarcoplasmic reticulum and two local release sites at 2 and 4µm distance from the sarcolemma (E) and in the cytosol (F), at 1 Hz pacing. (G) Comparison of AP characteristics in the hiPSC-CM model (red bars) to in vitro data (blue bars; mean ± SEM) listed in Supplementary information, Supplementary Table 4.

RYRs and inositol-1,4,5-trisphosphate receptors (IP3Rs) (Itzhaki et al., 2011). That is, released calcium increases the cytosolic calcium concentration ([Ca2+]i) and triggers a depolarizing current via sodium-calcium exchanger (NCX) (Kim et al., 2015), serving as a trigger for AP. In line with previous reports (Fine et al., 2013; Zhang X.-H. et al., 2013), our data shows a strong expression (Supplementary Figure 1) and function (Supplementary Figure 2) of NCX in hiPSC-CMs. Furthermore, immunostaining of IP3R shows their strong presence around the nucleus (Supplementary Figure 1), confirming previous findings (Itzhaki et al., 2011).

Based on this data we constructed the new model by first merging the cell geometry and ultrastructure of mouse embryonic myocyte model (Korhonen et al., 2010) with the membrane electrophysiology of a recent hiPSC-CM model (Paci et al., 2015) (**Figure 1D**). After this step, extensive model parameter fitting was done based on our own in vitro measurements and literature data (Supplementary Tables 1– 3). The resulting model recapitulates the central immature characteristics of hiPSC-CMs, such as spontaneous activity (Kim et al., 2015) and inhomogeneous subcellular calcium distribution (Lee et al., 2011; Zhang G. Q. et al., 2013) (**Figures 1E,F**, **2A** and Supplementary Figure 3). Moreover, basic characteristics of calcium signaling parameters, such as calcium transient and caffeine pulse decays and ratio between SR and SL calcium fluxes, are in line with the in vitro values (Supplementary Figures 2A–C). Finally, as the comparison of AP characteristics with literature data shows, the hiPSC-CM model is well within the range of reported in vitro values (**Figure 1G**, Supplementary Table 4).

# Mode of Activation Alters Membrane Currents and Calcium Cycling

A common feature of hiPSC-CMs separating them from mature atrial or ventricular CMs is their spontaneous beating. In literature, it appears that experimental results obtained in both modes of excitation, spontaneous and stimulated, are considered equivalent. Also in our in silico model, the AP morphology varies rather little depending on mode of activation (**Figure 2B**). AP amplitude and upstroke velocity are smaller in spontaneous vs. paced mode, while AP duration is almost identical. However, the fundamental ion currents and order of their activation are quite different depending on mode of activation (**Figures 2D–F**). In the spontaneous mode, the excitation trigger is the calcium release from the SR (**Figures 2A,C**), and thus the first membrane current to activate is INCX (**Figure 2D**). In the paced mode, the activation sequence is reversed and therefore the timing and dynamics of intracellular calcium is different, resulting in smaller calcium removal (18%, forward) and entry (54%, reverse) via NCX in spontaneous than paced mode. Depolarization of the membrane potential leads to activation of INa, which then further leads to activation of ICaL. As the rate of depolarization is much slower in spontaneous vs. paced mode, the amplitude of INa is drastically smaller, −91%, (**Figure 2E**); a result of a phenomenon known as accommodation. The same phenomenon, affects ICaL and Ito amplitudes as well, which are 45 and 54% smaller in spontaneous vs. paced mode, respectively (**Figures 2E,F**). The total sodium and calcium entries are only 3 and 17% smaller, respectively, in the spontaneous mode and the amplitude of the calcium transient (CaT) is only 10% smaller in the spontaneous vs. evoked mode.

Longer time course and altered timing of CaT in respect to AP also impacts the AP repolarization in spontaneously activated cells, enhancing calcium extrusion by NCX, which causes a depolarizing inward current at the late repolarization phase, thus creating a "tail" for the AP (**Figure 2B**). While this difference is subtle, it has a significant effect on excitability, as the availability of INa, and thus refractoriness, has a very steep dependence on membrane potential in this voltage range (Skibsbye et al., 2016). NCX function is also strongly affected by the diastolic membrane potential, which is typically depolarized by up to 30– 40 mVs in hiPSC compared adult CMs (Supplementary Figure 8). The detailed analysis show that forward mode is hampered and reverse mode enhanced at more depolarized potentials (Supplementary Figure 8F).

Sensitivity analysis of the hiPSC-CM model activated with either of the two modes demonstrates that if the cell is activated spontaneously, the AP parameters (triangulation, APtri and duration, APD90) depend more on NCX current and less on potassium currents (IKr, IK1) compared to stimulated cells (**Figure 2G**). These findings highlight that the impact of any intervention aimed at modulating a specific component in hiPSC-CMs E-C coupling will depend on whether the cells are spontaneously active or electrically stimulated.

#### Functional Dissimilarities of hiPSC-CM Compared to Adult Human Cardiomyocytes

To elucidate the contribution of basic components to calcium cycling, we simulated the effect of 50 and 90% block of ICaL, NCX and SERCA (**Figures 3A–D**). While some of the changes are similar, the effect of ICaL block on AP amplitude and duration is more dramatic in hiPSC-CMs (**Figure 3B**) and blocking of SERCA reduces the CaT amplitude much more in adult CM (**Figure 3D**). Sensitivity analysis (**Figure 3E** and Supplementary Figures 4A–D) indicates that the contribution of ICaL on CaT is more significant in adult CMs. In hiPSC-CMs, APD is much more sensitive to changes in the rapid delayed rectified (IKr) and inward-rectified (IK1) potassium currents, indicating that adult CMs have a stronger repolarization reserve. According to a sensitivity analysis based similarity index (**Figure 3F**), the AP of hiPSC-CM shares underlying mechanisms with both adult ventricular and atrial CMs, while the CaT dependencies are more similar between adult ventricular and atrial CMs than between hiPSC-CMs and either adult cell type. Interestingly, even though mouse embryonic cardiomyocytes lack two potassium currents (Ito, IKr), hiPSC-CMs appear to be functionally very similar with mouse embryonic myocytes as well (Supplementary Figure 4).

### Limited Translation of Pathology from hiPSC-CMs to Adult Cardiomyocytes

To assess the translational potential of hiPSC-CMs and directly compare hiPSC-CMs and adult cardiomyocytes to each other, we next implemented the modifications involved in Brugada Syndrome (BrS), Long QT Syndrome (LQTS) and catecholaminergic polymorphic ventricular tachycardia (CPVT).

We simulated BrS by replicating a Navβ1b/H162P mutation (Yuan et al., 2014) (**Figure 4A**). In hiPSC-CMBrS model variant, the normal activation of INa does not elicit an AP (Supplementary Figure 5A). However, it is possible to overcome the increased

FIGURE 2 | Two modes of Excitation-Contraction coupling in hiPSC-CMs. (A) Transient increase of intracellular Ca2<sup>+</sup> concentration and Ca2<sup>+</sup> diffusion in spontaneous (left) and paced (right) mode in silico measurements. The spatiotemporal representation is analogous to a line scan measurement in vitro. (B) AP in spontaneous (left) and paced, 1 Hz, (right) modes. (C) Ca2<sup>+</sup> concentration in central sarcoplasmic reticulum and two local release sites at 2 and 4µm distance from the sarcolemma. Sodium-calcium exchanger current (D), sodium and calcium current (E), and transient outward and delayed rectified potassium currents (F) in spontaneous (left) and paced (right) mode. The values in legends (D,E) indicate the ion flux integral over one AP cycle. Note: the direction of INCX in paced mode changes biphasically, while the spontaneous mode involves three phases. (G) Heatmap presentation of correlation coefficients of varied cellular components with eight different biomarkers in spontaneous (left) and paced (right) mode. MDP, minimum diastolic membrane potential; APamp, amplitude of the action potential; DDRtrimax, maximum diastolic depolarization rate; APtri, action potential triangulation; APD90, action potential duration at 90% repolarization; Cadias, minimum calcium concentration during diastole; CaTamp, amplitude of the calcium transient.

excitation threshold by using a stronger stimulus current, which depolarizes the membrane potential enough to activate the ICaL (Supplementary Figure 5C). Interestingly, the AP morphology in the hiPSC-CMBrS model differs very little from the control (**Figure 4A**). The peak of AP is reached 3.9 ms later and there is a slight deceleration of the late phase of AP repolarization (APD<sup>90</sup> +10%, +25.2 ms). In adult CM, BrS blunts the initial spike of AP and slows the late repolarization slightly more (APD<sup>90</sup> +14%, +35.8 ms). INa is so small in hiPSC-CM, and BrS reduces it even further to the extent, that ICaL becomes the predominant depolarizing current (**Figure 4B**).

In a previously reported LQT2 mutation (c.A2987T KCNH2), the conductance of IKr was reduced by 33%, which resulted in increased action potential duration in hiPSC-CMs in vitro (APD<sup>50</sup> +38% and APD<sup>90</sup> +41%) (Bellin et al., 2013). The simulations with hiPSC-CMLQT2 model replicates those

ventricular (haV) myocyte, hiPSC vs. human adult atrial (haA) myocyte, and human adult ventricular vs. atrial myocyte.

findings nicely (APD<sup>50</sup> +29% and APD<sup>90</sup> +60%, **Figures 4C,D**). However, running the same simulations with the adult CM model predicts substantially smaller changes (APD<sup>50</sup> +13% and APD<sup>90</sup> +12%, **Figure 4C**). This finding demonstrates that the repolarization reserve is much smaller in hiPSC-CMs compared to adult CMs, which also causes arrhythmias in the virtual hiPSC-CMLQT2 cell (Supplementary Figure 6).

Next, we simulated CPVT-type arrhythmias in hiPSC-CM and adult CMs with randomly timed SR Ca2<sup>+</sup> releases via RyRs (**Figures 4E–H**). According to the simulations, due to

c.A2987T KCNH2 mutation on AP repolarization in hiPSC (left) and adult (right) cardiomyocytes in silico. (D) AP duration in silico and in vitro mean ± SEM, as reported by Bellin et al. (2013). (E) Sarcoplasmic reticulum Ca2<sup>+</sup> release (Jrel) caused by random RyR openings (CPVT-like condition) in hiPSC (left) and adult (right) cardiomyocytes in silico. (F) Example of a primary (1) and secondary (2) Jrel in hiPSC-CM during one AP cycle. (G) Early and delayed after depolarizations in hiPSC (left) and adult (right) CM in silico. (H) Arrhythmogenic coupling efficiency (ACE) in hiPSC and adult CM, quantified as deviations in membrane voltage compared to control, is much stronger in hiPSC-CMs.

the self-propagating nature of the hiPSC-CM calcium release (**Figure 1**), spontaneous RyR openings result in a complete release of SR calcium and whole cell CaT (**Figures 4E,F**). Moreover, as NCX has a larger role in calcium cycling of hiPSC-CMs (**Figure 3**), they are more prone to extra SR calcium release (Jrel) induced membrane depolarizations CMs (**Figure 4E**) and have a higher arrhythmogenic coupling efficiency (ACE) than adult CMs (**Figures 4G,H**).

#### Immature E-C Coupling Is the Limiting Factor of hiPSC-CM Functional Phenotype

As hiPSCs are differentiated into hiPSC-CMs with variable techniques in different laboratories, they display a wide range of phenotypes (**Figure 5A** and Supplementary Tables 1–4). To analyse this huge variability, we created a database (Prinz et al., 2003) of 3,000 in silico hiPSC-CMs (**Figure 5B**), in which the parameter space was defined based on >25 publications (Supplementary Tables 1–4). As the time period of differentiation is variable in the published data, the resulting parameter space covers a wide field of theoretically possible hiPSC-CMs phenotypes. I<sup>f</sup> and IKs conductances were not varied in the database, as in the in vitro ranges they had virtually no effect on the AP dynamics, please see section Database Simulations and Sensitivity Analysis for further details. We ran simulations both in the spontaneous and evoked/paced mode for all the virtual cells in the database. Some combinations of parameter values resulted in nonviable phenotypes (exclusion criteria described in section Materials and Methods). As a result, the number of viable in silico cells in database was reduced from 3,000 to 940 and 235 in the evoked (freq = 1 Hz) and spontaneous mode, respectively (**Figures 5D,E**).

One of the key features of mature myocardium and cardiomyocytes is AP duration restitution (APDR): action potential becomes shorter, when the heart beat rate or the pacing frequency is increased (Figure 5 in Grandi et al., 2010). Thus, we explored the in silico database to see what kind of parameter value combinations would result in such a phenotype. In the database, it is possible to plot a biomarker such as APD<sup>90</sup> (APD at 90% repolarization) as a function of the parameters that have

database analysis. (C) 3D surface plot of APD90 as a function of three ion current parameters. The variable color of the data points is not quantitative or related to the color bar scale. Instead, it is just a way to increase the contrast of the dots against the surfaces. Histograms of maximum diastolic potential (D) and AP peak potential (E) in spontaneous and paced modes. Histograms of maximal frequency of AP duration restitution (APDR) (F) and force-frequency response (FFR) (G). Maximum pacing frequency for monotonic APDR and FFR. (H) Relative parameter values in the (1) spontaneous and (2) paced modes, as well as, (3) in the monotonic APD restitution and force-frequency response subpopulations, compared to the whole database.

been varied to build the population of models (**Figures 5A,C**). While there are a small number of cells that had a monotonically decreasing AP duration even up to ∼2 Hz (**Figure 5F**), APD restitution is relevant only if there is a positive force-frequency relation (FFR) as well. Monotonically positive FFR was present up to 1.4 Hz (**Figure 5G** and Supplementary Figure 7) in the in silico cell database. Cross-comparison of the APDR and FFR subcollections showed that just 30 of 3,000 virtual cells recapitulated these basic features. The average parameter values of INa (+13%), IKr (+5%), IK1 (−59%), NCX (−10%) and SERCA (+16%) were statistically different (p < 0.05) in the spontaneously active subpopulation of 235 cells compared to the whole database (**Figure 5H**, blue bars). In the paced mode, the subpopulation of virtual cells with proper excitability (n = 940) had smaller, yet statistically significant deviations in the average parameter values for INa (+4%), IKr (+3%), IK1

(−40%), NCX (−3%) and SERCA (+3%). Surprisingly, cell variants recapitulating APDR+FFR (n = 30) had only a stronger IK1 (18%) and a weaker SERCA (−20%) (**Figure 5H**, red bars). From those 30 APDR+FFR in silico cells only two had an APD<sup>90</sup> in the range of 250–300 ms. Interestingly, both of these ideal in silico hiPSC-CMs actually have about 40% smaller IK1 current density than on average in the database (**Figure 6A**), which contradicts the view that weak IK1 would be one of the limiting immature features of hiPSC-CMs (Meijer van Putten et al., 2015; Vaidyanathan et al., 2016). A side-by-side comparison shows that even though there is a rather good match in AP morphology with adult CM, the underlying ion currents and dynamics of the ideal hiPSC-CM still differ substantially from their mature counterparts (**Figure 6**). As in previous comparison scenarios, it appears that the ultrastructure-related differences in intracellular calcium handling cannot be overcome.

We also repeated the simulations with Brugada syndrome, LQT2 and CPVT-like model variants using a parameter combination that was found to be most favorable in the database analysis. The simulation shown in Supplementary Figure 9

FIGURE 6 | Comparison of ideal hiPSC-CM and adult CM in silico. (A) The most favorable parameter combination (red line) plotted with the full parameter range of the database on background (gray bars). Action potential (B), calcium transient (C), sodium current (D), calcium current (E), sodium-calcium exchanger current (F) transient outward, rapid and slow delayed rectified potassium currents (G–I), inward rectified potassium current and sodium-potassium pump current (J), and RyR-mediated Ca2<sup>+</sup> release fluxes from the sarcoplasmic reticulum (K). In the hiPSC-CM model, there are three spatially distinct release locations, as described in detail in Figure 1.

indicate that the hiPSC-CM model with ideal parameters is slightly closer to the adult CM phenotype. That is, in the hiPSC-CMBrS model, INa persists as the main depolarizing current. In the virtual hiPSC-CMLQT2 cell, increase of APD is also slightly smaller than in the model that has average parameters. However, the susceptibility to arrhythmogenic CPVT-like events is not changed.

#### DISCUSSION

Human iPSC-cardiomyocytes have emerged as popular cell models to study a variety of human cardiac diseases as well as for drug testing. In theory, hiPSC-CMs provide the first routinely accessible equivalent for native human cardiac myocytes, and solve the problems related to inter-species comparisons, which potentially hinder the development of therapies for human diseases. However, as more hiPSC-CM data is cumulating, concerns have risen regarding whether they are useful models for studying arrhythmias (Knollmann, 2013; Sinnecker et al., 2013) and electrophysiology (Han et al., 2014; Christ et al., 2015), or if their calcium signaling is comparable with that of adult cardiomyocytes (Hwang et al., 2015; Kane and Terracciano, 2015). To address these open questions, we have developed a novel mathematical model that recapitulates the functional characteristics of hiPSC-CMs, allowing us to compare them systematically and quantitatively with their adult counterparts.

# How Does Immaturity of hiPSC-CMs Shape Calcium Dynamics?

According to our in silico analysis, many of the immature functional features are related to structures involved in intracellular calcium handling. Adult cardiomyocytes are relatively large cells, capable of generating strong, spatially homogenous Ca2<sup>+</sup> signals at high frequency (Cannell et al., 1995; Bers, 2002). Although hiPSC-CMs express the same components for calcium handling, their Ca2<sup>+</sup> signals are substantially slower and show much higher degree of spatial inhomogeneity (Li et al., 2013) (**Figures 2**, **3**). This is not a surprise since spatiotemporal properties of calcium signals are not only affected by the efficiency of release and uptake but also Ca2<sup>+</sup> propagation in the cytosol, which is relatively slow (diffusion constant ≈ 30 ms/µm) even at short (<15µm) distances and is exponentially slower at longer distances (Korhonen et al., 2010). To overcome this biophysical obstacle, adult ventricular cardiomyocytes have unique cell membrane invaginations called T-tubules, which form a 3-D structure linking membrane and SR Ca2<sup>+</sup> channels, thus minimizing the calcium diffusion distances in the cytosol (Cannell et al., 1995; Bers, 2002). Even though hiPSC-CMs have subcellular structures for enhancing Ca2<sup>+</sup> propagation (**Figure 1** and Supplementary Figure 1), the lack of T-tubules has profound functional effects. Firstly, there is a substantial delay of about 100 ms between the central and peripheral calcium signals (**Figures 1**, **2**), which poses an absolute lower limit for the length of single E-C coupling cycle, and thus limits the maximal beating rate (**Figure 5**) (Korhonen et al., 2010). Secondly, this delay slows down the upstroke and decline rates of the whole cell CaTs in hiPSC-CMs, making them substantially slower than adult cardiomyocytes (**Figure 3**) (Lee et al., 2011; Hwang et al., 2015). This may appear as a minor detail, however, slower CaT kinetics change the timing of [Ca2+]<sup>i</sup> -dependent currents during AP. Therefore, e.g., INCX contributes much more to the late AP repolarization in hiPSC-CMs than in adult CMs (**Figure 3**). In addition, compared to adult CMs, hiPSC-CMs rely more on sarcolemmal (ICaL, INCX) than SR (RyR) calcium sources (**Figure 3**) (Lee et al., 2011). Importantly, larger INCX enhances the link between [Ca2+]<sup>i</sup> and V<sup>m</sup> and thus makes hiPSC-CMs more susceptible to after depolarization-triggered arrhythmias such as those triggering CPVTs (**Figure 4**). These features are important to consider, as hiPSC-CM should reflect the electrical stability/instability of adult human CMs, when they are used for drug testing or disease modeling.

### What Are the Functional Implications of Spontaneous vs. Evoked Mode in hiPSC-CMs?

While hiPSC-CMs are excitable and capable for CICR upon electrical excitation, one sign of their immaturity is that alongside with the normal E-C coupling they have the ability to generate spontaneous calcium oscillation for pacemaking (**Figure 2** and Supplementary Figure 3) (Kane et al., 2015). Our detailed comparison of two modes of hiPSC-CMs activation (spontaneous vs. evoked) shows that there are substantial differences in the dynamics and magnitudes of ion currents, even though AP morphology was roughly similar in both modes (**Figure 2**). In the spontaneous mode, the rate of depolarization is much slower than in paced mode, during both triggering and upstroke phase of the AP. This causes a so-called accommodation phenomenon to happen in many of the ion channels: activation is so slow that inactivation starts to take place simultaneously. Therefore, the amplitudes of INa, ICaL and Ito are drastically smaller in spontaneous than paced mode. There is also a subtle difference in the final phase of AP repolarization: in the paced mode hiPSC-CMs display a very slow "tail" in the AP. As there is a very steep dependence of INa availability on membrane potential in this voltage range, this influences cardiac refractoriness, contrary to adult human ventricular CMs. It is important to consider these mode-dependent mechanisms, when utilizing hiPSC-CMs in experiments. For example, in drug screening, the effect of an ion channel blocker will be different in spontaneous vs. evoked mode of activation of the cells.

## How Well Do Pathologies Translate from hiPSC-CMs to Adult Cardiomyocytes?

Human-iPSC-CMs exhibit a heterogeneous phenotype, usually representing a mixed population of cells with diverse electrophysiological characteristics (Ivashchenko et al., 2013; Uzun et al., 2016). While the profile of ion channel expression is qualitatively similar to adult CM, the functional immaturity of hiPSC-CMs has raised concerns about their usability as disease models. Our analysis of BrS, LQT2 and CPVT scenarios confirms the doubts (**Figure 4**). For example, implementing a Brugada syndrome associated loss-of-function INa into the hiPSC-CM model reduces the excitability drastically and ICaL becomes the main depolarizing current instead of INa, which does not happen in adult CMs. The LQT2 simulation results demonstrate concretely the effect of a much smaller repolarization reserve in hiPSC-CMs, which together with the immature calcium handling makes them also much more sensitive to repolarization abnormalities, such as spontaneous SR Ca2<sup>+</sup> release events in CPVT.

#### What Are the Building Blocks of a Mature as Possible hiPSC-CM Phenotype?

Clearly, the electrophysiological differences between hiPSC-CMs and adult CMs complicate the comparison of these two cell types. Among the attempts aimed at reducing these differences, increased density of inward rectifying potassium current, IK1, has gained a lot of attention. As IK1 is important in stabilizing the resting membrane potential in adult cells, enhancing its magnitude has the potential to stop spontaneous beating of hiPSC-CMs (Meijer van Putten et al., 2015; Vaidyanathan et al., 2016). However, our database analysis suggests that modification of IK1, or any other ion current, is not enough to induce functional properties characterizing adult CMs such as action potential duration restitution or force-frequency relationship in hiPSC-CMs. Single modification of any of the varied parameters do not appear to solve these problems, which are mostly contributed by the immaturity of intracellular calcium handling.

Conclusive consensus of the physiological properties of hiPSC-CMs is lacking partly because the reported in vitro data is rather variable. As long as standardized experimental protocols do not exist, wealth of the variability originates form divergence of the maturity of cells used and the experimental conditions. Therefore, validation of hiPSC-CMs as a human cardiomyocyte model should take into account the variability as one of the features the hiPSC-CMs. Database analysis was used here to simulate the impact of the variability in the reported hiPSC-CM parameters to the phenotype of the cells. In practice, database analysis answers the question: what is the best possible hiPSC-CMs phenotype that the current methods can produce? Only 30 out of 3,000 parameter combinations produced a phenotype with fundamental physiological cardiomyocyte properties (APD restitution and FFR), and only in a very limited frequency range (up to ∼1.5 Hz). Even though, the analysis was done in "ideal conditions": the variables did not have any interdependence, i.e., all of them were varied independently, which is not likely the case in biological context. This finding also raises anticipation for the more advanced, and hopefully standardized, hiPSC-CM maturation protocols that are expected to deliver more mature-like cardiomyocytes.

#### Limitations of the Study

The chamber-specificity of hiPSC-CMs is a rather controversial topic, and there is no standard way for making this distinction. The most common way has been to use some sort of AP morphology index; however, this simplified technical approach has been rightfully criticized (Kane and Terracciano, 2017). Therefore, we opted not to implement separate atrial- and ventricular-like hiPSC-CM model versions. When reliable quantitative physiological criteria for determining the chamberspecificity have been established and taken into use, the developed hiPSC-CM model should be updated to have atrialand ventricular-like versions accordingly.

We have not done a detailed comparison of the mechanisms of the "Ca2<sup>+</sup> clock" and the "membrane clock" in hiPSC-CM vs. SANC. An in-depth analysis of the principal cellular components contributing to spontaneous activation would be very interesting and timely, as a model incorporating more in vitro human SANC data was recently published (Fabbri et al., 2017). However, this kind of a comparison is beyond the scope of this study.

Cellular signaling forms another layer of complexity to the regulation rhythmic activity in cardiomyocytes. As more in vitro hiPSC-CM data emerges on phosphatases, Ca2+/calmodulindependent protein kinase II, Phospholipase C pathway, guanylate cyclase, etc., the developed hiPSC-CM model needs to extended so that it can be employed in future research on those topics.

The spontaneous activation frequency of the novel hiPSC-CM model is 45.1 BPM, which is within the range of values reported in vitro (Supplementary Table 4). Accordingly, pacing experiments could not be simulated at 0.5 Hz frequency, which has been used in many in vitro studies. Instead, we used 1 Hz as the standard pacing frequency.

In the database simulations, the sample size of the spontaneously beating virtual cells was significantly smaller (n = 235) than the subpopulation that had proper excitability under pacing conditions (n = 940). However, in both scenarios, deviations of the same five parameter values (INa, IKr, IK1, NCX, and SERCA) from the average still reached statistical significance. Furthermore, the more focused analysis was done with the paced virtual cell population. So, the starting size of the database (n = 3,000) should not affect the conclusions made in that part of the study.

#### Conclusion and Future Perspectives

The presented computational platform provides a quantitative tool for assessing hiPSC-CM properties, as well as comparing and translating hiPSC-CM findings to adult CMs. Our analysis suggests that the physiological properties of hiPSC-CMs differ from adult CMs in a way that warrants caution. As hiPSC-CMs show less robustness and greater tendency for arrhythmic events than adult CMs, translation of findings from e.g., particular ion channel mutation or pharmacological interventions is not straightforward. There is variability between different cell lines and culture conditions; however, the main bottleneck appears to be the structural immaturity of hiPSC-CMs. Recent efforts by multiple laboratories have succeeded in producing hiPSC-CMs with features, including e.g., functional T-tubule development (Parikh et al., 2017), more mature-like excitability (Lemoine et al., 2017) and contractile function (Mannhardt et al., 2016). This study provides a useful modeling framework for analyzing and improving those methods and techniques further.

# MATERIALS AND METHODS

# Derivation of Induced Pluripotent Stem Cells

Healthy fibroblast donor was recruited from Kuopio University Hospital (Kuopio, Finland; Approved by the committee on Research Ethics of Northern Savo Hospital district (license no 64/2014). Written informed consent was obtained from the donor. Skin biopsy derived fibroblasts were reprogrammed with CytoTune <sup>R</sup> iPS Sendai Reprogramming kit (Thermo Scientific, MA, USA) as previously described (Holmqvist et al., 2016), with slight modifications. Briefly, fibroblasts (1 × 10<sup>5</sup> ) were transduced with 3 or 4 separate vectors including the four Yamanaka factors OCT-3/4, KLF-4, SOX-2 and c-MYC. One week after transduction, 0.75 × 10<sup>5</sup> cells were seeded on the top of mitotically inactivated (10µg/ml mitomycin-C for 2.5 h in 37◦C) human foreskin fibroblast feeder cells (CRL-2429, ATCC, Manassas, VA) growing in 10 cm petri dish. First colonies started to appear a week later, and they were re-seeded by picking up individual colonies. The pluripotency of created hiPSC line was assessed as in our earlier studies (Qu et al., 2013).

# Maintenance of iPS Cells and Cardiomyocyte Differentiation

IPS cells were maintained in mTESR1 medium (Stem Cell Technologies, Canada) on human recombinant laminin-521 (Biolamina, Sweden) coated dishes at 37◦C in a humidified 5% CO<sup>2</sup> incubator. Cells were passaged with Tryple Express dissociation reagent (Thermo Fisher Scientific, MA, USA) 1–2 times a week just before cultures became confluent. Cells used in this study were between passages 5 and 23.

IPS cells were differentiated into cardiomyocytes using a protocol based on modulation of Wnt pathway (Lian et al., 2012). After dissociation into single cell suspension with Tryple Express, cells were plated on Matrigel (Corning Incorporated, NY, USA) coated dishes in mTESR1 medium. When the cells had reached full confluency, medium was changed to RPMI medium [RPMI 1640 Medium (Thermo Fisher Scientific, MA, USA) 1X B27 (Thermo Fisher Scientific, MA, USA), 100 U/mL penicillin-100µg/mL streptomycin (Thermo Fisher Scientific, MA, USA)] supplemented with 12µM CHIR99021 (Tocris, UK). After 24 h, CHIR99021 was removed and cells were kept in RPMI medium for 48 h. Next, cells were incubated in RPMI medium supplemented with 5µM IWP2 (Tocris, UK) for 48 h, after which cells were kept in RPMI medium for 3–8 weeks, before preparing them for experiments.

For immunocytochemistry, patch-clamp and Ca2<sup>+</sup> imaging spontaneously contracting hiPSC clusters were dissociated to single cells with a solution containing 2 mg/mL collagenase type II (Worthington, NJ, USA) and 2 mg/mL pancreatin (Sigma-Aldrich, MO, USA). Cells were plated in RPMI medium on glass coverslips coated with laminin (Sigma-Aldrich, MO, USA) at a density that allowed analysis of single cardiomyocytes. Cells were kept in RPMI medium for 3–7 days after plating, after which solution was changed to serum containing medium {Dulbecco's Modified Eagle Medium (Thermo Fisher Scientific, MA, USA) [10% fetal bovine serum (GE Healthcare Life Sciences, UT, USA), 100 U/mL penicillin-100µg/mL streptomycin]}. Cells were kept in serum containing medium for another 3–10 days before immunological or live cell analysis.

#### Electrophysiological Recordings in Isolated hiPSC Cardiomyocytes Patch-Clamp Experiments

All experiments were carried out at 37◦C (TC2BIP, Cell MicroControls, USA). Coverslips with attached cells were transferred to the recording chamber (Cell MicroControls, USA, flow rate approx. 1–2 mL/min, chamber volume 0.4 mL) perfused with Dulbecco's modified Eagle medium plus glutamax I (DMEM, bubbled with 95% O2, 5% CO2). Whole-cell voltageclamp (Axopatch 200B, Digidata 1440A, Molecular Devices Inc., USA) was used for Ca2<sup>+</sup> current and current-clamp (I = 0) for action potential (AP) recordings. Patch electrodes (Harvard Apparatus, United Kingdom) were pulled and fire polished with Sutter P-97 (Sutter Instrument Company, Novato, CA). Patch electrodes for current recordings had resistances of 1.5–2.5 M and 5–7 M for AP recording and Ca2<sup>+</sup> solution injection. Recordings were carried out after a membrane rupture of 5 min. The cell capacitance and series resistance were compensated electronically. The cells with an unstable or high access resistance were discarded. Under voltage clamp control cells were held at −80 mV. Membrane capacitance and resistance were estimated in response to a 5 mV pulse. The current amplitudes were normalized to cell capacitance. Recordings were carried out at a sampling rate of 10 kHz, and low-pass Bessel filtered at 5 kHz was used.

#### L-Type Ca2<sup>+</sup> Current Recordings

To characterize the L-type Ca2<sup>+</sup> current (ICaL) we used the protocol described previously (Xu et al., 2011). The cells were perfused with Tyrode solution containing (in mM): 130 NaCl, 5.4 KCl, 1 CaCl2, 1 MgCl2, 0.3 Na2HPO4, 10 HEPES, and 5.5 glucose, pH 7.4 with NaOH, after establishment of whole-cell was switched to recording solution (solutions were bubbled with 100% O2). The internal solution contained (in mM): 110 CsOH, 90 aspartic acid, 20 CsCl, 10 tetraethyl ammonium chloride (TEA chloride), 10 HEPES, 10 EGTA, 5 Mg-ATP2, 5 Na2-creatine phosphate, 0.4 GTP-Tris, 0.1 leupeptin (pH 7.2 with CsOH) and bath solution: 125 N-methyl-glucamine, 5 4-aminopyridine, 20 TEA chloride, 2 CaCl2, 2 MgCl2, 10 glucose, 10 HEPES (pH 7.4 with HCl). After an initial 1-sec prepulse at −40 mV, Ca2<sup>+</sup> currents were elicited using 200-ms voltage steps from −30 to +50 mV in 10-mV increments. Voltage-dependence of inactivation was assessed by holding cells at various potentials from −40 to +10 mV for 2 s, followed by a 100-ms test pulse to +10 mV.

#### AP Recordings

Action potentials were elicited by a 1-ms current injection, and recorded using the current-clamp mode (Yang et al., 2005). Only well attached hiPSC-CMs with visible spontaneous contractions we included in the analysis. The cells that had APs without overshoots (peak amplitude at positive membrane potential) or/and with prominent membrane voltage drop were discarded. The intracellular solution contained (in mM): 120 K-aspartate, 8 KCl, 1 MgCl2, 7 NaCl, 2 Na2-phosphocreatine, 5 Mg-ATP, 0.3 Na-GTP, and 10 HEPES, (pH 7.2 with KOH) and the bath solution was DMEM.

# Confocal Calcium Imaging

Calcium imaging was performed as previously described (Mutikainen et al., 2016). Cardiomyocytes were loaded with Fluo-4-acetoxymethyl (AM)-ester (2µM, Invitrogen) in DMEM for 20 min in an incubator (37◦C, 5% CO2) and then coverslips with attached cells were placed into the recording chamber. Experiments were carried out after a period of 20 min to allow deesterification of the dye. [Ca2+]<sup>i</sup> measurement was performed with a confocal inverted microscope (FluoView 1000; Olympus, Japan). To measure myocyte calcium [Ca2+]<sup>i</sup> transients, the cells were excited at 488 nm and the emitted light (500–600 nm) was collected through water immersion 60X objective lens, using the line-scan mode. To stimulate the cells, myocytes were stimulated with 1-ms voltage square pulses (Grass stimulator, S48) 50% over the excitation threshold through platinum electrodes. In some experiments, caffeine (10 mM, Sigma) was applied directly to the studied area with a local perfusion manifold (Cell MicroControls, USA). Fluo-4 fluorescence intensity is expressed as an F/F0-ratio, where F is the background subtracted fluorescence intensity and F<sup>0</sup> is the background subtracted minimum fluorescence value measured from each cell at rest. The images were analyzed with FluoView and ImageJ (imagej.nih.gov/ij/) softwares.

#### Calcium Injections for Measuring Diffusion

The whole-cell voltage-clamp mode was used for 1µM Ca2<sup>+</sup> solution injection into fluo2-loaded cells (5µM; TEFLabs, Inc; Austin, USA). The pipette was attached to a membrane with a Giga-seal (>3G). Patch-pipettes were filled with injection solution containing (in mM): 0.84 CaCl2, 130 KCl, 5 Na2 creatine phosphate, 5 Mg-ATP2, 1 EGTA, 10 HEPES, pH 7.2 with KOH, 1.042µM free Ca2<sup>+</sup> (Smith et al., 1984). Injection of pipette solution was performed immediately after cell membrane rupturing, as previously described (Korhonen et al., 2010), by a 3 ms pressure pulse through pipette holder with microinjector (Picopritser II, Parker Instrumentation). The cells were held at a −70 mV.

#### Immunofluorescence Labeling

Cells cultured on glass coverslips were washed once with Dulbecco's phosphate buffered saline (PBS, Sigma-Aldrich, MO, USA), fixed with 4% paraformaldehyde (in PBS) for 5 min and permeabilized with 0.5% Triton-X (in PBS) (Sigma-Aldrich, MO, USA) for 10 min. Coverslips were washed twice with PBS for 5 min after which they were incubated with blocking buffer [PBS (10% FBS, 0.05% Triton-X)] for 1 h. After blocking, cells were incubated with primary antibody in blocking buffer for 1 h, washed, and incubated with secondary antibody in blocking buffer for 1 h. All labeling steps were performed at room temperature. Nuclei were stained with 14.3µM DAPI (Thermo Fisher Scientific, MA, USA). Primary antibodies used were: Serca2 ATPase (mouse monoclonal, ab2861, Abcam, UK) (1:500 dilution), Ryanodine receptor (mouse monoclonal, ab2827, Abcam, UK) (1:100), IP<sup>3</sup> receptor type 1 (rabbit polycolonal, ab111087, Abcam, UK) (1:100) and Sodium/calcium exchanger (mouse monoclonal, MA3-926, Thermo Fisher Scientific, MA, USA) (1:100). Secondary antibodies were, anti-Mouse IgG (goat polyclonal, A11001, Thermo Fisher Scientific, MA, USA) (1:750) and anti-Rabbit IgG (goat polyclonal, A21245, Thermo Fisher Scientific, MA, USA) (1:750).

# Statistics

Data and statistical analyses were made using Origin9 software (OriginLab Corp., Northampton, MA, USA).

# Novel in Silico hiPSC-CM Model

The usefulness of mathematical modeling as a tool requires that the fundamental properties of the cell are recapitulated accurately. In the special case of hiPSC-CMs, this means that the model needs to have a proper representation of the mechanisms of automaticity: the so-called calcium and membrane clocks. Previous mathematical hiPSC-CM models focused mainly on the action potential morphology and sarcolemmal ion currents (Zhang H. et al., 2012; Paci et al., 2015) and did not recapitulate the spontaneous SR Ca2<sup>+</sup> release, which is a central feature of hiPSC-CMs. Accordingly, we developed a new in silico model that merges the cell geometry and immature intracellular calcium handling of a previously published mouse embryonic ventricular myocyte model (Korhonen et al., 2010) with the membrane electrophysiology of a recent hiPSC-CM model (Paci et al., 2015), using the ventricular-like variant of that model (**Figure 1D**).

As shown by the time-to-target analysis of intracellular Ca2<sup>+</sup> diffusion (**Figure 1C**) and cell size comparison (Supplementary Figure 2I and Supplementary Table 3), the geometry and calcium handling of the embryonic cell model is applicable to hiPSC-CM modeling as well. Furthermore, to properly recapitulate the mechanisms of automaticity, three components of the electrophysiology part of the model were modified to be better in line with in vitro data (Supplementary Figure 2). Firstly, new formulation (Skibsbye et al., 2016) was adopted for the INa and fitted to the Ma et al. (2011) in vitro hiPSC-CM data. Secondly, the ICaL formulation with a new one (Koivumäki et al., 2014), and fitted the properties to our own in vitro data. Thirdly, activation kinetics of the funny current (I<sup>f</sup> ) were modified to be better in line with Sartiani et al. (2007) in vitro data.

The virtual hiPSC-CM model (**Figure 1D**) accounts for


Importantly, the novel in silico model recapitulates the mechanisms of automaticity, as reported in previous in vitro studies (Supplementary Figure 3). That is, a full block of sodium calcium exchanger (NCX) stops the spontaneous activity, while a partial I<sup>f</sup> block (corresponding to 3µM Ivabradine) has virtually no effect on automaticity (Kim et al., 2015). Recapitulating the cell-type-specific interplay between Ca2<sup>+</sup> signals and membrane voltage is a central requirement for making comprehensive in silico comparisons between adult CMs and hiPSC-CMs, both in physiological and pathophysiological scenarios.

The parameter values for the main ion currents were defined based on an exhaustive literature search, the results of which are shown in **Figure 5** and in the supplementary material (Supplementary Tables 1–4). The parameter set was frozen on 06/2016. The chamber-specificity of hiPSC-CMs is rather controversial topic, as there is no standard way for making this distinction (Kane and Terracciano, 2017). Furthermore, many of the publications do not make a distinction, so we decided not to do it either. This way we were able to include much more in vitro data for model parameterization.

The basic outputs of the average model, in spontaneous and evoked mode, are shown in **Figures 1**, **2**, **6B–K**.

Source code of the developed hiPSC-CM model will be freely available via email upon request, as well as distributed via the ResearchGate networking portal in Matlab format.

#### Experimental Protocols in Silico

Unless stated otherwise, all the in silico results were obtained either at spontaneous or stimulated steady-state. In the stimulated mode, action potentials were evoked by using a current pulse, whose amplitude was 1.5-times the threshold and length 0.5 ms. In the voltage clamp experiments (INa and ICaL), we used protocols and conditions identical to the in vitro measurements.

The following biomarkers were measured from the in silico data:


Caffeine application experiments were simulated by holding the RyR constantly open (50%), while blocking LTCC and SERCA. The time-to-target analysis of intracellular Ca2<sup>+</sup> diffusion was done from data obtained while holding the virtual cell in voltage clamp (Vhold = −80 mV). Time for Ca2<sup>+</sup> diffusion to a certain distance was defined with a threshold of 220 nM. A 2µM Fluo-4 (Kd = 335 nM) was included in the cytosolic Ca2<sup>+</sup> buffer composition. To mimic the Ca2<sup>+</sup> puff from the patch pipette, the L-type Ca2<sup>+</sup> channel held constantly open [ICaL = 0.5 <sup>∗</sup> (Vm - ECa)] for 10 ms.

To define the dependence of NCX function on diastolic membrane potential (Supplementary Figure 8), a standard current stimulus pulse was used together with steadily changing baseline. During the 60-s protocol diastolic membrane potential was depolarized from about −80 to about −60 mV.

To elucidate the contribution of basic calcium cycling components, we simulated the effect of 50 and 90% block of ICaL, NCX and SERCA (**Figures 3B–D**), both in the novel hiPSC-CM model and in the previously published human ventricular (Grandi et al., 2010) CM model. The blocking effects were implemented by reducing maximum conductance/current/turnover rate by either 50 or 90% from the control parameter value.

# Database Simulations and Sensitivity Analysis

We used both a conventional sensitivity analysis and the so-called database approach or population-based method for exploring biological robustness and variability. For the sensitivity analysis, we varied the parameter values for the maximum conductances of Ito, IKr, IK1, ICaL, and INa, as well as maximum transport rates of SERCA and NCX by ±10% (n = 14). Correlation coefficients were calculated using Matlab's built-in function corrcoef. Similarity index for APD<sup>90</sup> and CaTamp was calculated as a sum of the relative contribution of the seven cellular components on the chosen set of biomarkers (APD<sup>90</sup> and CaTamp).

In the database approach, we varied the same seven key parameters in the model according to available literature in vitro data (**Figure 5**, Supplementary Table 1). This experimentallycalibrated approach of creating a population of models was introduced by Prinz et al. (2003) in the context of in silico studies of neurons, and later applied also in computational cardiac studies by e.g., Romero et al. (2009).

We excluded the hyperpolarization activated or funny current (I<sup>f</sup> ) and slow delayed rectified potassium current (IKs) from the group of varied parameters. This was done to limit the computational load of database simulation, which is exponentially proportional to number of varied parameters. Also, the exclusion was physiologically justified, as changing I<sup>f</sup> and IKs conductances in the in vitro ranges had virtually no effect on the AP dynamics. Instead, we studied I<sup>f</sup> contribution separately to test if the current is large enough to contribute to spontaneous activity (Supplementary Figure 3E).

Database simulation were carried out with three protocols:


All simulations were started from the control 1 Hz pacing steadystate. The 260-s simulation duration was justified by the estimate that the time constants for settling of [Na+]<sup>i</sup> and [K+]<sup>i</sup> was about 130 s in the model. In the database simulations, we used a slightly larger current pulse (amplitude 2-times the threshold) to evoke action potentials. APD restitution was measured as the shortening of APD<sup>90</sup> and FFR as the increase of CaT amplitude (surrogate measure of force, as the model does not include the description of the contractile element).

#### Pathological in Silico Model Variants

We chose Brugada Syndrome (BrS), Long QT Syndrome (LQTS) and catecholaminergic polymorphic ventricular tachycardia (CPVT) as the three principal types of inherited arrhythmia that have electrical origin and manifest as abnormalities in excitation, repolarization and depolarization.

Multiple ion channel mutations are associated with BrS. We chose a Navβ1b/H162P (Yuan et al., 2014) mutation as an example case, in which the properties of INa are altered so that (1) current amplitude is reduced by 48%, (2) steady-state inactivation curve is shifted by 6.7 mVs toward negative potentials, and (3) slow and fast recovery from inactivation are 75 and 46% slower, respectively.

To quantify the effect of LQT2-associated c.A2987T KCNH2 mutation on AP repolarization in both hiPSC and adult cardiomyocytes, conductance of rapid delayed inward rectifying potassium current (IKr) was decreased by 33%, based on the in vitro data from Bellin et al. (2013).

CPVT-like conditions were elicited both in hiPSC and adult cardiomyocytes, by forcing random RyR openings and subsequent calcium releases from the SR. Early and delayed afterdepolarizations caused by forced random RyR openings (**Figure 4**). Arrhythmogenic coupling efficiency (ACE) was quantified as deviations in membrane voltage compared to control.

#### Human Adult Cardiomyocyte in Silico Models

To compare the hiPSC phenotype and human adult cardiomyocytes, we used the previously published ventricular (Grandi et al., 2010) and atrial (Grandi et al., 2011) cell

# REFERENCES


models. In the BrS, LQT2 and CPVT-like model variants, the same pathology related modifications of model parameters were implemented as in the hiPSC-CM model. We chose to use ventricular and atrial CM models from the same Grandi et al. model familiy, so that a direct comparison between human adult ventricular and atrial myocytes was possible.

#### AUTHOR CONTRIBUTIONS

Conception and design of the experiments: PT and JTK. Collection, analysis and interpretation of data: JTK, NN, TT, JT, JKu, ML, JKo, and PT. Drafting the article or reviewing it critically for important intellectual content: JTK, NN, TT, JT, JKu, ML, JKo, and PT. All authors approved the final version of the manuscript.

# FUNDING

This work was supported by Academy of Finland (#267637, to PT) Academy of Finland (#292540, to JKu, ML, JKo, PT) Sigrid Juselius Foundation (to PT), the Finnish Foundation for Cardiovascular Research (to JTK) and the Finnish-Norwegian Medical Foundation (to JTK).

## ACKNOWLEDGMENTS

We gratefully thank Anne Karppinen, Laila Kaskela, and Eila Korhonen for their outstanding technical assistance and Marika Ruponen, Marja Koskuvi, Yanyan Gao, and Ida Hyötyläinen for helping with characterizations of hiPSC cultures.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2018.00080/full#supplementary-material


pluripotent stem cells: comparative ultrastructure. J. Cell. Mol. Med. 15, 2539–2551. doi: 10.1111/j.1582-4934.2011.01417.x


temporal modulation of canonical Wnt signaling. Proc. Natl. Acad. Sci. 109, E1848–E1857. doi: 10.1073/pnas.1200250109


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Koivumäki, Naumenko, Tuomainen, Takalo, Oksanen, Puttonen, Lehtonen, Kuusisto, Laakso, Koistinaho and Tavi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing

Francis A. Ortega<sup>1</sup> , Eleonora Grandi <sup>2</sup> , Trine Krogh-Madsen<sup>3</sup> and David J. Christini 1, 3 \*

*<sup>1</sup> Physiology, Biophysics, and Systems Biology Graduate Program, Weill Cornell Graduate School of Medical Sciences, New York, NY, United States, <sup>2</sup> Department of Pharmacology, University of California, Davis, Davis, CA, United States, <sup>3</sup> Greenberg Division of Cardiology, Weill Cornell Medical College, New York, NY, United States*

Dynamic clamp, a hybrid-computational-experimental technique that has been used to elucidate ionic mechanisms underlying cardiac electrophysiology, is emerging as a promising tool in the discovery of potential anti-arrhythmic targets and in pharmacological safety testing. Through the injection of computationally simulated conductances into isolated cardiomyocytes in a real-time continuous loop, dynamic clamp has greatly expanded the capabilities of patch clamp outside traditional static voltage and current protocols. Recent applications include fine manipulation of injected artificial conductances to identify promising drug targets in the prevention of arrhythmia and the direct testing of model-based hypotheses. Furthermore, dynamic clamp has been used to enhance existing experimental models by addressing their intrinsic limitations, which increased predictive power in identifying pro-arrhythmic pharmacological compounds. Here, we review the recent advances of the dynamic clamp technique in cardiac electrophysiology with a focus on its future role in the development of safety testing and discovery of anti-arrhythmic drugs.

Keywords: dynamic clamp, cardiac electrophysiology, cardiac modeling, arrhythmia mechanisms, antiarrhythmic drugs, pharmacology & drug discovery

# INTRODUCTION

The search for successful anti-arrhythmia therapeutics is rooted in the voltage clamp and current clamp techniques, which have provided the mechanistic details behind the ionic membrane currents that compose the cardiac action potential (AP). While basic science has made great leaps in identifying and characterizing the basic factors involved in arrhythmia, the translation of these advances into successful therapies has been lackluster. Nonetheless, investigators have been using a combination of experimental and computational approaches to unravel the complex mechanisms underlying cardiac arrhythmia. Using this approach, experimental measurements, typically in single cells from mammalian hearts, are used to develop biophysically detailed mathematical models that can be scaled up to the tissue and whole-organ levels where arrhythmia occurs. Unlike experiments, computational modeling readily allows for the precise perturbation of particular parameters individually or in controlled combinations (simulating, e.g., the multifactorial nature of many disorders), but results are reliant on the accuracy of the model and its many components. The dynamic clamp technique is a merger between experimental and computational techniques that has been gaining traction as a hybrid method for elucidating

#### Edited by:

*Catherine Proenza, University of Colorado Denver, United States*

#### Reviewed by:

*Arie O. Verkerk, University of Amsterdam, Netherlands Andrew F. James, University of Bristol, United Kingdom T Alexander Quinn, Dalhousie University, Canada*

> \*Correspondence: *David J. Christini dchristi@med.cornell.edu*

#### Specialty section:

*This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology*

Received: *01 September 2017* Accepted: *13 December 2017* Published: *04 January 2018*

#### Citation:

*Ortega FA, Grandi E, Krogh-Madsen T and Christini DJ (2018) Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing. Front. Physiol. 8:1099. doi: 10.3389/fphys.2017.01099*

**323**

arrhythmia mechanisms and possible therapeutics.

Traditional patch clamp protocols are typically static and predetermined, such as sequential voltage steps used to study membrane current dependencies. Dynamic clamp is an extension of patch clamp, where measurements from the cell are used to modify a continuously changing experimental protocol in a real-time feedback loop (Robinson and Kawai, 1993; Sharp et al., 1993). Earlier work has shown broad application—coupling of separate cardiomyocytes through an artificial gap junction (Tan and Joyner, 1990; Joyner et al., 1991; Spitzer et al., 1997; Verheijck et al., 1998; Zaniboni et al., 2000; Huelsing et al., 2001), injection of measured current from a transfected cell into a primary isolated myocyte (Berecki et al., 2005, 2006), antrhomorphization of mouse cardiac APs (Ahrens-Nicklas and Christini, 2009; Bot et al., 2012), and more recently in the study of cardiomyocyte coupling to unexcitable cells (McSpadden et al., 2012) and fibroblasts/myofibroblasts (Nguyen et al., 2012; Brown et al., 2016). The history of dynamic clamp has been reviewed in detail elsewhere (Prinz et al., 2004; Wilders, 2006; Ravagli et al., 2016). Here, we focus on a specific configuration of this technique, called the dynamic model clamp (referred hereafter as dynamic clamp), where a mathematically based model of a conductance is injected to the cell in real-time. Characteristically, this mathematical model describes a specific voltage and time-dependent membrane current determined by a set of differential equations. Measured voltage of a cell in a patch clamp configuration is fed into a mathematical model at high rates, from which the calculated current is injected back into the cell (**Figure 1A**).

Central to the dynamic clamp experimental rig is the software, which acts as the interface between the patch-clamp hardware and mathematical models. Accurate and rapid sampling of the membrane potential and computation of the virtual conductance is required to mimic sufficiently a biological conductance (Bettencourt et al., 2008). These requirements necessitate hard real-time control. In this context, the feedback loop must complete every iteration within a specified time constraint, typically 50–100 µs (10–20 kHz) in cardiomyocyte dynamic clamp experiments, a feat not possible on standard operating systems and software due to technical limitations. The works discussed here predominately use two software platforms— DynaClamp (Berecki et al., 2005, 2006) and the Real-Time eXperimental Interface (RTXI, www.rtxi.org; Ortega et al., 2014; Patel et al., 2017). Both platforms utilize a customized real-time Linux operating system and are freely available.

In this review, we discuss how investigators have used the dynamic clamp technique to test theoretical drug targets, validate and improve existing cardiac mathematical models, and design assays for cardiotoxicity testing.

#### INVESTIGATION OF ARRHYTHMIA MECHANISMS

#### Drug Target Identification

Dynamic clamp studies on the cardiac L-type Ca2<sup>+</sup> current (ICaL) by Madhvani et al. identified arrhythmia mechanisms, which could potentially be targeted by anti-arrhythmic drugs (Madhvani et al., 2011, 2015). The authors specifically focused on the role of ICaL in the formation of early after depolarizations (EADs), i.e., secondary depolarizations during phase 2 and 3 of the AP resulting from a transient failure of AP repolarization. EADs are used as a marker of cardiac arrhythmia due to its propensity to trigger a premature AP and subsequently initiate cardiac arrhythmias, such as Torsades de pointes (TdP) or ventricular fibrillation, which in turn can lead to sudden cardiac death (Cranefield and Aronson, 1991). EADs require an inward current that can overcome and reverse repolarization, which can be fulfilled by ICaL, the major inward current during phase 2 and 3 of the AP. Madhvani et al. aimed to investigate the dependence of EADs on the biophysical properties of ICaL, but the lack of an assortment of drugs known to finely alter this current makes traditional patch clamp experiments impractical. Thus, to mimic theoretical perturbations to ICaL properties in vitro dynamic clamp was used instead.

In rabbit ventricular myocyte exhibiting EADs, induced with either hydrogen peroxide (**Figure 1B**, top) or hypokalemia, they replaced native ICaL (blocked with nifedipine) with a virtual model-based ICaL, which was injected using dynamic clamp (**Figure 1B**, middle). The consequences of alterations in ICaL biophysical properties were investigated by manipulating the parameters underlying the modeled current. For example, shifting the half-maximal activation voltage by 5 mV abolished EADs and returned AP duration (APD) to normal values (**Figure 1B**, bottom). Note that H2O<sup>2</sup> affects multiple inward currents in addition to ICaL, such as the late sodium current (Xie et al., 2009), but modification of ICaL alone was able to eliminate EADs.

The mechanistic basis for the observed behavior was established in earlier work describing a window current region between −40 and 0 mV (January and Riddle, 1989) where the steady-state activation and inactivation curves overlap. In this region, a fraction of the L-type Ca2<sup>+</sup> channels are not inactivated and available for possible reactivation and generation of an EAD. A positive shift in the steady-state activation curve reduces this window region and eliminates EADs. In their later work, Madhvani et al. systematically perturbed all ICaL model parameters and measured the consequences to EAD formation, confirming that parameter changes that reduced the window current region (depolarizing shifts to steady-state activation, or hyperpolarizing shifts to steady-state inactivation) were highly effective at EAD prevention (Madhvani et al., 2015). Based on these observations, the authors identified the purine analog Roscovitine, originally developed as an anti-cancer agent, as a promising anti-arrhythmic due to its ability to decrease the window current through a reduction to the late component of ICaL. Preliminary work has shown Roscovitine did indeed abolish EADs in myocytes and terminated ventricular tachycardia/fibrillation in whole rat hearts (Karagueuzian et al., 2017), supporting its therapeutic potential. Notably, this work illustrates a new paradigm in the search for new classes of anti-arrhythmic drugs.

Using a similar approach to the ICaL studies, Altomare et al. investigated the human ether-a-go-go related gene (hERG)

channel responsible for the rapid portion of the delayed rectifier K<sup>+</sup> current (IKr) (Altomare et al., 2015). Mutations and drug perturbations to IKr result in abnormal repolarization, clinically highlighted by long- or short- QT syndrome. The authors examined how IKr biophysical properties influenced APD and its temporal variability by blocking and subsequently replacing native IKr in guinea pig ventricular cardiomyocytes using dynamic clamp. The modeled current was shown to recover control AP parameters adequately, which reveals the properties described in the model are sufficient to describe the contribution of IKr to APD and its stability. The voltage and time dependent properties of IKr were systematically perturbed, and then compared to control and drug block conditions. This approach allowed a detailed examination of the consequences of each current property in isolation. The study showed both APD and its variability were most sensitive to changes to steadystate inactivation. Alternatively, while steady-state activation had little impact on APD, significant changes to APD variability were observed. This suggests that variability in APD, rather than mean APD, may be more sensitive in detecting IKr-dependent repolarization abnormalities.

Dynamic clamp has also been used successfully in studies of the transient outward K<sup>+</sup> current (Ito), where dynamic clamp was used to vary Ito conductance in ventricular (Dong et al., 2006, 2010; Nguyen et al., 2015) and atrial cardiomyocytes (Workman et al., 2012). Given the fact existing Ito blocking drugs are nonselective (Ridley et al., 2003; Aréchiga-Figueroa et al., 2010), these studies provided important insight into the relationship between Ito and the morphology and duration of the AP. Dong et al. sought to understand the impact of Ito on the mechanical properties of cardiomyocytes. Ito is responsible for the presence of the characteristic phase-1 notch of the AP, and conflicting evidence suggested notch prominence can either increase or decrease ICaL, respectively, enhancing or reducing contraction. Canine ventricular epicardial myocytes are characterized by a prominent phase-1 notch, which endocardial myocytes generally lack (Antzelevitch et al., 1991). By swapping Ito conductance levels of both cell-types using dynamic clamp, Dong et al. found that endocardial cells in which the small native Ito was substituted by a larger epicardial-like Ito displayed diminished contractility, and demonstrated that Ito acts as a negative regulator of contractility through reduction of ICaL peak magnitude (Dong et al., 2010).

Workman et al. investigated the influence of Ito on atrial arrhythmogenesis, a topic which was unclear due to the lack of Ito specific drugs (Workman et al., 2012). Reduction of Ito through dynamic clamp revealed AP prolongation, and additional β-adrenergic stimulation evoked EADs. Ito increase or exposure to the β-blocker atenolol prevented EAD formation. This suggests Ito enhancement holds promise in arrhythmia prevention, at least in the atrium. On the other hand, the dynamic clamp study by Nguyen et al. showed that Ito enhancement potentiated EADs in rabbit ventricular myocytes with reduced repolarization reserve, i.e., the intrinsic redundancy against excessive APD (Roden, 1998). By affecting the early AP phases, Ito augmentation can alter other voltage-dependent repolarization currents, leading to decreased late repolarization reserve and increased EAD formation (Nguyen et al., 2015).

It is important to note that the dynamic clamp technique suffers from a major limitation, i.e., the lack of ion selectivity in the current injection. Given physiological intracellular solutions contain predominantly K+, dynamic clamp of ICaL current will be carried mainly by K+, and not Ca2+. Thus, the simulated conductance—which should be Ca2+-dependent per se, is unable to trigger secondary intracellular Ca2<sup>+</sup> release and contraction. In an attempt to compensate for this limitation, Madhvani et al. simulated the intracellular Ca2<sup>+</sup> transient, which was then fed back into the ICaL model (Madhvani et al., 2011, 2015), whereas Devenyi et al. included ion selectivity in their simulations (Devenyi et al., 2017). While especially true for Ca2<sup>+</sup> due to its major role as a secondary messenger, caution should be applied when interpreting results of virtual conductance injection, as transient changes in intracellular concentrations can affect ion channel behavior.

# Improvement of Cardiac Computational Models

The Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative seeks to introduce a new cardiac drug safety testing paradigm that combines in vitro drug effects on multiple ion channels, computational modeling of cardiac currents and AP, and the use of human stem-cell derived cardiomyocytes (Sager et al., 2014; Colatsky et al., 2016). Computational modeling has proven to be a vital tool in cardiac arrhythmia research, and is expected to be instrumental in the future pipeline in drug testing. Confidence in model accuracy is directly tied to dynamic clamp results, as errors in the formulation of the mathematical model used can skew results. However, this limitation can be exploited because only accurate models can fully rescue behavior after drug block.

Ravagli et al. compared two computational models of the hyperpolarization-activated funny current, I<sup>f</sup> (Ravagli et al., 2016), which plays a major role in the pacemaker activity current of sinoatrial node (SAN) cells. The authors used a dynamic clamp rescue experiment, where ivabradine was used to partially block I<sup>f</sup> current, and a dynamic clamp injected model current was used to rescue control behavior. They showed one model significantly outperformed the other by restoring spontaneous activity in SAN cells, identifying the more accurate mathematical formulation of their experimental data. Bartolucci et al. used this strategy to validate an optimized formulation of the IKr current (Bartolucci et al., 2015). The original Luo-Rudy model (Luo and Rudy, 1994), derived from voltage clamp step protocols (Sanguinetti and Jurkiewicz, 1990), fit poorly to their experimentally measured IKr current data obtained with AP clamp. After optimization to the AP clamp data, their new model strongly diverged from the widely used Luo-Rudy formulation and fully reversed IKr block during dynamic clamp.

Devenyi et al. used dynamic clamp to artificially scale multiple cardiac currents in guinea pig ventricular myocytes using a single whole cell model (Devenyi et al., 2017). Altogether, this amounted to a rapid and efficient testing of multiple computationally-based hypotheses within the same cell under static conditions. By comparing their experimental results of the current perturbations to the predicted results from the computational model, the authors noted significant discrepancies (**Figure 1C**). First, the basal APD was shorter, and second, current perturbations in the experiment were generally larger than predicted by the model. The authors then used the new experimental data to reparameterize the model through unbiased fitting with a genetic algorithm, yielding a new model that could recapitulate the experimental data well. Interestingly, while the original model had a large ratio between the slow (IKs) and rapid (IKr) portions of the delayed rectifier K<sup>+</sup> current, the fitting consistently reversed this ratio. This finding was then verified experimentally, and further in-silico investigation into the consequences to cardiac arrhythmia showed IKs is better able to prevent EADs during increased L-type Ca2<sup>+</sup> current.

These studies illustrate how dynamic clamp can be used to experimentally validate computational models, which are typically built from heterogenous data sets spanning numerous experiments, under consistent conditions. Thereafter, new data can be used to further refine the models and advance mechanistic understanding.

#### DRUG SAFETY TESTING PLATFORMS

Dynamic clamp has also been utilized in the development of new assays for assessment of drug proarrhythmic risks. The current regulatory framework used to prevent approval of drugs with the potential to induce TdP is focused on two main areas: the propensity of the drug to block the hERG channel in vitro, and whether the drug prolongs the QTc interval of the ECG. Though largely successful at preventing proarrhythmic drugs from entering the market, the approach has been criticized due to its low specificity, as hERG block and QT prolongation do not always carry torsadogenic risk (Sager et al., 2014; Colatsky et al., 2016). Consequently, it is generally agreed that many promising drugs that may have little arrhythmogenic risk have their development terminated due to failing either criteria. As mentioned previously, the CiPA initiative considers human stem-cell derived cardiomyocytes a key component in future drug safety assays (Sager et al., 2014; Colatsky et al., 2016), and dynamic clamp has been used to address key limitations.

Human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CMs) are being used as an alternative to traditional animal models, cell lines, and heterologous expression systems in the study of cardiac electrophysiology mechanisms and druginduced arrhythmia. Due to the inherent difficulty in obtaining human cardiac tissue for study, hiPSC-CMs may provide an accessible source of human cell lines and includes the additional capacity to produce patient-specific lines. However, as with human embryonic stem cell derived cardiomyocytes, hiPSC-CMs exhibit an immature phenotype. These cells are stereotypically characterized by spontaneous activity, elevated maximum diastolic potentials, low maximum upstroke velocity, and highly variable APD (Hoekstra et al., 2012). A major contributing factor for these issues is hiPSC-CMs lack of the inward rectifying K<sup>+</sup> current (IK1), which plays a major role maintaining a stable resting potential in quiescent cardiomyocytes (Doss et al., 2012). The lack of IK1 is a cumulative issue, in that a generally depolarized membrane potential influences other cardiac currents, such as lowering the availability of fast Na<sup>+</sup> channels due to inactivation, which reduces upstroke velocity.

Bett et al. implemented a dynamic clamp based approach to resolve the immaturity issue in hiPSC-CMs through the addition of a virtual IK1 current (Bett et al., 2013). The original erratic AP morphology of hiPSC-CMs (**Figure 2A**) was transformed to an AP profile similar to those seen in adult human cardiomyocytes (**Figure 2B**), with a stable resting membrane potential and fast upstroke velocity. Seeking to test the impact of the dynamic clamp transformation in response to drug perturbation, hiPSC-CMs were exposed to the Ca2<sup>+</sup> agonist BayK-8644 at room temperature. Without dynamic clamp, drug addition ceased spontaneous AP generation (**Figure 2C**) most likely due to BayK-8644 induced Ca2<sup>+</sup> loading. This is in stark contrast to what is expected from ventricular cardiomyocytes in humans and other mammalian species, where an increase in depolarizing Ca2<sup>+</sup> currents is expected to increase APD and abnormal activity, such as EADs. With IK1 dynamic clamp, however, APD prolongation is evident in stimulated APs (**Figure 2D**). This illustrates that while hiPSC-CMs are sensitive to BayK-8644, lack of IK1 can mask the relevance of drug effects.

Building upon this work, Putten et al. used multiple IK1 models in their dynamic clamp experiments to examine the impact of varying degrees of rectification (Meijer van Putten et al., 2015), a biological feature of the IK1 current due to differential expression of the channel (Kir2.x) subunits (Wang et al., 1998). Additionally, IK1 channelopathies were investigated by modifying their Kir2.1 model to represent gain-of-function and loss-of-function mutations. The gain-of-function mutation was based on the E299V mutation associated with short QT syndrome 3, and the loss-of-function mutation was based on the heterozygous dominant-negative mutation in KCNJ2 associated with Andersen-Tawil syndrome. The top panel of **Figure 2E** plots the different current-voltage relationships of the modified models. The bottom panel of **Figure 2E** shows the corresponding APs when these models are used in the calculation of the virtual IK1 current during dynamic clamp. Consistent with short QT, the gain-of-function mutation significantly decreased APD, while the loss-of-function had only a marginal effect.

More recently, hiPSC-CM studies augmented with IK1 dynamic clamp have provided insight into cardiac abnormalities such as Brugada syndrome (Veerman et al., 2016), long QT syndrome (Rocchetti et al., 2017), and familial atrial fibrilliation (Marczenke et al., 2017). While ion channel dysfunction has been associated with Brugada Syndrome, mainly the cardiac fast Na<sup>+</sup> current, Veerman et al. found no clear cellular electrophysiological abnormalities in patient-derived hiPSC-CMs, suggesting that other factors, such as fibrosis, could also be underlying mechanisms (Veerman et al., 2016). Rocchetti et al. recently studied hiPSC-CMs derived from a long QT patient carrying a heterozygous mutation in one of the three calmodulin encoding genes (Rocchetti et al., 2017). The patient-specific cells exhibited prolonged APD and failure to shorten with increased pacing rate, which the study linked to impairment of Ca2+-dependent inactivation of ICaL. The ICaL blocker verapamil reversed mutation-induced repolarization abnormalities. Marczenke et al. explored the role of mutations of the KCNA5 gene, encoding the channel responsible for the ultrarapid delayed rectifier K<sup>+</sup> current, in familial atrial fibrillation (Marczenke et al., 2017). The authors generated a functional KCNA5 knockout hiPSC-CM line combining CRISPR/Cas9-mediated mutagenesis and atrial- or ventricularspecific differentiation through manipulation of retinoic acid signaling (Devalla et al., 2015). They observed a strictly atrialspecific disease phenotype, where atrial KCNA5 knockout hiPSC-CMs exhibited prolonged APD and EADs at low stimulation frequencies vs. insignificant changes in the ventricular variant. These works highlight the potential of hiPSC-CMs in cardiac patient-specific and subtype-specific disease modeling.

IK1 dynamic clamp is becoming more common to hiPSC-CM studies to reduce variability in experimental metrics, eliminate spontaneity due to elevated resting membrane potential, and yield a more physiological relevant phenotype. Verkerk et al. systematically analyzed the impact of IK1 dynamic clamp on AP characteristics in atrial and ventricular hiPSC-CMs, and provided an in-depth comparison of the methodology and experimental variability of the studies discussed above (Verkerk et al., 2017). While IK1 dynamic clamp appears to reduce the variability of most AP parameters, enthusiasm of reducing the large experimental variability of hiPSC-CMs is tempered by the observation that APD variability is not affected. However, elimination of spontaneous depolarizations allows for stimulus at static frequencies, permitting investigation into rate-dependence. More importantly, static pacing reduces beat-to-beat variability, granting a greater ability to detect AP parameter changes. Verkerk et al. also investigated the impact of different mathematical formulations of the injected

IK1 current, by comparing the models used in several studies discussed previously (Bett et al., 2013; Meijer van Putten et al., 2015; Rocchetti et al., 2017). Not surprisingly, the parameter selection of IK1 current density and kinetics can influence relevant AP metrics. Conversely, the flexibility inherent to model modification provides a means to tailor the IK1 current to specific cell types, such as ventricular or atrial.

The low throughput of dynamic clamp is a major limitation to its use as part of a drug testing hiPSC-CM platform. Techniques to increase maturation and IK1 density, such as 3D culturing (Lemoine et al., 2017) and adenovirus-mediated overexpression of IK1 (Vaidyanathan et al., 2016), may circumvent the need for dynamic clamp, but are currently not widely used. Automated patch clamp offers a possible route to increase throughput, but brings a new set of issues, such as interfacing with proprietary equipment and the use of single suspended cells. In a promising recent advance, Goversen et al. have successfully combined IK1 dynamic clamp with automated patch clamp of hiPSC-CMs, suggesting the feasibility of high-throughput application as a drug testing platform (Goversen et al., 2017).

In summary, dynamic clamp has been utilized in a number of exciting studies to address some of the inherent limitations of hiPSC-CMs, suggesting a promise as a component of safety pharmacology testing. Furthermore, the ability to modify the underlying mathematical models to examine channelopathies expands the capabilities of this platform.

# CONCLUSION

By coupling mathematical models with biological experiments, dynamic clamp has provided a powerful tool in the search for potential anti-arrhythmic therapies through modelbased perturbations, enhanced hiPSC-CMs as a platform for pharmacological safety testing, and used to clarify and improve mathematical models of cardiac electrophysiology. Dynamic clamp allows fine manipulation of numerous parameters like in-silico studies, but is performed in the context of experimental biology. This approach has enabled investigators to test theoretical perturbations in real-time and in live cells, and the power of this technique is represented by the broadness seen in the studies discussed here. It is expected dynamic clamp will continue to elucidate the mechanisms underlying cardiac arrhythmia and identify novel drug targets, and could evolve into a high-throughput assay, e.g., on automated patch clamp platforms to improve maturity of hiPSC-CMs.

# AUTHOR CONTRIBUTIONS

FO, EG, TK-M, and DC all contributed to the planning, writing, and editing of the manuscript and figures contained herein.

#### REFERENCES


#### FUNDING

This work was funded by NIH grants U01HL136297 (to DC) and R01HL131517 (to EG), and the American Heart Association (15SDG24910015 to EG).


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Ortega, Grandi, Krogh-Madsen and Christini. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A Hybrid Model for Safety Pharmacology on an Automated Patch Clamp Platform: Using Dynamic Clamp to Join iPSC-Derived Cardiomyocytes and Simulations of Ik1 Ion Channels in Real-Time

#### Edited by:

Blanca Rodriguez, University of Oxford, United Kingdom

#### Reviewed by:

David Christini, Weill Cornell Medical College, Cornell University, United States Antonio Zaza, Università degli studi di Milano Bicocca, Italy Patrick M. McDonough, Vala Sciences, United States

#### \*Correspondence:

Teun P. de Boer t.p.deboer@umcutrecht.nl

† These authors have contributed equally to this work.

#### Specialty section:

This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology

Received: 29 June 2017 Accepted: 12 December 2017 Published: 19 January 2018

#### Citation:

Goversen B, Becker N, Stoelzle-Feix S, Obergrussberger A, Vos MA, van Veen TAB, Fertig N and de Boer TP (2018) A Hybrid Model for Safety Pharmacology on an Automated Patch Clamp Platform: Using Dynamic Clamp to Join iPSC-Derived Cardiomyocytes and Simulations of Ik1 Ion Channels in Real-Time. Front. Physiol. 8:1094. doi: 10.3389/fphys.2017.01094 Birgit Goversen1†, Nadine Becker 2†, Sonja Stoelzle-Feix <sup>2</sup> , Alison Obergrussberger <sup>2</sup> , Marc A. Vos <sup>1</sup> , Toon A. B. van Veen<sup>1</sup> , Niels Fertig<sup>2</sup> and Teun P. de Boer <sup>1</sup> \*

<sup>1</sup> Division of Heart & Lungs, Department of Medical Physiology, University Medical Center Utrecht, Utrecht, Netherlands, <sup>2</sup> Nanion Technologies, Munich, Germany

An important aspect of the Comprehensive In Vitro Proarrhythmia Assay (CiPA) proposal is the use of human stem cell-derived cardiomyocytes and the confirmation of their predictive power in drug safety assays. The benefits of this cell source are clear; drugs can be tested in vitro on human cardiomyocytes, with patient-specific genotypes if needed, and differentiation efficiencies are generally excellent, resulting in a virtually limitless supply of cardiomyocytes. There are, however, several challenges that will have to be surmounted before successful establishment of hSC-CMs as an all-round predictive model for drug safety assays. An important factor is the relative electrophysiological immaturity of hSC-CMs, which limits arrhythmic responses to unsafe drugs that are pro-arrhythmic in humans. Potentially, immaturity may be improved functionally by creation of hybrid models, in which the dynamic clamp technique joins simulations of lacking cardiac ion channels (e.g., IK1) with hSC-CMs in real-time during patch clamp experiments. This approach has been used successfully in manual patch clamp experiments, but throughput is low. In this study, we combined dynamic clamp with automated patch clamp of iPSC-CMs in current clamp mode, and demonstrate that IK1 conductance can be added to iPSC-CMs on an automated patch clamp platform, resulting in an improved electrophysiological maturity.

Keywords: automated patch clamp electrophysiology, cardiomyocyte, stem cell, dynamic clamp, inward rectifying potassium ion channels, safety pharmacology

# INTRODUCTION

The Comprehensive In Vitro Proarrhythmia Assay (CiPA) initiative aims to find new means of predicting the proarrhythmic risk of newly developed drugs (Gintant et al., 2016), which do not rely exclusively on hERG block, and not on QT prolongation at all. Key aspects are to include results of computer simulations of drug effects on heart rhythm and in vitro assays using human stem cell-derived cardiomyocytes (hSC-CMs).

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Characterization of the hSC-CM electrophysiological phenotype has so far shown that these CM express most, but not all cardiac ion channels, which has implications for their use in safety pharmacological assays (Jonsson et al., 2012; van den Heuvel et al., 2014). Importantly, the inward rectifying potassium current, IK1 (de Boer et al., 2010), that is highly expressed in adult CMs is not, or hardly, expressed by hSC-CMs (Doss et al., 2012; Goversen et al., 2017), while the pacemaker current I<sup>f</sup> is expressed consistently. As a result, hSC-CMs display a pacemaker-like phenotype, with a depolarized and unstable resting membrane potential, resulting in spontaneous triggering of action potentials. This is an important issue, as the action potential waveform affects the activity and availability of many cardiac ion channels, as these are voltage-sensitive and rely on a negative resting membrane potential between beats to recover from inactivation after an action potential. For example, in hSC-CMs, sodium channel availability during the action potential is minimal, even though the channels are expressed in sufficient levels. As a consequence, we found in a previous study that, except for drugs blocking the hERG channel, none of the tested drugs that are known to be proarrhythmic in adult cardiomyocytes triggered arrhythmias (early-afterdepolarizations) in hSC-CMs (Jonsson et al., 2012). More recent studies have found that iPSC-CMs are not sufficiently mature to detect risks associated with inhibition of the late sodium current (Blinova et al., 2017), or peak sodium current (Ando et al., 2017). Interestingly, adenovirus mediated overexpression of IK1 channels in iPSC-CM was demonstrated to improve drug responses (Li et al., 2017).

Several approaches are being adopted to improve the electrophysiological phenotype, for instance overexpression of the IK1 channel, which has shown promising results (Vaidyanathan et al., 2016). Another, more controllable approach is to use dynamic clamp to add simulated IK1 channels to hSC-CMs (Wilders, 2006; Ortega et al., 2017). The essence of dynamic clamp is that a hybrid model is created by connecting a real cell with a computer simulation of (parts of) a cell. For this to work, one needs a computer simulation that is running in real-time—simultaneously with the experiment on the real cell so there is an instantaneous interaction between the real cell and the simulation. This works well, and has been described by several groups that applied it in manual patch clamp experiments (Bett et al., 2013; Meijer van Putten et al., 2015). Addition of simulated or overexpressed IK1 channels results in a stable, more negative resting membrane potential, increased action potential amplitude, and upstroke velocity, thereby bringing the action potential waveform much closer to that of adult human ventricular cardiomyocytes. The expectation is that this approach will result in a more reliable prediction of drug effects, but this hypothesis has yet to be studied systematically (Goversen et al., 2017).

When considering the use of dynamic clamp in safety pharmacology, the low throughput and complex nature of manual patch clamp in combination with dynamic clamp is problematic. Additionally, as noted in the literature (Meijer van Putten et al., 2015), current implementations require the simultaneous use of two computers that both require user interaction during the experiment, which is not very practical. In this study, we have developed a remote-controlled dynamic clamp system with the purpose to couple and integrate it with automated patch clamp devices, in order to increase throughput and develop new predictive assays using hSC-CMs that are in line with the aims of the CiPA initiative. In this study, we demonstrate its application by creating hybrid human cardiomyocyte models by the addition of virtual IK1 current to single, suspended human iPSC-CMs, and recording action potentials on an automated patch clamp device.

# MATERIALS AND METHODS

### iPSC-CM Culture and Dissociation

Differentiated iPSC-derived cardiomyocytes (Cor.4U, kindly provided by Axiogenesis AG, Germany and Cellartis Cardiomyocytes, kindly provided by Takara Bio Europe AB, Sweden) were cultured according to the suppliers' instructions. The cells were dissociated by incubating them for 15–30 min in TrypLE (Gibco) until detached from the surface of the culture flask, and then kept at 4◦C for 30 min before pipetting them to individualize the cells.

#### Automated Patch Clamp Electrophysiology

Recordings from single iPSC-CMs were done using a Nanion Patchliner automated patch clamp device at 20◦C and standard medium resistance NPC-16 chips. After catching an iPSC-CM, obtaining a gigaseal and breaking into whole cell configuration, several experiments were performed.

From a holding potential of −100 mV, current-voltage recordings were made using voltage steps from −80 to 40 mV for 20 ms increasing in 10 mV steps at 2 s intervals (sodium ion currents), and from −40 to 40 mV for 200 ms increasing in 10 mV steps at 5 s intervals (calcium ion currents), with a 100 ms pre-pulse to −40 mV to inactivate sodium ion currents. IK1 current were recorded from a holding potential of −40 mV, with voltage steps from −120 to +30 mV for 1,200 ms increasing in 10 mV steps. IK1 was blocked by adding 10µM Ba2+, from these recordings we calculated the Ba2+-sensitive steady-state current and report these in I-V diagrams.

Next, the recording mode was switched to current clamp and the effect of adding simulated IK1 conductance to the iPSC-CM using dynamic clamp was tested. To this end, a current stimulus was optimized for each cell individually to reliably induce action potentials (APs) at a rate of 0.5 Hz. The stimulus was 1 ms long and ranged from 0.6 to 3 nA. The same stimulus was used to trigger APs while exposing the cells to increasing simulated IK1 conductance. If the conductance was set too low, no effect on the AP was detectable, if set too high, no AP could be induced. The simulated IK1 conductance range varied considerably between individual cells, 200 to 2,000 pS/pF were used across cells.

All experiments were done using extracellular solution containing (in mmol/L) 140 NaCl, 10 HEPES, 5 Glucose, 4 KCl, 2 CaCl2, 1 MgCl2, pH 7.4 (NaOH), 298 mOsm, and intracellular solution containing 110 KF, 10 KCl, 10 NaCl, 10 HEPES,

TABLE 1 | iPSC-CMs can be captured efficiently using automated patch clamp and display Na<sup>+</sup> and Ca2<sup>+</sup> currents.


Six experiments were performed using a total of 3 chips, therefore 48 potential sites on the chip were available and 28 Cellartis iPSC-CMs were captured (with seal resistance >150 MΩ) resulting in a success rate of 58% for capture.

10 EGTA, pH7.2 (KOH), 285 mOsm. In some experiments, potassium salts were replaced by cesium salts to expose calcium ion currents otherwise obscured by potassium ion currents. Since potassium currents turned out to be negligible, no difference referring to (real) potassium conductance was observed between those recordings.

TABLE 2 | Average electrophysiological parameters iPSC-CMs.


Shown are values for seal resistance (RSeal), cell capacitance (Cm) and series resistance (Rs) for Cellartis Cardiomyocytes captured with seal resistance > 150 MΩ. Na<sup>+</sup> current at −30 mV and Ca2<sup>+</sup> current at 10 mV is also shown. Number of cells shown in brackets. Note that the average current is taken from the IV curves and not all cells which had a detectable Na<sup>+</sup> current were used for the IV analysis.

#### Dynamic Clamp System

Experiments were done using a dynamic clamp system developed in house at UMC Utrecht, Utrecht, The Netherlands. The system runs on the Labview RT operating system, and simulates IK1 current in response to membrane potential measured

IC<sup>50</sup> = 252 ± 186 nM (n = 5).

block) for nifedipine for an average of 5 cells. The average concentration response curve was fitted with a standard Hill-equation which revealed an

from the iPSC-CM. Real-time simulation of the IK1 current was done using the model by Ishihara et al. (2009), and simulations were done at 20 kHz, on four independent channels, allowing simultaneous dynamic clamp of four iPSC-CMs. We have included as supplementary information the used IK1 model (**Supplementary Data Sheet 1**), a diagram explaining our dynamic clamp implementation (**Supplementary Figure 1**) and a flowchart describing the various steps taken during the dynamic clamp experiments (**Supplementary Figure 2**).

The dynamic clamp system is coupled to the HEKA EPC-10 Quattro amplifier that is part of the Patchliner setup (see **Figure 1**). The connections couple the membrane potential of each iPSC-CM with each IK1 simulation channel and return the computed IK1 current to the iPSC-CM via the external stimulus input of the EPC-10 amplifier. Remote control is achieved via additional couplings that allow bi-directional communication between the dynamic clamp system and the Patchliner setup. For this we use the standard digital input and output channels of the HEKA EPC-10 Quattro amplifier. These are used to continuously read dynamic clamp system status and set model parameters (e.g., IK1 conductance, membrane capacitance or external K<sup>+</sup> ion concentration) when needed. Converting a model parameter to a digital command was done using macros in Patchmaster.

Because of this tight integration with the APC and its software, no direct user interaction with the dynamic clamp setup is necessary. The dynamic clamp system is completely controlled from within the HEKA PatchMaster or the Patchliner PatchControlHT software used to run experiments, and can be set automatically using the programming features in these software programs (i.e., Protocol Editor in PatchMaster or Tree Editor in PatchControlHT).

#### Statistics

All results are presented as mean ± standard error of the mean (s.e.m.). Differences in mean outcomes were tested using a Oneway ANOVA followed by Tukey's multiple comparisons test, p-values smaller than 0.05 were considered significant.

# RESULTS

# Na<sup>+</sup> and Ca2<sup>+</sup> Currents in iPSC-CMs

Single iPSC-CMs dissociated from iPSC-CM cultures were loaded in the automated patch clamp device and studied in voltage clamp mode to record Na<sup>+</sup> and Ca2<sup>+</sup> currents. Capture of the iPSC-CM in the patch clamp chip was efficient, with appropriate seals in 58% of captured cells (see **Table 1**). After obtaining whole cell configuration, Na<sup>+</sup> and Ca2<sup>+</sup> currents could be recorded in ∼70% of iPSC-CMs (see **Table 2**).

Current-voltage relations of both currents were similar to those reported for iPSC-CMs in manual patch clamp experiments (Ma et al., 2011), showing maximal peak current amplitudes at −30 mV for Na<sup>+</sup> currents (**Figures 2A,B**) and 10 mV for Ca2<sup>+</sup>

currents (**Figures 2C,D**). The Ca2<sup>+</sup> currents could be blocked by nifedipine with an IC<sup>50</sup> of 252 ± 186 nM, confirming we recorded current conducted by L-type Ca2<sup>+</sup> channels (**Figures 2E,F**).

# IK1 Currents in iPSC-CMs

Functionality of IK1 currents was studied in single dissociated iPSC-CMs that were loaded in the automated patch clamp device. Voltage clamp studies in control solution, and in presence of 10µM Ba2<sup>+</sup> to block IK1 currents, showed that we could record Ba2+-sensitive currents with some resemblance of IK1 in 7 out of 12 cells. Examples of cells showing Ba2+-sensitive and insensitive currents can be found in **Figures 3A,C**, respectively. However, current densities were low, and both the reversal potential (which was less negative than expected) and the rectification of the currents were not as observed in adult cardiomyocytes (**Figures 3B,D**).

# Single Suspended iPSC-CMs Have Depolarized Membrane Potentials

While the voltage clamp experiments demonstrated that the cardiac Na<sup>+</sup> and Ca2<sup>+</sup> channels remain functional after dissociation, recording action potentials from iPSC-CMs in suspension was challenging. After switching to current clamp mode, the resting membrane potential of iPSC-CMs was typically between 0 and −15 mV. A negative resting membrane potential close to the reversal potential of K<sup>+</sup> could be achieved by injecting a small constant, negative holding current. After that, action potentials could be triggered with a brief depolarizing stimulus. However, the action potentials were very short and

had a monotonic repolarization without a plateau phase, which does not match well with adult human cardiac action potentials (see **Figure 4**, black trace labeled "−180 pA"). The IK1 channels expressed in fully differentiated human cardiomyocytes hyperpolarize the resting membrane potential of these cells, bringing it close to EK. An important difference with a constant hyperpolarizing current is that IK1 channels close upon strong depolarization, allowing development of the plateau phase of the cardiac action potential. In order to improve our methods, and obtain better action potential recordings from suspended single iPSC-CMs, we implemented the dynamic clamp technique on our automated patch clamp device in order to inject simulated IK1.

### Hybrid Models of Suspended iPSC-CMs and Simulated Ik1 Channels Produce Longer Action Potentials with a Plateau Phase

Our dynamic clamp implementation is in many ways similar to other published implementations (Bett et al., 2013; Ortega et al., 2014; Meijer van Putten et al., 2015), but differs in two aspects: the functional integration with existing patch clamp control software,

FIGURE 5 | Effects of adding simulated IK1 on AP parameters. (A) Adding IK1 prolongs the APD90 of action potentials recorded from Cellartis Cardiomyocytes (n = 4) compared to constant current injection. With increasing IK1 conductance, the prolongation of the action potential becomes smaller, consistent with the role of IK1 in the final repolarization of the cardiac action potential. (B) Upstroke velocity of the action potentials after addition of simulated IK1 is high, as with constant current injections, and decreases slightly with increasing IK1 conductance.

and the model used to compute IK1. Earlier work has used IK1 formulations that model the current as a steady-state current, i.e., without time-dependence. The model by Ishihara et al. used in this study is a more detailed, time-dependent model that includes the rectifying effects of Mg2<sup>+</sup> and polyamines, as well as two modes of channel closure by spermine (Ishihara et al., 2009). Including this more detailed model is relevant, as time and voltage dependent Mg2<sup>+</sup> block or unblock can significantly affect action potential duration (Ishihara et al., 2002).

In current clamp experiments with suspended iPSC-CMs, we injected virtual IK1 current with varying conductance densities (GK1), depending on the specific cell. At depolarized potentials (>−40 mV), the Ishihara model does not generate much outward current, therefore increasing GK1 did not immediately induce hyperpolarization. This could be solved by briefly injecting a hyperpolarizing current, bringing the membrane potential to values inducing a sufficiently large outward IK1 current. As a result, the membrane potential was maintained at or close to E<sup>K</sup> (which was −95 mV for the simulated IK1 channels) due to the injected virtual IK1 current. After this, the constant hyperpolarizing current was switched off, as it was only needed to start the experiment.

Action potentials recorded from iPSC-CMs with addition of virtual IK1 differed from the earlier recorded brief and

monotonically repolarizing action potentials. Injecting IK1 resulted in a stable resting membrane potential, fast upstroke velocities, and prolonged action potential duration with a clear plateau phase (**Figure 4**). Further increasing GK1, resulting in injection of more IK1, caused a small additional hyperpolarization, but more significantly, also shortened action potential duration (**Figure 5A**) and slightly decreased upstroke velocity (**Figure 5B**). This is consistent with the role of IK1 in cardiomyocyte electrophysiology, as it contributes to resting membrane potential stability and the final repolarization phase of the action potential (de Boer et al., 2010). A benefit of our newly developed approach is that experimental throughput can be moderately increased as we can record from, and inject IK1 into, 4 cells in parallel. In **Figure 6** we show an example of an experiment in which we were able to record APs from 3 iPSC-CM in parallel (**Figure 6A**) and have also plotted the injected IK1 (**Figure 6B**). The fourth channel was available but for this channel no cell was captured successfully. Additional experiments, in which we studied the effect of GK1 on upstroke velocity, showed that we could perform a dynamic clamp experiment in 20 out of 28 wells in 7 experimental runs that used 4 wells per run (71% success rate), see **Supplementary Figure 3**.

#### Addition of Virtual Ik1 Channels Restores Sensitivity of the Plateau Phase to Pharmacological Modulation

In earlier experiments, it proved difficult to observe effects of Ca2<sup>+</sup> channel antagonists or agonists on the action potential shape of suspended iPSC-CMs when injecting a constant hyperpolarizing current (data not shown), most likely due to suppression of the plateau phase. After observing the restoration of the plateau phase when injecting virtual IK1 current, we tested if the action potential became again sensitive to manipulation of the L-type Ca2<sup>+</sup> current. After injecting IK1 (on average GK1 was 267 ± 42 pS/pF) we observed an APD<sup>90</sup> of 118 ± 21 ms (n = 6), which significantly prolonged after enhancing the Ltype Ca2<sup>+</sup> channel with 1µM BayK-8644 to 155 ± 31 ms (n = 6, see **Figures 7A,B**). In contrast, blocking the L-type Ca2<sup>+</sup> channel with 30µM nifedipine caused a shortening to 81 ± 14 ms (n = 6). These findings demonstrate that enabling the plateau phase of the action potential of suspended iPSC-CMs by addition of virtual IK1 channels restores action potential sensitivity to L-type Ca2<sup>+</sup> channel modulation.

#### DISCUSSION

In this study, as a proof of principle, we have demonstrated that the dynamic clamp technique can be used in combination with automated patch clamp devices, thereby creating a higher throughput alternative to manual patch clamp. Using dynamic clamp to add virtual IK1 channels to suspended iPSC-CMs allowed us to record action potentials with waveforms that are more representative of the human fully differentiated ventricular cardiomyocyte. This is especially relevant to the CiPA initiative, which aims to use hSC-CMs in drug safety testing.

and RMP was −94 mV. (B) Average responses from 6 cells showing significantly increased APD90 after exposure to 1µM BayK-8644 (\*p < 0.05) and decreasing APD90 after exposure to 30µM nifedipine.

Achieving higher throughput evaluation of drug effects on action potentials generated by iPSC-CMs will most likely require the use of isolated, suspended cells, as these can be used with automated patch clamp devices. The depolarized resting membrane potential of freshly isolated iPSC-CMs is a challenge that can be overcome, at least to some extent, by using the dynamic clamp technique (this study), but will also require improvement in the dissociation methods used. Dissociation of cardiomyocytes with enzymes disrupting the extracellular matrix, whether native or created in culture, is known to affect the function of IKr, IKs, and IK1 channels (Yue et al., 1996; Hoshino et al., 2012). Hoshino et al. demonstrated that the approach used to isolate cardiomyocytes from neonatal mouse hearts has a significant impact on IK1 channel function and resting membrane potential. Using enzymatic perfusion of the hearts preserved IK1 channels, while the chunk digestion method resulted in four to five times smaller IK1 currents and a depolarization of ∼20 mV. The approach used in this and other studies to obtain single, suspended iPSC-CMs is very similar to the chunk digestion method, and we have indeed observed only small Ba2+-sensitive currents, which may be smaller than those observed in studies using adherent iPSC-CM (Ma et al., 2011; Doss et al., 2012; Nunes et al., 2013). Further improvement of cell dissociation protocols may improve results with iPSC-CMs on automated patch clamp devices. This is supported by recent work by Rajamohan et al. who have used a two-step dissociation protocol and recorded APs from the dissociated iPSC-CMs using both manual and automated patch clamping approaches (same device as used in this study). From the data in this study it appears that the twostep protocol yields cells with a more hyperpolarized membrane potential (Rajamohan et al., 2016).

In the present study, we provide proof-of-principle that automated patch clamp devices and dynamic clamp can be combined successfully. The resulting action potential durations and waveforms are very comparable to those obtained in manual patch clamp experiments in which IK1 was added to iPSC-CMs using dynamic clamp (Bett et al., 2013; Meijer van Putten et al., 2015), including the action potential prolongation in response to Bay-K8644. However, more research will be needed to establish the method, and to define its limits and benefits. A better insight into the effects of the specific IK1 model that is applied is needed, as well as a well-defined algorithm that allows us to determine which amount of added IK1 results in the most predictive results and therefore the best safety pharmacology assay. This should subsequently be demonstrated using the set of drugs defined by CiPA. If these goals can be reached, performing predictive patch clamp experiments with iPSC-CMs with an increased throughput becomes feasible.

#### AUTHOR CONTRIBUTIONS

BG: data acquisition, data analysis, data interpretation, revising; NB: data acquisition, data analysis, data interpretation, study

#### REFERENCES


design, writing; SS-F, AO: data analysis, data interpretation, revising; TvV, MV, NF: data interpretation, revising; TdB: data acquisition, data analysis, data interpretation, study design, writing, revising. All authors meet the following criteria: (i) Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work, (2) Drafting the work or revising it critically for important intellectual content, (3) Final approval of the version to be published, (4) Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

#### FUNDING

This study is supported by MKMD grants 114021501 and 114022502 from ZonMW (TvV and TdB), and a grant from Utrecht Holdings (TdB).

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.01094/full#supplementary-material

Supplementary Figure 1 | Diagram describing implementation of dynamic clamping.

Supplementary Figure 2 | Flowchart describing steps in dynamic clamp experiment.

Supplementary Figure 3 | Influence of IK1 conductance on upstroke velocity.

Supplementary Data Sheet 1 | CellML implementation of IK1 model used in this study.


cardiomyocytes: electrophysiological properties of action potentials and ionic currents. Am. J. Physiol. Heart Circ. Physiol. 301, H2006–H2017. doi: 10.1152/ajpheart.00694.2011


inherited arrhythmia syndromes. Am. J. Physiol. Heart Circ. Physiol. 310, H1611–H1621. doi: 10.1152/ajpheart.00481.2015


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Goversen, Becker, Stoelzle-Feix, Obergrussberger, Vos, van Veen, Fertig and de Boer. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Evaluation of Optogenetic Electrophysiology Tools in Human Stem Cell-Derived Cardiomyocytes

Susann Björk 1†, Elina A. Ojala1†, Tommy Nordström<sup>2</sup> , Antti Ahola<sup>3</sup> , Mikko Liljeström<sup>4</sup> , Jari Hyttinen<sup>3</sup> , Esko Kankuri <sup>1</sup> and Eero Mervaala<sup>1</sup> \*

<sup>1</sup> Department of Pharmacology, Faculty of Medicine, University of Helsinki, Helsinki, Finland, <sup>2</sup> Department of Physiology, Faculty of Medicine, University of Helsinki, Helsinki, Finland, <sup>3</sup> BioMediTech Institute and Faculty of Biomedical Sciences and Engineering, Tampere University of Technology, Tampere, Finland, <sup>4</sup> Department of Anatomy, Faculty of Medicine and HiLIFE, University of Helsinki, Helsinki, Finland

#### Edited by:

Stefano Morotti, University of California, Davis, United States

#### Reviewed by:

Daniël Antonie Pijnappels, Leiden University, Netherlands Joel Kralj, University of Colorado Boulder, United States

> \*Correspondence: Eero Mervaala eero.mervaala@helsinki.fi

† These authors have contributed equally to this work.

#### Specialty section:

This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology

Received: 30 June 2017 Accepted: 18 October 2017 Published: 02 November 2017

#### Citation:

Björk S, Ojala EA, Nordström T, Ahola A, Liljeström M, Hyttinen J, Kankuri E and Mervaala E (2017) Evaluation of Optogenetic Electrophysiology Tools in Human Stem Cell-Derived Cardiomyocytes. Front. Physiol. 8:884. doi: 10.3389/fphys.2017.00884 Current cardiac drug safety assessments focus on hERG channel block and QT prolongation for evaluating arrhythmic risks, whereas the optogenetic approach focuses on the action potential (AP) waveform generated by a monolayer of human cardiomyocytes beating synchronously, thus assessing the contribution of several ion channels on the overall drug effect. This novel tool provides arrhythmogenic sensitizing by light-induced pacing in combination with non-invasive, all-optical measurements of cardiomyocyte APs and will improve assessment of drug-induced electrophysiological aberrancies. With the help of patch clamp electrophysiology measurements, we aimed to investigate whether the optogenetic modifications alter human cardiomyocytes' electrophysiology and how well the optogenetic analyses perform against this gold standard. Patch clamp electrophysiology measurements of non-transduced stem cell-derived cardiomyocytes compared to cells expressing the commercially available optogenetic constructs Optopatch and CaViar revealed no significant changes in action potential duration (APD) parameters. Thus, inserting the optogenetic constructs into cardiomyocytes does not significantly affect the cardiomyocyte's electrophysiological properties. When comparing the two methods against each other (patch clamp vs. optogenetic imaging) we found no significant differences in APD parameters for the Optopatch transduced cells, whereas the CaViar transduced cells exhibited modest increases in APD-values measured with optogenetic imaging. Thus, to broaden the screen, we combined optogenetic measurements of membrane potential and calcium transients with contractile motion measured by video motion tracking. Furthermore, to assess how optogenetic measurements can predict changes in membrane potential, or early afterdepolarizations (EADs), cells were exposed to cumulating doses of E-4031, a hERG potassium channel blocker, and drug effects were measured at both spontaneous and paced beating rates (1, 2 Hz). Cumulating doses of E-4031 produced prolonged APDs, followed by EADs and drug-induced quiescence. These observations were corroborated by patch clamp and contractility measurements. Similar responses, although more modest were seen with the IKs potassium channel blocker JNJ-303. In conclusion, optogenetic measurements of AP waveforms combined with optical

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pacing compare well with the patch clamp gold standard. Combined with video motion contractile measurements, optogenetic imaging provides an appealing alternative for electrophysiological screening of human cardiomyocyte responses in pharmacological efficacy and safety testings.

Keywords: optogenetics, human iPSC-derived cardiomyocytes, optical action potential, contractile motion, hERG, cardiac electrophysiology, arrhythmia, safety pharmacology

# INTRODUCTION

Present cardiac safety assessments focus on the in vitro block of the human rapid component of the delayed inward rectifier IKr (hERG) channel, combined with in vivo QT prolongation for evaluating the arrhythmic risks of novel drug candidates in preclinical development. Block of the hERG channel delays cardiac repolarization, prolonging the action potential duration (APD) and the QT interval on ECG, and potentially increases the risk for the development of the cardiac arrhythmia Torsades de Pointes (TdP) (Sanguinetti et al., 1995; Redfern et al., 2003; Gintant et al., 2016). However, although these assays have been effective in preventing drugs that induce TdP proarrhythmia from entering the market, it has been recognized that a drug's proarrhythmic effect often is shaped by its action on multiple ion channels (Mirams et al., 2011). The lack of specificity of the hERG assay therefore often leads to unwarranted attrition of drugs, which is costly for the pharmaceutical industry. A more focused approach to address and eliminate cardiovascular toxicity early in development has thus been proposed by the Comprehensive in vitro Proarrhythmia Assay (CIPA) initiative (Gintant et al., 2016). CIPA proposes a multimodal approach of cardiac safety screening based on the integrated effects of drugs on the multiple cardiac ion channels that define cardiac excitability and repolarization and that play a role in delayed ventricular repolarization. Reconstructions of the drug effects are evaluated in silico on a computationally reconstructed human ventricular cardiomyocyte action potential (AP) (Cavero and Holzgrefe, 2014; Fermini et al., 2016; Gintant et al., 2016; Page et al., 2016). Finally, predicted effects are verified with electrophysiological experiments in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CM).

Numerous methodology development studies have appeared which have tried to assess the criteria set up by CIPA. Optical, non-invasive measurements of AP parameters performed in hiPSC-CM has been associated with great potential over the current gold standard, patch clamping, since it focuses on the AP waveform from multiple cells beating synchronously and thus assesses the contribution of several ion channels on the overall drug effect (Entcheva, 2013; Ambrosi and Entcheva, 2014; Chang Liao et al., 2015; Dempsey et al., 2016; Klimas et al., 2016). Optogenetics utilizes light sensitive proteins (microbial opsins), that are genetically encoded and expressed on the cardiomyocyte plasma membrane, where they function as optical actuators or sensors, which enables all-optical shaping of the AP. Hochbaum and colleagues developed several optogenetic constructs, of which Optopatch2 utilizes a modified version of the channelrhodopsin cation channel (CheRiff) that in response to blue light at 488 nm depolarizes the cardiomyocyte, enabling pacing of cardiomyocytes at elevated beating rates. By combining this optogenetic actuator with the genetically encoded voltage indicator QuasAr2, a modified, non-pumping version of the protein pump Archaerhodopsin3, which in response to red light at 640 nm generates an optical signal that is proportional to the membrane potential, all optical electrophysiological experiments were demonstrated in neuronal cells (Hochbaum et al., 2014), and later in hiPSC-CMs (Dempsey et al., 2016). Another construct CaViar, based on the genetically encoded voltage sensor Arch(D95N) combined with the genetically encoded calcium sensor, GCaMP5f, was developed to allow for simultaneous AP dynamics and intracellular calcium transient determinations (Hou et al., 2014).

Traditional electrophysiological methods, such as calcium imaging, measures the ionic functions which regulate the contractile movement of the cells. However, these measurements do not directly quantify the biomechanics of the cell. Different video-based block matching methods have been developed to non-invasively measure the contractile movement in cardiomyocytes and the results on cellular biomechanics have been linked to clinical findings (Kiviaho et al., 2015; Laurila et al., 2016). Since contractile cardiotoxicity also is a safety concern, combining optogenetic electrophysiology experiments with contractile measurements would therefore bring added value to safety screens. Furthermore, the arrhythmogenic sensitizing by light-driven pacing in combination with optical measurements of cardiomyocyte APs is essential to detect toxic drug effects evident only under elevated beat rates. Due to the stringent and meticulous requirements of cardiac safety testing it is of utmost importance that these novel tools are studied in detail to understand how the optogenetic modifications possibly alter human cardiomyocytes' electrophysiology. The purpose of this study was to characterize the optogenetic constructs (Optopatch and CaViar) against non-transduced cardiomyocytes, and more importantly, to compare how well-optogenetic analyses perform against the gold standard, patch clamp electrophysiology.

# MATERIALS AND METHODS

#### Cell Culture

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), Cor.4U <sup>R</sup> , were acquired from Axiogenesis Inc. (Germany). These spontaneously beating cells represent a mixture of atrial, nodal and ventricular cardiomyocytes, with 60% being of the ventricular type. Cor.4U <sup>R</sup> hiPSC-CMs were delivered as fresh cells in T25-flasks (Nunc©, Thermo Fisher Scientific) and kept in an incubator (5% CO2, 37◦C) and fed

daily with Cor.4U <sup>R</sup> complete culture medium (Axiogenesis Inc.) supplemented with 1X Antibiotic-Antimycotic (Thermo Fisher Scientific) to prevent bacterial and fungal infection. For further passaging T25 flasks were pre-coated with 10µg/ml fibronectin (Sigma) in PBS (with Ca2<sup>+</sup> and Mg2+, Gibco <sup>R</sup> , Thermo Fisher Scientific) for 3 h at 37 or at 4◦C o/n and the solution was removed shortly before plating the cells. For passaging, cells were detached using Accumax (Millipore) according to the manufacturer's instructions. The cells were collected by centrifugation (200 g, 3 min), the supernatant was removed and the cell pellet was gently re-suspended in the culture medium. Viable cells were counted using the trypan blue exclusion method and the cell density calculated according to viable cells. After plating, the cells were kept in the cell culture hood for 15 min to ensure that the cells settled evenly.

#### Lentiviral Transduction of Cardiomyocytes

To express light-gated voltage sensors and actuators on the plasma membrane of the hiPSC-CMs, the cells were transduced with lentiviral vectors bearing the constructs of interest. CaViar, pJMK019 (Addgene plasmid # 42168) and CMV-Optopatch2\_FCK, pMOS001 (Addgene plasmid # 62984) were gifts from Adam Cohen, acquired through the non-profit plasmid repository Addgene. The production of lentiviral particles, lentiviral titer determinations and replication competent virus (RCV) tests were purchased from the Biomedicum Virus Core Unit in the Faculty of Medicine, University of Helsinki. For the toxicological testing of lentiviral particles, four different amounts of lentivirus stock were tested for both optogenetic constructs (0.25, 0.50, 0.75, and 1.00 pg/cell for CaViar; 0.50, 0.75, 1.00, and 1.25 pg/cell for Optopatch, as determined by the p24 capsid protein concentration), where final concentrations used are underlined. For the transduction procedure, the lentiviral stock was diluted 1:2 in serum-free BMCC medium (Axiogenesis) supplemented with polybrene (4µg/ml final concentration) to assist the penetration of the viruses through the cell membrane. The cells were incubated for 6–7 h with the lentivirus mix and then washed with PBS to remove excess virus. The lentiviral transduction was confirmed by CheRiff-tagged GFP or GCaMP5f introduced in the transduced cells, imaged by an EVOS <sup>R</sup> FL Imaging System. After the lentiviral transduction, the cells were washed with 3x PBS and supplemented with fresh culture medium daily. 24 h after the transduction procedure the cells were screened for cytotoxicity and cytolysis using an absorbancebased lactate dehydrogenase (LDH) release assay (Pierce, Thermo Fisher Scientific). In order to get rid of the replicative virus prior to patch clamp measurements and optogenetic imaging, the transduced cells were passaged for two times during a time period of 2–3 weeks in a BSL2 safety level laboratory. Passaging was done as described above and cells were re-plated in fibronectin-coated T25 flasks.

# Patch Clamp Electrophysiological Measurements

Whole-cell recordings were performed using an EPC 9/2 double patch clamp amplifier and pulse v 8.80 software (HEKA Elektronik, Lambrecht, Germany). For current clamp recordings, non-transduced control hiPSC-CMs and hiPSC-CMs expressing the optogenetic constructs were plated as subconfluent monolayer in fibronectin-coated petri dishes (30 mm, Nunc), which were placed on an inverted microscope (Olympus IX71) and visualized using an AxioCam HRM digital camera (AxioVision 4.6 software). For the recordings cells were perfused with a bathing solution composed of 143 mM NaCl, 4 mM KCl, 1.2 mM MgCl2, 1.8 mM CaCl2, 5 mM D-glucose, and 10 mM HEPES (pH 7.4 NaOH). The internal pipette solution contained 122 mM K+-Gluconate, 30 mM KCl, 1 mM MgCl2, 5 mM HEPES (pH 7.2, KOH). The microelectrodes were pulled from borosilicate glass (outer diameter 1.5 mm) on a two-stage pipette puller (PC-10, Narishige) and heat polished with a Micro Forge MF-90 heater (Narishige). The resistance of the pipettes used in the experiments were 2.5–3.5 M. Membrane capacitance and series resistance were compensated electronically. The HEKA amplifier was set to current clamp at zero applied current, and spontaneous APs were recorded for 20 s in each data sweep. The cells were superfused with the bathing solution at a rate of 1.0 ml/min. All experiments were done at 37◦C by using a TC-344B Dual automatic temperature controller (Warner). To minimize the volume in the petri dish, a petri dish insert was used (Bioscience Tools). Action potentials were digitized at 10 kHz and low-pass filtered at 3 kHz.

# Preparation of Cells for Optogenetic Measurements

For the optogenetic imaging, transduced hiPSC-CMs were plated as confluent monolayer on Geltrex (Gibco <sup>R</sup> , Thermo Fisher Scientific)-coated glass-bottom dishes (10 mm Ø, P35G-1.5-10- C, MatTek), by seeding 90,000 cells per dish. Geltrex was pre-incubated on the glass-bottom dishes at 37◦C for 1 h and removed shortly before plating the cells. After plating, cells were left in the cell culture hood for 15 min to ensure an even monolayer of the cells. Cells were cultured on glass-bottom dishes for 1 week to ensure full integration of the beating monolayer. Just before the optogenetic imaging the culture medium was exchanged for imaging buffer, which was identical to the patch clamp bathing solution. Separate dishes were utilized for spontaneous beating, 1 and 2 Hz pacing (three dishes for each condition).

#### Drug Dilutions

Dried powders of E-4031 and JNJ-303 (Tocris) were dissolved in DMSO to make a stock concentration of 10 mM. Compounds were solubilized by vortexing the stock solution at RT and stock solutions were stored at −20◦C until use. The drug dilutions were prepared fresh at the day of the experiment from stocks in imaging buffer and kept at 37◦C in 5% CO2. For optogenetic imaging, the addition of drugs started from a blank (fresh imaging buffer) to check proper beating of the monolayer, followed by vehicle and drug doses. The entire volume (2 ml) in the dish was exchanged at each drug dose, as we noted that the cells needed fresh buffer at regular intervals for proper beating. A delay of ∼1 min before imaging was allowed in order for the drug to take effect. The vehicle DMSO concentrations were 0.001% (v/v) for E-4031 series and 0.03% (v/v) for JNJ-303 series. The final concentrations for E-4031 were 3, 10, 30, and 100 nM and the final concentrations for JNJ-303 were 0.03, 0.1, 0.3, 1, 3, and 10µM. For E-4031 patch clamp measurements drugs were diluted in bathing solution and administered through perfusion.

#### Optogenetic Measurement Setup

The optogenetic imaging platform was designed for fast photo manipulation and analysis of live cells. The platform included an environmental chamber (5% CO2, 37◦C, EMBL), a fully motorized inverted wide field epifluorescence microscope (Nikon Eclipse Ti-E equipped with a Nikon IR-based Perfect Focus System, PFS). Pulses (10 ms) of blue laser illumination (Argon, λ = 488 nm, 17 mW/mm<sup>2</sup> ) were used to pace CheRiff at 1 or 2 Hz frequencies and a red laser λ = 647 nm, E<sup>f</sup> = 550 mW/mm<sup>2</sup> excited fluorescence of QuasAr2. For CaViar imaging, the laser lines were used in combination with a beam splitter (Hamamatsu Gemini) to allow simultaneous use of the two separate illumination sources (λ = 647 nm, E<sup>f</sup> = 550 mW/mm<sup>2</sup> to excite fluorescence of ArchD95N and λ = 488 nm, E<sup>f</sup> = 3 mW/mm<sup>2</sup> for GCaMP5f). Fluorescence was collected via a 60× oil immersion objective (PlanApo VC) with a numerical aperture (NA) of 1.4. Illumination was limited to the ocular field of view (FOV, 22 mm) of the Nikon Ti-E inverted microscope by adjusting the field stop. The illuminated area was calculated from the FOV and the objective magnification (giving a surface area of 0.106 mm<sup>2</sup> ). Optical power was measured on the microscope sample plane with an EXFO X-Cite XR2100 power meter. Laser illumination at 488 nm was measured with the acousto-optic tunable filter (AOTF) set to 100% transmission (giving a power reading of 1.8 mW). At 647 nm the laser output was set to 100 mW and the AOTF transmission was limited to 50% to avoid saturation (giving a power reading of 9.7 mW). The actual laser power used for imaging at 647 nm (laser output 300 mW, AOTF 100%) was calculated assuming a linear response (resulting in a power of 58.2 mW). The software for the platform operation was NIS-Elements advanced research v. 4.2 with 6D image acquisition module. Signals were recorded with an Andor iXon3 897 backilluminated EMCCD camera (512 × 512 px) or Andor iXon+ 885 EMCCD camera (1,004 × 1,002 px) for CaViar. Imaging was conducted at a framerate of 50 frames per second. The raw imaging data from optogenetic imaging was recorded as image sequences, from which the total intensity signal was exported to MS Excel in numerical format. The raw data trace was acquired as an average signal from the cells in the whole FOV. To calculate averages for each condition or drug concentration, image sequences from six FOVs were recorded.

## Automated Data Processing and Curve Analysis

For the automated processing of optogenetic raw data traces and the analysis of key features of cardiac electrophysiology, we developed the cPot Cardiac Action Potential Calculator software, written in MATLAB. With cPot, all raw data traces from optogenetic imaging were normalized by fitting the acquired signal to an exponential function. Then, peaks with larger than a selected threshold (10% of maximum amplitude) were detected in the normalized signal. The detected peak time points and their respective signal values were then used to determine the AP parameters and other key features. The key features analyzed and reported in this study were APD at 90, 50, and 30% repolarization (APD90, APD50, and APD30, s, respectively), beat to beat interval (s), frequency (Hz), maximum signal level of the peak, i.e., amplitude (1F/F for optogenetics, mV for patch clamp) and minimum signal level between peaks (MDP). Respective percentage levels for APDs were determined so that 100% was the overall change in signal from Peak Height to the following MDP. Patch clamp data was analyzed with cPot in the same way, but without normalization since the baseline in patch clamp measurements is steady. Optogenetic calcium traces for contraction analysis were normalized by fitting the acquired signal to an exponential function.

# Simultaneous Contraction Analysis of Video Microscopy

The contractile movement of the cardiomyocytes was analyzed from Optopatch and CaViar video microscopy sets using a semiautomatic CellVisus tool (Ahola et al., 2014). It uses particle image velocimetry based on minimum quadratic difference to determine velocity vector fields between consecutive video frames. Directional motion velocity signals are calculated from AP video data by using an estimated beating focus point as a reference. Contraction signals are generated from these motion velocity signals by integrating with respect to time and fitting the signal on a spline for baseline correction. Contraction amplitude was normalized to comply with the AP and the calcium transient for illustration. Here, we analyzed the motion from AP measurement in both Optopatch and CaViar microscopy from 10 image sequences each.

For signal characterization, calcium transient duration (CTD) parameters at different amplitude levels were calculated. Calcium transient durations (CTD) parameters CTD90, CTD50, and CTD30 were calculated by determining percentage values so that 100% was the overall change in signal from Peak Height to the following MDP. For contraction movement, we calculated the contraction time and relaxation time, as well as total contraction duration (CD) parameters CD90, CD50, CD30 defined by the beginning of the contraction and the end of relaxation movement. Further, we measured the time difference between the AP, calcium transient and contraction signal peaks from the same region of interest. The effect of E-4031 to contraction was measured by analyzing in total 92 image sequences for vehicle and 3, 10, 30 and 100 nM drug concentrations. In addition to the CD parameters listed above, average motion magnitude was measured.

#### Statistical Testing

The APD-values were beat rate adjusted, so that beating intervals were corrected to 60 bpm by Fridericia's correction formula (based on the cube-root of beating interval). Statistical comparisons were done either with a Student's two-sample t-test, or for cumulating drug responses with a one-way ANOVA with Dunnett's test for statistical significance. Significant p-values were <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

# RESULTS

## Lentiviral Transduction of hiPSC-CMs with Optogenetic Constructs Exhibit No Significant Side Effect on the Electrophysiological Properties of Cardiomyocytes

To validate the effect of lentiviral transduction of hiPSC-CMs with the optogenetic construct Optopatch (Hochbaum et al., 2014), we measured AP parameters with patch clamp electrophysiology and optogenetic imaging and compared the results against non-transduced control cells (**Figure 1**). There were no significant changes in the APD at 90% repolarization (**Figure 1A**), at 50% repolarization (**Figure 1B**), at 30% repolarization (**Figure 1C**), nor in beating rates (**Figure 1D**) between non-transduced cells and Optopatch-transduced cells. Nor were there any significant changes between the two methods of measurement: patch clamp electrophysiology and optogenetic imaging. The same stemmed for peak amplitude (**Figure 1E**), although this could only be compared using patch clamp electrophysiology, as the measured parameter for patch clamp (mV) is not measured by optogenetic imaging. A summary for the numerical AP parameters measured on non-transduced and Optopatch-transduced cells in **Figures 1A–E** is outlined in **Figure 1F**. Pearson correlations for the measured APD parameters were 0.99 (p < 0.001) both for non-transduced against Optopatch-transduced cells, as well as for correlations between APD parameters measured by patch clamp and optogenetic imaging. Thus, we propose that inserting the Optopatch construct into cardiomyocytes does not affect the cardiomyocyte's electrophysiological properties. To determine the amount of viral particles for delivery of the constructs to the cells, initial optimizations were performed with four different lentiviral concentrations of Optopatch, in which the lowest concentration yielded a monolayer of cells that did not pace at elevated frequencies and the highest concentration resulted in some cell death, therefore the second highest concentration of virus was used. However, screened by an absorbance-based LDH cytotoxicity method, this toxicological measurement revealed no significant cytotoxicity or cytolysis in any of the used lentivirus concentrations compared to non-transduced Cor.4U <sup>R</sup> cells (**Supplementary Figure 1**).

The optogenetic construct CaViar (Hou et al., 2014) holds the potential to measure changes in intracellular calcium in addition to AP dynamics and we therefore additionally validated the effect of transducing hiPSC-CMs with CaViar, and measured AP parameters (**Figure 2**) similarly as for the Optopatch construct. There were no significant changes in APD90 (**Figure 2A**), APD50 (**Figure 2B**), APD30 (**Figure 2C**), beating rates (**Figure 2D**) nor in amplitude (**Figure 2E**) between non-transduced cells and CaViar-transduced cells, measured by patch clamp electrophysiology. Pearson correlation values for the measured APD parameters were accordingly 0.99 (p < 0.001). This indicated that inserting the CaViar construct into hiPSC-CMs does not affect the electrophysiology of the cardiomyocyte. Neither was there any toxicity in any of the used concentrations of CaViar in toxicological measurement. However, when comparing APD parameters for the CaViar construct acquired with optogenetic imaging against those acquired with patch clamp electrophysiology, modest, but still statistically significant changes for APD90 and APD30 were seen. Thus, e.g., APD90 measured by patch clamp (300 ± 16 ms) and optogenetic imaging (350 ± 4 ms) exhibited a statistical difference, whereas APD50 did not. However, correlations values for all measured APD-values were still 0.98 (p < 0.001). A summary for the numerical AP parameters measured on nontransduced and CaViar-transduced cells in **Figures 2A–E** is outlined in **Figure 2F**.

## Simultaneous Measurement of Action Potential, Calcium Transients, and Contractile Motion: Signal Characterization and Timings

Action potentials, calcium transients, and contractions were measured from CaViar and Optopatch recordings. Representative signals from a CaViar recording are shown in **Figure 3A**, and from an Optopatch recording in **Figure 3B**. The CaViar measurements displays the AP (red) preceding the calcium transient (green), which is then followed by a contraction (blue). Contraction ended rapidly after reaching a peak (slope coefficient −0.0108). The calcium transient curve showed very similar kinetics (slope coefficient −0.0114). The timing of peaks (**Table 1**) for both constructs well adheres to cellular physiology. There was ∼30 ms interval between the AP and calcium peaks, and a 10 ms interval between the calcium and contraction peaks, thus a total of 40 ms between the AP and contraction peaks in CaViar measurements. For Optopatch measurements, the same value was 50 ms, albeit with a 30 ms variance indicating a close similarity to the APcontraction dynamics of the two constructs. The Optopatch construct does not allow for calcium measurements and therefore the AP-Calcium interval could not be calculated. When measuring the directional velocities, contraction time was measured to be 180 ms in CaViar measurements and 180 ms in Optopatch measurements. Relaxation times were 270 and 230 ms, respectively. The difference was not statistically significant in a two-sample t-test.

The measured signals were further characterized by peak width parameters at 90, 50, and 30 signal amplitude levels. The results are shown in **Table 2**. None of the differences were statistically significant indicating very similar characteristics of the two constructs, CaViar and Optopatch. Linear correlations were calculated for the characterization parameters. The results were −0.14 for CD90/CTD90, 0.18 for CD50/CTD50, and 0.48 for CD30/CTD30.

# Optogenetic and Patch Clamp Measurements Show Dose-Dependent APD Prolongation and Early Afterdepolarizations upon Exposure to the hERG Potassium Channel Blocker E-4031

Many compounds have failed early on in drug development due to block of the hERG potassium channel, and we

therefore assessed whether optogenetic measurements can show proarrhythmia events or early afterdepolarizations (EADs), which are known effects of hERG channel block. We utilized the potent and selective hERG blocker E-4031, as it commonly has been used as a positive control. Cumulating doses of E-4031 (3–100 nM) were applied to Optopatch-transduced hiPSC-CMs, and drug effects were measured by optogenetic imaging and by patch clamp. In optogenetic measurements, both spontaneous and optically paced beating rates (1 and 2 Hz) were screened, whereas patch clamp measurements only enabled recordings at spontaneous beating rates. Cumulating doses of E-4031 produced prolonged APDs dose-dependently in both methods (**Figure 4**).

In optogenetic measurements, averaged APDs from three dishes showed that APD90 at 30 nM E-4031 concentration was prolonged to 176% over vehicle APD90 (spontaneous beating), 167% under 1 Hz pacing and 143% at 2 Hz, with EADs evident at 30 nM under spontaneous and 1 Hz beat rates. APD90 was further increased to 219% over vehicle at 100 nM for 1 Hz and to 158% at 2 Hz. At 100 nM E-4031, APD90 decreased to 136% over vehicle under spontaneous beating which represented an average of the different behaviors seen; either very prolonged APDs with EADs or a decrease in peak amplitude with an increase in frequency, finally followed by drug-induced quiescence until beating stopped (**Figures 4A,E**). Similarly, in patch clamp measurements, the prolongation of APD90 (140%) was accompanied by EADs at 30 nM E-4031. APD90 further increased to 247% at 100 nM. In optogenetic measurements, a significant (p < 0.001) dose-dependent decrease in peak amplitude was evident at both spontaneous (22% over vehicle), 1 Hz (37%) and 2 Hz (46%) at 100 nM of E-4031 (**Figure 4D**). Representative traces for each drug concentration are shown in **Figure 4E**.

Contractile measurements revealed a dose-dependent (E-4031), non-significant prolongation of CD90 up to 10 nM (**Table 3**). EADs were detected as small twitches from 30 nM onwards after contraction and initial relaxation had occurred. E-4031 dose-dependently increased total relaxation time, being significant at 30 nM (p < 0.05). Motion magnitude decreased dose-dependently, reaching significance at 30 nM (p < 0.05). At 30–100 nM level, some image sequences could not be analyzed due to the motion reaching levels undetectable by the method.

### The IKs Blocker JNJ-303 Prolongs APD Slightly and Decreases Peak Amplitude Dose-Dependently, under Both Spontaneous and Elevated Beating Rates

Cumulating doses of JNJ-303 (0.03–10µM) were applied to hiPSC-CMs, and drug effects were measured at both spontaneous and 1–2 Hz paced beating rates (**Figure 5**). Prolongation of APD90 was seen at 100–300 nM JNJ-303 under spontaneous

beat rates, and at 30–100 nM JNJ-303 under paced frequencies (**Figure 5A**). The prolongations were however statistically nonsignificant. A significant dose-dependent decrease in peak amplitude was evident already at 1µM (58% of vehicle), decreasing to 45% at 10µM under spontaneous beating. A similar decrease in the peak amplitude was also seen under 1 Hz pacing, whereas only 10µM exhibited a significant decrease in peak amplitude (49% of vehicle) under 2 Hz pacing (**Figure 5B**). The cells stopped responding to pacing frequencies already at 100 nM of JNJ-303, but AP recordings were still continued under light stimulation at indicated pacing rates.

# DISCUSSION

The present study was conducted to evaluate the optogenetic electrophysiology tools against the gold standard, patch clamp electrophysiology. Moreover, we evaluated how well-optogenetic tools and contractile motion measurements can predict proarrhythmia events and delayed repolarization (EADs) in cardiac drug safety screens.

Block of the potassium channel hERG plays a critical role in defining ventricular repolarization, however mechanistic and translational studies demonstrate that block of IKr alone is not highly specific for predicting either delayed repolarization or clinical proarrhythmia events (Gintant et al., 2016). Indeed, several drugs such as verapamil and ranolazine are potent hERG blockers, but are not associated with either QT prolongation or risk of TdP (Chouabe et al., 1998; Schram et al., 2004). It has been estimated that 60% of new molecular entities developed as potential therapeutic targets test positive in hERG blocking assays and are thus abandoned early on in the development pipeline (Gintant et al., 2016). However, these hERG-expressing immortalized cell-based assays do not represent the highly differentiated human cardiac myocyte. The technology of generating hiPSC-cardiomyocytes holds great potential for preclinical cardiac efficacy and safety screens (Grskovic et al., 2011; Matsa et al., 2014). These cells are somewhat immature, and phenotypically more close to an embryonic myocyte than adult, reflected in their less-negative resting potential, reduced upstroke velocities and spontaneous automaticity. In spite of this, hiPSC-CMs have been shown to respond in a highly predictable manner to over 40 compounds that have a known pharmacological effect on the human heart (Fermini et al., 2016). In addition, hiPSC technology enables the generation of cardiomyocytes from patients with e.g., congenital long-QT syndrome. Drug responses and toxicity measurements adapted on these cells could thus bring toxicity screens to a deeper level, stratifying patient responses and reducing late-stage clinical failures (Grskovic et al., 2011; Matsa et al., 2014). To overcome the shortcomings in current drug safety screens, the CIPA initiative proposes the investigation

insets are close-ups of a single peak.

TABLE 1 | Simultaneous measurement of CaViar and Optopatch peak intervals and contraction time parameters.


The measures illustrate mean ± standard deviation (ms), (n = 10), n.a., not applicable; AP, action potential.

of drug effects on multiple human cardiac currents, tested in hiPSC-CMs.

Although hiPSC-CM transmembrane potential measured with patch clamp electrophysiology provide the most detailed characterization of electrophysiological effects on cellular repolarization, this technique is slow, technically demanding and very low-throughput (Gintant et al., 2016). Extracellular field potential recordings obtained through multielectrode arrays provide a means of adapting the assay to a high-throughput format, and communicates the rate of electrical activity and the timing of repolarization, but lack information regarding the morphological changes in the configuration of the AP and the actual end of repolarization. Voltage sensing optical platforms however offers significant advantage over these platforms (Chang Liao et al., 2015; Dempsey et al., 2016; Hortigon-Vinagre et al., 2016; Klimas et al., 2016), as they provide information on the whole AP waveform, which represent a readout of the integrated activity of multiple cardiac ion channels. Additionally, since the cardiotoxic effect of some drugs is evident only at elevated beat rates, insertion of genetically encoded actuators enables light-induced pacing of cells to higher beat frequencies. Combination of optogenetic pacing and voltage sensitive dyes has been reported (Park et al., 2014; Klimas et al., 2016), however the suitability of fluorescence dyes for long term incubations is questioned since fluorescent dyes can cause photodynamic damage to isolated cardiomyocytes under prolonged incubation (Schaffer et al., 1994) or potentially alter the electrophysiological properties of the cells (Novakova et al., 2008). HiPSC-CMs can be maintained in culture for a long time, and thus these cells per se (in contrast to primary animal myocytes) permit long-term experiments. Noninvasive optogenetic measurements on hiPSC-CMs transduced with genetically encoded optical actuators and sensors therefore enable in vitro evaluation of chronic drug effects and delayed cardiotoxicity, as reported in (Dempsey et al., 2016). Optogenetic electrophysiology assessment tools thus have the potential to improve sensitivity and specificity in the early detection of genuine cardiotoxicity risks, thereby reducing the likelihood of mistakenly discarding viable drug candidates and speeding the progression of worthy drugs into clinical trials (Dempsey et al., 2016; Gintant et al., 2016; Klimas et al., 2016).

We have evaluated hiPSC-CMs transduced with the commercially available constructs Optopatch and CaViar (Hochbaum et al., 2014; Hou et al., 2014) against non-transduced cells with patch clamp electrophysiology and shown that none of the measured AP parameters were affected. There were no significant differences in APD at 90, 50, or 30% repolarization, nor in peak amplitude or beat rates. The APD90 for Optopatch was 300 ± 12 ms measured with patch clamp and 320 ± 8 ms measured with optogenetic imaging, both of which compare well to the computational human ventricle APD90-value of 300 ms (O'Hara et al., 2011), as well as to reported APD90-values for ventricular-like hiPSC-CMs (312– 320 ms) (Zhang et al., 2009; Lahti et al., 2012). The measured APD parameters were selected from recommendations by the CIPA initiative, and were calculated by a MATLAB-based software that was generated by us. When looking at how well the optogenetic imaging experiments compared to patch clamp measurements, we found no significant differences between the two techniques for the Optopatch construct (**Figure 1**), whereas for the CaViar construct the APD90- and APD30-values exhibited modest, but significant differences for APD parameters between the two techniques (**Figure 2**). We utilized the CaViar construct published by Hou et al. (2014) that contains the Arch(D95N) voltage indicator and not the QuasAr2 voltage indicator published by Dempsey et al. (2016), as this newer version of CaViar was not available from Addgene at the time of our experiments. Compared to QuasAr2, Arch(D95N) has been shown to exhibit slower responses to voltage transients (Gong et al., 2013), which might provide a possible explanation for the prolongation of the APD in the Caviar expressing cells measured with optogenetic imaging. The largest difference was seen at APD90, measured close to the base of the AP, where small changes in the AP waveform due to the slower kinetics of the Arch(D95N) can results in a broader AP waveform. The newer CaViar version based on the QuasAr2 voltage indicator might possibly alleviate this shortcoming.

In order to rule out most methodological restrictions related to the cellular material, we used only the well-documented, standardized and validated commercial Axiogenesis Cor.4U <sup>R</sup> hiPSC-CMs in our experimentations (typical confluent cell monolayer is illustrated in **Supplementary Figure 2**). Future experiments should be focused on ruling out the contribution of atrial hiPSC-CMs, as well as on comparing the results from Cor.4U <sup>R</sup> cells used in this study to ventricular-enriched hiPSC-CMs such as vCor.4U <sup>R</sup> cells. In the future, continued evaluation of the most optimal cell platform will provide great value in further validating the cellular system best compatible with the optogenetic electrophysiology tools. The experimental procedure for lentiviral delivery of the optogenetic constructs was quite time-consuming, as cells had to be kept at the viral core facility until RCV negative, which took 2–3 weeks, including washing and media exchange every day, as well as one passage of the cells which resulted in loss of cardiomyocytes. One of the bigger drawbacks of optogenetic imaging is the lack of ability to determine absolute values for the resting potential. However, the cardiac AP waveform is sensitive to resting membrane potential, and changes in APD are expected if compounds induce a shift in resting voltage (Dempsey et al., 2016). We can calculate percentile differences in amplitude peak height but not compare these to amplitudes measured by patch clamp, which yields accurate numerical values. The red voltage fluorescence trace photobleaches in the first few seconds of imaging, yielding a fluorescence trace with a steep descend. To solve this problem and to accurately measure AP parameters from curves, a normalization step was inserted in the automated processing of raw data by the cPot software. Dempsey et al. (2016) tested for photobleaching or phototoxicity arising from imaging of QuasAr2 in cardiomyocytes by measuring fluorescence during 500 s of continuous red laser illumination (500 mW/mm<sup>2</sup> ) and showed a modest signal amplitude decrease of 12% during the acquisition with a small variability in the AP width, which was within the natural variation in spontaneously beating hiPSC-CMs.

Contractile and structural cardiotoxicity, seen with e.g., some kinase-targeted cancer drugs, represent another safety concern (Cheng and Force, 2010). Cellular electric impedance assays have been implemented with multielectrode assays for contractility measurements (Obergrussberger et al., 2016), but do not provide the spatial resolution to detect movements within the cell in detail, in contrast to the minimum quadratic difference method based on video motion tracking used here (Ahola et al., 2014, 2017). We aimed to evaluate whether optogenetic measurements of cardiomyocyte electrophysiology can be combined with an assay measuring the end point of the cardiomyocyte electrical activity, i.e., contraction and relaxation. To our knowledge this is the first study to combine video motion tracking with optogenetic measurement of APD and calcium transients (**Figure 3**, **Table 1**). The measurement setup provided a detailed view on the key components related to cardiomyocyte function, and revealed a physiological order of AP, calcium and contraction peaks (Bers, 2002). It widens the scope of studying drug effects as changes in any of the three signals can be quantified simultaneously. Motion analysis can also reveal information that is beyond the


CTD, calcium transient duration; CD, contraction duration. The measures illustrate mean ± standard deviation (ms), (n = 10), n.a., not applicable.

TABLE 3 | The effect of cumulating doses of E-4031 on CD90, relaxation time and motion magnitude in spontaneously beating Optopatch-transduced hiPSC-CMs.


The measures illustrate mean ± standard deviation (ms) in CD90 and relaxation time and percentage change in motion magnitude, (n = 18, 17, 20, 21 and 16, for vehicle, 3, 10, 30 and 100 nM, respectively).

\*p < 0.05.

electrical properties and ion fluxes in cardiomyocytes, such as actual biomechanical timing and possible intracellular motion defects (Ahola et al., 2014). From the contractile motion point of view, Optopatch and CaViar appear to function similarly, as can be seen as the relatively similar values describing contractionrelaxation parameters between the two constructs (**Tables 1**, **2**). None of the differences found were statistically significant (p < 0.05). The correlations between CD and CTD parameters indicated that a connection between the two can be found, but one cannot be directly deduced from the other. A very low correlation value was found in CD90, indicating high variance near baseline. This is not unexpected, as a prolongation in calcium transient near baseline does not equate to longer cell relaxation. The measured correlation values are lower than previously reported by Ahola et al. (2017) where the correlations were in the range of 0.6–0.7. However, the differences may be explained by a different calculation method of the measurement parameters in these two studies.

To assess how optogenetic measurement can reveal changes in cardiomyocyte repolarization we exposed the hiPSC-CMs to the hERG potassium channel blocker E-4031 (**Figure 4**). IKr inhibition by E-4031 prolonged APD in the late phase of repolarization consistent with the role of IKr in phase 3 of repolarization in the adult ventricular myocyte (Gintant, 2000). Cardiomyocytes showed cellular arrhythmias in response to cumulating doses of E-4031. 100 nM E-4031 has been shown to induce EADs in stem-cell derived cardiomyocytes (Peng et al., 2010). We, similarly to Obergrussberger et al. (2016) detected significant APD90 prolongation already at 30 nM under both spontaneous and paced beat rates in optogenetic measurements as well as under spontaneous beating measured by patch clamp. In both methods, the prolongation of APD under spontaneous beat rate was followed by EADs at 30–100 nM concentration of E-4031. In optogenetic imaging, however, exposure to 100 nM E-4031 more often resulted in a decrease in signal amplitude with an increase in frequency, followed by drug-induced quiescence. In patch clamp, the somewhat large variations in APD S.E.M.s were due to a small sample size in the labor-intensive patch clamp method. However, the two methods showed significant prolongation of APD90, as well as EADs detected at the same concentration (30 nM E-4031). Thus, we show that E-4031, which in clinical settings has been shown to cause the proarrhythmic event TdP, also when measured with optogenetic tools caused an increase in the APD and induced EADs. In contraction signals, E-4031 increased relaxation duration, decreased motion magnitude and caused EADs at 30 nM levels. The results suggest that contraction analysis can be a feasible tool in detecting drug responses in high-throughput applications. However, large sample sizes are required for definite conclusions as high concentrations applied to individual cells or small clusters may terminate the beating altogether, causing variances in measured parameters.

Repolarization of the cardiac AP is not only dependent on the hERG channel but on several ion channels including the IKs, the second main potassium channel involved in ventricular repolarization, and thus the length of the QT interval. To assess whether optogenetics could detect activities of this channel, we applied JNJ-303, a potent blocker of IKs, to hiPSC-CMs. Previous studies using this drug revealed no peculiar activity in standard hERG screens, but subsequently evoked unprovoked TdP in vivo in an anesthetized dog model (Towart et al., 2009). Our results (**Figure 5**) revealed a statistically nonsignificant, yet visible prolongation of the APD90 already at low concentrations of JNJ-303 under both spontaneous and paced rates, accompanied by possible delayed afterpolarizations (DADs). A significant decrease in signal amplitude starting from 1µM JNJ-303, accompanied by an increase in frequency, which was followed by drug-induced quiescence and finally beating arrest, thus indicating blocking activity of cardiomyocyte repolarization. Additional experiments with a sodium channel blocker could have shed light on how inhibited depolarization could be measured by optogenetic imaging, though this has been already reported by Dempsey et al. (2016).

Finally, we have shown that optogenetics reliably can detect changes in the AP waveform, including APD prolongation, EADs, and drug-induced quiescence. Yet, we do not propose that optogenetic electrophysiology experiments completely replace comprehensive patch clamp electrophysiological assessments, but it allows for a faster prediction of successful and safe drug candidates in a high-throughput screening (HTS) format. Optogenetics could be utilized in the early stages of preclinical drug development and could thus extensively reduce cost for the pharmaceutical industry. Selected candidates taken further for

statistical significance, where \*\*p < 0.01, \*\*\*p < 0.001.

clinical trials could then be studied in detail on a single cell level with patch clamp.

In conclusion, we have shown that optogenetic imaging allows for AP waveform recordings from a cardiomyocyte monolayer. Due to the non-invasiveness and non-toxicity of genetically encoded voltage sensors and actuators, chronic drug exposures are enabled. Furthermore, light-induced pacing of cells to elevated beat rates allows for arrhythmogenic sensitization. With the high throughput screening compatibility of hiPSC-CMs and the optogenetic technique, broader high content screens can be established with integrated contractility studies. Thus, optogenetic measurements provide an appealing alternative to electrophysiological screening of human cardiomyocyte responses for pharmacological efficacy and safety testing.

# AUTHOR CONTRIBUTIONS

SB, EO, TN, AA, ML, JH, EK, and EM: designed the research; SB, EO, and TN: collected the data; SB, EO, TN, and AA: analyzed the data; and SB, EO, and AA: wrote the manuscript. All authors reviewed the manuscript.

#### ACKNOWLEDGMENTS

We thank Prof. Adam Cohen and Prof. Emilia Entcheva for all their valuable advice when getting started in the field of optogenetics and Prof. Cohen for sharing his optogenetic constructs, and for his advice on curve processing. We thank COB Seppo Orsila and Dr. Petteri Uusimaa (Modulight) as well as Drs. Ari-Pekka Koivisto and Hugh Chapman (Orion Pharma) for meaningful insights on the research project and light sources. The fluorescence microscope instrumentation for optogenetic imaging was set up in collaboration with the Biomedicum Imaging Unit in the Faculty of Medicine and HiLIFE, University of Helsinki and we are grateful for their support. The cPot Cardiac Action Potential Calculator software was developed in collaboration with the Systems Biology Laboratory, University of Helsinki and we are grateful to Ville Rantanen for his support and expertise in MATLAB. This research was supported by the Academy of Finland, the Finnish Foundation for Cardiovascular Research, the Sigrid Jusélius Foundation, the Swedish Cultural Foundation in Finland, the Instrumentarium Science Foundation and Tekes, the Finnish Funding Agency for Innovation.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.00884/full#supplementary-material

Supplementary Figure 1 | Virus-induced cytotoxicity (LDH release) measurements. (A) Optopatch-transduced hiPSC-CMs revealed no significant increase in cytotoxicity or cytolysis compared to control (Cor.4U® non-transduced cells, dotted line), measured at 24 h after lentiviral transduction. (B) Neither CaViar-transduced hiPSCs revealed any significant cytotoxicity over control cells. Results are means ± S.E.M. from n = 3. OD, optical density.

#### REFERENCES


Supplementary Figure 2 | Confluent monolayer of hiPSC-derived cardiomyocytes. Phase contrast microscopy image (20X) showing typical structural characteristics and cell density of confluent monolayer of Cor.4U® hiPSC-CMs cultured on Geltrex-coated glass-bottom dishes for optogenetic imaging. Scale bar = 100µm.

characteristics and drug effects on human induced pluripotent stem cellderived cardiomyocytes. Toxicol. Sci. 154, 320–331. doi: 10.1093/toxsci/kfw171


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Björk, Ojala, Nordström, Ahola, Liljeström, Hyttinen, Kankuri and Mervaala. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Adult Human Primary Cardiomyocyte-Based Model for the Simultaneous Prediction of Drug-Induced Inotropic and Pro-arrhythmia Risk

Nathalie Nguyen, William Nguyen, Brynna Nguyenton, Phachareeya Ratchada, Guy Page, Paul E. Miller, Andre Ghetti and Najah Abi-Gerges\*

AnaBios Corporation, San Diego, CA, United States

Cardiac safety remains the leading cause of drug development discontinuation. We developed a human cardiomyocyte-based model that has the potential to provide a predictive preclinical approach for simultaneously predicting drug-induced inotropic and pro-arrhythmia risk.

Methods: Adult human primary cardiomyocytes from ethically consented organ donors were used to measure contractility transients. We used measures of changes in contractility parameters as markers to infer both drug-induced inotropic effect (sarcomere shortening) and pro-arrhythmia (aftercontraction, AC); contractility escape (CE); time to 90% relaxation (TR90). We addressed the clinical relevance of this approach by evaluating the effects of 23 torsadogenic and 10 non-torsadogenic drugs. Each drug was tested separately at four multiples of the free effective therapeutic plasma concentration (fETPC).

Results: Human cardiomyocyte-based model differentiated between torsadogenic and non-torsadogenic drugs. For example, dofetilide, a torsadogenic drug, caused ACs and increased TR90 starting at 10-fold the fETPC, while CE events were observed at the highest multiple of fETPC (100-fold). Verapamil, a non-torsadogenic drug, did not change TR90 and induced no AC or CE up to the highest multiple of fETPCs tested in this study (222-fold). When drug pro-arrhythmic activity was evaluated at 10-fold of the fETPC, AC parameter had excellent assay sensitivity and specificity values of 96 and 100%, respectively. This high predictivity supports the translational safety potential of this preparation and of the selected marker. The data demonstrate that human cardiomyocytes could also identify drugs associated with inotropic effects. hERG channel blockers, like dofetilide, had no effects on sarcomere shortening, while multi-ion channel blockers, like verapamil, inhibited sarcomere shortening.

#### Edited by:

Stefano Morotti, University of California, Davis, United States

#### Reviewed by:

RaffaEle Coppini, University of Florence, Italy Thomas O'Hara, Lawrence Livermore National Laboratory (DOE), United States

#### \*Correspondence:

Najah Abi-Gerges Najah.abigerges@anabios.com

#### Specialty section:

This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology

Received: 04 August 2017 Accepted: 06 December 2017 Published: 19 December 2017

#### Citation:

Nguyen N, Nguyen W, Nguyenton B, Ratchada P, Page G, Miller PE, Ghetti A and Abi-Gerges N (2017) Adult Human Primary Cardiomyocyte-Based Model for the Simultaneous Prediction of Drug-Induced Inotropic and Pro-arrhythmia Risk. Front. Physiol. 8:1073. doi: 10.3389/fphys.2017.01073

**355**

Conclusions: Isolated adult human primary cardiomyocytes can simultaneously predict risks associated with inotropic activity and pro-arrhythmia and may enable the generation of reliable and predictive data for assessing human cardiotoxicity at an early stage in drug discovery.

Keywords: human heart, adult human primary cardiomyocyte, pro-arrhythmia, inotropy, risk assessment, drug discovery and development

#### INTRODUCTION

Cardiac safety remains the leading cause of drug development discontinuation and withdrawal of marketed drugs (Piccini et al., 2009). Consequently, during the last decade strategies have been extensively employed to evaluate the cardiac safety of novel drugs at the preclinical stage. However, the strategies employed thus far have proven to be prone to false positive signals, which may lead to prematurely discontinue the development of potentially useful drugs. In other cases, the occurrence of false negative results has led to serious adverse events during clinical trials. The limited predictivity of the current strategies has stimulated a quest for more reliable tools (Sager et al., 2014; Holmes et al., 2015; Gintant et al., 2017). Given that the challenges in translating preclinical findings into successful clinical studies, seem to originate, at least in part, from the use of animal models and the inability of different species to quantitatively recapitulate human cardiac physiology and pharmacology (Perel et al., 2007; Seok et al., 2013), the use of adult human cardiac tissue has the potential to provide the preclinical models needed to enhance preclinical to clinical translation. Human heart tissues and human isolated myocytes have been used for decades in ex-vivo studies of human physiology (see, for example, Bustamante et al., 1982; Beuckelmann et al., 1992; Wettwer et al., 1993, 1994; Näbauer et al., 1996; Iost et al., 1998; Näbauer and Kääb, 1998; Jost et al., 2005; Brandenburger et al., 2012; Coppini et al., 2014; Boukens et al., 2015). However, the adoption of these methods to drug discovery has been hampered by the limited availability of human tissue for research, the variability in the quality of the samples, and the technical challenges related to human tissue's procurement and experimental interrogation. For human cardiac tissue to have practical utility in preclinical cardiac safety assessment, it is necessary to develop and validate: (i) methodologies that can provide tissue of high and consistent quality; (ii) assays that can generate predictive data and are relatively simple and scalable to medium or high throughput format. To this aim, we have developed procedures that consistently allow the procurement and experimental interrogation of human heart tissue preparations to reliably assess the toxicity risks of novel drugs (Page et al., 2016). In order to further increase the throughput and scalability of the human ex-vivo heart model, we are now reporting on the implementation of a cell-based assay that utilizes adult human primary cardiomyocytes.

Regular heart beat and myocardial contractility (inotropy) are the essential properties of cardiac function and depend on the electro-mechanical dynamics of cardiac tissue. The consequence of drug-induced irregular heart beat (pro-arrhythmia; Sager et al., 2014) and/or changes in contractility (inotropic liability; Harmer et al., 2012; Gallacher et al., 2016; Pugsley et al., 2017) can limit the utility of potential novel therapeutic applications. Therefore, it is highly recommended to assess the potential of novel drugs to induce pro-arrhythmia and inotropic risk early in the drug discovery process before advancing into later development work.

Abnormal ventricular repolarization, such as the kind observed in patients with long QT syndrome, can cause not only electrical disorders (pro-arrhythmia) but also affect the heart's contractile function (Belardinelli et al., 2009; De Ferrari and Schartz, 2009). Long QT syndrome patients exhibit abnormal left ventricular contraction, which can appear as single or double-peaked contraction transient (Nador et al., 1991; De Ferrari et al., 1994), increased dispersion of myocardial contraction and abnormal left ventricular relaxation (Nakayama et al., 1998; Haugaa et al., 2009). This correlation between electrical (action potential, AP) and mechanical (contraction) abnormalities is a consequence of the tight functional coupling (Lou et al., 2011; Kang et al., 2016), and suggest that similarly to the genetic disorders which affect the QT interval, druginduced ventricular repolarization abnormalities could lead to contractility changes. Along these lines, we investigated the possibility of developing a cardiomyocyte-based model that would allow the simultaneous evaluation of drug-related risks for pro-arrhythmia and inotropic liabilities. The main motivation of this investigation was to develop a cardiomyocyte-based model that uses adult human primary cardiomyocytes to provide a novel and predictive preclinical approach for the simultaneous prediction of drug-induced inotropic and pro-arrhythmia risk. In order to facilitate the scalability of the model, we focused on the simple measurement of a contractility-related parameter: we recorded the fractional sarcomere shortening, using a digital, cell geometry measurement system (IonOptixTM; Abi-Gerges et al., 2013) and then used measures of changes in the contractility transients to infer both inotropic as well as pro-arrhythmia risk. To address the clinical relevance of this approach, we performed a validation study to test the effects of a set of 33 reference drugs with well-characterized clinical outcomes. Both positive and negative controls were selected, including 23 torsadogenic and 10 non-torsadogenic drugs. We found that the isolated cardiomyocytes accurately exhibited drug-induced contractility changes and pro-arrhythmia that are consistent with the known clinical safety profiles of the drugs tested.

#### MATERIALS AND METHODS

#### Donor Heart Procurement

All human hearts used for this study were non-transplantable and ethically obtained by legal consent (first person or nextof-kin) from organ donors in the United States. Our recovery

#### TABLE 1 | Donor characteristics.


F, Female; M, Male; BMI, Body Mass Index; COD, Cause Of Death; EF, Ejection Fraction; CVA, Cerebrovascular Accident; ICH, Intracranial Hemorrhage; AS, Asphyxiation; HH, Human Heart; HHA, the 1st heart received on the day; HHB, the 2nd heart received the same day.

<sup>a</sup>Organ procurement organization could not transplant the heart and consequently no echocardiography was performed; N/A, Not available.

protocols were pre-approved by IRBs at each transplant center. Furthermore, all transfers of the donor hearts are fully traceable and periodically reviewed by US Federal authorities. Donor characteristics are shown in **Table 1** and exclusion criteria were previously described (Page et al., 2016).

#### Cardiomyocyte Contractility Measurement

Upon arrival at our laboratory, hearts were re-perfused with icecold proprietary cardioplegic solution as previously described (Page et al., 2016). Adult human primary ventricular myocytes were isolated enzymatically from the ventricles (Supplementary Figure 1). Digestion of the cardiac tissue was conducted at 37◦C for ∼25 min utilizing a proprietary solution which included a cocktail of proteolytic enzymes. Solutions and cells described in this paper will be available upon request. Contractility transients were measured as previously described (Harmer et al., 2012; Butler et al., 2015; Supplementary Video 1). Briefly, cardiomyocytes were placed in a perfusion chamber (FHC Inc., Bowdoin, ME, USA) mounted on the stage of an inverted Motic AE31E microscope (StellarScientific, MD, USA) and continuously perfused from a gravity fed system at 4 ml/min with myocyte Tyrode solution (see composition below) heated to ∼36◦C using an inline heater (Cell MicroControls, Norfolk, VA, USA). A video-based cell geometry system was used to measure sarcomere dynamics (IonOptix, MA, USA; Ren and Wold, 2001). The myocytes were field stimulated at voltage 50% above threshold at a 1 Hz pacing frequency, with a biphasic pulse of 3 ms duration, using a pair of platinum wires placed on opposite sides of the chamber and connected to a MyoPacer EP stimulator (IonOptix). Images were acquired at a rate of 240 Hz using an IonOptix MyoCam-S CCD camera. Digitized images were displayed within the IonWizard acquisition software (IonOptix). Optical intensity data were collected from a user-defined rectangular region of interest placed over the myocyte image. The optical intensity data represent the bright and dark bands corresponding to the Z-bands of the cardiomyocyte. The IonWizard software analyzes the periodicity in the optical density along the myocyte detecting the Z-bands by means of a fast Fourier transform algorithm.

The stability of sarcomere shortening transients was assessed by continuous recording for 2 min in Tyrode's solution establishing the vehicle control (in 0.1% dimethyl sulfoxide, DMSO). Subsequently, the test article concentration was applied for a minimum of 250 s period or until a steady-state effect was achieved. Four ascending concentrations of the test article were used, providing cumulative concentration-effect (C-E) curves. Analysis was performed using the IonWizard software. For each test condition, data for 15 contractions with or without AC or CE events were averaged, to obtain a single representative monotonic contractility transient. A series of polynomials were fitted to the five different phases of the monotonic transient. From this representative transient, fractional sarcomere shortening (which indicates the percentage of peak contraction relative to the resting length; µm) and TR90 (time to 90% relaxation; ms) were used to quantify sarcomere dynamics and delay in the relaxation of cardiomyocytes after contraction, respectively. An AC (after-contraction) was visually identified as change in the slope of the contractility transient that occurred before the next stimulus-induced contraction. CE (contractility escape) was also visually identified when the electrical stimulus did not result in a contraction transient. Presence or absence of AC and CE events was determined by examining non-averaged transients for the 4-min application article concentration. Results are expressed as mean ± s.e.m. Treatment effects on sarcomere shortening and TR90 were expressed relatively to the myocyte's specific baseline control period. AC and CE were expressed as incidence: number of cells showing events normalized by the total number of cardiomyocytes. Hill curves were fitted to sarcomere shortening C-E data using SigmaPlot v13 (Systat Software Inc., CA, USA) and used to determine IC<sup>50</sup> (concentration inducing 50% decrease in sarcomere shortening). A comparative set of experiments were also performed with quinidine and verapamil on ventricular myocytes isolated from beagle dog hearts as previously described (Abi-Gerges et al., 2013). The dog beagle hearts were obtained from BTS Research (CA, USA) following the vendor's Institutional Review Board-approved protocols. Differences were tested for statistical significance using the paired Student's t-test. A value of P < 0.05 was considered significant.

Assessment of variability was assessed as previously described (Page et al., 2016). The intra-heart and inter-heart total variabilities were evaluated as follows. For baseline vehicle condition, the intra-heart variability for each parameter of the contractility transient was calculated as the average of the all SDs (Standard Deviations) generated from all the individual cells for all of the hearts. Inter-heart (Total) variability was calculated as the SD of all cells pooled at each parameter for all hearts. For dofetilide, the mean and SD of the percent change effect in the cells from each heart were calculated separately for each of the four test concentration periods. For each concentration period, the intra-heart variability was then calculated as the average of


TABLE 2 | Concentrations tested in adult human primary cardiomyocyte-based model and ratio to clinical concentrations.

<sup>a</sup>CiPA-selected drug; <sup>b</sup>Redfern et al. (2003); <sup>c</sup>CiPA Stem Cell Working Group; TdP, Torsades de Pointes; fETPC, free Effective Therapeutic Plasma Concentration; Red, Positive pro-arrhythmia risk; Green, Negative pro-arrhythmia risk.

the all of the SDs generated from all the three individual hearts. Total variability was calculated as the SD of the mean percent change of all the cells pooled at each concentration period for dofetilide.

#### Solutions and Test Articles

The standard myocyte Tyrode solution contained (in mM): NaCl 145, KCl 4, CaCl<sup>2</sup> 1.8, MgCl<sup>2</sup> 1, glucose 11.1 and HEPES 10, pH 7.4 with NaOH. The reference drugs selected for this investigation were obtained from Sigma (CA, USA). Drugs were initially formulated in DMSO as a 1,000x stock solution. Stock solutions were diluted to the working concentrations in 0.1% DMSO on the day of the experiment. The test concentrations are indicated in **Table 2**. Ratio to fETPCs (free Effective Therapeutic Plasma Concentration) and replicates information are also shown in **Table 2**.

#### RESULTS

In order to record contractility transients in isolated cardiomyocytes, we utilized bright-field optical imaging and measured sarcomere length. With the ultimate goal of assessing both electrical (AP) as well as mechanical (contractility) drug-induced effects, we decided to focus our analysis on four parameters: TR90, incidence of AC, incidence of CE and sarcomere shortening. TR90 is correlated to the duration of the cardiac AP and delays in AP repolarization are expected to be associated with extension of the TR90 (Dipla et al., 1999; Undrovinas et al., 2006). Early-afterdepolarization (EAD) is an AP abnormality that results in a transient slope change of the AP during the repolarization phase. EAD is potentially of great relevance in the context of pro-arrhythmia risk assessment since this is believed to be the underlying cause of re-entrant


TABLE 3 | Distributions of baseline values of the contractility parameters in 189 human ventricular cardiomyocytes from 11 donor hearts.

Cont. vel., Contraction velocity; Sarc. short., Sarcomere shortening; Ret. Vel., Relaxation velocity; Tpeak, Time to peak; TR70, TR80, and TR90, Time to 70, 80, and 90% relaxation, respectively.

arrhythmia (Roden et al., 1996; El-Sherif and Turitto, 1999). The mechanical equivalent of EAD electrical abnormality is an after-contraction (Kaumann and Olson, 1968; Noda et al., 2004), a transient change of slope in the contractility transient, typically in the later portion of the relaxation phase. Drugs that interfere with cardiac depolarization or in other ways suppress the generation of a cardiac AP, result in complete inhibition of the contractility transient, an event we refer to as CE. Therefore, changes in three parameters measured from contractility transients, TR90, AC and CE can provide useful information with regards to the drug-induced alterations of the electrical behavior of cardiac cells. In addition, changes in fractional sarcomere shortening provide direct measurement of inotropic effects in cardiomyocytes.

#### Stability of the Contractility Transient in Adult Human Primary Ventricular Cardiomyocytes

Baseline properties of the contractility transients in adult human primary ventricular cardiomyocytes were investigated in 189 cardiomyocytes from 11 human donor hearts (**Table 1**). First, we calculated TR90, incidence of AC and CE, and sarcomere shortening in baseline vehicle control at a pacing rate of 1 Hz (**Table 3**). The distributions of the contractility parameters from all the vehicle baseline control periods show that at baseline, the physiological properties of isolated ventricular cardiomyocytes fall within the expected ranges (see section Discussion; **Table 3**; Supplementary Figure 2) with time to peak (TPeak) at 168 ± 3. ms and TR90 at 337 ± 8 ms. It is also important to note that during the vehicle baseline period, we never observed AC or CE events. We further assessed the intra-heart and inter-heart (Total) variability of contractility parameters in the presence of vehicle controls (Supplementary Figure 3). Our data showed that the intra-heart variability for sarcomere shortening, TPeak and TR70-90 accounted for almost 90% of the Total observed variability for each of these contractility transient parameters after exposure to the vehicle.

Next, we assessed the stability of the human cardiomyocyte preparation. We recorded vehicle time-control data in four cardiomyocytes (one heart) using multiple additions of vehicle solution spaced by 4 min each, to mimic the experimental conditions that we were set to use with the test drugs. Cardiomyocytes exhibited stable behavior for the duration of the recordings, up to 20 min (**Figure 1**). No AC or CE were observed and only a small, non-significant increase in TR90 was observed (1st, 2nd, 3rd, and 4th vehicle applications increased TR90 by 0.4 ± 2, 6 ± 2, 6 ± 3, and 5 ± 4%, respectively; p > 0.05; **Figure 1A**). Similarly, the measurements of sarcomere shortening in myocytes demonstrated good stability (**Figure 1B**).

#### Effects of Torsadogenic Drugs on Adult Human Primary Cardiomyocytes

To begin assessing the pharmacological responses of isolated adult cardiomyocytes, we selected 33 drugs, including 23 known torsadogenic (like cisapride, clarithromycin, d,l-sotalol, dofetilide, domperidone, quinidine) and 10 not previously associated with TdP arrhythmias (like mexiletine, ranolazine, verapamil; Johannesen et al., 2014; Colatsky et al., 2016; Fermini et al., 2016). Specifically, we were interested in establishing the correlation, if any, between the parameters measured in contractility transients, the clinical incidence of pro-arrhythmia and inotropic liability. The effects of the 23 torsadogenic drugs on adult human primary ventricular cardiomyocytes are shown in **Figures 2**–**4**, **Table 4,** and Supplementary Figures 4–12. Dofetilide most notably caused frequent occurrence of AC [in up to 50% of the recorded contraction transients; **Figure 2C**; n = 6 cells (1 heart)]. At the lower concentrations, the AC events consisted of a single ectopic small AC (**Figure 2A**), but at higher concentrations larger amplitude double-peak AC were also observed (**Figure 2B**). In addition, dofetilide resulted in a significant prolongation of the relaxation phase, with TR90 increase to 17 ± 6% at 10-fold of the fETPC and to 26 ± 7% at 100-fold of fETPC (**Figure 2C**). CE events were observed in 17% of the recordings, at the highest concentration tested (**Figure 2C**).

Cisapride resulted in AC events at all concentrations tested and with the highest incidence at the two highest concentrations tested: 43% at 30-fold fETPC and 30% at 100-fold fETPC [**Figure 3A**, n = 7 cells (2 hearts)]. CE events were observed at the highest concentration tested in 14% of the contraction transients. No significant changes in TR90 were observed at any concentration (**Figure 3A**). Domperidone induced AC events at all concentrations tested, CE at all concentrations

above the fETPC and significant and concentration-dependent prolongation of the relaxation phase [**Figure 3B**, n = 8 cells (1 heart)]. Quinidine and clarithromycin induced concentrationdependent increases in AC incidence, CE and prolongation of the relaxation phase [**Figure 3C**, n = 4 cells (1 heart) for quinidine; **Figure 4A**, n = 8 cells (2 hearts) for clarithromycin]. d,l-sotalol [**Figure 4B**, n = 8 cells (2 hearts)] also caused a concentrationdependent increase in TR90 and AC incidence but it did not induce CE events.

The translation predictivity of the AC parameter was used to calculate assay performance values for the adult human primary cardiomyocyte-based model (**Figures 2**–**4**; **Table 4**; Supplementary Figures 4–12). In comparison with clinical torsadogenic risk and when predicting pro-arrhythmic risk at 10-fold the fETPC of the 23 torsadogenic drugs, the human cardiomyocyte assay has an excellent sensitivity (96%) for predicting clinical pro-arrhythmic risk with very low false negative rate. This outstanding predictivity confirms the translational safety potential of the AC marker and sensitivity of human primary adult cardiomyocytes to the effects of the 23 torsadogenic drugs we tested; in particular this cellular preparation exhibits changes in contractility parameters that are

primary ventricular myocyte in the presence of vehicle control and after exposure to dofetilide at 0.02µM (A), 10-fold the fETPC, non-fitted averaged transients) and 0.06µM (B, 30-fold the fETPC, non-fitted and non-averaged transients) at a pacing frequency of 1 Hz. Note that contractility transients shown in this figure were obtained from the same cardiomyocyte. (C) Mean % change in TR90 and AC & CE incidence when cardiomyocytes were incubated with dofetilide at 1 Hz. \*P < 0.05 vs. values from vehicle.

related to the AP changes expected to be induced by the drugs (Redfern et al., 2003; CredibleMeds <sup>R</sup> , https://crediblemeds.org/). It is also important to note that the observed changes occurred at concentration ranges that are clinically relevant: all 23 drug induced contractility abnormalities, that are potentially related to pro-arrhythmia risk, starting at the fETPC.

To determine the reproducibility and reliability of adult human primary cardiomyocytes, dofetilide was tested in three donor hearts. Data summaries for the effects of dofetilide on sarcomere shortening, TR90, AC, and CE incidence are shown in

Supplementary Figures 13, 14. An unmarked level of variability was seen with sarcomere shortening (Supplementary Figure 13), TR90 (Supplementary Figure 14A), AC events (Supplementary Figure 14B), and CE incidence (Supplementary Figure 14C). For example, the mean dofetilide-induced % changes in TR90 at 30-fold the fETPC were found to be 21 ± 12, 24 ± 5, and 18 ± 5% in donor hearts 1 (n = 6 cells), 2 (n = 4 cells), and 3 (n = 5 cells), respectively. We further assessed the level of variability by assessing the intra-heart and inter-heart (Total) variability of cell responses to dofetilide (Supplementary Figure 15). Our data show that the intra-heart variability for TR90 accounted for 90% of the Total observed variability of the TR90 parameter after exposure to dofetilide concentrations (Supplementary Figure 15A). For the inter-heart variability for the dofetilide concentration period corresponding to the top test concentration, the total SD related to the mean percent

change in TR90 effects was 13.3, while the intra-heart SD for the same concentration period was 12.7. The same was true for the variability of sarcomere shortening (Supplementary Figure 15B). Taken together, these data establish that the interdonor variability is relatively small and does not add significant noise beyond what is inherent to this experimental approach.

We also confirmed that similar data could be obtained when the experiments were conducted in blinded or non-blinded fashion. For example, the effects of ibutilide were found to be similar in blinded experiments and in unblinded testing [Supplementary Figures 16, 17; n = 5 blinded cells (1 heart)].

Given that canine in-vivo models are extensively used for drug cardiac safety assessment (Pollard et al., 2010) and isolated adult cardiomyocytes from dog hearts are also commonly tested for early risk assessment (Abi-Gerges et al., 2010; Harmer et al., 2012), we compared the effects of quinidine in human and dog adult cardiomyocytes. Quinidine elicited a significantly larger increase in TR90 in myocytes from human hearts compared to canine hearts [Supplementary Figure 18A, n = 5 (1 heart)]. Furthermore, AC and CE events were only observed in quinidine-treated human myocytes (Supplementary Figure 18A). These data underscore the potential limitations of canine cardiomyocyte model in recapitulating the pharmacology observed in human cardiomyocytes.

#### Effects of Non-torsadogenic Drugs on Adult Human Primary Cardiomyocytes

Non-torsadogenic drugs, like mexiletine, ranolazine, and verapamil, are approved drugs with low clinical torsadogenic


TABLE 4 | Pro-arrhythmia prediction of the adult human primary cardiomyocyte-based model.

<sup>a</sup>CiPA-selected drug; Red, Positive pro-arrhythmia risk; Green, Negative pro-arrhythmia risk; Sarc. short., Sarcomere shortening; hiPSC-CM, human induced pluripotent stem cellderived cardiomyocyte; iCell®, hiPSC-CMs from Cellular Dynamics; MEA, Micro-electrode array; FPD, Field Potential Duration; JiCSA, Japan iPS Cardiac Safety Assessment; FDA, Food and Drug Administration; Cor.4U, hiPSC-CMs from Axiogenesis AG; EAD, Early afterdepolarization; fETPC, free effective therapeutic plasma concentration.

risk (Redfern et al., 2003; Colatsky et al., 2016; Fermini et al., 2016; CredibleMeds <sup>R</sup> ). While mexiletine and verapamil are not expected to delay ventricular repolarization, ranolazine can elicit prolongation of the QT interval in the electrocardiogram (ECG) (Duff et al., 1987; Giardina and Wechsler, 1990; Johannesen et al., 2014). None of the three drugs induced AC at any of the concentrations tested (**Figures 5**, **6**). However, mexiletine induced CE events in 30% of the transients, at the highest concentration tested [30-fold the fETPC; n = 7 cells (1 heart); **Figure 5A**]. This observation is consistent with the known sodium channel inhibitory activity of mexiletine (Qu et al., 2013). Relaxation time was significantly prolonged only by ranolazine at the highest concentration tested [100-fold of fETPC; 37 ± 11%; n = 3 cells (1 heart); **Figure 5B**]; this finding is consistent with the fact that ranolazine is known to induce QT interval prolongation at concentrations above the therapeutic dose (Chaitman, 2004; Johannesen et al., 2014). Ranolazine was also able to induce CE events, which is consistent with its known inhibitory action on sodium and calcium voltage gated channels (Antzelevitch et al., 2004). The data shows that the cardiac safety margins

are different for the three with mexiletine inducing CE events 10-fold above the fETPC, ranolazine above 30-fold the fETPC and verapamil not exhibiting any signal potentially predictive of pro-arrhythmia up to the highest concentration tested [220-fold of the fETPC; n = 4 (1 heart); **Figure 6**]. However, when the effects of verapamil were compared in dog and human adult cardiomyocytes, we observed that in dog cardiomyocytes verapamil induced a significant prolongation of the relaxation time: at 30- and 220-fold of fETPC, verapamil increased TR90 by 85 ± 19% [n = 4 cells (1 heart); Supplementary Figure 18B] and 3 ± 4% (**Figure 6B**), respectively. These results highlight the inability of the dog cardiomyocyte model to accurately predict the effects of verapamil on the human heart.

The AC parameter was again used to calculate specificity value for the adult human primary cardiomyocyte-based model (**Figures 5**, **6**; **Table 4**; Supplementary Figures 19–21). In comparison with clinical torsadogenic risk and when predicting risk at 10-fold the fETPC of the 10 non-torsadogenic drugs, the human cardiomyocyte assay has an excellent specificity (100%) for predicting the safety of the 10 non-torsadogenic drugs. Thus, adult human primary cardiomyocytes have a great value as a specific assay to predict the safety of drugs.

#### Effects of Reference Drugs on Sarcomere Shortening in Adult Human Primary Cardiomyocytes

We then analyzed the effects of the 33 reference drugs on sarcomere shortening in adult human primary ventricular

from an adult human primary ventricular myocyte in the presence of vehicle control and after exposure to verapamil at 0.01, 0.1, 1, and 10µM (0.2-, 2-, 22-, and 222-fold the fETPC, respectively) at a pacing frequency of 1 Hz. (B) Mean % change in TR90 and AC & CE % incidence when cardiomyocytes were incubated with verapamil at 1 Hz. P > 0.05 vs. values from vehicle.

cardiomyocytes. For example, while dofetilide and d,lsotalol, hERG channel blockers, had no effects on sarcomere shortening (**Figures 7A,B**), multi-ion channel blockers, like cisapride, clarithromycin, domperidone, mexiletine, ranolazine, quinidine, and verapamil all inhibited sarcomere shortening (**Figure 7**). Additionally, the concentration-dependence of the negative inotropic effects of these multi-ion channel blockers (**Figures 7A,C**) is also evaluated in the context of the fETPC (**Figures 7B,D**). The same was true for other hERG channel blockers (like erythromycin, moxifloxacin and sematilide) and multi-ion channel blockers (Supplementary Figures 4–12 and 19–21; **Table 5**). Thus, these data demonstrate that human cardiomyocytes are of great value to screen/identify drugs associated with inotropic effects, help ranking compounds for progression to next drug discovery phases and establish human safety margins (**Table 5**).

When the effects of quinidine on sarcomere shortening were compared in human and dog cardiomyocytes, we found that the drug was 11-fold more potent in human ventricular myocytes compared to canine cells (Supplementary Figures 22A,B). Conversely, the negative inotropic effect of verapamil was similar between human and canine cells (Supplementary

Figures 22C,D). These data clearly show the ability of isolated human cardiomyocytes to identify multi-ion channel drugs associated with inotropic risk and further stress the challenges in cross-species translation for cardiac risk assessment.

## DISCUSSION

In the present work, we wanted to evaluate the potential of a novel strategy for addressing pre-clinical cardiac risk assessment. The goal was to establish and validate, a novel approach that would be: (i) human-relevant and cell-based; (ii) amenable to high-throughput screening; (iii) reliant on non-invasive measurements; (iv) simple to implement and yet able to provide a rich data set that could address both pro-arrhythmia as well as inotropic risks. We have recently established methods that enable standardized organ procurement protocols and the experimental utilization of ventricular trabeculae from human donor hearts for ex-vivo cardiac safety studies (Page et al., 2016). Our previous work established the low donor-to-donor variability with regards to physiological and pharmacological properties of these ex-vivo preparations and provided evidence for the ability of that model to distinguish between pro-arrhythmic and non-pro-arrhythmic drugs. We now further extend the previous work by reporting on the isolation and experimental interrogation of human ventricular cardiomyocytes. We describe the use of ventricular human cardiomyocytes for drug cardiac safety assessment using an ex-vivo model which addresses all four features discussed above: (i) the assay we developed is based on human cells; (ii) it relies on the measurement of contractility, an endpoint for which numerous options are available for performing mediumor high-throughput assays; (iii) it utilizes bright field optical imaging for measuring sarcomere shortening. This provides a non-invasive methodology which avoids the use of fluorescent dyes and the potential for chemo- or photo-toxicity; and (iv) the optically-based measurement of sarcomere shortening is simple to implement but, thanks to the utilization of refined analysis endpoints of the contractility transients, enables tracking parameters relevant to pro-arrhythmia risk as well as inotropic risks.

One critical component of our work is the utilization of data obtained from contractility measurements to infer the effects of drugs, not only with regards to inotropic effects, but also for making prediction of pro-arrhythmia risk. The justification for this approach derives from the tight functional coupling between the electrical and mechanical behavior of cardiac cells (Lou et al., 2011; Kang et al., 2016). It is well-documented that abnormal ventricular repolarization leads to contraction abnormalities: for example, delays in the repolarization phase of the cardiac AP and triggered EADs, result in delays of relaxation phase and AC events in the contraction cycle (Nador et al., 1991; De Ferrari et al., 1994; Nakayama et al., 1998; Belardinelli et al., 2009; De Ferrari and Schartz, 2009; Haugaa et al., 2009).

We first established that our methods could provide human adult myocytes exhibiting the functional parameters expected of healthy and functionally competent cardiac tissue. Our data on the contractility parameters (summarized in **Table 3**) are in agreement with previous reports (Gerdes et al., 1992; Davies et al., 1995, 1996; del Monte et al., 1995). Furthermore, our



IC50; Concentration inducing 50% decrease in sarcomere shortening; Hill equation using SigmaPlot v13 was fitted to sarcomere shortening concentration-effect curves, assuming drugs would eventually cause complete inhibition of the contractility when they decreased sarcomere shortening by ≥25%. <sup>a</sup>CiPA-selected drug; fETPC, free effective therapeutic plasma concentration.

measurements of sarcomere shortening, as well as the findings from the previously cited papers, are all well within the range of the distance between the Z-bands (i.e., sarcomere length) of 1.6–2.2µm in human hearts (Klabunde, 2005). Our baseline sarcomere shortening, TPeak and TR90 values agree with those reported by Lyon et al. (2009), although they are not consistent with the data reported by del Monte et al. (1995): TPeak and TR90 were higher in the del Monte study. A plausible explanation for the discrepancy is that, in del Monte study, the cardiomyocytes were paced at lower frequency, 0.2 Hz, compared to the 1 Hz pacing frequency used throughout our study. Interestingly, the TR90-values that were observed in this study and in the study by Lyon et al. (2009) are almost identical to the values previously reported for AP duration at 90% repolarization (Franz et al., 1988; Kang et al., 2016; Page et al., 2016), further supporting the functional interrelation between the electrical (AP) and mechanical (contractility) in cardiomyocytes (see also Lou et al., 2011). Additionally, cardiomyocytes obtained from 11 donor hearts showed a relatively low total variability for the contractility parameters after exposure to the vehicle control. The stability of the human adult cardiomyocyte preparation was then evaluated in time-matched vehicle control experiments. During the course of these experiments, and for the total of 20 min per experiment, no significant change was observed in sarcomere shortening and TR90, and AC or CE were not observed.

Next we assessed the effects of reference drugs with wellcharacterized clinical outcomes, including 23 torsadogenic and 10 non-torsadogenic drugs. Torsadogenic drugs, like dofetilide and d,l-sotalol, two hERG blockers, caused an increase of TR90 and evoked AC events starting at 10-fold fETPCs. These findings agree with clinical measurements of the QT interval following administration of these drugs, as well as reports of TdP arrhythmia for the same molecules (see, for example, Soyka et al., 1990; Torp-Pedersen et al., 1999; Johannesen et al., 2014; Colatsky et al., 2016). Moreover, dofetilide and d,l-sotalol did not significantly affect sarcomere shortening up to the highest multiple of fETPCs (100- and 30-fold, respectively). Dofetilide and d,l-sotalol lack of effect on cardiomyocyte contractility is in agreement with myocardial contractility data reported in clinical studies (FDA labels for both drugs; Brooks et al., 1970; Rasmussen et al., 1992; Holubarsch et al., 1995). Similarly to dofetilide and d,l-sotalol, other torsadogenic drugs (like cisapride, clarithromycin, domperidone, and quinidine) also increased TR90 and induced ACs. While cisapride, domperidone and quinidine induced ACs starting at fETPCs, clarithromycin induced ACs starting at 10-fold the fETPC. These findings agree with the data reported for these 4 drugs in humans (see, for example, Koster and Wellens, 1976; Roden et al., 1986; Lee et al., 1998; Vitola et al., 1998; Kamochi et al., 1999; Barbey et al., 2002; Johannes et al., 2010; van Noord et al., 2010; Johannesen et al., 2014; Colatsky et al., 2016). In contrast to dofetilide and d,lsotalol, cisapride, clarithromycin, domperidone, and quinidine inhibited sarcomere shortening in cardiomyocytes, as had been previously shown in human myocardium (Nawrath and Eckel, 1979; Kirch et al., 1992). This effect on sarcomere shortening is in line with the ability of these drugs to simultaneously block, not only the hERG potassium channel (Redfern et al., 2003), but also other cardiac ion channels, like Na<sup>+</sup> and Ca2<sup>+</sup> channels (Gluais et al., 2003; Harmer et al., 2011; Mirams et al., 2011; Kramer et al., 2013; Crumb et al., 2016). The remaining 17 torsadogenic drugs displayed similar torsadogenic and inotropic behaviors. Additionally, AC incidence seen at fETPCs in our study is consistent with reports of TdP cases with therapeutic concentrations (like with quinidine; Koster and Wellens, 1976; Roden et al., 1986). TdP risk is also known to increase with increasing concentrations as a result of administering a high dose or drug accumulation in plasma or in cardiac tissue (Mounsey and DiMarco, 2000; Reiffel and Appel, 2001). Such a dose-risk relationship was observed in our study in which AC incidence increased as the testing concentration was elevated. Moreover, human cardiomyocytes identified with excellent sensitivity (96%) drugs associated with pro-arrhythmic risk, displayed consistent reproducibility of ibutilide- and dofetilide-induced inotropic and pro-arrhythmia risk with a relatively low total variability of the pharmacological response to dofetilide. Altogether, our data with the 23 torsadogenic drugs support the potential of these human cardiomyocytes, combined with measurement of contractility transients, to significantly enhance preclinical cardiac safety assessment by stopping true positive compounds from being developed as novel therapies. Pacing frequency may influence kinetic drug binding in ion channels and usage of one pacing frequency may lead to false negative outcomes. However, human cardiomyocytes assessed at only 1 Hz pacing frequency (our study) had an excellent sensitivity. This indicates that these 1 Hz-paced cells would only be associated with 4% chance in incorrectly categorizing drugs as false negatives. If the chemical space of a drug discovery project is found to be frequency-dependent, re-assessment of 1 Hz-categorized true negative compounds at slower or faster pacing rate would be recommended. Finally, cell-to-cell coupling may attenuate AC events in multicellular cardiac preparations compared to isolated uncoupled cardiomyocytes. Preliminary findings show that ventricular trabeculae, like human cardiomyocytes, could differentiate between the safety of ranolazine and the torsadogenic potential of dofetilide, and identify the inotropic risk associated with ranolazine (data not shown). Although these data are very encouraging, a future study is necessary to determine the influence of cell-to-cell coupling on the prediction of drug-induced pro-arrhythmic risk.

The 10 non-pro-arrhythmic drugs used in this study are multi-ion channel blockers (Liu et al., 1998; He et al., 2003; Antzelevitch et al., 2004; Kramer et al., 2013; Anon, 2014; Crumb et al., 2016); possibly due to their multi-ion channel activity, they were also able to decrease sarcomere shortening in human isolated cardiomyocytes. Importantly though, none of these non-pro-arrhythmic drugs induced AC events, even when tested at large multiples of fETPCs. For example, mexiletine, ranolazine, and verapamil induced no AC events at 30-, 100- and 222-fold above fETPCs, respectively. The lack of clinical QT interval prolongation and pro-arrhythmia risk with these three drugs (see, for example, Ritchie et al., 2006; Johannesen et al., 2014; Vicente et al., 2015) has been explained with their ability to simultaneously inhibit the hERG channel and Ca2<sup>+</sup> channels (verapamil; Vicente et al., 2015; Crumb et al., 2016) or late Na<sup>+</sup> inward currents (mexiletine and ranolazine; Johannesen et al., 2016; Vicente et al., 2016). In fact, these electrophysiological effects may explain the antiarrhythmic activity of mexiletine and ranolazine (Duff et al., 1987; Giardina and Wechsler, 1990; Moss et al., 2008). In agreement with our sarcomere shortening data, verapamil and mexiletine (dosed at high multiples of the therapeutic plasma levels) were found to reduce contractility and cardiac ejection fraction (Gottlieb and Weinberg, 1992; Ritchie et al., 2006). Moreover, mexiletine (Shanks, 1984; Stein et al., 1984; Sami and Lisbona, 1985) and ranolazine (Murray and Colombo, 2014) were shown to not affect contractility at therapeutic plasma levels. This emphasizes the importance of assessing drug effects as a function of the fETPC. Therefore, use of C-E curves normalized to the fETPC enables a more accurate ranking of drug risk and consequently more educated decision at early drug discovery stage. Consequently, human cardiomyocytes identified with excellent specificity (100%) the safety of the 10 nontorsadogenic drugs tested in this study and, when combined with measurement of contractility, they may have a great value in identifying true negative compounds and hence supporting the development of new drugs without inotropic and pro-arrhythmia risk.

Side by side comparison in human and canine adult cardiomyocytes for two of the compounds highlighted the potential for interspecies differences in pharmacological responses. In our experiments cardiomyocytes from dog exhibited limited sensitivity to the effects of quinidine, with a right shift in the concentration dependence of TR90 prolongation and no observed AC or CE events, which in our model would result in underestimation of the pro-arrhythmic risk of this drug. In addition, quinidine had a more potent negative inotropic effect in human compared to dog myocytes. The underlying cause for these discrepancies could be the different affinities of the drug for canine and human K+, Na+, and Ca2<sup>+</sup> channels; it is also possible that species-specific differences in the relative levels of expression of channels responsible for inward and outward currents, may lead to the discrepancy in pharmacological responses. In the case of verapamil, both human and dog myocytes exhibited similar inotropic effects, but in dog myocytes a significant prolongation of the TR90 was observed, which was not measured in the human cells. Such a lack of cross species consistency of drug effects is an obvious concern, given how much reliance is still placed on the use of animal models for complex in-vivo cardiovascular safety studies. Given the discrepancies that we and others have highlighted (Perel et al., 2007; Seok et al., 2013), it would seem prudent to assess each new drug candidate using the approach we have described to circumvent the translatability issues of the animal model.

Recent efforts to develop and validate new robust, reliable and predictive human cardiac safety assessment tools (Sager et al., 2014; Holmes et al., 2015; Gintant et al., 2017) have been focused primarily on human stem cell-derived cardiomyocytes (hSC-CMs) (see, for example, Zhao et al., 2016; Gintant et al., 2017). It has been pointed out that hSC-CM lack several features found in their adult primary homologs (van Meer et al., 2016) and attempts at improving the extend of hSC-CMs maturation have been made (Veerman et al., 2015; Sala et al., 2016). In **Table 4** we have summarized the findings of different studies in which the same 33 drugs presented in this study were used. While the degree of success of hSC-CMs in correctly classifying pro- and non-proarrhythmic drugs varies, it is also apparent that hSC-CMs have a particularly high rate of false positive and false negative findings when multi-ion channel blockers are tested. This is not surprising, given the known challenges in fully differentiating these cells into a desired cardiac subtype and maturing them to the adult phenotype, which most likely results in non-physiological levels of expression of the conductances that govern the cardiac AP (Qu et al., 2013; Blinova et al., 2017).

Another major initiative currently underway to improve the existing cardiac safety paradigm is the CiPA (Comprehensive in vitro Pro-arrhythmia Assay; Sager et al., 2014; Fermini et al., 2016). Functional assessment of drug effects on multiple cardiac ion channels from cell lines and in-silico modeling of drug effects, to generate a pro-arrhythmia score, are the core elements of the CiPA initiative (Sager et al., 2014). Under the strategy being currently evaluated, CiPA-derived prediction of risk could then be confirmed in hSC-CMs (Sager et al., 2014; Colatsky et al., 2016; Crumb et al., 2016; Fermini et al., 2016; Gintant et al., 2016; Li et al., 2017; Windley et al., 2017). Each element of the CiPA strategy faces significant challenges. Predictive in-silico modeling of drug effects critically depends on the accurate measurement of drug effects for each one of the ion channels included in the simulation (Fermini et al., 2016). This is of fundamental importance both at the stage of algorithm parameters' tuning as well as at the later stage of drug risk evaluation. While the experimental measurement of IC<sup>50</sup> for each one of the channels being modeled is a seemingly straightforward task, two often overlooked challenges, undermine the reliability of these measurements. While many technologies are available for obtaining precise measurements of the concentration-response inhibition curves, obtaining accurate measurements is extremely difficult. In particular, a very large proportion of small molecules active on the principal inward conductances (Na<sup>+</sup> and Ca2<sup>+</sup> inhibitors) exhibit use dependence. This renders the magnitude of observed inhibition completely dependent upon both the specific voltage waveform as well as the stimulation frequency. Therefore, a truly accurate IC<sup>50</sup> could only be obtained by performing the measurement using voltage clamp recordings while stimulating the cells with the cardiac AP waveform at the physiological rate of about 1 Hz. Technical and biological constraints render this experimental design extremely challenging and impractical with the result that the IC<sup>50</sup> for the inward conductances are often not accurate. This is compounded by the second challenge, which is created by the fact that the cardiac AP is the result of the non-linear interaction of many inward and outward conductances. The non-linearity amplifies the effects of errors in the IC50, when one attempts to combine all the drug's effect on the various ion channels in a simulation aimed at modeling the pharmacological effects on the cardiac AP.

In principle, human adult primary cardiomyocytes could bypass all the above-mentioned challenges and limitations. These cells provide a naturally integrated system and are the minimal unit recapitulating all the key features of cardiac function: AP generation and excitation-contraction coupling. By virtue of their derivation from human adult hearts, they do not require any re-engineering or other artificial manipulation of their gene expression profile. In fact, they could provide the most clinically relevant model for the early assessment of potential cardiac risks of new drugs. This strategy would require adequate throughput to enable the screening of tens to hundreds of molecules per week. The endpoint we have used in the present study provide both low technical complexity and high degree of information with regards to drug's effect and pro-arrhythmia and inotropic risks. Recent technological developments hold great promises for the ability to implement optically based contractility measurements in high throughput platforms and could greatly facilitate the adoption of this innovative approach. Importantly, the data generated in the model we have developed, could be used to fine tune the parameters of in-silico models of the human heart (see Britton et al., 2017), without requiring any reliance on difficulty to measure individual ion channel effects. The in-silico models could then be invaluable for deconvoluting the signals that a drug may generate in the human adult myocyte assay, providing specific guidance as to the mechanism underpinning the observed signals and therefore guiding targeted medicinal chemistry effort to remove the undesired activity. This new paradigm may potentially have the following core elements: (i) Functional evaluation of drug effects on human ventricular myocytes; (ii) modeling-based deconvolution of the observed drug effects, if any, and identification of the potential undesired activities; (iii) mitigation of the liability with medicinal chemistry; and (iv) confirmation of successful elimination of the liability in cardiomyocytes. If the compound is found not to be associated with inotropic and pro-arrhythmia risk, it could simply progress to next discovery milestone. Finally, in addition to the study of normal adult human primary cardiomyocytes presented in the present study, the opportunity now exists for the use of adult cardiomyocytes from highly prevalent disease conditions (diabetes, cardiac hypertrophy, heart failure, etc.) or disease- and patient-specific hSC-CM lines, and therefore, for the ability to assess how cardiac toxicity risk may be affected by common comorbidities.

In conclusion, the results of the present investigation suggest that the adult human primary cardiomyocyte-based model has the potential to simultaneously predict risk associated with inotropic activity and pro-arrhythmia, and enables, for the first time, the generation of reliable and predictive human cardiotoxicity data during early phases of the drug discovery process.

#### AUTHOR CONTRIBUTIONS

NN, GP, PM, AG, and NA-G: designed the study; NN, WN, BN, and PR: performed experiments; NN, WN, GP, and NA-G: analyzed data; PM, AG, and NA-G: wrote the article.

#### ACKNOWLEDGMENTS

This work was supported by AnaBios Corporation.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.01073/full#supplementary-material

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**Conflict of Interest Statement:** All authors are employed by AnaBios Corporation.

Copyright © 2017 Nguyen, Nguyen, Nguyenton, Ratchada, Page, Miller, Ghetti and Abi-Gerges. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Action Potential Recording and Pro-arrhythmia Risk Analysis in Human Ventricular Trabeculae

Yusheng Qu<sup>1</sup> \*, Guy Page<sup>2</sup> , Najah Abi-Gerges <sup>2</sup> , Paul E. Miller <sup>2</sup> , Andre Ghetti <sup>2</sup> and Hugo M. Vargas <sup>1</sup>

*1 Integrated Discovery and Safety Pharmacology, Amgen Inc., Thousand Oaks, CA, United States, <sup>2</sup> AnaBios Corporation, San Diego, CA, United States*

#### Edited by:

*Esther Pueyo, University of Zaragoza, Spain*

#### Reviewed by:

*Jose Vicente, United States Food and Drug Administration, United States Masamichi Hirose, Iwate Medical University, Japan Tamas Banyasz, University of Debrecen, Hungary Norbert Jost, University of Szeged, Hungary*

> \*Correspondence: *Yusheng Qu yqu@amgen.com*

#### Specialty section:

*This article was submitted to Cardiac Electrophysiology, a section of the journal Frontiers in Physiology*

Received: *31 August 2017* Accepted: *14 December 2017* Published: *05 January 2018*

#### Citation:

*Qu Y, Page G, Abi-Gerges N, Miller PE, Ghetti A and Vargas HM (2018) Action Potential Recording and Pro-arrhythmia Risk Analysis in Human Ventricular Trabeculae. Front. Physiol. 8:1109. doi: 10.3389/fphys.2017.01109* To assess drug-induced pro-arrhythmic risk, especially Torsades de Pointe (TdP), new models have been proposed, such as *in-silico* modeling of ventricular action potential (AP) and stem cell-derived cardiomyocytes (SC-CMs). Previously we evaluated the electrophysiological profile of 15 reference drugs in hESC-CMs and hiPSC-CMs for their effects on intracellular AP and extracellular field potential, respectively. Our findings indicated that SC-CMs exhibited immature phenotype and had the propensity to generate false positives in predicting TdP risk. To expand our knowledge with mature human cardiac tissues for drug-induced pro-arrhythmic risk assessment, human ventricular trabeculae (hVT) from ethically consented organ donors were used to evaluate the effects of the same 15 drugs (8 torsadogenic, 5 non-torsadogenic, and 2 discovery molecules) on AP parameters at 1 and 2 Hz. Each drug was tested blindly with 4 concentrations in duplicate trabeculae from 2 hearts. To identify the pro-arrhythmic risk of each drug, a pro-arrhythmic score was calculated as the weighted sum of percent drug-induced changes compared to baseline in various AP parameters, including AP duration and recognized pro-arrhythmia predictors such as triangulation, beat-to-beat variability and incidence of early-afterdepolarizations, at each concentration. In addition, to understand the translation of this preclinical hVT AP-based model to clinical studies, a ratio that relates each testing concentration to the human therapeutic unbound Cmax (Cmax) was calculated. At a ratio of 10, for the 8 torsadogenic drugs, 7 were correctly identified by the pro-arrhythmic score; 1 was mislabeled. For the 5 non-torsadogenic drugs, 4 were correctly identified as safe; 1 was mislabeled. Calculation of sensitivity, specificity, positive predictive value, and negative predictive value indicated excellent performance. For example, at a ratio of 10, scores for sensitivity, specificity, positive predictive value and negative predictive values were 0.88, 0.8, 0.88 and 0.8, respectively. Thus, the hVT AP-based model combined with the integrated analysis of pro-arrhythmic score can differentiate between torsadogenic and non-torsadogenic drugs, and has a greater predictive performance when compared to human SC-CM models.

Keywords: action potential, Pro-arrhythmic risk, human ventricular tissue, TdP assessement, In-vitro models

# INTRODUCTION

The pharmaceutical industry has been conducting studies according to ICH S7B guideline (ICH S7B, 2004) for preclinical assessment and ICH E14 (ICH E14, 2005) guideline for clinical evaluation since 2005 to understand drug-induced proarrhythmic risks, especially Torsades de Pointes (TdP). In July of 2013, a novel paradigm, the comprehensive in-vitro pro-arrhythmic assessment (CiPA), was proposed (FDA-HESI-Cardiac Safety Research Consortium Workshop, Sager et al., 2014) as a definitive approach for directly assessing proarrhythmic risks using in-vitro and in-silico approaches that incorporate multi-ion channel potencies, i.e., moving beyond hERG potency alone. The CiPA approach for assessing proarrhythmic risk is composed of 3 models (Sager et al., 2014), (1) potency determination of 3–7 cardiac ion channels; (2) insilico action potential (AP) modeling; and (3) drug effects on the electrical activity of human stem cell-derived cardiomyocytes (hSC-CM). The CiPA initiative has propelled a multitude of invitro activities in assay development and validation, in particular in regard to hSC-CM and in-silico modeling of ventricular electrophysiology (e.g., Abi-Gerges et al., 2017; Ando et al., 2017; Blinova et al., 2017).

For understanding the potential of hSC-CM in assessing proarrhythmic risk, we have tested a set of 15 compounds (ten hERG blockers; four Na channel blockers; one IKs blocker) with a well understood pro-arrhythmic potential in two models of hSC-CM: (1) human embryonic stem cell (hESC)-CM model using traditional patch clamp technique (Qu et al., 2013), and (2) human induced pluripotent stem cell (hiPSC)-CM model using Maestro multi-electrode array (MEA) platform (Qu and Vargas, 2015). This set includes 6 compounds that are included in the CiPA calibration set: dofetilide, sotalol, cisapride, terfanadine, mexiletine, and ranolazine, with 2 in each TdP risk categories (high, intermediate, and low). We found that AP recordings in hESC-CM are sensitive to repolarization delay induced by hERG blockers, but less sensitive for identifying Nav1.5 inhibition, and insensitive to a potent and specific IKs blocker. Consistently, MEA recordings in hiPSC-CM demonstrate that this model would have a high false positive rate when evaluating proarrhythmic risk, which could lead to premature termination of drug candidates, a highly undesirable outcome for early safety screening assays. In addition, this model is not able to differentiate Na<sup>+</sup> channel blockade from hERG blockade due to reduced repolarization reserve in hSC-CM. Our experiences with hSC-CM indicate that pro-arrhythmia risk assessment in hSC-CM is not ready for primetime. Our findings are consistent with the outcome of a recent industry survey conducted by the Safety Pharmacology Society (Authier et al., 2017), which reported that only 21% of responders considered hSC-CM representative of adult cardiomyocytes and provide reliable data as a nonclinical safety assay.

To calibrate the performance of in-silico modeling of ventricular AP and hSC-CM, it is important to benchmark adult human ventricular APs, presently regarded as the gold standard for the investigation of pharmacological targets and for the prediction of the pro-arrhythmic potential of novel compounds. A recent publication by Page et al. (2016) described the AP recordings in human ventricular trabeculae for assessing pro-arrhythmia risk by testing 3 TdP agents and 2 non-TdP agents. The TdP risk of these 5 agents were differentiated clearly in this human tissue-based platform by measuring AP-related parameters. To validate this approach independently, we tested and analyzed blindly the same 15 agents that have been tested in hSC-CM (Qu et al., 2013; Qu and Vargas, 2015) in human ventricular trabeculae so that a head-to-head comparison could be performed between electrophysiological recordings in hSC-CM and AP recordings in mature human ventricular tissue.

# METHODS

# Donor Heart Procurement

All human hearts that were used for this study were obtained by legal consent from organ donors in the US. Policies for donor screening and consent are the ones established by the United Network for Organ Sharing. Organizations supplying human tissues to AnaBios follow the standards and procedures established by the US Centers for Disease Control and are inspected biannually by the Department of Health and Human Services. Tissue distribution is governed by internal IRB procedures and compliance with HIPAA regulations regarding patient privacy. All organ donor transfers to AnaBios are fully traceable and periodically reviewed by US Federal authorities.

AnaBios obtained donor hearts from adults aged 17–60 years old. Some donors were trauma victims but the following conditions were excluded: Ejection fraction <45%, HIV, cardiac death, HBV, congenital LQT syndrome, HCV, LOT syndrome, MRSA, downtime >20 min, ongoing infections, positive blood cultures without treatment and 48-h results.

Donor hearts from males and females were harvested using AnaBios' proprietary surgical techniques and tools and were shipped to AnaBios via dedicated couriers. Upon arriving at AnaBios, each heart was assigned a unique identifier number that was reproduced on all relevant medical history files, data entry forms and electronic records.

# Recording of Action Potentials in Human Ventricular Trabeculae

Tissue dissection: the procedures of tissue dissection and recording were similar to what had been previously described (Page et al., 2016). Briefly, the human heart was transferred into a dissection vessel containing a cold (4◦C), fresh proprietary dissection solution. The heart was maintained completely submerged in dissection solution. Ventricular trabeculae were dissected and transferred to the recording chamber.

Recording of APs: The approach used to record APs is similar to that in a recent study (Page et al., 2016). Briefly, a single tissue was mounted into the experimental chamber filled with oxygenated Tyrode's external solution. The temperature of the solution was maintained at 37◦C with flow rate at 5 mL per minute. The tissue was allowed to equilibrate for 30–60 min with stimulation (3 V, 3 ms) at a frequency of 1.0 Hz. High impedance borosilicate microelectrodes were prepared with a tip resistance of 10–20 M once filled with 3 M KCl. Upon tissue impalement, the membrane potential was allowed to stabilize (typically, around −85 mV). Tissues with resting membrane potentials more positive than −75 mV were rejected. Bipolar stimulation at 1.5x threshold was applied and recordings were performed in continuous mode with sampling at 20 kHz using ADInstruments and LabChart Software.

Tissue exclusion Criteria: (1).Interruption of perfusion/oxygenation; (2). Absence of Aps following stimulation at baseline; (3). Time frame of drug exposure not respected; (4). Unstable response to stimulation at baseline; (5). Resting membrane potential (RMP) > −75 mV; 7). Maximal amplitude of AP (AMAX) < 70 mV; 8). AP duration at 90% repolarization (APD90) < 200 ms or >450 ms.

Experimental Procedure: Each test article was evaluated at 4 concentrations in 4 ventricular trabeculae derived from a minimum of 2 donor hearts. Testing concentrations were chosen based upon human free ETPC, aiming to cover 1– 100-fold of human free ETPC. All tissues tested respected the treatment sequence and time course designated in **Figure 1**. Briefly, following stabilization of each tissue, APs were collected and assessed for 31 min in vehicle control solution (Tyrode with 0.1% DMSO) at stimulation frequencies of 1 Hz for 25 min, 2 Hz for 3 min and then 1 Hz for 3 min. Following this vehicle control period, 4 concentrations of a test compound were applied sequentially and cumulatively. Each concentration was applied for 31 min with the same stimulation sequence as in vehicle controls.

#### Data Analysis

For each frequency tested, the last 30 APs acquired at the end of the period were averaged for vehicle controls and for each test article concentration. Analysis at 1 Hz included only the last 30 APs of the initial 25-min incubation period. The following AP parameters and pro-arrhythmia variables were analyzed offline upon the completion of recordings:


as STV from APD90 Poincare plots over a period of 30 sec. STV for all APDs was calculated as STV = 6|APDn+1−APDn|/(30× √ 2), where APD (n) and APD(n+1) are the APDs for the nth AP and the following one, respectively.


Compound effects were quantified relative to the data collected during the vehicle control period (see **Figure 1**). Threshold values for changes over baseline control for APD30, APD50, APD90, Triangulation and STV at 1 and 2 Hz pacing frequencies have been determined in a previous validation study (Page et al., 2016). Additionally, based on AnaBios historical data, threshold values for changes over baseline control for AP instability, APD alternans, Maximum APD dispersion and ERP (APD) were based upon an effect level of 10%. When applicable, differences were tested for statistical significance using the unpaired Student's t-test. A value of P < 0.05 was considered significant.

AP parameters and pro-arrhythmia variables were combined into a meaningful, single score to assess the pro-arrhythmic risk of a compound at each concentration tested. The pro-arrhythmic potential of compounds at 1 or 2 Hz was determined by assigning a weighted scale to each variable (**Table 1**). The maximum score (the sum) calculated at either 1 or 2 Hz was selected as The Pro-Arrhythmic Potential Score for each concentration. Based on historical data of this APD assay, a score ≤ 10 indicates

#### TABLE 1 | Determination of the pro-arrhythmia score.


*Similar weighted scales were used for STV(APD90) at 2 Hz, although increase or decrease % changes in STV(APD90) were as follows: 0–164%,* >*164–200%,* >*200–220%,* >*220– 240%,* >*240–260%,* >*260–300% and* >*200%. A linear weighted scale was assigned to each variable and this assignment took into consideration (i) the role of each variable during pro-arrhythmia and (ii) drug-induced % change or % incidence. To identify the pro-arrhythmic risk of each drug, a pro-arrhythmic score was calculated as the weighted sum of % drug-induced changes in various AP parameters at each concentration. Score was determined at 1 and 2Hz pacing frequencies and the maximum score at 1 or 2Hz was selected as The Representative Score. Based on historical AP data analysis, a score size of 10 was applied to all drugs: score* ≤*10 indicated no pro-arrhythmic potential, while a score* >*10 indicated a pro-arrhythmic potential. Whereas decrease or increase in weighted scales for each variable indicated anti-pro-arrhythmic potential or potential pro-arrhythmia risk, respectively, a significant decrease in APD90 or triangulation indicated potential pro-arrhythmia risk. Threshold values for changes over baseline control for AP parameters in this human* ex-vivo *AP model were reported in Page et al. (2016).*

a non-pro-arrhythmic potential, while a score ≥ 10 indicates pro-arrhythmic potential.

#### Reagents

Sertindole (CAS # 106516-24-9) and Moxifloxacin (151096- 09-2) were purchased from ChemPacific (MD, USA), L768673 (Selnick et al., 1997) was purchased from Albany Molecular Research Inc. (N Y, USA), Cisapride (81098-60-4) was from Tocris Bioscience (MO, USA), Ranolazine, Alfuzosin, Mexiletine, Flecainide, Terfenadine, Lamotrigine, DL-sotalol, and Terodiline were from Sigma-Aldrich (MO, USA), Dofetilide was synthesized at American Custom Chemicals Corporation (San Diego, CA), Tolterodine (214601-13-5) was from Toronto Research Chemicals (Toronto, Canada), and AMG 1 was synthesized at Amgen Medicinal Chemistry (Thousand Oaks, CA). All compounds were dissolved in DMSO to make stock solutions.

## RESULTS

#### Effect of Tolterodine and Terodiline on AP in Human Ventricular Trabeculae

Both tolterodine and terodiline are relatively potent hERG blockers (Martin et al., 2006), yet tolterodine is considered safe in the clinic (Malhotra et al., 2007), whereas terodiline was withdrawn from the market due to adverse cardiac events (Thomas et al., 1995). To understand the performance of AP recording and analysis in hVT, Tolterodine and terodiline profiles were characterized side-by-side.

The concentration-dependent effects of tolterodine and terodiline on AP in human ventricular trabeculae are shown in **Figure 2**, which were recorded separately in 2 example tissues. To understand the translation from ex-vivo AP recordings to clinical observations, the testing concentrations were converted to multiple of free effective therapeutic concentrations (ETPC) in the clinic, which equals testing concentrations divided by free ETPC. As shown in **Figure 2**, tolterodine increased the duration of AP repolarization at 0.1 and 1µM with predominant prolongations of phase 3 without notably affecting phase 2. In addition, tolterodine had negligible effects on the amplitude of AP up to the highest testing concentration, 1µM.

On the other hand, terodiline significantly modified the AP morphology by lengthening the phase 3 while shortening the phase 2 of AP repolarization, in addition, terodiline decreased the amplitude of AP, especially at 30µM.

To further analyze the effects of tolterodine and terodiline on hVT AP, percent changes of APD normalized by baseline values, including APD30, APD50, and APD90, were derived at stimulation frequencies of 1 Hz and 2 Hz (**Figure 3**). Consistent with the observation in **Figure 2**, tolterodine induced a concentration-dependent increase of APD50 and APD90, which represent the early and late stages of the phase 3 repolarization. On the other hand, APD30, the phase 2 repolarization, was not affected. Effects of terodiline on AP duration exhibited a differing profile compared to tolterodine (**Figure 3B**). The late stage of phase 3 repolarization, APD90, was prolonged, however, phase 2, APD30, and the early stage of phase 3, APD50, were shortened.

#### Effects of Tolterodine and Terodiline on Pro-arrhythmic Parameters in Human Ventricular Trabeculae

To understand beat-to-beat variability of repolarization, the short-term variability (STV) of AP duration was quantified from APD90 Poincare plots over a period of 30 beats in control and under treatments of tolterodine (A) and terodiline (B) in **Figure 4**. As shown in **Figure 4**, under the stimulation frequency of 2 Hz, there is minimal variation of APD90 in the presence of tolterodine, however, significant increase of APD90 oscillation was observed in the presence of terodiline.

The concentration and frequency-dependent effects of tolterodine and terodiline on pro-arrhythmic parameters,

including APD90, triangulation, STV and EAD incidence were described and overlaid in **Figure 5**. Tolterodine (A) and terodiline (B) did not induce EAD at any testing concentrations under either stimulation frequencies. For both compounds, the changes in APD90 and triangulation are not frequencydependent, while effects on STV are more prominent under 2 Hz than under 1 Hz, a characteristic of use-dependent effect.

Effects of tolterodine (A) and terodiline (B) on STV and triangulation as a function of APD90 change were described under stimulation frequencies of 1 Hz and 2 Hz in **Figure 6**. For both compounds, triangulation became greater with APD90 prolongation, however, the relationship between triangulation and APD90 was linear in the case of tolterodine (**Figure 6A**). While for terodiline, it is a non-linear relationship with accelerated increase of triangulation with lengthening of APD90. The initial 3 testing concentrations of terodiline, APD90 was not affected by less than 10%, however, change in triangulation increased to 20% and greater. This accelerated increase of triangulation was observed at both stimulation frequencies (**Figure 6B**). The effect of triangulation was not use-dependent for tolterodine, but reverse use-dependent for terodiline.

Both tolterodine and terodiline produced minimal changes in STV as a function of APD90 prolongation at 1 Hz, and increase of stimulation frequency from 1 to 2 Hz augmented STV (**Figure 6**). While the increase of STV by tolterodine was minimal as a function of APD90 prolongation, terodiline produced magnified changes of STV at 2 Hz as a function of APD90 prolongation. With less than 10% change in APD90 at the first 3 testing concentrations of terodiline, STV was increased to 2.2 (third concentration) from 0.9 (first conccentration), a 144% increase. Therefore, effects of tolterodine and terodiline on STV were usedependent, and had distinct profiles as a function of APD90 prolongation.

#### Assessment of Pro-arrhythmic Risk-Based on Multiples of Clinical Exposure

All compounds were evaluated in the same manner as tolterodine and terodiline, the raw data and percent changes of each parameters were described in the Supplementary Material. The value of APD and its derived pro-arrhythmic parameters in human ventricular trabeculae for predicting pro-arrhythmic risk was evaluated by integrating and deriving a pro-arrhythmic score at each testing concentration of each compound (**Table 1**). Testing concentrations were converted to a multiple of human effective therapeutic plasma concentrations in the unbound fraction. **Figure 7** showed the pro-arrhythmic scores as a function of the multiple of free ETPC for tolterodine and terodiline. **Figure 8** included the subsequent compounds tested. Two agents, AMG1 and L 768,673 were not displayed due to a lack of human exposure data. Pro-arrhythmic scores were classified into 2 categories based upon the score: unsafe (>10) and safe (<10). Assay performance of pro-arrhythmic scores at a 10-fold of human free ETPC for predicting TdP risk was calculated for the 13 compounds that have human clinical data (**Table 2**). As shown in **Table 2**, at a pro-arrhythmic score of > 10, 7 out of 8 compounds are identified correctly as TdP positive, while sertindole was incorrectly identified as a TdP negative. At a pro-arrhythmic score of < 10, 4 out of 5 TdP negative compounds were correctly identified, while lamotrigine was identified incorrectly as TdP positive. However, the TdP risk of sertindole and the lack of TdP risk of lamotrigine have been challenged, this will be discussed in detail later.

Consistent with initial observations, at 10-fold human free ETPC, pro-arrhythmic score had high sensitivity (0.88), specificity (0.8), positive predictive value (0.88), and negative predictive value (0.8) (**Table 2**).

#### DISCUSSION

Drug-induced pro-arrhythmia was assessed by determining the pro-arrhythmic score, a comprehensive score derived from APD and other AP-associated parameters, in hVT. Risk assessment was performed by comparing the pro-arrhythmic score to known clinical exposure, free Cmax. To the best of our knowledge, this is the first blinded study with an extensive reference compound

FIGURE 4 | Poincaré plots of APD90 in the presence of increasing concentrations of tolterodine (A) and terodiline (B) under 2 Hz stimulation. Tolterodine induced minimal APD90 variation, while terodiline produced concentration-dependent increase of APD90 oscillation.

set tested for their effects on ventricular APs in authentic healthy human cardiac tissues. The comprehensive analysis of multiple AP parameters and comparison of the pro-arrhythmic risk of various drugs using a single score in the context of their human clinical exposure clearly distinguished TdP-positive and TdPnegative compounds (**Table 2**).

As shown in **Table 2**, at a pro-arrhythmic score of >10, 7 out of 8 compounds were identified correctly as TdP positive, while sertindole was incorrectly identified as a TdP negative. At a pro-arrhythmic score of <10, 4 out of 5 TdP negative compounds were correctly identified, while lamotrigine was identified incorrectly as TdP positive.

# Assay Performance Depends Critically Upon Categorization of TDP Risk in Human

Sertindole is an antipsychotic medication developed for the treatment of schizophrenia (Karamatskos et al., 2012). In Europe, sertindole was approved and marketed in 1996, but the drug was withdrawn from the market in 1998 due to concerns of QTc prolongation and potential high risk of fatal arrhythmias in patients. Further clinical epidemiological studies did not provide clear evidence that patients on sertindole were at a significantly increased risk of cardiac arrhythmia and cardiac death (Toumi et al., 2003; Lindström et al., 2005; Spina and Zoccali, 2008). In 2002, sertindole was reintroduced for restricted use in clinical trials. It is a potent hERG blocker with a submicromolar IC50 (Rampe et al., 1998; Qu and Vargas, 2015). However, preclinical electrophysiological studies conducted in animal models of pro-arrhythmia have demonstrated that QTc prolongation induced by sertindole does not sufficiently elicit serious and fatal ventricular arrhythmias (Eckardt et al., 2002; Thomsen et al., 2003; Lindström et al., 2005). Therefore, the outcome of current study is consistent with the risk profile of sertindole in both preclinical and clinical settings. If sertindole is categorized as TdP-negative, the assay sensitivity would be perfect with a value of 1.

Lamotrigine has been approved for the treatment of generalized seizures, partial seizures, Lennox–Gastaut syndrome, and bipolar disorder (Rogawski and Loscher, 2004). It inhibits the voltage-gated sodium channels, including Nav1.5, it also inhibits hERG channels (Danielsson et al., 2005). It has an IC50 value of 110 µM for hERG, and 40 µM for Nav1.5 in our previous experiments (Qu and Vargas, 2015). Therefore, at free therapeutic exposure (approximately 17µM, Dixon et al., 2008) inhibition of hERG channels does not translate into an effect on QT or a pro-arrhythmia risk, which has been demonstrated in a TQT study (Dixon et al., 2008). This correlates well with the current finding that at therapeutic exposure the pro-arrhythmic score is below 10 and lamotrigine is not associated with a pro-arrhythmic risk.

However, when tested at concentrations of 100, 300, and 1,000µM, lamotrigine blocks hERG channels in addition to inhibition of Nav1.5 and consequently increases its association with pro-arrhythmia risk and conduction delay. The conduction delay further enhances the reverse use-dependence block of hERG channels by lamotrigine. Our findings clearly indicate that this is the case (pro-arrhythmic score is above 40 at these concentrations). There are many clinical case studies for understanding the risk of lamotrigine in terms of its risk of sudden unexpected death, the reported results are conflicting. On one hand, no statistically significant difference in rate of sudden unexpected death between lamotrigine and control groups (e.g., Tomson et al., 2013) has been reported. On the other hand, Aurlien et al. (2012) have shown the evidence that incidence of sudden unexpected death was significantly higher among female patients with epilepsy who were being treated with lamotrigine than among female patients with epilepsy who were not taking lamotrigine. In addition, FDA requires warning labels on the risk of sudden unexpected death in association with the use of lamotrigine. Clinically, overdose of lamotrigine has been shown to be linked to QTc prolongation and pro-arrhythmic risk (e.g., Chavez et al., 2015). In summary, pro-arrhythmia classification of lamotrigine depends on its exposure level and safety margin. At super-therapeutic concentrations, lamotrigine is associated with arrhythmic risk. If lamotrigine is classified as pro-arrhythmic,

then the outcome of our current study is perfect with a specificity of 1.

## Pro-arrhythmia Risk Assessment in Mature Human Cardiac Tissue with Sharp Electrode AP Recording: Superior to Stem-Cell Derived Cardiomyocytes with MEA Recording

Previously, we have tested the same 15 compounds and characterized their pharmacological profiles in human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CM) with extracellular field potential recordings (Qu and Vargas, 2015). Our study results indicate that hiPSC-CM would have a high false positive rate when evaluating pro-arrhythmic risk (**Table 3**). In contrast, current study using the same 15 compounds demonstrated excellent assay performance with sensitivity, specificity, positive predictive value, and negative predictive value all 0.8 and above (**Tables 2, 3**). This side-by-side comparison with the same set of compounds gives us a greater understanding of the models tested. The results provide us with more confidence that authentic mature human cardiac tissue with sharp electrode AP recording is superior to stem-cell derived cardiomyocytes with MEA recording in assessing a drug's pro-arrhythmic risk.

### EAD Is a Rare Electrical Event in Normal Human Ventricular Trabeculae

Early afterdepolarization of ventricular myocytes represents a trigger event that has been implicated as the primary mechanism for ventricular arrhythmia induction in acquired and congenital long QT syndromes, including TdP (Weiss et al., 2010). Interestingly, at the concentration ranges used in our study, some of them are at greater than 100-fold of human free therapeutic Cmax, EAD was only detected in one trabecula, which was under the treatment of moxifloxacin at 91-fold hETPC. None of the other TdP-positive compounds elicited EAD in hVT. Two compounds, dofetilide and sotalol, have previously been tested in a similar experimental design (Page et al., 2016). Lack of EAD was also observed for sotalol. For dofetilide, Page et al. (2016) had observed EAD in 9 out of 21 trabeculae at a testing concentration of 0.1 uM, a 33% incidence. In the current study, dofetilide was tested at 0.003, 0.01, 0.03, and 0.3µM without any EAD in a total of 4 trabeculae. However, dofetilide did prolong APD starting at 0.003 uM in a concentration-dependent manner with 105% increase of APD90 at 0.3 uM (data not shown), which is comparable with the magnitude of APD90 prolongation observed at 0.1 uM in Page et al. (2016) (∼100%). The lack of EAD in the current study could be due to the combination of low incidence (33%) and much smaller number of trabeculae (n = 4) compared to the previous study (Page et al., 2016). Therefore, EAD incidence in AP recordings is not a sensitive biomarker for pro-arrhythmic risk in normal human ventricular trabeculae, false negative rate would be very high if pro-arrhythmic risk was based solely upon EAD incidence.

TABLE 2 | Performance of action potential recordings and Pro-arrhythmic score analysis in hVT.


## An Integrated Analysis of AP and Associated Parameters Is Powerful in Differentiating TDP-Positive from TDP-Negative Agents

In analyzing electrophysiological data, multiple endpoints can be derived. For pro-arrhythmic risk assessment, it's a major challenge to determine which endpoint is more important and has more predictive value. Combinations of various endpoints in a weighted manner with expression as an integrated arrhythmic score have been previously successfully used in the A-V ablated isolated rabbit heart model (Hondeghem and Hoffman, 2003; Hondeghem et al., 2003; Lawrence et al., 2006). A similar approach has been taken for the current study with a quantitative arrhythmic score determined by combining all parameters of AP and AP-related parameters, including APD30, APD50, APD90, triangulation, STV, AP instability, APD alternans, Maximum APD dispersion and ERP, etc (details shown in **Table 1**). In addition, pro-arrhythmic scores are considered in relation to human free ETPC and at multiples above the highest free ETPC. The validation with 8 TdP-positive and 5 TdP-negative agents has demonstrated that this approach is able to differentiate the positive from the negative drugs with high sensitivity and specificity values (**Tables 2**, **3**).

Take an example of tolterodine and terodiline. Both agents are relatively potent hERG blockers (Martin et al., 2006), yet tolterodine is considered safe in the clinic (Malhotra et al., 2007), whereas terodiline was withdrawn from the market because of adverse cardiac events (Thomas et al., 1995). We tested both compounds in ion channel assays, including hERG, Nav1.5, and L-type Ca channel assays (Qu and Vargas, 2015), confirming that both agents are potent hERG channel blockers. In human TABLE 3 | Comparison of Assay Performance.


ventricular trabeculae, both compounds increased AP duration, increased triangulation and short-term variability (**Figures 2**– **5**). If examining each of the parameter in isolation, it's difficult to distinguish one from the other in regard to their proarrhythmic potentials. When a single pro-arrhythmic score was derived by combining all the parameters in a weighted manner and then related to their human free ETPC, their TdP risks were clearly separated (**Figures 7A,B**). This case study indicates that AP recordings in hVT combined with analysis of proarrhythmic score can differentiate agents that inhibit hERG with significant QTc prolongation and associate with TdP risk, such as terodiline, from agents that inhibit hERG with significant QTc prolongation but not associated with TdP risk, such as tolterodine.

#### LIMITATIONS

There were several limitations in this study: (1) The tissue in this study came from the trabeculae of the left and right ventricles, which may or may not represent the characteristics of the entire ventricles, because myocardium from different regions of the heart reflect the specialized electrophysiological functions of the region, have different configurations of APs (Schram et al., 2002); To our knowledge, ion channel (hERG, SCN5A, KvLQT1, and KCNE1) distribution at the gene and protein levels in human ventricular trabeculae has not been published. However, it has been shown that SCN5A expression is greater in the endothan the epi- myocardium, which cause the maximal rate of depolarization (dV/dtmax) higher in the endo-myocardium than in the epi-myocardium (Gaborit et al., 2007). Ikr (hERG) is expressed throughout the myocardium of the human heart with higher expression in epimyocardium than in endomyocardium (Szabo et al., 2005). A more relevant study was performed in human ventricular trabeculae (Jost et al., 2005) that recorded Ikr and Iks (KvLQT1 + KCNE1) with patch clamp technique and specific blockers of Ikr and Iks were used for inhibiting the currents. In addition, this study and a recent study (Jost et al., 2013) showed that there is a robust prolongation of APs in human ventricular trabeculae in response to specific hERG blockers, therefore it is reasonable to postulate that there is abundant hERG in human ventricular trabeculae. (2) Our evaluation was limited by the trabeculae sample size utilized for each concentration. In the previous study (Page et al., 2016), it was recommended that a sample size of at least 2 hearts and 3 trabeculae per heart is necessary to detect drug-related AP changes. In the current study, 2 hearts and 2 trabeculae from each heart were tested for each concentration, a design may not be sufficient for small drug-induced changes; (3) Our conclusion are limited by the number of agents tested, a larger panel of test compounds, including both TdP-positive and TdP-negative standard compounds, would provide increased confidence, and assist in understanding the performance of AP recordings in hVT and analysis of pro-arrhythmic score as a new model for assessing pro-arrhythmic risk; (4) A single calculation of human free ETPC data is a limitation, because there are multiple sources for clinical exposure data, which could introduce selection bias into the ratio calculation.

#### CONCLUSIONS

This study has tested multiple compounds in authentic human ventricular tissue for their effects on AP, and subsequent determination of pro-arrhythmic scores by calculating the weighted sum of drug-induced changes in various AP parameters and pro-arrhythmia variables. The outcome reported here has demonstrated that this approach yields better performance compared to hSC-CM. Importantly, this approach is able to differentiate agents that inhibit hERG with significant QTc prolongation and associate with TdP risk from agents that inhibit hERG with significant QTc prolongation but not associated with TdP risk.

Therefore, use of primary human cardiac tissues to evaluate pro-arrhythmia risk in vitro (Page et al., 2016) could prevent the confounding influences of the embryonic ion channel expression and spontaneous beat rate observed with hSC-CM, and enable a robust and definitive electrophysiological evaluation in mature ventricular myocytes. The performance characteristics of mature ventricular tissue shown here surpass the reliability of iPSC-CM for pro-arrhythmia detection, which give us confidence in employing them for cardiac safety assessment. While the use of mature cardiac tissues does not provide a good screening tool due to the low throughput nature of the assay and the requirement for large numbers of human hearts, this limitation may be overcome by placing this model later in

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#### AUTHOR CONTRIBUTIONS

YQ: Designed the experiment, wrote the manuscript. HV: designed the experiment, wrote and reviewed the manuscript. GP: performed the study and analyzed data. NA-G: performed the study, analyzed data, wrote and reviewed the manuscript. PM and AG: wrote and reviewed the manuscript.

#### ACKNOWLEDGMENTS

We thank Phachareeya Ratchada, Ashley Alamillo, and Yannick Miron for their excellent technical support and Joe Alsadi (AnaBios) for technical assistance.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphys. 2017.01109/full#supplementary-material

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**Conflict of Interest Statement:** YQ and HV were employed by company Amgen Inc. GP, NA-G, PM, and AG were employed by company AnaBios Corporation. All authors declare no competing interests.

Copyright © 2018 Qu, Page, Abi-Gerges, Miller, Ghetti and Vargas. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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