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

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


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 K V 1.5, carrying the ultra-rapid delayedrectifier K + current (I Kur ). Genetic mutations causing both lossand gain-of-function of I Kur 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 K V 1.5-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 I Kur 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 I Kur 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 K V 1.5 inhibitors in clinical trials is lacking (Ravens et al., 2013). However, recent studies have suggested an anti-arrhythmic potential of I Kur -targeting drugs in cAF (Christ et al., 2008;Ford et al., 2013Ford et al., , 2016Loose 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 I Kur 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 I Kur results in prolongation and elevation of the AP plateau, which augments the Ca 2+ transient (CaT) amplitude (CaT amp ), thereby eliciting a positive inotropic effect . Thus, I Kur 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).

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 Morotti et al., 2016b). I Kur gating was described by a 6-state Markov type model ( Figure 1A) as in Ellinwood et al. (2017), and I Kur maximal conductance (G Kur ) in cAF was reduced by 50% compared to nSR .
Simulations were equilibrated for 300 beats at 1-Hz pacing or 900 beats at 3-Hz pacing. After the 300 th or 900 th beat, the time to 40 and 90% repolarization of the AP (APD 40 and APD 90 ) were calculated, along with diastolic intracellular Ca 2+ concentration ([Ca 2+ ] i ), CaT amp and time to 50% CaT decay. The atrial ERP was determined using a standard S 1 -S 2 premature stimulation protocol (Wang et al., 1996;Shinagawa et al., 2000;Christ et al., 2008;Zhao et al., 2009), where the S 1 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 2 stimulus (5 ms in duration, 2-fold the diastolic threshold of excitation) at progressively smaller S 1 -S 2 intervals from 700 ms to refractoriness by decrements of 2 ms. The longest S 1 -S 2 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 S 1 ).
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 (E m ), APD 90 , and CL was tracked over the course of the simulation.

Parameter Sensitivity Analysis
Parameter sensitivity analysis was performed with the population-based approach described in Sobie (2009), , and  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.

K V 1.5 Drug-Binding Model
We utilized our recent I Kur Markov formulation and approach to describe various drug-K V 1.5 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 K V 1.5 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 (k on ) and reverse (k off ) drugbinding rates to the open and inactivated states of the K V 1.5 channel in the predicted physiological range of 0.01-100 s −1 (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 −1 ). For a particular state of the channel, dissociation constants (K d ) for our drug scenarios were calculated as k off /k on , and affinity constants were calculated as k on /k off . To investigate the effects of these drug characteristics, for a given state-dependent binding inhibitor, we varied k on and k off together (k on = k off ) 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 K V 1.5 channel, we also varied the relative affinity to open (K O ) vs. inactivated state (K I ). 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 I Kur (i.e., IC 50 ). IC 50 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 50 values were calculated at 1and 3-Hz pacing rates as the [drug] causing a 50% reduction in peak I Kur 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 K V 1.5 channel during a physiological atrial AP, as we have shown in (Ellinwood et al., 2017).

Role of I Kur in nSR and cAF Atrial Electrophysiology
We built 900 variations of our nSR and cAF human atrial cardiomyocyte models  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 APD 40 , APD 90 , ERP, CaT amp , diastolic [Ca 2+ ] i , 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 G Kur in nSR and cAF conditions at 1-and 3-Hz pacing are in Figure 1C. The values are negative because an increase in I Kur shortens APD 40 , APD 90 , and ERP on average according to the regression algorithm. The analysis revealed that, while at a slow pacing rate APD 90 and ERP 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 −1 using half-logarithmic increments, whereby k off = k on , K d = 1 µM. 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 G Kur (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 IC 50 value. (C,E,H,J) show the closed, open, inactivated and drug-bound (d B , i.e., Od or Od+Id) state occupancies during an AP for three different drug-binding kinetics (k off = k on = 0.01, 3, and 100 s −1 ).
Frontiers in Pharmacology | www.frontiersin.org are more sensitive to changes in G Kur , APD 40 is similarly sensitive in nSR and cAF ( Figure 1C). At 3-Hz pacing, G Kur impacts AP and ERP prolongation more in cAF vs. nSR despite the fact that G Kur is smaller in cAF conditions. This points to I Kur 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 I Kurtargeting drug properties that exhibit anti-AF selectivity and efficacy along with minimized proarrhythmic risk in cAF.

Figure 2 shows changes in APD caused by O and O & I inhibitors
at varying drug-binding kinetics, whereby k on is set equal to k off (i.e., K d = 1 µM). These are compared to no block, 50, and 100% reduction in G Kur 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 G Kur 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 −1 for the open state blocker and 1-30 s −1 for the open and inactivated state blocker), and goes well beyond the little APD prolongation resulting from a constant 50% reduction in G Kur . 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 G Kur . However, drugs with intermediate drugbinding kinetics (3-30 s −1 for the O blocker and 10-30 s −1 for the O & I blocker) did extend the APD at 3-Hz pacing above the APD in nSR conditions given no block of I Kur . Thus, even though G Kur is reduced by 50% in cAF as compared to nSR, Figure 2 illustrates that I Kur 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 −1 ), intermediate (3 s −1 ), and fastest (100 s −1 ) 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 I Kur . 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, K V 1.5 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 I Kur inhibitors affected the time course of E m ( Figure 3B) and APD 90 ( 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 k on = k off (K d = 1 µM) in Figure 3 again demonstrate a biphasic relationship between drug-binding kinetics and average APD 90 (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 I Kur 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, I Kur inhibitors cause minimal ERP prolongation at slow drug-binding rates (≤0.3 s −1 for O blockers and ≤1 s −1 for O & I blockers) and fast drug-binding rates (100 s −1 ). Although substantial ERP changes are predicted at intermediate drug-binding rates (1-30 s −1 for O blockers and 3-30 s −1 for O & I blockers), ERP prolongation remains ∼62 ms lower than the ERP in nSR given no block of I Kur for both inhibitors.
At 3-Hz pacing, however, I Kur 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 G Kur (Figures 4B,D). Notably, for intermediate drug-binding kinetics (3-30 s −1 for O inhibitors and 10-30 s −1 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 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 d on APD, ERP, and Ca 2+ 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 (k on = k off , K d = 1 µM), but even closely related I Kur inhibitors can have dissimilar K d values (Lagrutta et al., 2006). Thus, we simulated all permutations of the nine different rates of drug binding (0.01 to 100 s −1 ), yielding 81 different combinations of k on and k off 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 50 concentration) on APD, ERP, CaT amp , and diastolic [Ca 2+ ] i . 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 k on = k off (K d = 1 µM). Except for the drugs with the largest K d values (k off >> k on ), when k on is held constant, APD, ERP, and Ca 2+ handling are not very sensitive to changes in k off. Thus, the effects of I Kur inhibitors on atrial electrophysiology and Ca 2+ handling are largely driven by k on rates as compared to k off rates.
In cAF conditions, ideal I Kur 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 CaT amp at 1-Hz pacing). O & I inhibitors with a large K d do not display any of the desired favorable drug properties including prolongation of ERP at 3-Hz pacing ( Figure 5B) or increase in CaT amp (Figures 5C,D), as their effects on APD, ERP, and Ca 2+ handling are minimal, resembling drug-free conditions. Intermediate k on rates (3-30 s −1 for 1-Hz pacing and 10-30 s −1 for 3-Hz pacing) cause the most significant increase in all the outputs displayed in Figure 5. For example, drugs with a k on rate equal to 10 s −1 cause the greatest ERP prolongation at 3-Hz pacing ( Figure 5B) and increase in CaT amp and diastolic [Ca 2+ ] i (Figures 5C,E). Note, there is also significant APD prolongation at 1-Hz pacing when k on 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 Simulations were also run in nSR and cAF drug-free conditions, and in cAF given a 50 and 100% reduction in G Kur .
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 CaT amp and diastolic [Ca 2+ ] i mirrors the prolongation in APD and ERP at 3-Hz pacing (Figures 5D,F). While an excessive increase in diastolic [Ca 2+ ] i 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 −1 ) 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 k on rate in the intermediate drug-binding range (3-30 s −1 ) 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 I Kur inhibitors bind to multiple states of K V 1.5 with variable affinity (Bouchard and Fedida, 1995;Lagrutta et al., 2006;Ford et al., 2016), we allowed k on for the open state (k on,O ), k off for the open state (k off,O ), k on for the inactivated state (k on,I ), and k off for the inactivated state (k off,I ) to have any of the three binding rates (0.01, 3, and 100 s −1 ), and varied them independently to yield 81 different drug combinations. We studied the effects of these I Kur blockers in cAF conditions using a [drug] equal to their IC 50 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 G Kur 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 K O /K I . Data points in Figure 6A are separated by IC 50 cutoffs of 0.1 µM, 10 µM, and 1 mM, and show that when K O /K I < 1, we almost always obtain maximal AP prolongation (this also corresponds to larger IC 50 values). In Figure 6B, we separated the points according to the drug's k off,O rate (0.01, 3, or 100 s −1 ), which revealed that when K O /K I > 1, we only obtain significant AP prolongation when k off,O is equal to 3 s −1 (i.e., the intermediate drug-binding rate). These results in the cAFremodeled atrial cardiomyocyte correspond well with the results from our previous study of I Kur 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 K O /K I ratio. In Figure 6C, light gray symbols correspond to K O /K I ≤ 1, and dark symbols correspond to K O /K I > 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 K O /K I > 1, except if k off,O equals 3 s −1 . 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  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% I Kur block, respectively. Diastolic [Ca 2+ ] 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% I Kur block, respectively. percent increase in CaT amp . 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., k off,O = 3 s −1 ) may thus be favorable given their stronger inotropic effect.

DISCUSSION
In this study, we sought to determine if I Kur 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 I Kur inhibitors in cAF atrial cardiomyocyte models, and identified metrics for delineating ideal K V 1.5 blockers against AF. Our results point to I Kur 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 K V 1.5-targeting drugs as compared to nSR (Ellinwood et al., 2017; Figure 7). Figure S7 shows the differences in the time courses of E m , I Kur , and closed, open, and inactivated state occupancies of K V 1.5 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 I Kur inhibition, including the extent of AP FIGURE 7 | Summary of main findings. Atrial cardiomyocytes in cAF (solid lines) vs. nSR (dotted lines) have different AP trajectories, including a shorter APD and more depolarized plateau (top left). The latter causes longer open state occupancy (right, blue solid vs. dashed lines) and stronger inactivation of the channel in cAF conditions (especially at fast pacing rates, right, green solid vs. dashed lines). I Kur inhibitors appear also more potent in cAF vs. nSR (bottom left). These factors render APD and ERP more sensitive to inhibition by O and O & I inhibitors of K V 1.5, thus increasing efficacy of these drugs in cAF vs. nSR. Because basal APD is shorter in cAF, there are potentially less safety concerns due to drug-induced AP prolongation and subsequent afterdepolarization-driven proarrhythmia. and ERP prolongation, depend not only on I Kur magnitude (i.e., maximal conductance), but also on other fluxes affected by AFinduced remodeling, which affect E m and thus E m -dependent properties of I Kur (Figure 7). For example, our group and others have hypothesized that the extent of AP and ERP prolongation due to I Kur blockade depends on the AF-induced remodeling of other K + currents (Lagrutta et al., 2006;Morotti et al., 2016a;Aguilar et al., 2017;Colman et al., 2017), and relative strengths of I CaL and I Kur (Wettwer et al., 2004;Grandi and Maleckar, 2016). Our sensitivity analysis (Figure 1C and Figures S1-S6) revealed that APD 90 and ERP are more sensitive to changes in G Kur at fast vs. slow pacing rates. Aguilar et al. recently determined that the relative contribution of I Kur to AP repolarization increases at higher frequencies because of reduced activation of the rapid delayed-rectifier current I Kr (Aguilar et al., 2017). Our results concur with these findings, as our sensitivity analysis shows that APD 90 and ERP are less sensitive to changes in G Kr at 3-Hz pacing as compared to 1-Hz pacing in nSR conditions ( Figures  S2, S3). Most importantly, we also found that G Kur 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 I Kur block is not affected by I Kur downregulation.

Enhanced Efficacy and Safety of I Kur 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 k on = k off (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 I Kur 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 K V 1.5 block in cAF patients. At 3-Hz pacing, ERP prolongation is at least equivalent to that caused by a constant 50% reduction in G Kur , 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 −1 , 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 I Kur inhibitors by also accounting for changes in Ca 2+ -handling parameters, namely CaT amp and diastolic [Ca 2+ ] i (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 CaT amp . Increasing force generation might be a useful outcome after cardioversion to nSR.
When K O = K I , the best-performing O & I inhibitors were those with intermediate k on rates (3-30 s −1 ), because they prolonged ERP at 3-Hz pacing and increased CaT amp and diastolic [Ca 2+ ] i at 1-Hz pacing (Figure 5). These inhibitors also prolonged the AP at 1-Hz pacing and increased CaT amp and diastolic [Ca 2+ ] i at 3-Hz pacing-thus potentially predisposing to harmful AP prolongation and Ca 2+ overload. However, we note that such cardiotoxicity is unlikely considering the fact that the maximum increases of APD and CaT amp 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 Ca 2+ handling.
When K I and K O were varied, the relationships between APD at 1-Hz pacing and affinity ratio (K O /K I ) 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) I Kur 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 I Kur 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 I Kur 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 K V 1.5, and future analysis should consider multi-channel effects of I Kur 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 I Kur in ventricles prevents ventricular proarrhythmia. However, this might not be true for real I Kur blockers with off-target effects. Here, we simulated I Kur block at the cellular level with no contribution of structural tissue remodeling and defined I Kur inhibitors' efficacy and toxicity by tracking only electrophysiological properties such as APD, ERP, CaT amp , and diastolic [Ca 2+ ] i . 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 I Kur 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), I Kur 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 I Kur 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 I Kur 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 I Kur inhibitors, i.e., degree and heterogeneity of I Kur 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-I Kur 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;. This information could be useful for a personalized (precision) medicine approach to AF treatment or helpful in suggesting potential combination therapies with I Kur 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 K V 1.5-selective compounds for the desired kinetics, state-dependence, and rate-dependence of I Kur 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 K V 1.5 (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 I Kur inhibitors were assessed in silico. We concluded that I Kur is a promising anti-AF target, even if strongly downregulated in cAF condition. We confirmed that steady-state IC 50 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 efforts to identify the complex net impact of I Kur 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.