# AXON NEUROBIOLOGY: FINE-SCALE DYNAMICS OF MICROSTRUCTURE AND FUNCTION

EDITED BY : Haruyuki Kamiya and Dominique Debanne PUBLISHED IN : Frontiers in Cellular Neuroscience

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ISSN 1664-8714 ISBN 978-2-88966-187-9 DOI 10.3389/978-2-88966-187-9

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# AXON NEUROBIOLOGY: FINE-SCALE DYNAMICS OF MICROSTRUCTURE AND FUNCTION

Topic Editors: Haruyuki Kamiya, Hokkaido University, Japan Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France

Citation: Kamiya, H., Debanne, D., eds. (2020). Axon Neurobiology: Fine-Scale Dynamics of Microstructure and Function. Lausanne: Frontiers Media SA. doi: 10.3389/978-2-88966-187-9

# Table of Contents

*05 Editorial: Axon Neurobiology: Fine-Scale Dynamics of Microstructure and Function*

Haruyuki Kamiya and Dominique Debanne


Wei Zhang, Angela Bonadiman, María Ciorraga, María José Benitez and Juan José Garrido

*47 Technologies to Study Action Potential Propagation With a Focus on HD-MEAs*

Vishalini Emmenegger, Marie Engelene J. Obien, Felix Franke and Andreas Hierlemann


Cheng-Hsin Liu and Matthew Neil Rasband

*111 Glutamate Imaging Reveals Multiple Sites of Stochastic Release in the CA3 Giant Mossy Fiber Boutons*

Sylvain Rama, Thomas P. Jensen and Dmitri A. Rusakov

*117 Dynamic Regulation of Synaptopodin and the Axon Initial Segment in Retinal Ganglion Cells During Postnatal Development*

Annabelle Schlüter, Sabrina Rossberger, Dominik Dannehl, Jan Maximilian Janssen, Silke Vorwald, Janina Hanne, Christian Schultz, Daniela Mauceri and Maren Engelhardt


Torsten Bullmann, Milos Radivojevic, Stefan T. Huber, Kosmas Deligkaris, Andreas Hierlemann and Urs Frey

*156 Axonal Computations* Pepe Alcami and Ahmed El Hady


# Editorial: Axon Neurobiology: Fine-Scale Dynamics of Microstructure and Function

Haruyuki Kamiya<sup>1</sup> \* and Dominique Debanne<sup>2</sup> \*

<sup>1</sup> Department of Neurobiology, Graduate School of Medicine, Hokkaido University, Sapporo, Japan, <sup>2</sup> Unité de Neurobiologie des canaux Ioniques et de la Synapse, UMR1072, INSERM, Aix-Marseille Université, Marseille, France

Keywords: action potential, axon, excitability, modeling, subcellular recording

**Editorial on the Research Topic**

#### **Axon Neurobiology: Fine-Scale Dynamics of Microstructure and Function**

The axon has been considered as a high-fidelity digital cable that reliably conducts action potentials toward the presynaptic terminals (Rama et al., 2018). Comprehensive understanding of cell biology and physiology of the axons is the key step in a bottom-up approach in cellular neuroscience, although the small structure of the axon, as well as ultrafast signaling by action potentials, have made the experimental analysis extremely difficult (Ohura and Kamiya, 2016). In this Research Topic, we aimed at illuminating recent advances in the study of axon neurobiology, with a focus on the cell biology of the axon initial segment (AIS), electrophysiology and modeling of axon excitability and transmitter release. These studies highlighted that axonal spike signaling is regulated much dynamically than previously thought, and substantially involved in fine-tuning of neuronal information transfer both in time and space.

Action potentials are generated at the AIS or in the proximal axon near the soma, and therefore the excitability of the AIS is the critical determinant of encoding output trains of the action potential. In a series of papers, this Research Topic gained insight into our understanding of the AIS structure and function. Raghuram et al. analyzed the AIS length and distance from the soma in mice retinal ganglion cells and attempted to correlate AIS length with cell size, and shown that both parameters are linked. Computational modeling suggested that this scaling adjusts the spiking threshold, spike rate to support the light responses unrelated to the cell size of the ganglion cells. A study by Kim et al. addressed an important aspect of auditory experience-dependent AIS structure plasticity of the medial nucleus of trapezoid body (MNTB) neurons, a relay of the ascending auditory pathway, during development and aging. It was shown that AIS length and distance from the soma change with age and auditory experience, and that these structural changes account for the modifications in the excitability of MNTB neurons, as supported by modeling. The paper by Zhang et al. examined the roles of purinergic signaling in the development and maintenance of AIS. Using mouse cultured hippocampal neurons, they demonstrated that P2Y<sup>1</sup> purinergic receptors determine the initial development of AIS structure and function. On the other hand, P2X<sup>7</sup> receptors are involved in the maintenance of AIS maturation. The study by Alpizar et al. explored the roles of the cell adhesion molecule neurofascin-186 (NF-186) in the arrangement of ankyrin G and sodium channels in the AIS. Ablation of NF-186 perturbed ankyrin G accumulation at the AIS and altered expression of sodium channels and therefore suggested the possible contribution of this cell adhesion molecule in AIS-specific molecular organization. Schlüter et al. reported the maturation of AIS in retinal ganglion cells with a focus on the cisternal organelle, a presumed Ca2+-store of the AIS, using the marker synaptopodin. Since retinal development, as well as visual deprivation, alter the AIS

#### Edited and reviewed by:

Arianna Maffei, Stony Brook University, United States

\*Correspondence:

Haruyuki Kamiya kamiya@med.hokudai.ac.jp Dominique Debanne dominique.debanne@univ-amu.fr

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 13 August 2020 Accepted: 24 August 2020 Published: 23 September 2020

#### Citation:

Kamiya H and Debanne D (2020) Editorial: Axon Neurobiology: Fine-Scale Dynamics of Microstructure and Function. Front. Cell. Neurosci. 14:594361. doi: 10.3389/fncel.2020.594361

**5**

and synaptopodin distribution, the authors suggested the activity-dependent structural plasticity occur in both retinal ganglion cells and pyramidal cells in the visual cortex.

This Research Topic puts special emphasis on the understanding of basic mechanisms underlying fine-tuning of the excitability of the axons. In this line, a few articles nicely reviewed and summarized the current understandings of the functional significance of the excitability tuning of the axons as well as the underlying molecular identities. In combination with the historical views as well as the recent updates on the biophysical properties of axons, Alcami and El Hady offered a comprehensive review of the computational abilities of axons and the dynamic control of generation and propagation of action potentials. This paper also lights up the issues to be investigated in future studies with cutting-edge technologies. The authors suggested the importance of "hybrid computation" of analog and digital signals and their interplay. Burke and Bender reviewed the mechanisms as well as the functional significance of modulation of ionic channels in axons. Action potential generation and propagation, as well as neurotransmitter release and its short-term plasticity, are critically and dynamically regulated by modulation of ion channels in axonal membranes. The future perspective of looking for the functional consequence of modulation of axonal excitability in vivo is of extreme interest. Liu and Rasband provided a nice overview of the axonal spectrin, a key cytoskeletal molecule determining the microstructure of the axons. Thanks to the recent development of super-resolution microscopy, the periodic spatial organization of ring-like structures of actin and subcellular arrangement of spectrin implicate the pivotal role of actin-spectrin cytoskeletons in determining axonal excitable domains such as AIS and nodes of Ranvier. Bonetto et al. reported the early steps of compartmentalization of Kv1 channels and associated molecules preceding myelination of axons in cultured hippocampal GABAergic neurons. Although K<sup>+</sup> channels are well-known to localized at nodes and juxtaparanodes to secure spike propagation along myelinated axons, they demonstrated that Kv1.2 channels are highly expressed all along the axons and the AIS before myelination, in contrast with "pre-nodes" localization of NaV1 channels. Rozov et al. provided an overview of the current understanding of the underlying mechanisms for asynchronous transmitter release from the axon terminals. Ca2<sup>+</sup> sensors, Ca2<sup>+</sup> sources, and Ca2<sup>+</sup> extrusion mechanisms may coordinate to limit the prolonged time course of the asynchronous release. Although high-affinity Ca2<sup>+</sup> sensor Syt7 has been suggested to play key roles in the asynchronous release, the contribution of other synaptotagmins as well as the Na+/Ca2<sup>+</sup> exchanger (NCX) which determine the rate of Ca2<sup>+</sup> extrusion is needed to be determined in future investigation. Goaillard et al. summarized the roles of dendrite geometry in the output of action potentials and transmitter release. The authors overviewed the examples of "non-canonical polarity neurons" and even axon-less neurons. They also discussed the case of dorsal root ganglion neurons as an example of unipolar neurons. The diversity of axonal and dendritic roles in shaping neuronal output is of importance for the understanding of neuronal functions.

Several studies also illustrate novel experimental methods to overcome the limitation of previous approaches. Emmenegger et al. provided a nice and concise overview of the methods for studying the propagation of action potential along the axons, i.e., subcellular patch-clamping from the axon, genetically encoded voltage imaging, and CMOS technology-based highdensity microelectrode arrays (HD-MEAs). With high temporal resolution and spatial information obtained by recordings with HD-MEAs covering the entire course of axon arbors of cultured hippocampal neurons, the authors focused on fundamental studies on action potential propagation. Bullmann et al. introduced a novel approach for high-throughput scanning of axonal arbors and mapping of axonal delays using cultured cortex neurons grown on HD-MEAs. With a high temporal and spatial resolution of HD-MEA recordings of axonal spikes, they provided the evaluation of axon segmentation and enabled high-throughput functional mapping of axon arbors. Rama et al. adopted simultaneous imaging of presynaptic Ca2<sup>+</sup> entry and glutamate release at the hippocampal mossy fiber boutons using biolistic transfection of glutamate sensor SF-iGluSnFR and introduction of Ca2<sup>+</sup> indicator Cal-590 in granule cells from organotypic hippocampal cultures. This technique offers a unique opportunity to evaluate the relationship between presynaptic Ca2<sup>+</sup> and glutamate release across multiple release sites within the individual presynaptic terminals. With this multiplexed imaging, they demonstrated the evidence for the existence of distinct release sites of glutamate at the mossy fiber synapse. Nagendran and Taylor investigated the intrinsic injury mechanisms following axotomy. Using cultured hippocampal neurons grown on microfluidic chambers, they revealed that Na<sup>+</sup> influx and reversal of NCX induce dendritic spine loss. The authors also report that Ca2<sup>+</sup> release from the axonal endoplasmic reticulum (ER) plays a critical role in trans-synaptic hyperexcitability following axotomy.

This Research Topic also highlighted the advantage of modeling approach due to the limitation of the experimental approach in axon physiology. Since the information based on the experimental findings is limited for quantitative evaluation, a simulation approach based on a simple assumption might help in testing the quantitative validity of the hypothesis. Using computer modeling, Zbili and Debanne addressed the contribution of myelination on length constant of analogdigital facilitations (ADFs), a graded modulation of transmitter release due to subthreshold depolarization of axonal membranes. This study demonstrated that myelination enhances the axonal length constant thus suggesting a possible functional significance of ADFs in myelinated axons. An important notion is that the enhanced spatial extent of ADFs with myelination may enhance the contribution of ADFs in fine-tuning of neuronal information processing. An advantage of the modeling approach was further highlighted by the review by Kamiya which focused on the mechanism underlying afterdepolarization that follows axonal action potentials. Using a realistic model of hippocampal mossy fibers in combination with a direct recording from the axon terminals, the author clearly shows the substantial contribution of a capacitive component in axonal afterdepolarization. This study also suggests that voltagedependent K<sup>+</sup> and Na<sup>+</sup> conductance play a critical role in shaping time course of afterdepolarization lasting for several tens of ms. Holland et al. discussed alternative solutions for the famous Hodgkin-Huxley (HH) model of the action potential that entirely lies on the electrical nature of the nerve impulse propagating along the axon. Non-electrical factors such as the mechanical and/or thermal changes are taking into account for an attempt to propose a unified model that takes into account the mechanical wave by the pressure pulse of axoplasm and represents the process of nerve impulse propagation accurately. This paper gave insight into the fundamental understanding of the neve impulse propagating axon. Daur et al. addressed the interaction of different spike initiation sites of proximal and distal axons of the unmyelinated motor axon of the lobster with the simultaneous recordings from the two sites of the same axons. The author points to the fact that centrally generated bursts occurring in the proximal axons and peripheral "ectopic" spike initiation from distal axon show mutually suppressive influence. Although the functional significance of ectopically generated action potentials is not fully understood, this implies that they play an important role in shaping the output of the neuronal network. It is also noteworthy that these rules can be generalized to understanding

#### REFERENCES


axonal information processing in the mammalian central nervous system.

As overviewed above, this Research Topics illustrated the current state of knowledge on axon neurobiology, of fundamental importance for the bottom-up approach in the understanding of brain functions. It is also obvious that our continuing efforts to understand axon function will require a combination of cutting edge optical techniques for imaging fine structures with super-resolution technologies (Chéreau et al., 2017), direct electrophysiological recordings from the axon (Kawaguchi and Sakaba, 2015), optogenetic tools (Kim et al., 2017), calcium imaging (Hanemaaijer et al., 2020; Zbili et al., 2020), and computer modeling analysis (Goethals and Brette, 2020).

#### AUTHOR CONTRIBUTIONS

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

#### FUNDING

This work was supported by the KAKENHI from the JSPS (18K06514) to HK and by the Agence National de la Recherche (ANR-14-CE13-0003) to DD.


**Conflict of Interest:** 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 © 2020 Kamiya and Debanne. 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(s) 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.

# Loss of Neurofascin-186 Disrupts Alignment of AnkyrinG Relative to Its Binding Partners in the Axon Initial Segment

Scott A. Alpizar <sup>1</sup> , Arielle L. Baker <sup>2</sup> , Allan T. Gulledge<sup>2</sup> and Michael B. Hoppa<sup>1</sup> \*

<sup>1</sup>Department of Biological Sciences, Dartmouth College, Hanover, NH, United States, <sup>2</sup>Department of Molecular and Systems Biology, Geisel School of Medicine at Dartmouth College, Hanover, NH, United States

The axon initial segment (AIS) is a specialized region within the proximal portion of the axon that initiates action potentials thanks in large part to an enrichment of sodium channels. The scaffolding protein ankyrinG (AnkG) is essential for the recruitment of sodium channels as well as several other intracellular and extracellular proteins to the AIS. In the present study, we explore the role of the cell adhesion molecule (CAM) neurofascin-186 (NF-186) in arranging the individual molecular components of the AIS in cultured rat hippocampal neurons. Using a CRISPR depletion strategy to ablate NF expression, we found that the loss of NF selectively perturbed AnkG accumulation and its relative proximal distribution within the AIS. We found that the overexpression of sodium channels could restore AnkG accumulation, but not its altered distribution within the AIS without NF present. We go on to show that although the loss of NF altered AnkG distribution, sodium channel function within the AIS remained normal. Taken together, these results demonstrate that the regulation of AnkG and sodium channel accumulation within the AIS can occur independently of one another, potentially mediated by other binding partners such as NF.

Keywords: ankyrin G, axon initial segment, voltage gated sodium channels, neurofascin-186, cultured hippocampal neurons

#### INTRODUCTION

Neurons are the most polarized electrically excitable cells, allowing for the rapid transfer of information throughout the nervous system. Postsynaptic electrical currents are received primarily by the dendrites and cell bodies, while chemical neurotransmitters are predominantly released from presynaptic boutons in the axon. The proximal region of the axon, known as the axon initial segment (AIS), maintains the molecular underpinnings of polarity (for reviews see Rasband, 2010; Huang and Rasband, 2016; Leterrier, 2018) and functionally links electrical inputs with chemical outputs through the generation of action potentials (for reviews see Clark et al., 2009; Bender and Trussell, 2012; Kole and Stuart, 2012). Action potential generation at the AIS relies on the local enrichment of a high density of voltage-gated sodium channels (Nav), whose arrangement within the AIS directly influences cellular excitability (Kuba et al., 2010; Grubb et al., 2011; Gulledge and Bravo, 2016). A second important factor that modulates firing of the action potential is the isolation of the AIS from the somatodendritic compartment,

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France

#### Reviewed by:

Matthew S. Grubb, King's College London, United Kingdom Maren Engelhardt, Universität Heidelberg, Germany

#### \*Correspondence:

Michael B. Hoppa michael.b.hoppa@dartmouth.edu

> Received: 20 October 2018 Accepted: 07 January 2019 Published: 22 January 2019

#### Citation:

Alpizar SA, Baker AL, Gulledge AT and Hoppa MB (2019) Loss of Neurofascin-186 Disrupts Alignment of AnkyrinG Relative to Its Binding Partners in the Axon Initial Segment. Front. Cell. Neurosci. 13:1. doi: 10.3389/fncel.2019.00001 which generates a capacitive and conductive load that acts as a Na<sup>+</sup> current sink and inhibits excitation (Brette, 2013; Eyal et al., 2014). The degree of this Na<sup>+</sup> current sink is influenced by the morphology of the somato-dendritic compartment (Gulledge and Bravo, 2016; Hamada et al., 2016; Jamann et al., 2018; Kole and Brette, 2018). Taken together, factors controlling the location and function of Na<sup>v</sup> within the AIS are critical influences on excitability, though this influence will vary across cell types due to their respective morphology.

The molecular development of the AIS is led by the scaffolding protein ankyrinG (AnkG), which has been dubbed the ''master regulator'' of the AIS (Jenkins and Bennett, 2001; Rasband, 2010; Grubb et al., 2011; Leterrier et al., 2015). AnkG typically arrives during the first few days of development, at about the same time that a single neurite adapts an axon-like extension (Boiko et al., 2007; Hedstrom et al., 2007; Galiano et al., 2012; Le Bras et al., 2014; Kyung et al., 2017). Unsurprisingly, due to its early arrival during axon extension, AnkG is thought to directly influence the subsequent arrival of Nav, with various Na<sup>v</sup> isoforms arriving throughout AIS maturation, including Nav1.6 (Boiko et al., 2007; Hedstrom et al., 2007). A number of other proteins containing AnkG binding domains also enrich during this time period, including the cell adhesion molecules (CAMs) neurofascin-186 (NF-186) and neuronal CAM (NrCAM; Hedstrom et al., 2007). Genetic ablation of AnkG after AIS formation causes the dispersion of other AIS proteins, including Na<sup>v</sup> and NF (Hedstrom et al., 2008). Additionally, mutations in the AnkG binding site of Na<sup>v</sup> disrupt its targeting and accumulation at the AIS (Gasser et al., 2012). Indeed, when exogenously expressed, the fragment of the Na<sup>v</sup> containing this targeting motif can enrich within the AIS (Garrido et al., 2001) through a process involving homogenous delivery to the somatic membrane and selective endocytic elimination from areas outside the AIS (Fache et al., 2004). However, these results do not eliminate other mechanisms that may be controlling enrichment. Addition of an AnkG binding motif to other ion channels does not cause enrichment of these channels at the AIS, suggesting this motif alone is not solely regulating the delivery of Na<sup>v</sup> to the AIS for enrichment (Akin et al., 2015). Furthermore, Na<sup>v</sup> often exist in neurons as heteromeric trimers with a single alpha (α) subunit and two transmembrane beta (β) subunits, which add additional layers of interactions to their trafficking (Catterall, 2000). The knockout of the Na<sup>v</sup> β1 subunit in mice results in a failure to accumulate Nav1.6 at the AIS, but instead leads to elevated levels of Nav1.1 accumulation as a compensatory mechanism (Brackenbury et al., 2010). The β1 subunit also contains its own AnkG binding motif (Malhotra et al., 2002) and, along with β3 subunits, interacts with NF through extracellular immunoglobulin (Ig) domains (Ratcliffe et al., 2001). These interactions suggest that the coupling and alignment of AnkG and Na<sup>v</sup> within the mature AIS may experience additional regulation outside of their direct interaction.

NF has been implicated in cellular functions outside of the AIS. For instance, NF null mice die by postnatal day 7 (P7) and fail to recruit Na<sup>v</sup> to CNS nodes of Ranvier (Sherman et al., 2005). In addition, while NF null mice show a normal initial recruitment of Na<sup>v</sup> to the AIS in cerebellar Purkinje cells, this is followed by a complete loss of both Na<sup>v</sup> and AnkG after 15 days (Zonta et al., 2011). Knocking down NF in hippocampal cultures also leads to an impairment in AnkG enrichment (Leterrier et al., 2017). Thus, AnkG is sensitive to the overall stability of interacting partners at the AIS. Therefore, while NF may be influencing the biophysical properties of Na<sup>v</sup> directly through preferential recruitment or retention of specific β subunits, these data also suggest that NF may influence Na<sup>v</sup> accumulation and localization indirectly through its interaction with AnkG. To further clarify the role of NF at the AIS during maturation, we measured parameters of AIS development, composition, and cellular function in wild-type and genetically manipulated neurons. Utilizing the CRISPR/Cas9 system, we targeted a single guide RNA (sgRNA) to NF in cultured hippocampal neurons shortly after initial AIS development. Neurons expressing NF sgRNA exhibited a loss of AnkG enrichment as well as a distal shift in the AnkG localization independent of Na<sup>v</sup> within the AIS, suggesting a previously unreported and selective role for NF in the localization and enrichment of AnkG within the mature AIS.

## MATERIALS AND METHODS

#### Animals

This study was carried out in accordance with the recommendations of Dartmouth College's Institutional Animal Care and Use Committee (IACUC). The protocol was approved by Dartmouth College's Institutional Animal Care and Use Committee—Protocol 00002115.

#### Cell Culture

Neurons from the hippocampal CA1–CA3 regions were dissected from P1 Sprague-Dawley rats, dissociated (bovine pancreas trypsin; 5 min at room temperature), and plated on polyornithine-coated coverslips inside a 6 mm diameter cloning cylinder as previously described (Hoppa et al., 2012). Calcium phosphate mediated transfection was performed on 5-day-old cultured neurons with the described plasmids (below).

#### Antibodies and Plasmids

Mouse monoclonal antibodies to AnkG (1:1,000, 75-187 NeuroMab), panNa<sup>v</sup> (1:1,000, S8809 Sigma), and NF (1:1,000, 75-172 NeuroMab for external; 1:1,000, 75-027 NeuroMab for internal), rabbit polyclonal antibodies to AnkG (1:500, 386-003 Synaptic Systems), NrCAM (1:1,000, ab24344 Abcam) and mCherry (1:2,000, ab167453 Abcam), a chicken polyclonal antibody to GFP (1:2,000, A10262 Thermo Fisher, Waltham, MA, USA), a guinea pig polyclonal antibody to MAP2 (1:2,000, 188-004 Synaptic Systems), and a 565-FluoTag camelid monoclonal antibody to RFP (1:250, N0404-At565-S Synaptic Systems) were used (Grubb and Burrone, 2010a; Xu et al., 2013; Leterrier et al., 2017; Lezmy et al., 2017). Alexa Fluor 488-, 546-, and 647-conjugated goat anti-rabbit, anti-mouse, and anti-chicken IgG (Cat. #s A11034, A11039, A11029, A11074, A11035, A21236, A21245) were used for secondary staining (1:1,000, Thermo Fisher, Waltham, MA, USA).

To construct the NF sgRNA, we inserted a guide RNA (sgRNA) targeting NF-186 specifically (using the sequence caccgTCAACATTGCCAAGGACCCA for the forward primer and GTCAACATTGCCAAGGACCCAgttt for the reverse primer) into the pU6-(BbsI)CBh-Cas9-T2A-mCherry plasmid purchased from Addgene (plasmid 64324). The empty pU6- (BbsI) CBh-Cas9-T2A-mCherry plasmid was used as the sgRNA control. Nav1.6-GFP was cloned as previously described (Gasser et al., 2012).

#### Immunofluorescence

To visualize AIS proteins, days in vitro (DIV) 14–17 neurons were fixed with 4% paraformaldehyde and 4% sucrose in phosphate buffered saline (PBS) and permeabilized with 10% Triton X-100 and 10% goat serum in PBS for 30 min, a procedure to help visualize Na<sup>v</sup> localization at the AIS (Akin et al., 2015). Neurons were then incubated with the appropriate primary antibodies overnight (∼16 h) and visualized using Alexa Fluorconjugated secondary antibodies, both in 5% goat serum.

#### Image Acquisition

Images of stained neurons were primarily obtained using an Olympus microscope (IX-83) equipped with a 40× 1.35 NA oil immersion objective (UAPON40XO340-2). Illumination was generated with a halogen light source (X-Cite 120PC Q; Excelitas) and images captured with an IXON Ultra 897 EMCCD camera (Andor). Green fluorescence was captured using filter sets including ET470/40×, ET525/50m, and T495lpxr filters; red fluorescence was captured using filter sets including ET560/40×, ET630/75m, and T585lpxr filters; and far-red fluorescence was captured using filter sets including ZET635/20×, ET655lpm, and ZT640rdc filters (all from Chroma). All images were captured as a time series of 15 brief exposures which were then maximum intensity projected for analysis. In order to eliminate increased levels of background in the staining, z-stacks were obtained for NrCAM stained neurons using confocal imaging on a Zeiss LSM 880 microscope with a 40×, 1.3 NA objective. Z-stacks contained a step size of 0.35 µm and ranged from 3 to 6 µm in height to ensure all AIS signal was captured. For MATLAB intensity profiling (see below), channels were merged together to create an RGB image using Fiji<sup>1</sup> .

#### Electrophysiology

Neurons were cultured and grown as indicated above for 14–18 days before being transferred to a recording chamber for electrophysiological recording. Neurons were continuously perfused (at 35–36◦C) with oxygenated artificial cerebrospinal fluid composed of the following (in mM): 125 NaCl, 25 NaHCO3, 3 KCl, 1.25 NaH2PO4, 2 CaCl2, 1 MgCl2, and 25 glucose (saturated with 95% O2–5% CO2). Neurons were visualized with a 60x water immersion objective on an Olympus BX51WI microscope. Whole-cell current-clamp recordings of neurons were made with patch pipettes (5–7 MΩ) filled with a standard intracellular solution containing (in mM): 135 K-gluconate, 2 NaCl, 2 MgCl2, 10 HEPES, 3 Na2ATP, and 0.3 NaGTP (pH 7.2 with KOH). Wide-field epifluorescence illumination using a 550 nm LED was used to identify transfected neurons for whole-cell recording. Data were acquired with Axograph software (Axograph Scientific) using BVC-700 amplifiers (Dagan Corporation) and ITC-18 digitizers (HEKA Instruments). Membrane potentials were sampled at 25 kHz, filtered at 5 kHz, and corrected for the junction potential of +12 mV. Capacitance was maximally compensated and bridge-balance used to compensate for series resistance [∼10–25 MΩ, which was stable (within ±5 MΩ) throughout experiments] as previously described (Gulledge et al., 2009). Cells that showed large changes in series resistance were discarded for data analysis purposes. Depolarizing current injections were titrated to evoke just-suprathreshold action potentials and measurements were made of spike threshold as well as the peak, rise time, width, and decay time of the action potential waveform. Input resistance was calculated from the slope of the linear portion of the steadystate voltage-current relationship established with a sequence of somatic current injections (usually −50 to +50 pA). All analyses of action potentials were made from 10 or more trials of the stimulus protocol. Action potential threshold was defined as the voltage at the time corresponding to the slope exceeding 50 mV/ms. Action potential amplitudes were measured as the absolute peak positive amplitude of the voltage response following the current step, relative to the membrane potential occurring just before the initiation of the action potential. Action potential rise time was calculated as time from 10 to 90% of the peak. Full width at half maximum amplitude (FWHM) refers to the broadness of the action potential measured at 50% of peak amplitude. Decay time was calculated as time from 100 to 50% of the peak.

#### Image and Data Analysis

For intensity measurements, images were analyzed in Fiji<sup>1</sup> . A 2-pixel wide line was drawn from the soma to the distal axon to a minimum length of ∼40 µm. The start of the AIS was identified by the morphological constriction of the soma. In cases where an AIS was found on a proximal dendrite, the constriction of the dendrite was used in the same manner as if it were the soma. The raw fluorescence values were then copied into a custom-written Excel spreadsheet to define the AIS (continuous normalized fluorescence intensity above 0.33 for more than 5 µm; termination of the AIS was identified if the normalized fluorescence intensity dropped below 0.33 for more than 2 µm). This region was averaged, and the background was subtracted. Intensity values are represented as the ratio of fluorescence intensity of transfected neurons to the fluorescence intensity of multiple untransfected neurons in the same image (Leterrier et al., 2017). For determination of AIS distance from the soma and length, MATLAB software was used<sup>2</sup> . A previously published MATLAB code (Grubb and Burrone, 2010a) downloaded from the Grubb Lab (ais\_z3.m from http://grubblab.org/resources/) was used to obtain raw 3 × 3 pixel measurements that were normalized and adjusted in a custom-written Excel spreadsheet to obtain length and distance from the soma of the AIS. AIS localization index was calculated

<sup>1</sup>https://fiji.sc/

<sup>2</sup>https://www.mathworks.com/products/matlab.html

for each antibody from untransfected cells using the following formula:

#### AIS Localization Index =

(MeanAIS − Meannon-AIS)/(MeanAIS + Meannon-AIS)

where MeanAIS is the mean fluorescence within the AIS region as defined above and Meannon-AIS is the mean fluorescence over all points outside of the AIS as previously described (Grubb and Burrone, 2010b). All measurements of enrichment at the AIS comparing AnkG and Na<sup>v</sup> localization in both sgRNA control and NF sgRNA conditions were independently replicated blind to experimental conditions. All physiological data were analyzed using Axograph software.

#### Statistical Analysis

All data are presented as mean ± standard error of the mean (SEM). Significance was calculated for two conditions using two-tailed Student's t-test, except in paired distance from the soma measurements, where a Wilcoxon signed-rank test was used. For three or more conditions, a one-way ANOVA followed by Tukey's multiple comparison analysis was performed, except for any distance from the soma measurements, where a Kruskal-Wallis ANOVA followed by a Dunn's post-test with Bonferroni correction was performed. In all figures significance is indicated as: <sup>∗</sup>p < 0.05; ∗∗p < 0.01; ∗∗∗p < 0.001. All statistical tests were performed using OriginPro 8 or R software.

#### RESULTS

#### AnkG and NF Arrive at the AIS Prior to Na**<sup>v</sup>**

One of the earliest proteins to localize to the proximal axon during the establishment of the AIS is AnkG, as previously demonstrated both in vitro (Boiko et al., 2007; Hedstrom et al., 2007) and in vivo (Galiano et al., 2012; Le Bras et al., 2014). We sought to determine the time course of AIS enrichment for NF and Nav, which both contain different AnkG binding domains. Hippocampal neurons from P1 rat pups were dissociated, plated, and then fixed at specific 24-h time points until DIV20. At each time point, we evaluated protein enrichment using immunostaining against AnkG, panNav, and NF. Accumulation of AnkG staining at the AIS was rapid, with discernable enrichment compared to the soma found in 10 ± 2% of neurons at DIV1 (n = 39 fields of view; an average of five cells were contained in each field of view), and appeared in a majority of neurons on DIV3 (**Figures 1A,B**). NF was the next observable protein to enrich within the AIS, present in over 50 ± 6% (n = 25 fields of view) of neurons at DIV7. Na<sup>v</sup> were the last to enrich in the AIS, reaching 50 ± 6% (n = 18 fields of view) of neurons at DIV9, as detected by a panNa<sup>v</sup> antibody in good agreement with previous findings (Yang et al., 2007). Expression of all three proteins gradually increased after their initial observations, becoming evident in greater proportions of neurons in subsequent days, with more than 75% of neurons expressing all three proteins by DIV10 (AnkG 98 ± 1%, NF 89 ± 4%, Na<sup>v</sup> 82 ± 6%; n = 26, 11, and 15 fields of view, respectively).

AIS enrichment. Scale bar: 10 µm. (B) Percentages of neurons containing discernable enrichment at the AIS compared to the soma for AnkG (black), Na<sup>v</sup> (red), and NF (cyan) during development (≥10 images/fields of view were quantified for all proteins in all DIV). Error bars indicate mean ± standard error of the mean (SEM). Cyan line at top indicates statistical significance between NF and AnkG, red line indicates statistical significance between Na<sup>v</sup> and AnkG, and purple line indicates that Na<sup>v</sup> is statistically significant from NF. All significance indicates p < 0.05, ANOVA with Tukey's post hoc comparisons.

To determine the relative localization of AIS proteins with respect to each other at the AIS, intensity profiles of immunostaining within the axon were obtained. A line was drawn over the AIS from the point at which the soma meets the axon and extended distally. An intensity profile plot was obtained, and a continuous portion having greater than 33% normalized intensity and longer than 5 µm was defined as the AIS as previously described (Grubb and Burrone, 2010a) and detailed in the ''Materials and Methods'' section (**Figure 2A**). Intensity profiling allowed us to obtain the distance from the soma as well as the length of AnkG, panNav, and NF in untransfected DIV14 neurons (**Figures 2B–G**). AnkG was most often localized proximal to both Na<sup>v</sup> and NF enrichment. To systematically quantify this distal localization of NF and Nav, we immunostained identical cells with AnkG and either NF or

panNav. While all three proteins exhibited enriched AIS staining of similar length, there were protein-specific differences in their relative location within the AIS. The start of Na<sup>v</sup> enrichment was localized distal to that of AnkG (3.3 ± 0.7 µm and 6.4 ± 1.0 µm for AnkG and Na<sup>v</sup> respectively, n = 40), as was the start of enrichment for NF [2.7 ± 0.76 µm and 7.5 ± 1.0 µm for AnkG and NF respectively, n = 40; **Figure 2F**. Start positions of both Na<sup>v</sup> (3.0 ± 0.6 µm) and NF (4.8 ± 0.9 µm) relative to AnkG start can be seen in **Figure 2G**]. We used a heavy detergent (10% Triton X-100) permeabilization to optimize Na<sup>v</sup> detection as previously described (Akin et al., 2015). To ensure that this did not contribute to our findings of relative enrichment, we directly compared AnkG and NF under high (10% Triton X-100) and low (0.2% Triton X-100) detergent conditions and found that the distance from the soma and length of the two proteins were not altered by permeabilization (**Supplementary Figure S1**). A final concern when using this quantification of AIS parameters as determined by immunostaining is comparable signal to noise. To address this, we calculated the AIS localization index (Grubb and Burrone, 2010b) for each antibody used and found that each had a high localization value that was statistically indistinguishable from the others, validating the method (**Supplementary Figure S2A**).

## Knockout of NF Influences AnkG Localization and Enrichment at the AIS

While Na<sup>v</sup> α subunits have an AnkG binding domain sufficient to target them to the AIS, it has also been shown that Na<sup>v</sup> accumulation stabilizes AnkG enrichment within the AIS (Leterrier et al., 2017). Moreover, Na<sup>v</sup> are most commonly found in the brain as heterotrimeric complexes with one α subunit and two β subunits (Catterall, 2000; Namadurai et al., 2015). NF is uniquely positioned to bind to both AnkG intracellularly through its FIGQY motif and extracellularly with Na<sup>v</sup> β subunits through its Ig domains (Ratcliffe et al., 2001). To elucidate how these interactions may be involved in the localization of Na<sup>v</sup> relative to AnkG post-development, we measured enrichment levels of both AnkG and Na<sup>v</sup> after acute depletion of NF from the maturing AIS. We developed a CRISPR-based method to ablate endogenous protein levels of NF. We combined this with a sparse transfection method (Ca2+-phosphate) that targeted ∼1% of neurons for NF depletion. Recent work has demonstrated that large scale changes in electrical activity within a dish can alter AIS localization relative to the soma (Grubb and Burrone, 2010a). Thus, this combination of CRISPR and sparse transfection closely simulates knockout and avoids any potential large-scale alterations in the overall electrical activity within the culture. A single plasmid encoded the sgRNA, Cas9 enzyme, and a fluorescent protein marker of transfection (mCherry) with cDNA coexpressed using a ribosomal cleavage site as previously described (Cho et al., 2017). This provided both a means to visualize the transfected neurons as well as ensured proper CRISPR component targeting. To test the effectiveness of our sgRNA for CRISPR depletion during AIS maturation, neurons were transfected at DIV5 with either NF sgRNA or an ''empty'' sgRNA control plasmid that only expressed Cas9 and mCherry (sgRNA Ctl.). Neurons were then fixed and immunostained for mCherry, NF and AnkG. We verified the efficiency of our NF sgRNA construct by measuring the NF labeling intensity (**Figures 3A,B**). The intensity of NF labeling, as detected using an antibody directed against an extracellular domain of NF, was severely reduced in NF sgRNA neurons to 7 ± 2% (n = 15) of that observed in untransfected neurons in the same image. In contrast, neurons without sgRNA, but expressing Cas9 and mCherry served as our control condition and did not show significant depletion of NF (88 ± 5%, n = 15; **Figure 3C**). To ensure that the use of a CRISPR InDel for knockout did not produce a NF truncation mutant, we also probed NF levels using an antibody directed against the intracellular N-terminal domain of NF and observed similar reductions in NF protein in sgRNA transfected neurons (**Figures 3D–F**, **F**: 99 ± 9% for sgRNA Ctl. and 10 ± 1% for NF sgRNA, n = 15 for both conditions). Additionally, this intracellular NF antibody showed a similar distal localization relative to AnkG in untransfected cells (**Supplementary Figures S2B,C**) compared to measurements using the extracellular NF antibody (**Figure 2F**).

Previous studies have found that NF is more important for the stabilization of AIS components than for their delivery to the AIS (Zonta et al., 2011). Given that NF has binding sites for both AnkG and Na<sup>v</sup> β subunits, we wanted to determine whether our NF CRISPR knockout would destabilize the arrangement of molecular components within the AIS. In DIV14 neurons AnkG labeling intensity was significantly decreased in neurons transfected with the NF sgRNA construct compared to the sgRNA control (100 ± 4% for sgRNA Ctl., 81 ± 3% for NF sgRNA; n = 55 and 63, respectively; **Figures 4A,B**), results that are in good agreement with those of a previous study using shRNA in hippocampal neurons (Leterrier et al., 2017). We additionally undertook detailed measurements of AnkG localization within the axon using

intensity for external NF at the AIS using an internally targeting antibody in sgRNA control or NF sgRNA expressing neurons, normalized to untransfected neurons in the same image (n = 15 for both conditions; ∗∗∗p < 0.001, Student's t-test). Error bars indicate mean ± SEM.

a previously developed MATLAB code (Grubb and Burrone, 2010a). First, we quantified the distance from the soma that the AIS started, as measured by AnkG staining. Interestingly, we measured a distal shift in the start point for AnkG enrichment in NF sgRNA neurons (8.3 ± 1.2 µm, n = 44) compared to sgRNA control (5.0 ± 1.0 µm, n = 52) and untransfected neurons (4.5 ± 0.9 µm, n = 31; **Figure 4C**). Despite the change in start location, the overall length of the AnkG enrichment was similar in the various conditions (18.1 ± 1.0 µm for untransfected, 18.4 ± 1.0 µm for sgRNA Ctl., 19.8 ± 1.3 µm for NF sgRNA; n = 31, 52, and 44, respectively; **Figure 4D**). Therefore, the loss of

NF results in a decrease in the overall enrichment of AnkG and a distal shift in its distance from the soma.

## NF Knockout Disrupts Stereotypical Alignment of Na**<sup>v</sup>** Relative to AnkG Within the AIS

Next, we sought to determine if the loss of NF caused a uniform shift in the enrichment and localization of Na<sup>v</sup> as a result of their AnkG binding motif dictating a distal shift coupled to AnkG. Previous experiments investigating translocation of the AIS during plasticity indicate that AnkG, Nav, and NF move uniformly together, without noticeable changes in overall enrichment (Grubb and Burrone, 2010a). Despite a ∼20% decrease in AnkG enrichment, Na<sup>v</sup> enrichment at the AIS was unchanged compared to adjacent untransfected neurons (102 ± 6% for sgRNA Ctl.; 94 ± 5% for NF sgRNA; n = 51 and 61, respectively; **Figures 4E,F**). Moreover, when we measured the distance from the soma of AIS start as well as the length of the AIS in untransfected, sgRNA control, and NF sgRNA neurons using Na<sup>v</sup> staining, we found that AnkG and Na<sup>v</sup> were uncoupled. While the start of AnkG enrichment was distally shifted by 3.3 microns (see above), we observed no differences in either the start locations (7.0 ± 1.3 µm for untransfected, 5.9 ± 0.9 µm for sgRNA Ctl., 7.5 ± 1.7 µm for NF sgRNA; n = 29, 62, and 43, respectively; **Figure 4G**) or length (18.2 ± 1.4 µm for untransfected, 18.4 ± 0.9 µm for sgRNA Ctl., 16.3 ± 1.0 µm for NF sgRNA; n = 29, 62, and 43, respectively; **Figure 4H**) of Na<sup>v</sup> enrichment. Collectively, these data demonstrate, to our knowledge, the first changes in AnkG localization that are independent of Na<sup>v</sup> within the AIS, suggesting a unique role for NF to align the enrichment between AnkG and Na<sup>v</sup> in the mature AIS (summary in **Figure 4I**).

## Overexpression of Na**<sup>v</sup>** Restores AnkG Enrichment, but Not Relative Localization

The loss of NF caused a ∼20% depletion of overall AnkG enrichment (**Figures 4A,B**). Recent studies have demonstrated that AnkG can be stabilized by any proteins that contain an AnkG binding domain (Leterrier et al., 2017). Thus, we sought to restore AnkG levels in NF depleted neurons by overexpressing the most distally enriched Na<sup>v</sup> isoform at the AIS, Nav1.6 (Boiko et al., 2003), to determine if its increased presence would rescue the distal translocation of AnkG. To enable visualization of channel overexpression, we expressed a fluorescent chimera, Nav1.6-GFP, which has been previously shown to properly traffic to the AIS (Akin et al., 2015) and to exhibit normal gating kinetics (Gasser et al., 2012). Neurons were transfected with both NF sgRNA or a sgRNA control plasmid and Nav1.6-GFP, and immunostained for mCherry, GFP, and AnkG or panNav. Nav1.6 overexpression rescued the deficient enrichment levels of AnkG in NF sgRNA neurons (81 ± 3% for NF sgRNA, 112 ± 1% for NF sgRNA + Nav1.6-GFP; n = 63 and 18, respectively; **Figures 5A,B**; NF sgRNA originally from **Figure 4B**) as expected. However, overexpression of Nav1.6 did not rescue the distal shift of AnkG enrichment we previously observed in NF sgRNA neurons (5.0 ± 1.0 µm for sgRNA Ctl., 8.3 ± 1.2 µm for NF sgRNA, 8.8 ± 1.5 µm for NF sgRNA and Nav1.6-GFP; n = 52, 44, and 44, respectively; **Figure 5C**; sgRNA Ctl. and NF sgRNA originally from **Figure 4C**). These experiments also confirm successful AIS targeting of Nav1.6 channels in the absence of NF.

Additionally, we investigated the influence of Nav1.6 overexpression on total Na<sup>v</sup> expression at the AIS to determine if their enrichment or location were altered. Despite normal levels of Na<sup>v</sup> labeling intensity in NF sgRNA only neurons (**Figure 4F**), overexpression of Nav1.6 did significantly increase the total Na<sup>v</sup> enrichment as detected by a pan-Na<sup>v</sup> antibody when NF sgRNA was co-transfected with Nav1.6-GFP (94 ± 5% for NF sgRNA, 117 ± 6% for NF sgRNA + Nav1.6-GFP; n = 61 and 28, respectively; **Figures 5D,E**; NF sgRNA originally from **Figure 4F**), further supporting the proper localization of this channel. Additionally, Na<sup>v</sup> overexpression had no influence on the start of Na<sup>v</sup> enrichment at the AIS (5.9 ± 0.9 µm for sgRNA Ctl., 7.5 ± 1.7 µm for NF sgRNA, 7.6 ± 1.3 µm for NF sgRNA and Nav1.6-GFP; n = 62, 43,

FIGURE 5 | Nav1.6 overexpression rescues AnkG enrichment, but not translocation. (A,D) Representative images for NF sgRNA + Nav1.6-GFP co-transfected neurons stained for mCherry, GFP, and AnkG (A) or panNa<sup>v</sup> (D). Red arrows indicate the AIS of transfected neurons. Scale bars: 10 µm. (B,E) Ratio of mean fluorescence intensity for AnkG (B) and Na<sup>v</sup> (E) at the AIS in NF sgRNA (originally from Figure 3) or NF sgRNA + Nav1.6-GFP expressing neurons normalized to untransfected neurons in the same image (B: NF sgRNA n = 63; NF sgRNA + Nav1.6-GFP n = 18; ∗∗∗p < 0.001, Student's t-test. E: NF sgRNA n = 61; NF sgRNA + Nav1.6-GFP n = 28; ∗∗p = 0.0099, Student's t-test). (C,F) Distance from the soma to start of AIS for AnkG (C) and Na<sup>v</sup> (F) in NF sgRNA (data originally from Figure 4) or NF sgRNA + Nav1.6-GFP neurons (C: NF sgRNA n = 44; NF sgRNA + Nav1.6-GFP n = 44; asterisks indicate statistical significance from sgRNA Ctl.; NF sgRNA <sup>∗</sup>p = 0.012, NF sgRNA + Nav1.6-GFP ∗∗p = 0.0073, Kruskal-Wallis ANOVA followed by Dunn's post-test with Bonferroni correction. F: NF sgRNA n = 43; NF sgRNA + Nav1.6-GFP n = 26). sgRNA Ctl. is displayed as a dashed line for comparison. Error bars indicate mean ± SEM. (G) To-scale distribution of AnkG (black) and Na<sup>v</sup> (red) in NF sgRNA (left) and NF sgRNA + Nav1.6-GFP (right) neurons. Color saturation of bars are indicative of average labeling intensity of the population. Dashed black line indicates start of AnkG enrichment in sgRNA control (data originally from Figure 4). Left error bar indicates SEM for distance from the soma, right error bar indicates SEM for length; data taken from (B,C) and (E,F).

and 26, respectively; **Figure 5F**; sgRNA Ctl. and NF sgRNA originally from **Figure 4G**), demonstrating that the loss of AnkG enrichment is not an indirect effect of other altered binding partners, but is specific to the loss of NF (summary in **Figure 5G**).

## NF Knockout Neurons Do Not Exhibit Altered Action Potential Initiation, but Generate Wider Action Potentials

Although we found no intensity or localization changes in Na<sup>v</sup> at the AIS of NF sgRNA neurons, functional differences may be present if NF has an influence directly or indirectly (via Na<sup>v</sup> β subunits) on the kinetics of Na<sup>v</sup> α subunits (Brackenbury and Isom, 2011). Thus, we investigated the electrical properties of control and NF sgRNA neurons using whole-cell patch clamp electrophysiology. Neurons were transfected with either NF sgRNA or a sgRNA control plasmid and recordings were performed on DIV14–18 in untransfected, NF sgRNA, and sgRNA control neurons. No differences in baseline physiological properties, including resting membrane potential (RMP) and input resistance, were observed across conditions (**Table 1**). If NF was in fact influencing Na<sup>v</sup> gating kinetics, one might expect to observe changes in spike threshold (Platkiewicz and Brette, 2011). Thus, we induced action potential generation through just-suprathreshold current injections to closely examine the kinetic parameters of the action potential waveform in each condition (**Figure 6A**). No significant changes in the spike threshold were observed across conditions (−43.0 ± 0.7 mV for untransfected, −41.4 ± 1.1 mV for sgRNA Ctl., −42.6 ± 0.7 mV for NF sgRNA; n = 36, 25, and 30, respectively; **Figure 6B**). Peak amplitude and rise time, both of which are also indicative of Na<sup>v</sup> kinetics, also remained unchanged in NF sgRNA neurons (Peak amplitude: 38.9 ± 2.0 mV for untransfected, 39.1 ± 3.0 mV for sgRNA Ctl., 35.5 ± 1.9 mV for NF sgRNA; n = 36, 25, and 30, respectively; **Figure 6C**. Rise time: 0.14 ± 0.01 ms for untransfected, 0.15 ± 0.01 ms for sgRNA Ctl., 0.17 ± 0.01 ms for NF sgRNA; n = 36, 25, and 30, respectively; **Figure 6D**). There was, however, a significant slowing of the action potential between untransfected and NF sgRNA neurons as measured by FWHM (0.44 ± 0.02 ms for untransfected, 0.47 ± 0.03 ms for sgRNA Ctl., 0.51 ± 0.03 ms for NF sgRNA; n = 36, 25, and 30, respectively; **Figure 6E**) and decay time (0.26 ± 0.01 ms for


Properties of resting membrane potential (RMP), input resistance, spike threshold, peak amplitude, rise time, full width at half maximum amplitude (FWHM), and decay time are shown. All recordings were made between days in vitro (DIV) 14–18 for untransfected (n = 36), single guide RNA (sgRNA) Ctl. (n = 25), and neurofascin-186 (NF) sgRNA (n = 30) cells. Transfections for sgRNA Ctl. and NF sgRNA were identified with an mCherry marker. untransfected, 0.28 ± 0.02 ms for sgRNA Ctl., 0.32 ± 0.02 ms for NF sgRNA; n = 36, 25, and 30, respectively; **Figure 6F**). All electrophysiological properties of the neurons recorded in the three groups are summarized in **Table 1**. These data indicate that Na<sup>v</sup> gating kinetics are likely unaltered in NF sgRNA neurons, but that other changes result in the widening of action potentials and the increase in decay time. Phase plots of the action potentials (**Supplementary Figure S3**) demonstrate that the overall threshold for firing (arrow in **Supplementary Figure S3B**) is similar and the rising and polarizing phases are largely unchanged between conditions.

## Knockout of NF Does Not Influence NrCAM Enrichment or Relative Localization at the AIS

Previous studies in Purkinje neurons using a NF knockout mouse reported impaired action potential generation as well as a loss of NrCAM localization at the AIS (Zonta et al., 2011). However, using shRNA in hippocampal neurons produces only a very moderate effect on NrCAM accumulation (Hedstrom et al., 2007). Given the modest functional effects of NF sgRNA on action potential firing in our neurons, we next investigated how the loss of NF might alter NrCAM enrichment at the AIS using more efficient depletion methods. Neurons were transfected with NF sgRNA or a sgRNA control plasmid and fixed and immunostained for mCherry, NrCAM, and AnkG or NF. In NF sgRNA neurons, there was no decrease in NrCAM intensity compared to the sgRNA control (97 ± 11% for sgRNA Ctl. and 105 ± 8% for NF sgRNA; n = 15 for both conditions; **Figures 7A,B**). NrCAM's AIS localization index was also statistically indistinguishable from AnkG (**Supplementary Figure S2D**). Moreover, there were no changes in the AIS start (2.8 ± 0.8 µm for untransfected, 3.5 ± 0.7 µm for sgRNA Ctl., and 4.2 ± 1.1 µm for NF sgRNA; n = 30 for all conditions; **Figure 7C**) or length (18.0 ± 1.2 µm for untransfected, 15.7 ± 1.1 µm for sgRNA Ctl., and 17.6 ± 1.1 µm for NF sgRNA; n = 30 for all conditions; **Figure 7D**) as measured through NrCAM labeling. To ensure that the NF sgRNA construct was still efficient in our NrCAM measurements, a subset of neurons from the same culture transfected with either the sgRNA control or NF sgRNA was stained for NF and quantified for enrichment levels. These neurons also exhibited a significant decrease in NF labeling intensity, similar to that shown in **Figure 3** (93 ± 10% for sgRNA Ctl. and 12 ± 3% for NF sgRNA; n = 10 for both conditions; **Figure 7E**). Likewise, measuring AnkG staining in the same neurons as NrCAM was quantified and also confirmed NF-dependent modulation of AnkG enrichment levels and localization (**Figures 7F–H**, **F**: 102 ± 6% for sgRNA Ctl. and 80 ± 8% for NF sgRNA; n = 10 for both conditions; **G**: 1.8 ± 0.6 µm for untransfected, 2.2 ± 0.6 µm for sgRNA Ctl., and 4.5 ± 0.9 µm for NF sgRNA; n = 30 for all conditions; **H**: 22.1 ± 1.2 µm for untransfected, 19.5 ± 1.2 µm for sgRNA Ctl., and 18.9 ± 1.2 µm for NF sgRNA; n = 30 for all conditions). Together, these results indicate that NrCAM expression is undisturbed by NF depletion and, like Nav, display

a relative localization uncoupled from AnkG (summary in

n = 36; sgRNA Ctl. n = 25; NF sgRNA n = 30; <sup>∗</sup>p < 0.05, ANOVA with Tukey's post hoc comparisons). Error bars indicate mean ± SEM.

## DISCUSSION

**Figure 7I**).

The AIS has been an area of interest for understanding neuronal excitability for nearly 50 years. This unique neural compartment has been extensively studied, and while the primary molecular components have been identified, their interplay is yet to be completely explained. Multiple studies agree that AnkG is a master regulator of this structure, necessary for both its formation and maintenance (Zhou et al., 1998; Zhang and Rasband, 2016). AnkG also interacts with the majority of other AIS proteins (Nav, NF, βIV-spectrin), further confirming its critical role in AIS organization (Xu et al., 2013; Leterrier et al., 2015). These interactions are typically thought to create a tightly-linked structure with slow turnover and negligible diffusion (Hedstrom et al., 2008; Akin et al., 2015). Here, we describe a disruption in AnkG accumulation as well as an uncoupling of AnkG localization relative to Na<sup>v</sup> and NrCAM caused by the acute loss of NF (**Figure 4B**). These data agree with a recently published study showing more promiscuous interactions of proteins containing AnkG binding motifs that ensure a stable ''interactome'' for enrichment of AIS components (Leterrier et al., 2017). However, the relative arrangement of proteins within the

AIS seems quite specific, as the selective depletion of NF causes a distal shift in AnkG localization without changing the location of Na<sup>v</sup> (**Figures 4C,G**) or NrCAM (**Figure 7C**). Overexpression of Nav1.6 was unable to restore proximal relative localization of AnkG when NF was depleted despite restoring overall levels of AnkG (**Figures 5B,C**). Moreover, given no functional changes in Na<sup>v</sup> as a result of altered AnkG localization (**Figures 6B–D**), NF does not appear to directly influence cellular excitability through modulation of Na<sup>v</sup> channels. These results suggest that the anchoring of Na<sup>v</sup> is not solely controlled by AnkG and that NF plays a role in stabilization of the mature AIS but does not directly alter Na<sup>v</sup> kinetics.

Although NF can bind to both Na<sup>v</sup> and AnkG, its loss influences them differently. The knockout of NF had a two-fold effect on AnkG, altering its concentration at the AIS and shifting its overall localization within the AIS (**Figure 4**). Typically, depletion of either AnkG or Na<sup>v</sup> leads to a loss of the other and eventually a destabilization of the AIS as whole (Zhou et al., 1998; Xu and Shrager, 2005). Conversely, without NF the two proteins act independently. Indeed, we now appreciate that the AIS is not a static structure, as several studies have observed alterations in AIS morphology through manipulations of neural input (Grubb and Burrone, 2010a; Kuba et al., 2010; Evans et al., 2015). This plasticity occurs through shifts in AIS location relative to the soma (Grubb and Burrone, 2010a) or alterations in AIS length (Kuba et al., 2010; Evans et al., 2015). In all cases, Na<sup>v</sup> and AnkG have been shown to transform in tandem, maintaining their relative proximal and distal enrichment patterns (along with NF and β-spectrin). Most studies of AIS structural plasticity have only shown that dynamic relocations occur during very early development or in vitro (Yamada and Kuba, 2016), a limitation of this study as well. It would be increasingly exciting to study AIS plasticity in vivo (Jamann et al., 2018). We propose that the coupling of AnkG to Na<sup>v</sup> and NrCAM minimally requires a contribution from NF. Therefore, NF may be one of multiple players required for specific interactions that stabilize the AIS.

There are conflicting data regarding the exact role of NF from studies of Purkinje neurons in NF knockout mice and those using RNA interference in hippocampal or cortical neurons. Purkinje neurons in knockout mice have fairly normal AIS development, including AnkG and Na<sup>v</sup> enrichment, with only a loss of NrCAM. However, during maturation, NF knockout leads to a complete dismantling of the AIS (Zonta et al., 2011). Using shRNA to deplete NF in hippocampal neurons had a much milder phenotype, where the AIS still recruits Na<sup>v</sup> and AnkG (Hedstrom et al., 2007), though complete enrichment of AnkG is impaired (Leterrier et al., 2017). This differs from studies at the nodes of Ranvier, where NF is crucial to recruiting Na<sup>v</sup> (Sherman et al., 2005). Using a CRISPR strategy to more thoroughly deplete NF from the AIS, we observed a significant loss of AnkG accumulation that did not lead to the disassembly of the mature AIS (**Figure 4**), in agreement with previous knockdown experiments (Leterrier et al., 2017). Additionally, we did not see the disruption of NrCAM enrichment (**Figure 7**), which was observed in cultured slices of Purkinje neurons (Zonta et al., 2011). We speculate that there are at least three possibilities for these discrepancies between our study and others. First, there are differences in the temporal windows over which manipulations to NF were applied. We do not, however, believe this to be the cause since even in null mice initial AnkG localization and Na<sup>v</sup> recruitment were normal. Second, there are differences between the firing frequencies of the neurons studied. The firing rates of Purkinje (>100 Hz) and hippocampal (<10 Hz) neurons differ by an order of magnitude. We do not believe this is the cause of instability, as while the loss of NF decreased excitability in Purkinje neurons (Zonta et al., 2011), decreasing excitability is not usually detrimental to the stability of the AIS. Interestingly, we did detect some changes in width and decay time of the somatically-recorded action potential waveform, which may indicate that NF influences K<sup>+</sup> channels in the AIS. That being said, the phase plots (**Supplementary Figure S2**) and overall properties of the cells (**Table 1**) were not telling as to a mechanism. These results could be due to other compensatory mechanisms. In our study we only compared the firing of single action potentials, but perhaps a slight increase in action potential width and decay time as we observed could indirectly impair the ability of neurons to maintain high frequency firing as seen in Purkinje neurons (Zonta et al., 2011), especially given the different cell shape and physiology. Third, there are additional isoforms of NF present in our cultures that were not targeted by our sgRNA. There is the glial isoform, NF-155, as well as the more recently discovered NF-140 (Zhang et al., 2015). While in null mice the glial NF-155 is also ablated (Sherman et al., 2005), these isoforms remain in our cultures. However, the selective knockout of NF-155 produces independent impairments (Smigiel et al., 2018), arguing against potentially redundant transcellular signaling by NF-155 within the extracellular matrix (ECM). Furthermore, NF-140 has remained understudied until recently. This isoform has been shown to be expressed in the AIS of cerebellar Purkinkje neurons in a developmental manner, and while it plays complementary roles in Na<sup>v</sup> and NrCAM clustering (Zhang et al., 2015), our staining with a pan-NF antibody showing nearly complete lack of staining at the AIS suggests that this isoform is not present at the AIS in our neurons (**Figure 3**). Thus, we argue that additional factors may be responsible for the more drastic destabilization previously seen in Purkinje neurons (Zonta et al., 2011).

Without the presence of NF during development, the AIS may be lacking critical extracellular interactions. Among these could be interactions with ECM proteins such as brevican. The clustering of brevican and formation of a specialized brevicancontaining matrix at the AIS has been shown to be dependent on NF, and has been speculated as important for stabilizing axo-axonic synapses (Hedstrom et al., 2007). Additionally, NF may play a more direct role in the formation of axo-axonic GABAergic synapses along the axon hillock (Kriebel et al., 2011). Coincidently, Purkinje neurons have one of the largest inhibitory inputs onto their AIS from basket cells that form Pinceau synapses in this region. This innervation is dramatically disrupted by the loss of NF (Ango et al., 2004), which may contribute to the more dramatic phenotype observed in those neurons. Moreover, axo-axonic inhibitory synapses are also found in the cortex, hippocampus, and amygdala. These connections appear to be disrupted in schizophrenia (Lewis, 2011), and genetic depletion of NF in mature neurons within the amygdala was recently demonstrated to alter reversal learning in fear-conditioning studies (Saha et al., 2018), further pointing to a highly important role for these connections. Additionally, during acute changes in AIS location in cultured neurons, GABA receptors were destabilized within the AIS (Muir and Kittler, 2014), though their relative location during plasticity-induced relocation of AnkG remained stable (Wefelmeyer et al., 2015). Functional studies of the relatively static inhibitory synapses at the AIS could not be performed, but were modeled and observed to change the relative inhibition of neurons in a homeostatic manner during AIS distal shifts (Wefelmeyer et al., 2015). Given our results that NF helps to couple the localization of both AnkG and Na<sup>v</sup> within the AIS, this protein is well positioned to influence GABAergic innervation and function within the AIS and could be studied in relation to AnkG and Na<sup>v</sup> translocation in axons heavily innervated with GABAergic synapses.

After revealing that NF ablation reduces the distal enrichment of AnkG relative to Nav, we are left to speculate about the molecular control of this alignment within the AIS. A number of other dynamic factors can alter channel density and availability at the AIS including channel endocytosis (Benned-Jensen et al., 2016), Ca2<sup>+</sup> influx (Bender et al., 2010; Martinello et al., 2015), intracellular fibroblast growth factor homologous factors (Pablo and Pitt, 2016), and AIS-specific kinases and phosphatases (Bréchet et al., 2008; Hien et al., 2014; Xu and Cooper, 2015; Lezmy et al., 2017). Our work cannot directly link to any of these particular mechanisms. Protein kinase CK2 is highly enriched at the AIS and within the nodes of Ranvier of hippocampal neurons in vitro and in vivo as is AnkG, Na<sup>v</sup> and NF. CK2 has been found to regulate the interaction of both Na<sup>v</sup> and the voltage-gated potassium channel (Kv) Kv7 in a potentially competitive manner with AnkG, and is also important in enabling a form of Kv7-dependent AIS plasticity (Lezmy et al., 2017). Pharmacological inhibition of CK2 causes reduced enrichment of both AnkG and Na<sup>v</sup> at the AIS suggesting a critical role for the kinase to ensure a stable interaction and enrichment of these two proteins at the AIS. How CK2 is localized within the AIS to control the important interaction between Nav, Kv, and AnkG remains to be determined, but data suggest that the Na<sup>v</sup> themselves recruit the kinase to the AIS (Hien et al., 2014). We speculate that NF may actually play a role in facilitating this localization between CK2, Nav, and AnkG, perhaps at the expense of Kv7. This may partially explain why AnkG enrichment is selectively reduced without NF because of a mismatch in localization between AnkG and CK2-phosphorylated Nav. Future development of genetically encoded fluorescent Na<sup>+</sup> and K<sup>+</sup> indicators (Shen et al., 2018) to study channel function within the AIS as well as the continued development of super-resolution microscopy (Sigal et al., 2018) may help investigate this mechanism further.

#### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and the supplementary files.

## AUTHOR CONTRIBUTIONS

SA: conception and design, experiments and data acquisition, analysis and interpretation of the data, draft and revision of the article. AB: experiments and data acquisition, analysis and interpretation of the data, draft and revision of the article. AG

#### REFERENCES


and MH: concept and design, interpretation of data, draft and revision of the article.

## FUNDING

This work was supported by the Esther A. and Joseph Klingenstein Fund (MH), the National Institute of General Medical Sciences (NIGMS; MH; P20-GM-113132), the Brain Research Foundation (MH; BRFSF\_2015-05), the U.S. Department of Education (SA; P200A150059), and the National Institute of Mental Health (NIMH; AG; R01 MH099054).

## ACKNOWLEDGMENTS

We thank current Hoppa Laboratory members Lauren Panzera and In Ha Cho for critical reading of the manuscript; former Hoppa Laboratory member Ryan O'Toole for thoughtful insight and Excel spreadsheet template; Nina Rhone and Mia Drury for blind analysis of AIS measurements; and Song Heui Cho for cloning sgRNA construct.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00001/full#supplementary-material


**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 © 2019 Alpizar, Baker, Gulledge and Hoppa. 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(s) 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 Ever-Growing Puzzle of Asynchronous Release

#### Andrei Rozov 1,2\*, Alexey P. Bolshakov 3,4 and Fliza Valiullina-Rakhmatullina<sup>1</sup>

<sup>1</sup>Laboratory of Neurobiology, Institute of Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia, <sup>2</sup>Department of Physiology and Pathophysiology, University of Heidelberg, Heidelberg, Germany, <sup>3</sup> Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences (RAS), Moscow, Russia, <sup>4</sup>Laboratory of Electrophysiology, Pirogov Russian National Research Medical University, Moscow, Russia

Invasion of an action potential (AP) to presynaptic terminals triggers calcium dependent vesicle fusion in a relatively short time window, about a millisecond, after the onset of the AP. This allows fast and precise information transfer from neuron to neuron by means of synaptic transmission and phasic mediator release. However, at some synapses a single AP or a short burst of APs can generate delayed or asynchronous synaptic release lasting for tens or hundreds of milliseconds. Understanding the mechanisms underlying asynchronous release (AR) is important, since AR can better recruit extrasynaptic metabotropic receptors and maintain a high level of neurotransmitter in the extracellular space for a substantially longer period of time after presynaptic activity. Over the last decade substantial work has been done to identify the presynaptic calcium sensor that may be involved in AR. Several models have been suggested which may explain the long lasting presynaptic calcium elevation a prerequisite for prolonged delayed release. However, the presynaptic mechanisms underlying asynchronous vesicle release are still not well understood. In this review article, we provide an overview of the current state of knowledge on the molecular components involved in delayed vesicle fusion and in the maintenance of sufficient calcium concentration to trigger AR. In addition, we discuss possible alternative models that may explain intraterminal calcium dynamics underlying AR.

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France

#### Reviewed by:

Marco Capogna, Aarhus University, Denmark Michael Beierlein, University of Texas Health Science Center at Houston, United States

#### \*Correspondence:

Andrei Rozov andrei.rozov@physiologie.uniheidelberg.de

Received: 31 October 2018 Accepted: 22 January 2019 Published: 12 February 2019

#### Citation:

Rozov A, Bolshakov AP and Valiullina-Rakhmatullina F (2019) The Ever-Growing Puzzle of Asynchronous Release. Front. Cell. Neurosci. 13:28. doi: 10.3389/fncel.2019.00028 Keywords: presynaptic, calcium, synaptotagmins, calcium extrusion, synaptic release

## INTRODUCTION

In most of the synapses in the central and peripheral nervous system, release of synaptic vesicles is tightly temporally coupled to presynaptic action potentials (APs). Usually synaptic delay, the time between the peak of the AP and the onset of the postsynaptic response, does not exceed a few milliseconds. This holds true even for synapses where APs can trigger multi vesicular release (Watanabe et al., 2005). Short synaptic delay also suggests a small range of synaptic jitter, which, in turn, provides the functional basis for the synchronization of postsynaptic responses (Burkitt and Clark, 1999). This feature of synaptic transmission allows rapid information transfer between connected cells and within neuronal networks. The level of synchronization between APs and synaptic vesicle fusion is mainly determined by the affinity of vesicular Ca2<sup>+</sup> sensors and Ca2<sup>+</sup> dynamics within presynaptic microdomains. In most cases, Ca2<sup>+</sup> concentration collapses below the threshold level for triggering vesicle fusion within a few milliseconds of the AP reaching the presynaptic terminal. Generally, even high frequency bursts of APs result in highly synchronized postsynaptic activity. However, at some synapses high frequency stimulation can trigger not only synchronized phasic transmitter release but can also generate vesicle fusion that lasts for tens or hundreds of milliseconds after the end of the AP burst (**Figure 1A**; Hefft and Jonas, 2005; Daw et al., 2009; Ali and Todorova, 2010; Wen et al., 2010; Jappy et al., 2016; Chen et al., 2017; Li et al., 2017; Luo and Sudhof, 2017; Turecek and Regehr, 2018). This phenomenon is known as asynchronous release (AR). Most likely, this mode of release is not involved in rapid information transfer within CNS, but plays an important role in the generation of long-lasting forms of synaptic plasticity especially at those synapses where plasticity requires the involvement of extrasynaptic metabotropic receptors (Jappy et al., 2016). Also, taking into account that the output of synapses with AR lasts for tens of milliseconds after the end of the presynaptic AP burst, neurons possessing the ability to release neurotransmitter in this delayed asynchronous fashion may participate in the generation of low frequency oscillations. For instance, hippocampal cholecystokinin (CCK) positive basket interneurons show prominent AR and play a key role in the maintenance of the hippocampal theta rhythm (Hefft and Jonas, 2005; Klausberger and Somogyi, 2008). Finally, similarly to phasic release, AR undergoes short-term plasticity dependent on presynaptic stimulation frequency and duration (Iremonger and Bains, 2007; Ali and Todorova, 2010). Thus, the understanding of mechanisms underlying AR will contribute to our knowledge on the generation of different forms of synaptic plasticity and network integration of distinct neuronal types.

Over the last couple of decades, the molecular components and mechanisms involved in delayed synaptic vesicle fusion have been extensively studied using different approaches. It has been proposed that the synchronous and asynchronous modes of release recruit different Ca2<sup>+</sup> sensors and are differentially regulated by proteins involved in the vesicle cycle. Both release modes are Ca2+-dependent, however, the number of Ca2<sup>+</sup> ions required to bind with Ca2<sup>+</sup> sensors that is necessary to trigger these distinct types of release might be different. Another question that remains a subject of discussion is: what are the Ca2<sup>+</sup> sources for triggering the two types of vesicle release? While there is a common agreement that synchronous release is mainly triggered by Ca2<sup>+</sup> influx through presynaptic voltage-gated Ca2<sup>+</sup> channels, the source of long-lasting Ca2<sup>+</sup> entry required for AR triggering remains poorly identified and, probably varies depending on the identity of the presynaptic neuron. The main differences in mechanisms underlying phasic and asynchronous modes of release have been discussed in an excellent review by Kaeser and Regehr (2014). However, it is still unclear why the same stimulation protocol on two types of presynaptic inputs to the same postsynaptic cell triggers highly synchronized release from one type of terminal and strong long lasting AR at the other (Hefft and Jonas, 2005). In this review article, we discuss the molecular players involved in AR generation in inhibitory and excitatory central synapses and in neuromuscular junctions. In addition to that, we review the current opinion on the mechanisms that allow a sufficient level of presynaptic Ca2<sup>+</sup> to trigger delayed fusion of synaptic vesicles. Finally, we suggest the possible involvements of calcium extrusion pumps in AR generation and maintenance.

FIGURE 1 | Asynchronous release (AR) is temporally separated from action potential (AP) generated calcium concentration microdomains. (A) Example traces of responses recorded from a pair of connected cells, a hippocampal presynaptic cholecystokinin (CCK)<sup>+</sup> basket cell (black) and postsynaptic CA1 pyramidal neuron (red, three subsequently recorded traces). Five APs (50 Hz) trigger synchronized phasic IPSC [labeled with (∧)] and delayed responses that can be observed both during the AP train [yellow window; labeled with (<sup>∗</sup> )] and after termination of presynaptic stimulation (green window). (B) Schematic drawing of the presynaptic calcium concentration dynamics after a single AP. Opening of the voltage gated calcium channel (VGCC) causes formation of a calcium concentration microdomain—a short-lasting local elevation of [Ca2+]<sup>i</sup> sufficient to trigger phasic release (left panel). After closure of the VGCC, [Ca2+]<sup>i</sup> radially diffuses and equilibrates within the terminal and then further declines due to binding to endogenous buffers and extrusion (right panel). (C) Schematic drawing of vesicle fusion driven by an AP evoked Ca2<sup>+</sup> micro/nano-domain (upper panel). Note that high synchrony arises from the low affinity of the Ca2<sup>+</sup> sensor (SytLA) and tight spatial coupling of the Ca2<sup>+</sup> source and Ca2<sup>+</sup> sensor. The lower panel shows delayed vesicle fusion mediated by residual [Ca2+]<sup>i</sup> remaining in terminals several milliseconds after the last AP. In this case recruitment of high affinity synaptotagmins (SytHA) is necessary, but vesicles can be spatially separated from VGCC, since release is triggered by bulk [Ca2+]<sup>i</sup> . (D) Schematic representation of the [Ca2+]<sup>i</sup> time course at the release site (blue) after AP. Dotted lines show time windows for synchronous (SR) and AR components of release that are probably mediated by synaptotagmins with different Ca2<sup>+</sup> affinities.

#### PRESYNAPTIC CALCIUM DOMAINS AND ASYNCHRONOUS RELEASE

According to the most widely accepted model, synaptic release is triggered in the active zones by Ca2<sup>+</sup> entering through voltage gated calcium channels (VGCCs). When these channels open during AP, short lasting and spatially restricted elevation of intraterminal Ca2<sup>+</sup> ([Ca2+]i) occurs in close vicinity to the channels or the cluster of the VGCCs known as nanoor microdomains (Chad and Eckert, 1984; Simon and Llinás, 1985; Neher, 1998; Eggermann et al., 2011). Although, direct measurements of [Ca2+]<sup>i</sup> dynamics in the active zone are technically challenging at this time, all existing mathematical models predict that [Ca2+]<sup>i</sup> elevation sufficient for triggering fast phasic release remains in the microdomain no longer than a few milliseconds after AP (Arai and Jonas, 2014). Then [Ca2+]<sup>i</sup> equilibrates within the terminal because of radial diffusion, and further declines due to binding to endogenous buffers and calcium extrusion (**Figures 1B,D**). The rapid temporal dynamics of calcium concentration in microdomains ensures high fidelity AP-driven phasic synaptic transmission. However, it seems very unlikely that the same calcium sensor (synaptotagmins) and calcium source are involved in the generation of both the phasic and asynchronous components of evoked release. Taking into account the duration of AR, at some synapses hundreds of milliseconds, the [Ca2+]<sup>i</sup> available at the release site should be substantially lower than that in the microdomain during phasic release. This assumption strongly suggests three possible scenarios for AR generation: (1) affinity of the calcium sensor mediating AR should be high enough so that fusion events may be triggered by the remaining bulk [Ca2+]<sup>i</sup> ; (2) invasion of APs to the presynaptic terminals, besides opening VGCC, triggers additional long lasting Ca2<sup>+</sup> entry; and (3) a combination of both high-affinity calcium sensors and an additional calcium source is necessary for AR generation.

## CALCIUM SENSORS UNDERLYING ASYNCHRONOUS RELEASE

One of the popular hypotheses to explain delayed vesicle fusion after high frequency presynaptic stimulation is that the synchronous and asynchronous modes of release are triggered by different types of Ca2<sup>+</sup> sensors (**Figure 1C**). The selective suppression of AR by moderate concentrations of EGTA (Hefft and Jonas, 2005; Iremonger and Bains, 2007) speaks in favor of this notion, suggesting both spatial separation of the asynchronously released vesicles from Ca2<sup>+</sup> microdomains and high affinity of the sensor mediating this mode of release. It is commonly accepted that the role of vesicular Ca2<sup>+</sup> sensor is played by proteins belonging to the synaptotagmin (Syt) family consisting of 17 members. They differ in their expression pattern and Ca2<sup>+</sup> binding properties (Bhalla et al., 2008; Gustavsson et al., 2008; Craxton, 2010; Moghadam and Jackson, 2013). The vital role in the generation of the phasic component of synaptic release is usually attributed to Syt1 and Syt2. Indeed, homozygous Syt1 knockout mice die within 48 h of birth. Analysis of synaptic transmission between cultured hippocampal pyramidal neurons has shown that deletion of Syt1 leads to the selective loss of fast evoked synaptic release while AR and spontaneous vesicle fusion remain unaffected (Geppert et al., 1994). Furthermore, point mutations in Syt1 that result in either reduction of Ca2<sup>+</sup> affinity or a decrease in phospholipid binding also selectively suppress the phasic component of evoked release (Pang et al., 2006; Fleidervish et al., 2010). Similarly to Syt1 omission, knockout of Syt2 results in severe desynchronization of synaptic release from presynaptic APs (Sun et al., 2007). In calyx of Held synapses, synaptic delay in Syt2-knockout mice was approximately 3–4 times longer than synaptic delay in wild type animals. Moreover, in wild type calyxes, when [Ca2+]<sup>i</sup> exceeded 1 µM most of the vesicles were released within first few milliseconds, resulting in fast rising excitatory postsynaptic currents (EPSCs); in knockout animals, using flash photolysis of caged Ca2+, release rate progressively increases reaching a peak about 100–200 ms after the flash that triggered Ca2<sup>+</sup> uncaging (Sun et al., 2007). The authors concluded that the presence of Syt2 is essential for rapid synchronization of vesicle fusion at high [Ca2+]<sup>i</sup> . The major role of Syt1 and Syt2 as the vesicular calcium sensors at GABAergic and glutamatergic synapses was further proven in a number of studies (Xu et al., 2007; Südhof, 2013; Chen et al., 2017; Li et al., 2017). Of the synaptotagmins Syt1 and Syt2 have the lowest Ca2<sup>+</sup> affinity (EC50 = 10–20 µM; Sugita et al., 2002). Therefore, although these Syts are suitable for triggering highly synchronized phasic release during the shortlived [Ca2+]<sup>i</sup> elevation within the microdomain, it seems unlikely that they can maintain vesicle fusion even a few milliseconds after VGCC closure.

Another isoform of synaptotagmin, Syt7, that has been proposed to mediate AR, has tenfold higher Ca2<sup>+</sup> affinity (EC50 = 1–2 µM; Sugita et al., 2002). At wild-type zebrafish neuromuscular junctions, high frequency stimulation leads to a high level of desynchronization of vesicle fusion that may be observed as a barrage of EPSCs between two subsequent APs. Knockdown of Syt7 almost completely abolished these events without having a major effect on the synchronous release occurring 1–3 ms after APs (Wen et al., 2010). Conversely, in a study conducted in T. Sudhof's laboratory (Maximov et al., 2008) deletion of Syt7 did not have any effect on either synchronous or AR measured at inhibitory synapses in cortical neuronal cultures. However, in a subsequent study the same group used a knockdown approach to eliminate the contribution of Syt7 to AR and they found that indeed, similarly to the neuromuscular junction, this isoform of synaptotagmin plays a significant role in AR generation (Bacaj et al., 2013). The authors explained the apparent discrepancy between these two reports as possible developmental compensation in Syt7 knockout animals. Finally, involvement of the Syt7 isoform in delayed vesicle fusion during neuroendocrine exocytosis has been demonstrated in numerous studies (Sugita et al., 2001; Shin et al., 2002; Fukuda et al., 2004; Tsuboi and Fukuda, 2007; Gustavsson et al., 2008; Schonn et al., 2008; Gustavsson and Han, 2009; Li et al., 2009; Segovia et al., 2010). Recently, the crucial role of Syt7 in AR generation has been confirmed in inhibitory hippocampal synapses (Li et al., 2017), cerebellar GABAergic (Chen et al., 2017) and glutamatergic (Turecek and Regehr, 2018) synapses, and at excitatory calyx of Held synapse (Luo and Sudhof, 2017).

However, despite the growing data pool supporting the notion that Syt7 is the AR calcium sensor, there are several features of this isoform suggesting a more complex mechanism underlying AR. First, in contrast to Syt1 and Syt2, Syt7 was found on the presynaptic plasma membrane and other internal membranes, but not synaptic vesicles (Sugita et al., 2001; Virmani et al., 2003; Takamori et al., 2006; Südhof, 2013) implying that this isoform either does not participate in vesicle exocytosis or does it in a non-canonical fashion. An alternative function of Syt7 was proposed by Liu et al. (2014) and they demonstrated the involvement of Syt7 in synaptic vesicle replenishment in response to high frequency depleting stimulation. In support of this hypothesis it has been recently shown that robust high frequency stimulation (20 Hz for 5 s) promotes Syt7-dependent endocytosis and formation of Syt7-containing vesicles, which might be later released asynchronously (Liu et al., 2014). This mechanism may underlay the delayed release observed at the cerebellar GABAergic basket to Purkinje cell synapses, where AR may be triggered by several repetitions of 20 Hz 50 APs trains (Chen et al., 2017), but fails to explain how in the terminals of hippocampal CCK-positive basket interneurons a single burst of a few APs (3–5 APs at 50 Hz; **Figure 1A**) generates AR lasing over 100 ms (Hefft and Jonas, 2005; Daw et al., 2009; Ali and Todorova, 2010; Jappy et al., 2016).

Second, the main evidence that Syt7 is the AR calcium sensor comes from experiments conducted on knockout animals. Indeed, deletion of this isoform leads to a reduction of the delayed release component in synapses which have a moderate contribution of AR to synaptic response (Bacaj et al., 2013; Chen et al., 2017; Turecek and Regehr, 2018). Nevertheless, there is evidence that the ''desynchronizing'' action of Syt7 depends on the identity of the interaction partners in the SNARE complex. For instance, in hippocampal cultured neurons substitution SNAP-25 by SNAP-23 in the presence of endogenous Syt7 resulted in strong desynchronization of evoked release, but omission of Syt7 in SNAP-23 expressing cultures made release even more asynchronous (Weber et al., 2014). Moreover, Weber and co-authors showed that asynchronously released vesicles carried Syt1, but not Syt7. Finally, the single-cell expression profile of synaptotagmins clearly shows that Syt7 is expressed in most hippocampal and neocortical neurons (Zeisel et al., 2015) and the level of Syt7 mRNA in excitatory hippocampal cells, which show very moderate AR, is substantially higher than in CCK/CB1-positive interneurons, which demonstrate pronounced AR (Zeisel et al., 2018). Recent articles proposed that this isoform is responsible for paired pulse synaptic facilitation at a number of excitatory synapses (Jackman et al., 2016; Turecek and Regehr, 2018) assuming that recruitment of Syt7 in synaptic release occurs during the second AP. Nevertheless, most of these connections, three hippocampal and one corticothalamic, do not show AR at a level that might have physiological relevance. Thus, one can conclude that different isoforms of synaptotagmins can play different roles in determining the modality of vesicle fusion at different synapses. Most likely, low-affinity isoforms Syt1 and Syt2 are responsible for the high level of synchronization of fast release with presynaptic APs, while high-affinity Syt7 participates in generation of delayed release. However, the mechanism of recruitment of Syt7 in phasic and AR needs to be identified.

Doc2 proteins were proposed as another candidate for the Ca2<sup>+</sup> sensor responsible for AR (Yao et al., 2011; Xue et al., 2015). However, the initial finding that knockout of cytosol soluble Doc2A reduces the asynchronous component of evoked release has not been confirmed by other groups (Groffen et al., 2010; Pang et al., 2011). More recently, it has been shown that proteins of the Doc2 family participate in spontaneous release rather than take part in AR generation (Ramirez et al., 2017). In particular, Doc2α is involved in spontaneous release at excitatory synapses while Doc2β knockout selectively affects spontaneous release from GABAergic terminals (Courtney et al., 2018). Finally, consideration of Doc2 proteins as specific Ca2<sup>+</sup> sensors for AR is challenged by single-cell RNA-seq data, according to which expression of Doc2 proteins is substantially higher in excitatory hippocampal and cortical neurons with very weak AR than in those subpopulations of interneurons that have very pronounced AR (Zeisel et al., 2018).

## CALCIUM SOURCES FOR TRIGGERING ASYNCHRONOUS RELEASE

Despite the fact that asynchronous and phasic releases can be triggered by distinct Ca2<sup>+</sup> sensors, the main prerequisite for triggering prolonged delayed release is long-lasting presynaptic [Ca2+]<sup>i</sup> elevation. Thus, the two main questions when studying AR are:


The suggested sources of Ca2<sup>+</sup> for AR generation are summarized on **Figure 2A**. It has been proposed that P2X2 receptors mediate/modulate AR at glutamatergic synapses formed by Schaffer collaterals on CA1 stratum radiatum interneurons. Here a high frequency train of 3 or 9 stimuli triggered AR lasting for several seconds (Khakh, 2009). In half of the neurons tested, the frequency of the post-train asynchronous event could be reduced by application of a P2X2 antagonist, however, drug application did not have any effect on the remaining interneurons. This finding has potential interest for two major reasons. First, it gives a hint that the P2X2 receptor is expressed in the brain in adulthood which so far has not been shown by RNA-seq (Zeisel et al., 2015; Cembrowski et al., 2016). Second, it shows that activation of Ca2+-permeable purinergic receptors may play a modulatory role in transmitter release at glutamatergic synapses.

In frog neuromuscular junctions, long-lasting amplification of Ca2<sup>+</sup> transients was suggested to be due to Ca2+-induced Ca2<sup>+</sup> release from intracellular stores. In two articles published by Narita et al. in 1998 and 2000, the authors claimed that during high frequency stimulation [Ca2+]<sup>i</sup> in motor neuron terminals reaches a sufficient level for the activation of ryanodine receptors located on presynaptic Ca2<sup>+</sup> depots (Narita et al., 1998, 2000). Subsequently, this can trigger massive Ca2<sup>+</sup> release from presynaptic intracellular stores. The major proof of this

(ii) calcium-dependent prolongation of calcium entry through VGCC.

(B) Schematic representation of a hypothetical [Ca2+]<sup>i</sup> time course at the release site during SR and AR. Conventional [Ca2+]<sup>i</sup> elevation due to the flux through VGCC during AP (blue) combines with Ca2<sup>+</sup> entry via an additional AP activated Ca2<sup>+</sup> source (green). Dotted lines show time windows for SR and AR.

conclusion is that, in the presence of thapsigargin, the amplitude of the [Ca2+]<sup>i</sup> transient evoked by high frequency afferent nerve stimulation was greatly reduced relative to control. The role of intracellular Ca2<sup>+</sup> depots in shaping fast synchronous release and the contribution to AR was later studied in cerebellar and hippocampal synapses (Carter et al., 2002). In both preparations, caffeine-induced Ca2<sup>+</sup> release from intracellular stores could be efficiently blocked by ryanodine or thapsigargin application. However, neither ryanodine nor thapsigargin had any effect on paired pulse facilitation in cerebellar parallel fibers or in most hippocampal excitatory synapses (Schaffer collaterals, associated commissural input, and mossy fiber input to pyramidal cells). In addition, both drugs failed to block AR evoked by stimulation of parallel fibers. Thus, additional experiments are necessary to determine the impact of Ca2<sup>+</sup> release from presynaptic intracellular stores on AR generation.

A very interesting hypothesis was proposed by Few et al. (2012). They showed that prolonged or repetitive activation of N- and/or P-types of VGCC triggers sustained Ca2+-dependent activation of these channels resulting in long-lasting Ca2<sup>+</sup> influx. Indeed, this current might be sufficient to trigger vesicle fusion. However, since the peak amplitude of the Ca2+-induced current is about 10% of the peak amplitude of the depolarizationinduced Ca2<sup>+</sup> current, the amplitude of asynchronous events should be substantially smaller than that of synchronous fast responses. This is probably the case at synapses formed by cerebellar parallel fibers, but seems to be unlikely in the case of AR from hippocampal CCK-positive basket cells. In the latter connection, the integral of asynchronously released IPSC detected after the bust of Aps is in the same range as the cumulative phasic response evoked during the AP train (Hefft and Jonas, 2005), suggesting similarity in release probability and [Ca2+]<sup>i</sup> during the synchronous and asynchronous phases of release. Even when taking into account the difference in the cooperativity of synchronous and AR (approximately 2–4 fold) and high Ca2<sup>+</sup> affinity of Syt7, the Ca2+-induced tail current through N- and P- type Ca2<sup>+</sup> channels is unlikely to be sufficient to trigger AR at CCK-positive synapses. In addition to that, activation of CB1 receptors expressed on these terminals leads to suppression of VGCC reducing overall Ca2<sup>+</sup> entry; this mostly affects synchronous release and has a weaker effect on the asynchronous component (Ali and Todorova, 2010). A similar picture was observed in the zebrafish neuromuscular junction, where blockade of voltage-gated P/Q Ca2<sup>+</sup> channels during a burst of APs did not prevent either delayed [Ca2+]<sup>i</sup> increase or AR (Wen et al., 2013). Taken together, the findings made by Ali and Todorova (2010) and Wen et al. (2013) suggest that a burst of APs may trigger some additional processes except from Ca2<sup>+</sup> entry via VGCC which may induce [Ca2+]<sup>i</sup> increase and trigger AR.

#### HYPOTHETICAL ROLE OF CALCIUM EXTRUSION IN ASYNCHRONOUS RELEASE

Most of the mechanisms of [Ca2+]<sup>i</sup> elevation discussed above, which trigger AR, consider the participation of either ligandgated or voltage-gated slow Ca2<sup>+</sup> conductances (**Figure 2B**). However, taking into account the fact that Syt7-mediated release can be triggered by [Ca2+]<sup>i</sup> in the range of 1 µM, the role of residual Ca2<sup>+</sup> in AR generation has to be considered. Disruption of Ca2<sup>+</sup> extrusion from presynaptic terminals might lead to a prolongation of [Ca2+]<sup>i</sup> transients and consequently evoke delayed vesicle fusion. Two major plasma membrane transport proteins are involved in the maintenance of presynaptic Ca2<sup>+</sup> homeostasis, these are: plasma membrane calcium-ATPase (PMCA) and the sodium/calcium exchanger (NCX; **Figures 2A**, **3A,C**). It was suggested that the major role of PMCA is the maintenance of low cytosolic Ca2+, since its affinity to Ca2<sup>+</sup> is rather high and the rate of extrusion was thought to be slow. In contrast, NCX can rapidly counteract large cytosolic Ca2<sup>+</sup> elevations especially in excitable cells. However, recently the roles of the two Ca2<sup>+</sup> extrusion systems have been revised, since it has been shown that some PMCA isoforms may be involved in the regulation of basal Ca2<sup>+</sup> concentration (in the 100 nM range) and in the Ca2<sup>+</sup> elevations generated by cell stimulation (in the µM range). For instance, PMCA2, in particular, PMCA2a, exhibits exceptionally rapid activation in response to a rise in [Ca2+]<sup>i</sup>

(Caride et al., 2001). PMCA2a is ideally suitable for quick Ca2<sup>+</sup> handling even during prolonged high-frequency firing. Interestingly, in hippocampal perisomatic inhibitory synapses this isoform is selectively expressed in parvalbumin-containing terminals (Jensen et al., 2007; Burette et al., 2009), while in CCK-terminals characterized by massive AR PMCA2a has not been detected.

NCX is a plasma membrane transport protein that exchanges 3 Na<sup>+</sup> for 1 Ca2+; its functioning is strongly dependent on Na<sup>+</sup> and Ca2<sup>+</sup> gradients and plasma membrane potential. Thus, strong Na<sup>+</sup> accumulation in the cytosol (for example, after a train of APs) substantially slows down NCX-mediated Ca2<sup>+</sup> extrusion resulting in elevation of residual [Ca2+]<sup>i</sup> . Presynaptic Na<sup>+</sup> dynamics are not well studied, however, several lines of evidence suggest that the decay time constant of Na<sup>+</sup> extrusion is in the range of hundreds of milliseconds (Regehr, 1997; Fleidervish et al., 2010). Thus, during a high frequency burst of APs Na<sup>+</sup> concentration can rapidly build up in the terminal and then slowly decay to the basal level; in this period NCX will extrude Ca2<sup>+</sup> at a substantially slower rate (**Figures 3B,D**). Elevation of residual [Ca2+]<sup>i</sup> due to Na+-dependent decelerating of NCX-mediated Ca2<sup>+</sup> extrusion is even more pronounced at synapses with reduced PMCA function (Roome et al., 2013a). Moreover, extreme elevation of [Na+]<sup>i</sup> may reverse NCX and result in Ca2<sup>+</sup> influx into the cell via this exchanger (Roome et al., 2013b; Khananshvili, 2014). The latter suggests that NCX may act either as a Ca2+-clearing protein or Ca2<sup>+</sup> source, depending on the intensity of presynaptic activity (**Figure 3A**). In the case of CCK-positive hippocampal basket cells, which do not express the fast isoform of PMCA, slowing of the rate of NCX-mediated extrusion or switching to NCX reverse mode might provide a level of [Ca2+]<sup>i</sup> sufficient for AR generation. Selective suppression of AR at these GABAergic synapses and at some excitatory terminals by moderate concentration of EGTA strongly suggests that residual Ca2<sup>+</sup> and Ca2<sup>+</sup> extrusion machinery, determining the kinetics of [Ca2+]<sup>i</sup> are involved in delayed release generation (Hefft and Jonas, 2005; Iremonger and Bains, 2007).

#### ASYNCHRONOUS RELEASE TRIGGERED BY STRONTIUM OR LANTHANIDES

Substitution of extracellular Ca2<sup>+</sup> with Sr2<sup>+</sup> or application of lanthanides reduces phasic release and greatly promotes AR (Dodge et al., 1969; Heuser and Miledi, 1971; Goda and Stevens, 1994; Xu-Friedman and Regehr, 2000; Shin et al., 2003). Although, the underlying mechanisms are certainly different from AR evoked at physiological conditions by high frequency stimulation, some of the effects of Sr2<sup>+</sup> and La3<sup>+</sup> on the timing of synaptic release can be explained by a reduction in the functioning of extrusion pumps.

Strontium can enter the terminals and trigger synaptic vesicle fusion via interaction with Syt1, although in a way that does not involve activation of SNARE (Shin et al., 2003; Li et al., 2017). However, in contrast to Ca2+, clearance of ''residual Sr2+'' from presynaptic terminals is significantly

FIGURE 3 | Possible role of the presynaptic calcium extrusion pumps in AR generation. (A) Schematic drawing of presynaptic sequence of Na<sup>+</sup> and Ca2<sup>+</sup> fluxes triggered by a single AP: (i) Na<sup>+</sup> entry trough voltage-gated sodium channels (VGSCs); (ii) Ca2<sup>+</sup> entry trough VGCC; (iii) Fast Ca2<sup>+</sup> extrusion via sodium/calcium exchanger (NCX); and (iv) Final clearance of the presynaptic Ca2<sup>+</sup> by plasma membrane calcium-ATPase (PMCA). (B) Massive elevation of intra-terminal Na<sup>+</sup> concentration during the high frequency train of APs can strongly reduce the NCX extrusion rate (a), or at extreme elevation of [Na+]<sup>i</sup> , reverse the direction of Na<sup>+</sup> and Ca2<sup>+</sup> fluxes (b) through NCX prolonging the time course of the presynaptic calcium clearance, especially in terminals with reduced function of PMCA. (C) Schematic representation of intraterminal [Ca2+]<sup>i</sup> (blue) and [Na+]<sup>i</sup> (red) time courses after a single AP. (D) Schematic representation of the [Ca2+]<sup>i</sup> time course (blue) after burst APs leading to the massive elevation [Na+]<sup>i</sup> (red) when NCX is the only extrusion pump. Note, that direct simultaneous measurements of intraterminal [Na+]i and [Ca2+]<sup>i</sup> are not technically possible at the moment. However, modeling studies suggest that in the case of PMCA absence the temporal dynamics of [Ca2+]<sup>i</sup> and [Na+]<sup>i</sup> are be tightly coupled.

slower (Xu-Friedman and Regehr, 2000), which can explain the extended time course of Sr2+-driven release. The rapid effect of La3<sup>+</sup> does not require La3<sup>+</sup> entry into the terminal, or binding to Syt1 and is independent of extracellular Ca2<sup>+</sup> concentration. Nevertheless, the delayed component of an La3+-evoked increase of spontaneous release frequency can be blocked by intracellular loading of Ca2<sup>+</sup> buffers (Chung et al., 2008). The latter, probably, can be attributed to the known ability of La3<sup>+</sup> to block PMCA (Shimizu et al., 1997) which results in elevation of [Ca2+]<sup>i</sup> and promotes vesicle fusion. Thus, one can assume that the lack or reduced function of one of the extrusion proteins may result in slowed presynaptic [Ca2+]<sup>i</sup> dynamics leading to prolongation of vesicle release.

#### CONCLUDING REMARKS

Currently, there is an agreement that the Ca2<sup>+</sup> sensors involved in fast and AR are different and that they have different Ca2+-binding kinetics. Syt7 has been proposed to perform the function of high affinity Ca2<sup>+</sup> sensors for AR generation that is spatially and temporally located outside Ca2<sup>+</sup> domains. However, Syt7 was found on the presynaptic plasma membrane and other internal membranes, but not on synaptic vesicles suggesting a non-canonical mechanism of Syt7-mediated of vesicle exocytosis. Thus, recruitment of Syt7 into evoked delayed release needs to be more thoroughly studied. In addition to that, involvement of other synaptotagmins to AR generation, which have high Ca2<sup>+</sup> affinity and neuronal expression, has to be investigated. Importantly, experiments with EGTA loading clearly show that AR requires the presence of long-lasting elevation of free intraterminal Ca2+. In this respect, it might be promising to study the possible role of modulation of Ca2<sup>+</sup> extrusion proteins. The role of NCX should be investigated, since

#### REFERENCES


the NCX-mediated extrusion rate depends on [Na2+]i, which is determined by the rate of presynaptic AP activity. Thus, Na<sup>+</sup> dependent modulation of NCX functioning might provide an alternative mechanism not only for AR generation but also for short-term plasticity.

#### AUTHOR CONTRIBUTIONS

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

#### FUNDING

This work was funded by RSF (17-75-10061), and performed within the Program of Competitive Growth of Kazan University.

#### ACKNOWLEDGMENTS

We thank David Jappy for useful comments on the manuscript.


**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 © 2019 Rozov, Bolshakov and Valiullina-Rakhmatullina. 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(s) 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.

# P2Y1 Purinergic Receptor Modulate Axon Initial Segment Initial Development

Wei Zhang<sup>1</sup> , Angela Bonadiman<sup>1</sup> , María Ciorraga<sup>1</sup> , María José Benitez 1,2 and Juan José Garrido<sup>1</sup> \*

<sup>1</sup>Spanish National Research Council (CSIC), Department of Molecular, Cellular and Developmental Neurobiology, Instituto Cajal, Madrid, Spain, <sup>2</sup>Departamento de Química Física Aplicada, Universidad Autónoma de Madrid, Madrid, Spain

Morphological and functional polarization of neurons depends on the generation and maintenance of the axon initial segment (AIS). This axonal domain maintains axonal properties but is also the place where the action potential (AP) is generated. All these functions require the AIS, a complex structure that is not fully understood. An integrated structure of voltage-gated ion channels, specific cytoskeleton architecture, as well as, scaffold proteins contributes to these functions. Among them, ankyrinG plays a crucial role to maintain ion channels and membrane proteins. However, it is still elusive how the AIS performs its complex structural and functional regulation. Recent studies reveal that AIS is dynamically regulated in molecular composition, length and location in response to neuronal activity. Some mechanisms acting on AIS plasticity have been uncovered recently, including Ca<sup>2</sup><sup>+</sup>, calpain or calmodulin-mediated modulation, as well as post-translational modifications of cytoskeleton proteins and actin-associated proteins. Neurons are able to respond to different kind of physiological and pathological stimuli from development to maturity by adapting their AIS composition, position and length. This raises the question of which are the neuronal receptors that contribute to the modulation of AIS plasticity. Previous studies have shown that purinergic receptor P2X7 activation is detrimental to AIS maintenance. During initial axonal elongation, P2X7 is coordinated with P2Y1, another purinergic receptor that is essential for proper axon elongation. In this study, we focus on the role of P2Y1 receptor on AIS development and maintenance. Our results show that P2Y1 receptor activity and expression are necessary during AIS initial development, while has no role once AIS maturity is achieved. P2Y1 inhibition or suppression results in a decrease in ankyrinG, βIV-spectrin and voltage-gated sodium channels accumulation that can be rescued by actin stabilization or the modulation of actin-binding proteins at the AIS. Moreover, P2X7 or calpain inhibition also rescues ankyrinG decrease. Hence, a dynamic balance of P2Y1 and P2X7 receptors expression and function during AIS assembly and maturation may represent a fine regulatory mechanism in response to physiological or pathological extracellular purines concentration.

Keywords: axon initial segment, purinergic receptors, P2Y1, ankyrinG, axon, myosin

#### Edited by:

Haruyuki Kamiya, Graduate School of Medicine, Hokkaido University, Japan

#### Reviewed by:

Hiroshi Kuba, Nagoya University, Japan Matthew S. Grubb, King's College London, United Kingdom

> \*Correspondence: Juan José Garrido jjgarrido@cajal.csic.es

Received: 14 February 2019 Accepted: 08 April 2019 Published: 24 April 2019

#### Citation:

Zhang W, Bonadiman A, Ciorraga M, Benitez MJ and Garrido JJ (2019) P2Y1 Purinergic Receptor Modulate Axon Initial Segment Initial Development. Front. Cell. Neurosci. 13:152. doi: 10.3389/fncel.2019.00152

## INTRODUCTION

The axon initial segment (AIS) plays a crucial role in neuronal physiology, being responsible for the coordination of the whole set of inputs that a neuron receives. This unique axonal domain generates the action potential (AP; Stuart et al., 1997; Kole et al., 2008) and has a high degree of plasticity that allows the control of AP amplitude and frequency. In fact, the AIS may undergo lengthening or shortening, changes in its composition and can move away from soma to control AP response (Grubb and Burrone, 2010; Kuba et al., 2010, 2015; Del Puerto et al., 2015). Further, axonal identity and neuronal polarity depend on AIS integrity (Schafer et al., 2009). Different mental disorders (e.g., bipolar disorder, schizophrenia) and genetic diseases (e.g., Angelman syndrome) are related to AIS alterations (Kaphzan et al., 2011; van der Werf et al., 2017; Zhu et al., 2017), as well as neurodegeneration related diseases, such as stroke, brain injury or Alzheimer's disease (Schafer et al., 2009; Sun et al., 2014; Del Puerto et al., 2015). Despite the importance of AIS, our knowledge is far from a complete understanding of its whole composition, structure and plasticity. In this sense, it remains mostly unknown which receptors and extracellular factors participate on AIS development, maintenance and modulation.

The AIS comprises around the first 20–60 microns of the axon, depending on the type of neuron and developmental stage (for a review see Leterrier, 2018). It is composed by a high density of voltage-gated sodium, potassium and calcium ion channels, and also contains among others, GABA, dopamine and serotonin receptors, which contribute to modulate APs (Rasband, 2010). These voltage-gated ion channels are anchored through interactions with AIS enriched scaffold proteins, such as AnkyrinG or PSD-93 (Garrido et al., 2003; Pan et al., 2006; Ogawa et al., 2008). AnkyrinG is the most important structural protein in the AIS and AnkyrinG suppression drives to the loss of polarity and axonal identity. Scaffold proteins also serve to anchor other membrane proteins, such as L1, neurofascin or ADAM-22 (Jenkins and Bennett, 2001; Ogawa et al., 2010). Other extracellular proteins, such as Lgi1 (Seagar et al., 2017) or brevican (Hedstrom et al., 2007) also contribute to this dense protein structure. This functional and structural membrane and submembranous scaffold are anchored to a complex cytoskeleton by βIV-spectrin (Komada and Soriano, 2002), which interacts with the actin cytoskeleton (Rasband, 2010). Although recent studies have contributed to a better knowledge of this actin cytoskeleton, whose roles in AIS maintenance, development and function are not well understood. The AIS contains regular actin rings and actin patches (Watanabe et al., 2012; Leterrier et al., 2015). Some AIS actin-interacting proteins are α-actinin-2 (Sánchez-Ponce et al., 2012), synaptopodin (Bas Orth et al., 2007) or myosins (Evans et al., 2017; Janssen et al., 2017). Also, the AIS contains a synaptopodin and actin-associated structure, the cisternal organelle (Benedeczky et al., 1994), which function is still elusive despite, changes in cisternal organelle structure occurs during development and AIS plasticity (Schlüter et al., 2017). Finally, a differential microtubules cytoskeleton supports this whole structure and contributes to axonal trafficking. This microtubules cytoskeleton contains acetylated and detyrosinated tubulin that confers a higher degree of stability to this cytoskeleton (Konishi and Setou, 2009; Tapia et al., 2010).

While our knowledge of this complex interplay between important structural and functional proteins of the AIS increases, we still have little information about the external regulatory mechanisms modulating the AIS and its structural and composition plasticity.

Recent studies have highlighted the role of some receptors at the AIS and outside the AIS on the control of AIS composition, integrity and structural plasticity. The function and plasticity of AIS seem to depend on the excitatory or inhibitory profile of hippocampal neurons, as well as the input they receive and their developmental stage (Grubb et al., 2011). However, the extracellular factors, receptors, and mechanisms controlling these adaptive modifications are unknown. This raises the question of what factors contribute to a physiological development and maintenance of the AIS. Recent results show that neurotransmitter receptors participate in AIS regulation. Dopamine, through D3R receptors, modulates T-type Ca2<sup>+</sup> channels at the AIS contributing to neuronal output (Bender et al., 2010; Clarkson et al., 2017). Serotonin receptors (5-HT1A) also contribute to the control of AP threshold by modulating AIS cyclic-nucleotide-gated channels (HCN1) in the medial superior olive (Ko et al., 2016). In addition, 5-HT1A receptors modulate Nav1.2 voltage-gated sodium channels in the AIS of cortical neurons, decreasing the success rate of AP generation (Yin et al., 2017). Cannabinoid receptor 1 (CB1R) is necessary to achieve a proper ankyrinG clustering at the AIS in the early developmental stages of AIS (Tapia et al., 2017). Other neurotransmitters such as ATP, through the purinergic receptor P2X7, modulate AIS composition (Del Puerto et al., 2015). Purinergic receptors are a wide family of receptors expressed in neurons and glial cells and are important regulators of neuronal excitability. They can be divided into three subfamilies, adenosine, P2X and P2Y receptors, all activated by different neuronal and glial secreted purines (Del Puerto et al., 2013). They have an important role not only in physiological but also in pathological processes (Burnstock, 2017). Among them, the ionotropic P2X7 receptors are activated by high concentrations of extracellular ATP, while the metabotropic P2Y1 receptor is preferentially activated by ADP (Burnstock, 2007). P2X7 and P2Y1 purinergic receptors have an antagonistic role and are coordinated during initial axon elongation (del Puerto et al., 2012). While P2X7 has a detrimental effect on axonal elongation, P2Y1 promotes axonal elongation during the first stages of axonal growth. These antagonistic actions are regulated by P2X7-mediated calcium entry that inhibits adenylate cyclase 5 (AC5), and P2Y1-mediated Gq-PKCζ activation of AC5. This generates a balance that controls cAMP production and modulates PI3K-Akt-GSK3 pathway activity. Our previous work demonstrated that P2X7 activation is detrimental for ankyrinG and voltage-gated sodium channels accumulation in AIS of mature neurons (Del Puerto et al., 2015). However, P2Y1 role on AIS regulation has not been studied. The objective of our study was to investigate whether P2Y1 purinergic receptor participates on AIS development or modulation. Our results show that P2Y1 activity is necessary for initial AIS development and ankyrinG accumulation while having no significant role in mature neuron AIS. Decreased ankyrinG accumulation due to P2Y1 suppression can be prevented through P2X7 or calpain inhibition, revealing the crosstalk of P2Y1 and P2X7 during AIS development. Further, P2Y1 suppression alters F-actin distribution in AIS and decreases phosphorylation of myosin light chain (pMLC) and ankyrinG which can be prevented by F-actin stabilizing agent Jasplakinolide or protein phosphatase 1 and 2A inhibitor Calyculin A. Together with previous results on purinergic regulation (del Puerto et al., 2012; Del Puerto et al., 2015), our results suggest a necessary role for P2Y1 for the early development of the AIS. However, with neuronal maturation, the importance of P2Y1 decreases while P2X7 gains and increasing relevance in AIS maintenance and modulation.

## MATERIALS AND METHODS

## Reagents and Plasmids

Reagents were obtained from the following manufacturers: Adenosine 5'-diphosphate sodium ADP (A2754), P2X7 antagonist, BBG (B0770), AC5 inhibitor, NKY80 (N2165) and PP1/PP2A phosphatases inhibitor calyculin A (C5552) were obtained from Sigma-Aldrich. P2Y Antagonist II (BPTU; 504187) was obtained from EMD Millipore. 2-Methylthioadenosine diphosphate trisodium salt (2-MeSADP; 1624), (N)-methanocarba-2MeSADP (MRS 2365; 2157), the calpain inhibitor MDL 28170 and jasplakinolide were obtained from Tocris. P2Y1 shRNA and scrambled shRNA plasmids have been previously published and validated (del Puerto et al., 2012).

#### Animals

Animals were housed in a room at controlled temperature and relative humidity with alternating 12 h light and dark cycles and free access to food and water ''ad libitum.'' Animal care protocols used in our laboratory are in conformity with the appropriate national legislation (53/2013, BOE no. 1337) and guidelines of the Council of the European Communities (2010/63/UE). All protocols were previously approved by the CSIC bioethics committee.

## Neuronal Culture

Mouse hippocampal neurons were prepared as previously described (del Puerto et al., 2012; Del Puerto et al., 2015). Neurons were obtained from E17 mouse hippocampi, which were incubated in a 0.25% trypsin solution in Ca2+/Mg2<sup>+</sup> free Hank's buffered salt solution (HBSS) and dissociated using fire-polished Pasteur pipettes. The cells were plated on polylysine-coated coverslips (1 mg/ml) at a density of 5,000 cells/cm<sup>2</sup> for 2 h in plating medium [minimum essential medium (MEM), 10% horse serum, 0.6% glucose and Glutamax-I]. Then coverslips were inverted and transferred to culture dishes containing astrocytes. Astrocytes medium was replaced by neuronal culture medium 24 h before neuronal culture (Neurobasal medium, B27 supplement, Glutamax-I). To avoid contact between neurons and astrocytes, paraffin beads were placed on coverslips before neuronal plating. Five micromolar 1-β-D-arabinofuranosylcytosine (AraC) was added after 2 days in culture to avoid glial cells proliferation. One-third of neuronal medium was replaced every week. Pharmacological treatments were applied as described in the ''Results'' section. In the case of pharmacological treatments in the absence of glial cell layer, coverslips were transferred to plates containing glial cells-conditioned medium. Primary hippocampal neurons were nucleofected using the Amaxa nucleofector kit for primary mammalian neural cells (Amaxa Bioscience) according to the manufacturer's instructions. Nucleofection was performed using 3 µg of total DNA and 3 × 10<sup>6</sup> cells for each nucleofection. Neurons were plated at a density of 10,000 cells/cm<sup>2</sup> as described above. Nucleofection efficiency was ∼15% of neurons, based on the number of GFP-positive neurons. For lipofection, neurons were plated at a density of 20,000 cells/cm<sup>2</sup> and transfected at 7 or 10 DIV. Lipofection was performed using Lipofectamine 2000 (Life Technologies) and 3 µg of total DNA following manufacturer instructions.

#### Immunofluorescence

Neurons from each experiment, containing all experimental conditions to be compared, were fixed in 4% PFA. To standardize staining, all these coverslips were treated at the same time for immunofluorescence following the same conditions. Briefly, coverslips were treated for 10 min with 50 mM NH4Cl and incubated in blocking buffer (0.22% gelatine, 0.1% Triton X-100 in PBS) for 30 min, before incubation with primary antibodies for 1 h at room temperature in blocking buffer. The primary antibodies used were: chicken anti-MAP2 (1:10,000, Abcam, ab5392), mouse anti-ankyrinG (1:100) from NeuroMab (clone N106/36), mouse anti-pan sodium channel (1:100) from Sigma (clone K58/35), rabbit anti-pMLC (1:200) from Thermo Fisher (PA5-17727) and rabbit βIV-spectrin (1:1,000; a gift from Dr. M. Rasband, Baylor College of Medicine, Houston, TX, USA). The secondary antibodies used were a goat or donkey antimouse, anti-rabbit or anti-chicken Alexa-Fluor 488, 594, or 647 (1:1,000). Phalloidin Alexa-Fluor 594 was used at a concentration of 1:100. Images from each immunofluorescence were acquired on a Leica SP5 confocal microscope maintaining the same acquisition parameters to compare intensities. Figures were prepared for presentation using the Adobe CS4 software.

## Dendrites and AIS Measurements

Quantification of fluorescence intensity at the AIS was performed on confocal images of neurons from at least three independent experiments. Neurons were randomly acquired without any bias by scanning each coverslip from top to bottom. All confocal images within the same experiment and immunofluorescence were acquired using exactly the same parameters of laser intensity, excitation and emission detection during the same working session for each Alexa fluorophore. Parameters were set in control neurons and maintained for the other experimental groups. After completing images acquisition of all conditions, ankyrinG and other AIS proteins staining were quantified using ImageJ software. We drew a line starting at the limit of neuronal soma identified by MAP2 staining and extended it along the ankyrinG staining or the GFP signal of the axon. Data from every 0.16 µm along the first 40 µm were obtained and smoothed using the Sigmaplot software to obtain average ankyrinG fluorescence intensity every 1 µm. Data were normalized in each neuron, within the same immunofluorescence, considering the value of maximum mean fluorescence in control neurons to be 100%. Total fluorescence intensity for each neuron was obtained by adding ankyrinG fluorescence values from 0 to 40 µm. In some experiments, the total ankyrinG intensity was calculated within each AIS length and data normalized to AIS length of each neuron. AIS start, end and maximum fluorescence intensity were determined following the criteria described in Grubb and Burrone (2010). Taking 100% fluorescence as the maximum fluorescence intensity point, start and end points were defined as the points were fluorescence intensity is lower than 33%. For actin patches quantification, neurons were stained with Phalloidin-Alexa 594 (1:100) and ankyrinG to detect the AIS. Puncta of relatively uniform diameter of less than 3 µm within AIS were considered to be patches (Balasanyan et al., 2017). To avoid any possible loss of actin patches by lower F-actin intensity, image intensity was increased for the purpose of identification and quantification of all possible actin patches.

Dendrites lengths were obtained based on MAP2 staining using NeuronJ software to measure the length of the dendritic arbor in each neuron. All dendrites and ramifications in each neuron were traced using NeuronJ and their total length added. GFP signal of neurons under analysis allowed discriminating from crossing dendrites from other neurons. In order to study correlations between dendrites and AIS fluorescence, both data were obtained from the same neurons.

#### Statistical Analysis

All statistical analyses were carried out in Sigmaplot v12.5 (Systat Software Inc.) and Prism 5 (GraphPad Software, Inc., La Jolla, CA, USA). Data for each independent sample were obtained from at least three independent experiments. For pharmacological experiments, data from each experiment were collected from at least 30 cells (between 30 and 50 cells) in each experimental condition. For nucleofection or lipofection experiments around 25 neurons from each experiment in each experimental condition were analyzed. Statistical analysis was performed by t-test for two group comparisons and one-way ANOVA for multiple group comparisons. When data were non-normally distributed, non-parametric tests were used: Mann-Whitney Rank test for two independent samples and Kruskal-Wallis for analysis of multiple groups. In the analysis of multiple comparisons, a post hoc analysis was performed using Dunn's test. All p-values were adjusted to account for multiple comparisons. Cell-tocell analysis of dendrite length and ankyrinG fluorescence was performed using Prism 5 and Sigmaplot v12.5. First, we tested the normality of data distribution on each variable using a Shapiro-Wilk or Kolmogorov-Smirnov normality test. As not all data passed normality test, the correlation was analyzed using the Pearson correlation function or Spearman correlation function when data failed normality test. Differences were considered significant when p < 0.05.

#### RESULTS

## ADP Activation of P2Y1 Increases AnkyrinG Levels in the Developing Axon Initial Segments

A previous study demonstrated that the AIS of mature cultured hippocampal neurons (21 DIV) is regulated by ATP and P2X7 receptor (Del Puerto et al., 2015). Due to the coordinated action of ATP and ADP during initial axon elongation, we have investigated whether ADP and P2Y1 play a role in AIS regulation. Hippocampal neurons were treated with vehicle or ADP 10 µM during the 3 days prior fixation at 10, 14 or 21 DIV. AnkyrinG levels were then analyzed after immunofluorescence (**Figures 1A–D**). ADP treatment increased ankyrinG fluorescence intensity at the AIS in neurons treated from 7 to 10 DIV (146.74 ± 2.48%) compared to 10 DIV control neurons (100 ± 1.76%). However, ADP treatment in 14 DIV neurons had no significant effect in ankyrinG levels (113.74 ± 3.81%) vs. 14 DIV control neurons (100 ± 3.78%), as also happened for ADP treatment in 21 DIV neurons (110.38 ± 3.89% vs. AIS of 10 and 21 DIV neurons (**Figures 1B,C**). Next, we treated neurons with two more P2Y1 agonists, 2MeSADP (10 µM) and MRS-2365 (10 µM). Both agonists also increased significantly ankyrinG intensity at the AIS of 7–10 DIV treated neurons (**Figures 1E,F**), suggesting a P2Y1 mediated effect of ADP.

## P2Y1 Receptor Suppression or Inhibition Decreases AnkyrinG Accumulation at the AIS During Initial Developmental Stages

In order to ensure that ADP effect was due to P2Y1 receptor activation, we nucleofected neurons before plating using scrambled (shscr) or P2Y1 (shP2Y1) interference RNAs that also express GFP. Neurons were left in culture for 4, 7, 14 or 21 DIV, fixed and stained with MAP2 and ankyrinG antibodies (**Figures 2A–D**). P2Y1 interference RNA significantly decreased ankyrinG intensity between 4 and 14 DIV (**Figure 2E**), with the maximum reduction found at 7 DIV (77.07 ± 3.79%) compared to 100 ± 4.75% in sh scrambled 7 DIV control neurons. Fourteen DIV neurons recovered when compared to 7 DIV neurons (86.58 ± 2.36%), and no significant change was observed in 21 DIV neurons. To ascertain that ADP treatment has no effect on ankyrinG intensity after P2Y1 suppression, nucleofected 7 DIV neurons were treated with ADP 10 µM for 3 days. Neurons nucleofected with scramble shRNA increased ankyrinG intensity after ADP treatment, while those expressing shP2Y1 did not respond to ADP treatment (**Figure 2F**). Next, we checked whether the fluorescence intensity of ankyrinG interacting proteins, βIV-spectrin and voltage-gated sodium channels, was also reduced in 7 DIV neurons (**Figure 2G**). Both proteins significantly decreased their expression at the AIS after P2Y1 suppression (72.19 ± 5.67%, panNaCh and 70.69 ± 6.46%, βIV-spectrin) and the percentage was similar to ankyrinG (**Figure 2E**). To rule out the possibility that shP2Y1 efficiency was progressively lost during in vitro development, we introduced

with MAP2 (blue) and ankyrinG antibodies (green). Scale bar = 100 µm. Four times-magnification of the ankyrinG staining (green) at the AIS is shown below images. (E) Normalized ankyrinG intensity at the AIS of 10 DIV neurons treated with ADP and P2Y1 agonists 2-methylthioadenosine diphosphate trisodium salt (2MeSADP) or MRS-2365 from 7 to 10 DIV. Data were acquired from three independent experiments (30 neurons/experimental condition in each experiment). ∗∗∗p < 0.001, two-tail t-test. (F) 10 DIV hippocampal neurons stained with MAP2 (blue) and ankyrinG antibodies (green) treated with 2MeSADP (10 µM) or MRS-2365 (10 µM). Data in graphs are represented as the mean ± SEM.

control scrambled shRNA and P2Y1 shRNA by lipofection in 7 or 10 DIV neurons. Neurons were left 2–3 days and ankyrinG signal was analyzed (**Figure 2H**). Lipofected neurons expressing shP2Y1 did not show any reduction of ankyrinG levels at neither 10 or 12 DIV, confirming that in cultured hippocampal neurons P2Y1 exerts its action only during the initial steps of AIS development. This timing correlates with the stages prior to which the AIS diffusion barrier is developed at 10 DIV (Brachet et al., 2010).

In view of these results, we next checked whether P2Y1 pharmacological inhibition was enough to reduce ankyrinG levels. For this purpose, we used the non-nucleotide allosteric and none ADP-competitive P2Y1 antagonist, BPTU (1-(2-(2-(tert-butyl)phenoxy)pyridin-3-yl)

(blue) and ankyrinG (red) antibodies. Nucleofected neurons were identified by GFP expression (green). Inserts show magnifications of AISs (gray) of each neuron. (E) Normalized ankyrinG intensity at different days post-nucleofection with scrambled shRNA (shscr, black) or P2Y1 shRNA (shP2Y1, red). shP2Y1 data are normalized to their respective shscr controls at each developmental stage. <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001, two-tail t-test. (F) Normalized ankyrinG intensity in 10 DIV neurons expressing shscr or shP2Y1 plasmids, treated with vehicle or ADP from 7 to 10 DIV. <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001, two-tail t-test. Data were acquired from three independent experiments (30 neurons/experimental condition in each experiment). (G) βIV-spectrin and voltage-gated sodium channels (PanNaCh) normalized intensity in 7 DIV control shscr and shP2Y1 expressing neurons. <sup>∗</sup>p < 0.05, ∗∗∗p < 0.001, two-tail t-test. Data were acquired from three independent experiments (at least 25 neurons/experimental condition in each experiment). (H) Normalized ankyrinG intensity in 10 and 12 DIV hippocampal transfected at 7 or 10 DIV, respectively, to express shscr or shP2Y1 interference RNAs. Data were acquired from three independent experiments (at least 20 neurons/experimental condition in each experiment). n.s., not significant, two tail t-test. Data in graphs are represented as the mean ± SEM.


treated from 7 DIV with increasing concentrations of the P2Y1 antagonist, BPTU (0.5, 1, 2, 5, 7 and 10 nM). Concentrations higher than 10 nM affected the morphology of supporting glial cells and were discarded to avoid secondary effects on neurons. (B) AnkyrinG intensity profile along the AIS of hippocampal neurons treated from 7 to 10 DIV with vehicle black line), DMSO (BPTU vehicle, gray line), ADP (green line) and BPTU (red line). (C) 10 DIV neurons stained with MAP2 (blue) and ankyrinG antibodies (green) and treated with vehicle (control) or 5 nM BPTU from 7 to 10 DIV. Inserts show a magnification of the respective AIS. (D) Normalized ankyrinG intensity on 10 DIV hippocampal neurons treated from 7 DIV with 10 µM ADP and BPTU 5 nM, alone or in combination. (E) Normalized ankyrinG intensity on 10 DIV shscr or shP2Y1 nucleofected hippocampal neurons treated with BPTU from 7 DIV. Data were acquired from three independent experiments (at least 30 neurons/experimental condition in each experiment). ∗∗p < 0.01, ∗∗∗p < 0.001, n.s. not significant, two-tail t-test. Data in graphs are represented as the mean ± SEM.

other hand, it is the first time that BPTU is used in neurons. We can not discard that BPTU is partially affecting other purinergic receptors. However, BPTU impairs ADP-mediated increase of ankyrinG fluorescence. Therefore, our results suggest that P2Y1 activation is necessary to maintain ankyrinG levels at the AIS during the first stages of AIS development. This led to the question which are the mechanisms or developmental events that are under P2Y1 regulation that contribute to AIS proteins accumulation.

### AnkyrinG and Dendrites or AIS Length do Not Correlate in Neurons Lacking P2Y1 Receptor

P2Y1 receptor is not detected at the AIS but is located in dendrites, distal axon and presynaptic terminals in cultured hippocampal neurons (del Puerto et al., 2012). We recently demonstrated that ankyrinG decrease at AIS was correlated with impaired dendrite development mediated by CB1R inhibition (Tapia et al., 2017) and previous studies demonstrated that P2Y1 modulate neuronal morphology during the initial stages of development (del Puerto et al., 2012). Dendrites start their development in cultured hippocampal neurons at 4 DIV (Dotti et al., 1988). In order to test whether P2Y1 may control dendrite development and also influence AIS development, we measured the cell-to-cell dendritic length and ankyrinG fluorescence intensity in 7 DIV shscr and shP2Y1 nucleofected neurons (**Figures 4A,B**). As happened when CB1 expression was reduced (Tapia et al., 2017), dendrites of 7 DIV shP2Y1 neurons were shorter (320.2 ± 14.1 µm) than in control neurons (397.1 ± 20.37 µm, **Figures 4C,E**). Moreover, ankyrinG expression at the AIS was also reduced by 20% (**Figures 4D,E**). Even though a similar percentage reduction of dendrites length and ankyrinG was observed (**Figure 4E**), we analyzed both parameters in each individual neuron (**Figure 4F**). While we found a significant correlation between dendritic arbor length and ankyrinG expression in sh scrambled control neurons (Spearman r = 0.3037, p = 0.0055), there was no significant correlation in shP2Y1 neurons (Spearman r = −0.1522, p = 0.1955).

On the other hand, the AIS is known to respond to stimulus or absence of stimulus with plasticity mechanisms that include changes in composition, length and position (Grubb and Burrone, 2010; Kuba et al., 2010; Del Puerto et al., 2015). Therefore, we analyzed AIS length in 7 and 14 DIV shscr and shP2Y1 neurons (**Figure 5**). No significant AIS length differences were found in 7 DIV shP2Y1 neurons (26.06 ± 1.03 µm) compared to control 7 DIV sh scrambled neurons (23.52 ± 0.97 µm), neither in AIS position or

maximum ankyrinG intensity position (**Figures 5A,B**). No significant change in AIS length was also obtained in 14 DIV neurons, being AIS length around 33 µm in sh scrambled and shP2Y1 neurons (**Figure 5E**). However, in 14 DIV neurons, P2Y1 suppression generated a significant proximal shift of ankyrinG maximum intensity of 2–3 µm (7.37 ± 0.41 µm vs. 9.58 ± 0.53 µm in sh scrambled neurons, **Figure 5I**), which can be observed in the mean profile of ankyrinG expression along the AIS (**Figure 5J**). Despite no AIS length mean changes were observed between scrambled sh and shP2Y1 neurons, there is variability of AIS length within each experimental group. Thus, we analyzed ankyrinG intensity within the AIS length of each neuron (**Figures 5C,F**). Our results show a significant reduction of the mean ratio ankyrinG/AIS length in shP2Y1 neurons at 7 DIV (around 30%, **Figure 5D**) and 14 DIV (around 10%, **Figure 5G**). Furthermore, we analyzed whether AIS length and ankyrinG intensity are correlated in 14 DIV scrambled sh and shP2Y1 neurons (**Figure 5H**). Both parameters were significantly correlated in control scrambled sh neurons, while no significant correlation was found in shP2Y1 neurons, demonstrating that ankyrinG intensity reduction in shP2Y1 neurons is not related to changes in AIS length. This data suggest that besides neuronal morphology

regulation, P2Y1 receptor maintain other mechanisms to regulate AIS development.

## P2X7 Inhibition Recovers AnkyrinG Expression

Our previous results showed that P2Y1 suppression produced a shorter axon, which was recovered by P2X7 inhibition with BBG (del Puerto et al., 2012). P2Y1-Gq and P2X7-mediated calcium entry are coordinated through AC5 activation (P2Y1) or inhibition (P2X7). This generates a cAMP balance that modulates the PI3K/Akt/GSK3 pathway. In addition, P2X7 modulate ankyrinG expression at the AIS through a calcium-calpain-dependent mechanism (Del Puerto et al., 2015). In order to test whether the same coordinated pathway is also related to AIS modulation, we treated neurons from 7 to 10 DIV with the adenylate cyclase inhibitor NKY80 (10 µM) and analyzed ankyrinG (**Figure 6A**). NKY80 significantly reduced ankyrinG expression by around 10%, suggesting a coordinated action of P2Y1 and P2X7. Next, 6 DIV sh scrambled and shP2Y1 neurons were treated for 24 h with BBG (100 nM), a well-characterized P2X7 inhibitor (**Figures 6B,D**). P2X7 inhibition resulted in a non-significant trend to increase ankyrinG fluorescence in sh scrambled neurons

FIGURE 5 | No correlation between P2Y1 suppression-mediated decrease of ankyrinG density and AIS length. (A) Graph represents AIS length of each 7 DIV neuron nucleofected with scrambled sh (black dots) or shP2Y1 (red dots). Lines represent the mean ± SEM. (B) Graph represents the mean ± SEM of AIS start point, maximum intensity point and end point of AIS in 7 DIV scrambled shRNA or P2Y1 shRNA nucleofected neurons. (C) Normalized ankyrinG intensity within the respective AIS length of neurons represented in (A). (D) Normalized AnkyrinG/AIS length ratio for each 7 DIV scrambled shRNA or P2Y1 shRNA nucleofected neuron. (E) Graph represents AIS length of each 14 DIV neuron nucleofected with scrambled sh (black dots) or shP2Y1 (red dots). Lines represent the mean ± SEM. (F) Normalized ankyrinG intensity within the respective AIS length of neurons represented in (E). Adjacent graph represents the mean ± SEM. (G) Normalized AnkyrinG/AIS length ratio for each 14 DIV scrambled shRNA or P2Y1 shRNA nucleofected neuron. Adjacent graph represents the mean ± SEM. (H) Correlation graph of AIS length and ankyrinG intensity for each individual 14 DIV neuron nucleofected with scrambled (black dots) or P2Y1 (red dots) shRNAs. Values are the same represented in (E,F). Data were analyzed first with two normality tests (Shapiro-Wilk and Kolmogorov-Smirnov). All data sets did fit a normal distribution and a Pearson correlation test was used. Regression lines are shown for shscr (black) and shP2Y1 (red) neurons. The number of neurons, Pearson r coefficient and p values are indicated in (H). A positive correlation is observed in control neurons, while there is no significant correlation in neurons expressing shP2Y1 interference RNA. (I) Graph represents the mean ± SEM of AIS start point, maximum intensity point and end point of AIS in 14 DIV scrambled shRNA or P2Y1 shRNA nucleofected neurons. Note a significant proximal shift of the maximum intensity point. (J) AnkyrinG profile along AIS length of 14 DIV neurons, indicating the proximal shift of the maximum ankyrinG intensity. Data are represented as the mean ± SEM of ankyrinG intensity every 1 micron. <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001, n.s., non-significant.

treated with the P2X7 antagonist, BBG (100 nM) from 6 to 7 DIV. Mean ± SEM for each condition is shown in the adjacent graph. Statistical differences were analyzed by a Kruskal-Wallis test followed by a Dunn's multiple comparisons post-test. <sup>∗</sup>p < 0.05, ∗∗∗p < 0.001, n.s., non-significant. (C) Mean ± SEM of normalized ankyrinG intensity in 7 DIV nucleofected with scrambled shRNA or P2Y1 shRNA and treated with the calpain inhibitor, MDL-28170 (50 nM) from 6 to 7 DIV. Statistical differences were analyzed by a Kruskal-Wallis test followed by a Dunn's multiple comparisons post-test. <sup>∗</sup>p < 0.05, ∗∗∗p < 0.001, n.s., non-significant. (D) Representative images of scrambled shRNA or P2Y1 shRNA treated with the P2X7 antagonist, BBG (100 nM). Neurons were stained with MAP2 (blue) and ankyrinG (red) antibodies. Nucleofected neurons were identified by GFP signal (green). Axon initials segments were magnified and presented in panels below.

(105.0 ± 4.59%), while P2Y1 suppression (shP2Y1 neurons) reduced ankyrinG fluoresecence around 25% (74.13 ± 3.98%). Interestingly, 24 h inhibition of P2X7 recovered ankyrinG intensity to control levels (92.7 ± 4.71%, **Figures 6B,D**). Further, 24 h treatment with the calpain inhibitor MDL-28170 (50 nM) recovered ankyrinG fluorescence (95.1 ± 4.49%) in shP2Y1 neurons (**Figure 6C**). This data suggests a coordinated and antagonistic action of P2Y1 and P2X7 receptors during initial stages of AIS development, which may depend on the amount of ATP and ADP in extracellular medium and their expression levels during AIS development. However, P2X7 inhibition did not completely recover ankyrinG intensity as previously observed in mature neurons (Del Puerto et al., 2015), suggesting that P2X7 participation is limited in young neurons. Thus, other AIS intrinsic mechanisms may be regulated by P2Y1 in AIS initial developmental stages.

#### P2Y1 Suppression Modifies AIS Actin Cytoskeleton and Myosin II Light Chain Phosphorylation

Recently, actin dynamics at the AIS were related to AIS plasticity (Berger et al., 2018). Activity-dependent AIS plasticity can produce a dramatic reorganization of the actin periodic structure (Berger et al., 2018) and P2Y1 signaling pathways can activate the RhoGTPase Rac, which modulates actin dynamics in migration and differentiation processes (Soulet et al., 2005). To understand whether our results can be attributable to actin cytoskeleton modifications mediated by

P2Y1 receptor, we stained neurons 7 DIV scrambled sh and shP2Y1 neurons with fluorescence phalloidin (**Figures 7A,B**) and quantified F-actin intensity along the AIS, as well as the number of actin patches (**Figures 7C,D**). Total F-actin intensity was reduced by around 30% in shP2Y1 neurons (**Figure 7D**), and so was ankyrinG intensity (**Figure 7F**). Besides, the F-actin intensity decrease in the AIS was confirmed by the profile (**Figure 7E**). While actin patches were visible in control AISs, these were highly reduced in intensity and visibility in shP2Y1 neurons (**Figures 7A,B**). Actin patches quantification, independently of their intensity, showed that scrambled sh neurons contained 4.8 ± 0.48 actin patches, while shP2Y1 neurons only 3.2 ± 0.41 patches (**Figure 7C**). If loss of P2Y1-dependent stabilization of the actin cytoskeleton results in the decrease in ankyrinG, then it may be recovered by actin stabilization. Thus, we treated scrambled and shP2Y1 neurons with an F-actin stabilizing agent, Jasplakinolide (10 nM) for 4 h (**Figure 7F**). AnkyrinG expression in shP2Y1 neurons was

test followed by a Dunn's multiple comparisons post-test. <sup>∗</sup>p < 0.05, ∗∗∗p < 0.001, n.s., non-significant.

significantly recovered by Jasplakinolide treatment (90.6 ± 4.7%) when compared to shP2Y1 neurons with no treatment (65.27 ± 2.59%, p = 0.0002). After recovery, the level was equivalent to sh scrambled control neurons (100 ± 4.36%). In control sh scrambled neurons, Jasplakinolide generated a decrease in ankyrinG expression (around 14%), which may be due to a deregulation of actin dynamics and higher actin stabilization.

How can actin cytoskeleton instability resulting from lack of P2Y1 activity modify ankyrinG in the AIS? Recently published work has highlighted the role of myosin II and myosin light chain phosphorylation (pMLC) on AIS (Evans et al., 2017; Berger et al., 2018). In platelets, ADP and P2Y1 activity contribute to shape changes by increasing pMLC levels in a calcium-calmodulin dependent manner (Paul et al., 1999). Therefore, we analyzed pMLC levels and localization in 7 DIV shP2Y1 neurons (**Figure 8A**). As previously demonstrated (Berger et al., 2018), pMLC was localized at the AIS in

7 DIV control neurons. However, pMLC staining in the AIS was 20% lower in shP2Y1 neurons (**Figure 8B**). Next, we analyzed whether treating neurons with CalyculinA to inhibit PP1/PP2A, the phosphatases acting on pMLC, could recover pMLC levels and, consequently, ankyrinG. Calyculin A (1 nM) treatment for 3 h increased pMLC intensity at the AIS of control neurons by 40%, while in non-treated shP2Y1 neurons it was reduced by 31% (**Figure 8C**). Calyculin A treatment in shP2Y1 neurons increased pMLC intensity by 25% when compared to control neurons without Calyculin A treatment. AnkyrinG intensity analysis in the same experimental conditions revealed a recovery of ankyrinG in shP2Y1 neurons treated with Calyculin A (87.82 ± 4.01%) compared to shP2Y1 neurons (72.04 ± 3.08%), which did not completely reach reference control levels (100 ± 4.16%, **Figure 8D**). Interestingly, 3 h treatment of calyculin A in control neurons reduced ankyrinG intensity (78.5 ± 3.89%). This may suggest

Dunn's multiple comparisons post-test. <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

that increased pMLC levels are also detrimental to ankyrinG clustering at the AIS, as happened with F-actin stabilization with jasplakinolide (**Figure 7F**).

Altogether, our results underscore the role of P2Y1 as one of the receptors that contribute to AIS plasticity during early events of AIS maturation. Further investigations are required to completely understand the signaling pathway and interactions with other receptors and neurotransmitters.

#### DISCUSSION

Relevant studies have recently underscored the importance of AIS in neurodevelopmental disorders and neurodegenerative diseases (Kaphzan et al., 2011; Sun et al., 2014; van der Werf et al., 2017). Changes in AIS protein composition have been detected in models of disease, such as Angelman syndrome or Alzheimer's disease (Kaphzan et al., 2011; Sun et al., 2014). However, our understanding of AIS composition, development and regulation is still limited. Which are the extrinsic and intrinsic mechanisms that modulate the AIS? The AIS has been proven to respond to external stimuli with a high degree of structural plasticity. However, our knowledge of the receptors, neurotransmitters and extracellular factors that modulate AIS remains limited. Understanding how the AIS can be deregulated may contribute to control and recover physiological neuronal function.

Prior studies demonstrated that the purinergic receptor P2X7 modulates AIS composition under pathological conditions (Del Puerto et al., 2015). Due to its relation with the P2Y1 receptor, the objective of our study was to decipher whether the purinergic receptor P2Y1 plays a role in AIS development and maintenance. Our results show that ADP-P2Y1 receptor contributes to the initial accumulation of ankyrinG at the AIS. P2Y1 suppression or inhibition decreases ankyrinG levels, as well as, voltage-gated sodium channels, βIV-spectrin and pMLC. P2Y1 is necessary for a proper elongation of the axon in early stages and is expressed in dendrites and axon terminals in cultured hippocampal neurons (del Puerto et al., 2012). P2Y1 expression is not detected in AIS, as previously mentioned for P2X7 (Del Puerto et al., 2015). Previous studies demonstrated a correlation between dendrites length or caliber and AIS properties (Hamada et al., 2016; Tapia et al., 2017). Our results show that, in control neurons, dendrites length and ankyrinG density is correlated, albeit there is no statistical correlation between both parameters after P2Y1 suppression. This suggests that P2Y1-mediated ankyrinG density regulation entails additional mechanisms triggered by P2Y1 alone or in coordination with other receptors. In fact, ankyrinG levels can be recovered through ATP-P2X7 receptor inhibition in neurons lacking P2Y1 receptor. A previous study demonstrated that high extracellular concentrations of ATP decrease ankyrinG density through P2X7 and calpain activation in mature cultured hippocampal neurons (Del Puerto et al., 2015). Here, we show that extracellular ADP or P2Y1 inhibition do not modify ankyrinG density in these mature neurons. However, through P2Y1 receptor, ADP is necessary to maintain ankyrinG density in young cultured hippocampal neurons. The P2Y1 regulation coincides with the initial stages of AIS development, between 4 and 10 DIV, when the diffusion barrier is being generated (Brachet et al., 2010) and is lost once the AIS achieve a certain degree of maturity and stability, around 10–14 DIV. In fact, P2Y1 suppression or ADP treatment after 7 DIV has no effect on ankyrinG density, while P2Y1 inactivation at 7 DIV or before decreases ankyrinG density. As happened during early axonal elongation (del Puerto et al., 2012), BBG-mediated P2X7 inhibition reverts the effects of P2Y1 suppression on ankyrinG density. However, P2X7 inhibition mediated recovery was not as high as previously observed in mature neurons (Del Puerto et al., 2015), suggesting that P2Y1 receptors decrease their expression or function during AIS development, while the importance of P2X7 increases. This recovery can be the result of decreased P2X7-mediated calcium entry and reduced calpain activation, but other mechanisms may also participate in this regulation. P2Y1 and P2X7 receptors are important regulators of neuronal excitability. P2Y1 receptors are expressed postsynaptically on dendrites of pyramidal cells and presynaptic terminals and participate in the regulation of neuronal plasticity (Bara´nska et al., 2017). Interestingly, P2X7 and P2Y1 are balanced over the regulation of cAMP and PKA activity, where P2Y1 contributes to increased cAMP levels (del Puerto et al., 2012). It was postulated that a PKA and phosphatases PP1 and calcineurin loop may regulate sodium channels phosphorylation modulating spike firing that correlates with AIS length in dentate granule cells (DGCs). In this study (Evans et al., 2015), PKA activation did not modify AIS length but did reverse the depolarizationinduced changes in sodium channels properties, increasing their phosphorylation and decreasing conductance. Our results show P2Y1 inhibition or suppression does not alter AIS length, but rather proximally shifts the maximum ankyrinG intensity while decreasing ankyrinG density. It remains to be determined whether this shift is due to PKA activity levels or modifications of sodium channels conductance. Nevertheless, our results show that PP1/PP2A inhibition with calyculin A is able to counteract the lack of P2Y1 expression, which may balance PKA-phosphatases loop. On the other hand, P2Y1 may participate in AIS modulation through regulation of its actin cytoskeleton. In support, P2Y1 regulates Rac and actin cytoskeleton in other cell types (Soulet et al., 2005). We show that F-actin distribution and intensity in AIS is modified after P2Y1 suppression, and actin cytoskeleton stabilization with jasplakinolide recovers ankyrinG density. In fact, short-time treatment with potassium chloride decreases ankyrinG density at the AIS while at the same time actin is destabilized (Berger et al., 2018). This may be caused by decreased phosphorylation of myosin II light chain ( pMLC) at the AIS (Berger et al., 2018). Our results demonstrate that P2Y1 suppression decreases pMLC levels at the AIS at the same time that ankyrinG density is reduced in a similar percentage. The lack of P2Y1 receptor is compensated by inhibition of MLC phosphatase using calyculin A. Interestingly, P2Y1 agonist, 2MeSADP, increases pMLC phosphorylation in platelets generating a shape change (Getz et al., 2010), through a Gq dependent mechanism. All these data suggest that P2Y1 receptor participate in the global regulation of AIS cytoskeleton dynamics during its initial development.

#### CONCLUSION

In conclusion, our work demonstrates that P2Y1 receptor participates only during initial AIS development. This may represent decreased expression or function during neuronal maturation, while other receptors, such as P2X7, increase their participation and function in more mature neurons. P2Y1 expression levels or functional activation/deactivation in coordination with other receptors and mechanisms may participate in the fine modulation of AIS development. Future work will be necessary to completely understand the molecular mechanisms underlying P2Y1 receptor; both at the level of plasticity and the modulation of AIS cytoskeleton.

#### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript.

#### ETHICS STATEMENT

Animals were housed in a room at controlled temperature and relative humidity with alternating 12 h light and dark cycles and free access to food and water ''ad libitum.'' Animal care protocols used in our laboratory are in conformity with the appropriate national legislation (53/2013, BOE no. 1337) and guidelines of the Council of the European Communities (2010/63/UE). All protocols were previously approved by the CSIC bioethics committee.

#### AUTHOR CONTRIBUTIONS

JG, WZ and AB conceived and designed the experiments. JG, WZ, AB, MC and MB performed

#### REFERENCES


the experiments and data acquisition. JG and WZ analyzed and interpreted the data. JG wrote the manuscript. AB, MB and MC contributed to acquiring and analyzing data. All authors read and approved the final manuscript.

#### FUNDING

This work was supported by a research grant from Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO) to JG (SAF2015-65315-R). We thank the China Scholarship Council for their support to WZ (fellowship number (No. 201506300085) and the support of the Erasmus+ Program and University of Trento for AB.

#### ACKNOWLEDGMENTS

We thank Dr Chaska Walton for critical reading of the manuscript, Cajal institute imaging service for their help in confocal images acquisition.

axon initial segment composition and function in physiological conditions and brain injury. Cereb. Cortex 25, 2282–2294. doi: 10.1093/cercor/ bhu035


**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 © 2019 Zhang, Bonadiman, Ciorraga, Benitez and Garrido. 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(s) 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.

# Technologies to Study Action Potential Propagation With a Focus on HD-MEAs

Vishalini Emmenegger<sup>1</sup> \*, Marie Engelene J. Obien1,2, Felix Franke<sup>1</sup> and Andreas Hierlemann<sup>1</sup>

<sup>1</sup> Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland, <sup>2</sup> MaxWell Biosystems AG, Basel, Switzerland

Axons convey information in neuronal circuits via reliable conduction of action potentials (APs) from the axon initial segment (AIS) to the presynaptic terminals. Recent experimental findings increasingly evidence that the axonal function is not limited to the simple transmission of APs. Advances in subcellular-resolution recording techniques have shown that axons display activity-dependent modulation in spike shape and conduction velocity, which influence synaptic strength and latency. We briefly review here, how recent methodological developments facilitate the understanding of the axon physiology. We included the three most common methods, i.e., genetically encoded voltage imaging (GEVI), subcellular patch-clamp and high-density microelectrode arrays (HD-MEAs). We then describe the potential of using HD-MEAs in studying axonal physiology in more detail. Due to their robustness, amenability to highthroughput and high spatiotemporal resolution, HD-MEAs can provide a direct functional electrical readout of single cells and cellular ensembles at subcellular resolution. HD-MEAs can, therefore, be employed in investigating axonal pathologies, the effects of large-scale genomic interventions (e.g., with RNAi or CRISPR) or in compound screenings. A combination of extracellular microelectrode arrays (MEAs), intracellular microelectrodes and optical imaging may potentially reveal yet unexplored repertoires of axonal functions.

Keywords: axon, action potential propagation, patch-clamp technique, genetically encoded voltage indicators, high-density microelectrode arrays

## INTRODUCTION

Intricate operations, performed by neuronal networks, emerge from the orchestrated interplay of individual neurons. Neurons use action potentials (APs) as a means to encode and relay information from the soma to the presynaptic terminal via reliable conduction through the axon. The three functional compartments of the axon include the axon initial segment (AIS), the axon proper, and the presynaptic terminal. Somato-dendritic integration of a number of synaptic inputs at the AIS are thought to shape the AP firing patterns. The axon proper is often conceived as a simple cable, whose function is the faithful transmission of the AP to distant presynaptic terminals in a digital (all or none) fashion. However, with the development of modern techniques that can directly access small axonal structures, an increasing body of work has emerged that challenges the traditional view on the role of the axon being purely limited to the transmission of the AP

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Zbili Mickael, Institut National de la Santé et de la Recherche Médicale (INSERM), France Michael Blake Hoppa, Dartmouth College, United States

\*Correspondence: Vishalini Emmenegger vishalini.emmenegger@bsse.ethz.ch

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

> Received: 28 February 2019 Accepted: 08 April 2019 Published: 26 April 2019

#### Citation:

Emmenegger V, Obien MEJ, Franke F and Hierlemann A (2019) Technologies to Study Action Potential Propagation With a Focus on HD-MEAs. Front. Cell. Neurosci. 13:159. doi: 10.3389/fncel.2019.00159

(Debanne et al., 2011; Sasaki et al., 2011; Sasaki, 2013; Bucher, 2016). It has been shown that the shape of the presynaptic AP can be modulated by subthreshold potentials, which, in turn, modulate the spike-evoked transmission through so-called "analog-digital facilitation" (Debanne, 2004; Alle and Geiger, 2008; Kress and Mennerick, 2009; Bucher and Goaillard, 2011; Debanne et al., 2011; Sasaki, 2013; Bucher, 2016). As AP propagation and synaptic transmission might undergo substantial modulation, the computational repertoires of single axons in the neuronal circuit may be more complex than commonly assumed.

Axonal membrane excitability and conduction velocity can change substantially with repeated activation. This can potentially alter the temporal patterns of spikes during propagation from the AIS to presynaptic sites. Such changes in temporal spike patterns may be an important feature of neural coding strategies (Izhikevich, 2006; Bucher and Goaillard, 2011; Bucher, 2016). Axonal conduction velocity in unmyelinated axons depends on several biophysical factors, such as ionchannel densities and kinetics, membrane capacitance, axial resistance, axon geometry, and, for myelinated axons, myelin thickness and internodal distances (Hodgkin, 1954; Manor et al., 1991; Shepherd and Harris, 1998; Ganguly et al., 2000; Fields, 2005; Cai et al., 2011). Axonal conduction velocity per se provides little information about the functional aspects of neuronal communication. On the other hand, axonal conduction delay, which depends on both, conduction velocity and axonal length, may have important functional implications in the integration of sensory information (Konishi, 2003). A plethora of diverse neurological disorders is associated with impaired axonal functionality (Suter and Scherer, 2003; Waxman, 2006; Krarup and Moldovan, 2009; Kullmann, 2010; Egawa et al., 2017; Khalilpour et al., 2017). Axonal dysfunction can be caused by missing or reduced myelination (e.g., multiple sclerosis) (Steinman, 1996; Trapp et al., 1999). Acute axonal damage (e.g., traumatic injury) (Smith and Meaney, 2000; Johnson V.E. et al., 2013), toxic entities, aggregated proteins, microgliosis and disrupted axonal transport (e.g., prion disease, Parkinson's disease, Alzheimer's disease) (Liberski and Budka, 1999; Millecamps and Julien, 2013) may directly affect axonal physiology. Lastly, abnormalities in the composition or function of ion channels (in channelopathies, e.g., in certain forms of migraine and epilepsy) are known to alter the conduction properties of axons (Goadsby et al., 2017; Oyrer et al., 2018; Pietrobon, 2018).

Recent advances in the understanding of axon physiology and pathophysiology have been driven by technological developments, such as optical imaging of the membrane potentials using genetically encoded voltage indicators (GEVI), subcellular patch-clamp recordings from thin axons and boutons, and high-density microelectrode array recordings (HD-MEA) (**Figure 1**; Shu et al., 2006; Kole et al., 2007; Sasaki et al., 2011; Bakkum et al., 2013; Novak et al., 2013; Hoppa et al., 2014; Kawaguchi and Sakaba, 2015; Müller et al., 2015; Rama et al., 2015a; Radivojevic et al., 2017). These techniques stand apart from other classical electrophysiological methods in their ability to monitor and interactively control subcellular components of single neurons at high spatial and microsecond temporal resolution. The above-mentioned techniques and devices were reviewed in-depth elsewhere (Hierlemann et al., 2011; Sasaki, 2013; Spira and Hai, 2013; Obien et al., 2015; Inagaki and Nagai, 2016; Ohura and Kamiya, 2016; Yang and St-Pierre, 2016; Xu et al., 2017; Zeck et al., 2017; Platisa and Pieribone, 2018; Rama et al., 2018; Wang et al., 2019). Here, we will briefly introduce these technologies with the focus on studying axonal signals, while we describe - in a bit more detail - recent investigations in axonal neurobiology by using HD-MEAs.

## TECHNOLOGICAL APPROACHES

In the following, we provide a brief overview of the three most commonly used recording modalities for measuring axonal signals. We describe the parameters that govern to the detection of neuronal signals and outline recent advances, including potential advantages and limitations. **Table 1** lists the key specifications of each methodology. Since several publications are available on each technology, we pooled the data from the most advanced and most recent publications. Given the plethora of applications for each methodology, we will restrict our comparison to the detection and measurements of AP propagation. A schematic overview on the different methodologies along with representative signals is displayed in **Figure 1**.

## Voltage Imaging

In order to monitor neural activity at single-cell resolution, optical methods, such as voltage-sensitive dyes and GEVI, make use of fluorescence signals to detect alterations in voltage (Peterka et al., 2011; Storace et al., 2016). Voltage-sensitive dyes have provided important insights into neuronal electrical signaling ranging from individual neurons to population dynamics (Grinvald et al., 1981; Gross and Loew, 1989; Petersen et al., 2003; Miller et al., 2012; Popovic et al., 2015). Yet, major limitations of voltage-sensitive dyes include cell toxicity, phototoxicity, indiscriminate neuronal and glial staining, and small signal-to-noise ratio (SNR) (Knöpfel et al., 2006; Mennerick et al., 2010).

In the last two decades, considerable efforts have been made to overcome these limitations, which have led to the development of GEVIs. The three main molecular designs of GEVIs – inserted into the plasma membrane – are (1) the fusion of fluorescent proteins (FP) to voltage-sensing domains, (2) the use of opsins, and (3) hybrid opsin-FP pairs (rhodopsin-FRET sensor) (Boyden et al., 2005; Kralj et al., 2011; Akemann et al., 2012; Jin et al., 2012; Tsutsui et al., 2013; Hochbaum et al., 2014; St-Pierre et al., 2014; Gong et al., 2015). Voltage sensitivity (dynamic range, %) is an important parameter of fluorescence indicators, expressed as 1F/F per 100 mV (−70 to 30 mV), which represents linear changes in fluorescence in response to voltage fluctuations. To detect neuronal activity with high SNR, a combination of key features of voltage indicators, such as bright fluorescence, fast kinetics (rapid response to changes in voltage), large dynamic range,

photostability, and efficient plasma membrane localization is desired (Lee et al., 2017; Xu et al., 2017; Piatkevich et al., 2018; Wang et al., 2019).

While there is constant development of new constructs, a recent work by Bando et al. (2019) provided a temporal snapshot of state-of-the-art GEVIs and compared their performances. The authors report that QuasAr2, a rhodopsin-based GEVI, outperforms other GEVIs concerning the optical detection of single APs of neurons in vitro, featuring high signal amplitude, fast kinetics and high SNR. In addition, Ace-2N-4AA-mNeon, a rhodopsin-FRET sensor, was shown to resolve individual spikes in single trials without averaging, while suffering from fast photobleaching.

A combination of a red-light-excited QuasAr2 with a spectrally compatible blue-light-activated channelrhodopsin (CheRiff) was co-expressed in neurons via a vector called "Optopatch," which was targeted at enabling simultaneous all-optical electrophysiology in neuronal cultures or organotypic brain slice cultures (Hochbaum et al., 2014; Kiskinis et al., 2018). The use of this construct enabled mapping of the dynamics of AP initiation and propagation across dendritic and axonal structures at high spatiotemporal resolution (**Figure 1**). However, significant multi-trial averaging (200–17,000 trials) was required for attaining good enough signal-to-noise characteristics (Hochbaum et al., 2014).

#### Subcellular Patch-Clamp Recordings

Patch-clamping is the gold standard technique for studying electrical properties of neurons at unprecedented resolution. The patch-clamp technique uses a glass micropipette that presses against the cell membrane to form a tight gigaohm seal resistance between the cell membrane and the rim of the glass micropipette. In the original cell-attached configuration, activity of single ion channels in the tiny patch of membrane surrounded by the tip of the pipette can be studied. If the patch of membrane under the pipette tip is ruptured by applying pressure, the electrode accesses the inside of the cell in the so-called wholecell configuration, where the trans-membrane voltage and currents can be directly recorded (Neher and Sakmann, 1976; Ogden and Stanfield, 1994).

Most patch-clamp studies have been conducted on the soma, which is the largest compartment of a neuron (8–30 µm in diameter). One of the limitations of the conventional patchclamp technique is that the studies on axons encountered technical difficulties due to the thin axonal structure (∼200 nm

TABLE 1 | Comparison of the three techniques in studies that showed AP propagation.


For subcellular patch-clamp, the device specifications of the Multiclamp 700 b have been taken. Feedback resistors: <sup>a</sup> 50 M, <sup>b</sup> 500 M. <sup>c</sup>With a gain of 1024; up to 1 V with reduced gain.

in diameter). Accordingly, axonal recordings have been mostly restricted to giant axon terminals, such as hippocampal mossy fiber boutons (Geiger and Jonas, 2000; Bischofberger et al., 2006; Boudkkazi et al., 2011) and the Calyx of Held (Forsythe, 1994; Borst et al., 1995; Awatramani et al., 2005). Recordings from thin axons have been obtained from axonal blebs (3–6 µm), which are resealed swellings at the cut ends of axons after brain slicing procedures (Shu et al., 2006, 2007; Kole et al., 2007; Kim, 2014; Rama et al., 2015a). Recently, recordings from intact thin axons have been made possible using a fluorescenceguided patch-clamp technique (Ishikawa et al., 2010; Sasaki et al., 2011, 2012; Hu and Jonas, 2014; Kawaguchi and Sakaba, 2015). Cell-attached extracellular recordings of APs in intact unmyelinated axons (∼1 µm in diameter) have been made using pipettes coated with fluorescently conjugated albumin. However, stable recording was possible for only less than 60 min with ∼50% success rate. Simultaneous whole-cell recordings have been performed from the soma and axon shaft of hippocampal basket cells in acute slices (Hu and Jonas, 2014) as well as in the presynaptic terminals in cerebellar Purkinje cells in cultures (Kawaguchi and Sakaba, 2015) to examine the fidelity of AP propagation.

In recent years, several studies were conducted using paired recordings from two distinct sites along a single axon or from a presynaptic axon terminal and a postsynaptic neuron. These experiments have made considerable contributions to understanding the mechanism of analog-digital facilitation, compartmentalized distribution of ion channels and gating properties, as well as the modulation of short- and long-term synaptic plasticity (Engel and Jonas, 2005; Alle and Geiger, 2008; Sasaki et al., 2011; Hu and Jonas, 2014; Kawaguchi and Sakaba, 2015; Rama et al., 2015b; Rowan et al., 2016). However, due to the limitation in simultaneously recording from multiple sites along the axon, the patch-clamp technique is not capable of tracking the modulation of AP propagation throughout the axon proper.

#### CMOS HD-MEAs

The electrical activity of neurons can also be detected extracellularly by means of metal electrodes, arranged in large arrays and known as MEAs. Microelectrodes can record changes in the electric field generated by the moving ions in the extracellular space during the electrical activity of a nearby neuron (Buzsáki et al., 2012; Anastassiou et al., 2013). During an AP, the fast Na<sup>+</sup> current flows away from the electrode into the cell and results in a negative peak in the extracellular action potential (EAP). Thereafter, a slower current of K<sup>+</sup> ions flows out of the cell toward the electrode resulting in a positive peak. Most axonal signals show a stereotypical positive-first, triphasic shape. The first, small amplitude positive peak corresponds to a capacitive current, the large negative peak to the Na<sup>+</sup> current, and the final

positive peak to the K<sup>+</sup> current (Gold et al., 2006). In general, EAPs show heterogeneity in signal shapes and amplitudes depending on the magnitude, polarity, and the distance from the recording site (Nunez and Srinivasan, 2006). In addition, the relative positioning of cells with respect to the location of electrodes has a strong influence on the amplitude of the EAP (Gold et al., 2006). EAPs signal amplitudes are in the range of µV and are usually around three orders of magnitude lower than intracellularly measured signals (mV) (Buzsáki et al., 2012).

Commercially available standard MEAs are an established technology for investigating neuronal network activity. However, they do not allow for targeting individual neurons in a network due to the limited number of electrodes (<300), arranged at a comparably large pitch (>30 µm) (Gross et al., 1993; Jimbo and Robinson, 2000; Stett et al., 2003; Rutten et al., 2007). In order to investigate the properties of individual neurons, CMOS (complementary metal oxide semiconductor) technology-based, planar, HD-MEAs can be used that enable simultaneous recording from a large number of sites at high spatiotemporal resolution (Eversmann et al., 2003; Berdondini et al., 2009; Frey et al., 2009; Huys et al., 2012; Johnson B. et al., 2013; Bertotti et al., 2014; Jackel et al., 2017; Ogi et al., 2017; Tsai et al., 2017). In contrast to a full-frame readout that is also used with CMOS cameras, our lab has developed a flexible readout approach, where a matrix of switches below the electrodes (total number: 26,000–59,000 electrodes) routes arbitrarily selectable subsets of 1024 or 2048 electrodes to a high-end readout circuitry placed outside the electrode array. This flexible readout approach enables (i) high spatial resolution with electrode densities of 3,000 to 5,000 electrodes per mm<sup>2</sup> at (ii) good signal quality. However, not all the electrodes can be simultaneously read out, but only subsets in a sequential approach [for technical details, cf. (Ballini et al., 2014; Müller et al., 2015; Dragas et al., 2017; Viswam et al., 2018; Yuan et al., 2018)].

The main advantage of the HD-MEAs is the high spatiotemporal resolution, which allows for detection of signals from thin axons (∼200 nm diameter) and the ability to record APs at microsecond temporal resolution. This degree of resolution helps to efficiently assign detected extracellular spikes to units or neurons through spike sorting (Einevoll et al., 2012; Diggelmann et al., 2018). HD-MEAs enable, owing to the high spatial resolution and non-invasive detection of EAPs, the simultaneous recording at EAPs at hundreds of sites simultaneously along the axonal arbor for up to several days (Bakkum et al., 2013; Radivojevic et al., 2017). CMOS-based HD-MEAs have been used with many in vitro preparations, such as dissociated cell cultures (Maccione et al., 2012; Bakkum et al., 2013; Yada et al., 2016; Amin et al., 2017; Radivojevic et al., 2017), cultures of induced pluripotent stem cells (iPSCs) (Amin et al., 2016; Fiscella et al., 2018), acute retinae (Menzler and Zeck, 2011; Fiscella et al., 2012; Jones et al., 2015), acute brain slices (Egert et al., 2002; Frey et al., 2009; Ferrea et al., 2012; Medrihan et al., 2014; Obien et al., 2019), and organotypic brain slice cultures (Gong et al., 2016). A disadvantage of HD-MEAs is that inferences with respect to analog signaling are difficult, as the subthreshold signals are not directly measurable.

## STUDIES OF AXONAL NEUROBIOLOGY USING HD-MEAs

The possibility to stimulate and record from a single axon, simultaneously at multiple spatial locations, enables to study axonal electrical properties in great detail. Capitalizing on this capability, our group investigated the possibilities to study neuronal cultures by using a combination of HD-MEA recordings, electrical extracellular stimulations, live staining of neurons directly on the HD-MEA, and patch-clamping of targeted individual neurons. For a long time, the soma and dendrites have been considered the main contributors to the EAP landscape, since most electrophysiological measurements, e.g., through whole-cell patch-clamp, have been done at the soma. Although the initiation of APs has been known to occur at the distal AIS (Kole et al., 2008; Hu et al., 2009; Foust et al., 2010; Popovic et al., 2011; Baranauskas et al., 2013; Debanne and Garrido, 2018; Leterrier, 2018), the contribution of axons to the EAP landscape has been assumed to be small, if not negligible due to the small dimensions of axonal structures – in contrast to the soma and dendrites. In order to investigate the contribution of different neuronal compartments to the EAP spatial landscape in detail, our group has used HD-MEAs to electrically image EAPs of cultured cortical neurons and of Purkinje cells in acute cerebellar slices (Bakkum et al., 2018). By using spike-triggered averaging, the EAP landscapes of more than 50 neurons were measured and compared to fluorescence images of the respective neuronal cells (Bakkum et al., 2013). We found that the largest measured EAP signal amplitudes originated from the AIS, instead of the soma. The dominant EAP signals, found at the AIS, featured negative polarity (charges entering the cell), while some EAP signals found in nearby dendrites had positive polarity (return currents or charges exiting the cell) (**Figures 2A,B**). These findings are relevant in interpreting results obtained with extracellular recording schemes (in vitro and in vivo), for setting up compartmental neuron models, and for developing methods to study the function of the AIS in healthy and diseased cellular cultures.

A characteristic parameter of axons is the conduction velocity, which determines how fast information is transferred between neurons. Detecting fluctuations or deviations in conduction velocity along the axon can provide an understanding of factors that affect conduction success or failure. Such detection poses a major challenge, as it requires a method to directly measure AP propagation at several points along the axon. Several groups have utilized PDMS tunnels, combined with MEAs, to confine the axons, to increase SNR (higher electrical resistance along the channels) and to track the AP propagation along axons and axonal bundles (Shimba et al., 2014; Lewandowska et al., 2015; Habibey et al., 2017). Our group used stimulustriggered averaging of EAPs to precisely measure the propagation of APs and quantify the conduction velocity along axonal branches (Bakkum et al., 2013). In general, the velocity of AP

with (red) application of synaptic blockers calculated by using a bootstrapping procedure. (Bottom) The same analysis was performed for an orthodromic action potential. The red cross indicates the stimulation electrode located near the soma. Propagation continued into two branches ("East" and "South"). (D) Stimulation-triggered EAP footprint superimposed with neuronal morphology, revealed by live-cell imaging using lipofection. Circle sizes indicate logarithmically scaled amplitudes of triggered APs, whereas colors indicate the occurrence times of the negative AP peaks relative to the stimulation time. The black arrow points to the stimulation electrode for orthodromic stimulation, whereas the pale red patch indicates the area affected by the stimulation artifact. (E) Two axonal branches, labeled "Branch 1" and "Branch 2," are marked by dark-green and light-green lines on a fluorescence image. White circles indicate the positions of the used recording electrodes. (F) AP propagation times obtained from the two branches: average propagation times are presented by solid lines; the standard deviations of the propagation times are represented by the pale bands in the background. Except Panel B, which is an acute cerebellar slice preparation, all other panels refer to cortical neuronal cultures. Images have been adapted with permissions from Bakkum et al., 2013, 2018 (A–C), Radivojevic et al., 2016, 2017 (D–F).

propagation along axons of wild-type primary rodent neuron cultures increases with age, as observed in our experiments and reported by other authors (Bakkum et al., 2013; Habibey et al., 2017). Both, antidromic (toward the soma) and orthodromic (away from the soma) AP propagations featured variations in conduction velocity along the axon (**Figure 2C**). The variations persisted upon application of synaptic blockers (100 µM APV, 10 µM CNQX, and 50 µM bicuculline methiodide), suggesting that variations in ion-channel properties and densities influence the conduction properties of axons, among others factors. Moreover, higher conduction velocities were observed in axonal segments closer to the soma as compared to the putatively thinner distal branches, which is in agreement with the theory that the action-potential propagation velocity is inversely proportional to the axon diameter (Goldstein and Rall, 1974). Pathological conditions affecting the axon may cause conduction delays, so that the capability to measure axonal signal propagation may allow for phenotyping cell cultures or brain slices that are characteristic of brain disorders and for identifying pharmacological effects.

The electrical properties of neurons, including their susceptibility to extracellular electrical stimulation, are highly variable across their morphology, so that stimulation efficiency with extracellular electrodes will strongly depend on where the neuron is stimulated. By combining optical imaging and electrically multisite stimulation, we could determine the electrical stimulation profiles of single neurons (Radivojevic et al., 2016). The AIS, the axonal arbor, and proximal somatodendritic compartments could be identified as prime stimulation targets (**Figure 2D**). Stimulation at the AIS required low voltages and provided immediate, selective and reliable neuronal activation, whereas stimulation at the soma required high voltages and produced delayed and unreliable responses. Subthreshold stimulation at the soma depolarized the somatic membrane

potential without eliciting APs. These findings provided a strategy to stimulate individual neurons with high specificity, by first measuring their EAP footprint to determine the likely location of their AIS (region of highest signal amplitudes) for subsequent electrical stimulation with low voltages.

A property of axons, which is of high biological relevance but is very hard to experimentally investigate, is the temporal precision with which axons conduct APs. The dendritic integration depends on the timing of incoming postsynaptic potentials. However, determining the temporal precision of axonal conduction, again, requires experimental access to a single axon at multiple locations and requires resolving single APs. As discussed previously, most recording modalities lack either the spatial or temporal resolution, or they rely on averaging many APs. Averaging, however, is not an option, when the timing of individual APs needs to be estimated. We demonstrated a method to non-invasively and directly record individual APs propagating along axons at microsecond temporal resolution using HD-MEA recordings and a template-matching technique relying on multi-electrode templates. We were able to detect individual APs propagating across entire neurons including axonal terminals, which were hundreds of micrometers away from the AIS by using optimized matched filters (Radivojevic et al., 2017). We found that cortical axons conduct single APs with high temporal precision and reliability. Individual APs travel along 1 mm of axons with a fixed travel time ± 100 µs, and we did not observe any conduction or branch-point failure in more than 8,000,000 recorded APs (**Figures 2E,F**).

#### DISCUSSION AND OUTLOOK

Based on the studies reviewed above, we think that HD-MEAs constitute a versatile tool to investigate neuronal information processing and axonal signaling. The possibility to conduct longterm, simultaneous, multisite recordings at high spatiotemporal resolution renders HD-MEAs an ideal technology for detailed characterizations of neurons and axons. HD-MEAs can be used to study alterations in axonal signal propagation and the effects of brain disorders on axonal signaling, as they provide a direct functional readout. Examples include the assessment of the effects of mutations in voltage-gated ion channels (e.g., in the case of channelopathies) on signal propagation velocity. The possibility to reliably electrically stimulate neurons at high frequencies can be used to study the modulation of axonal APs and the mechanisms of axonal conduction failures during repetitive neuronal activation (Geiger and Jonas, 2000; Debanne, 2004; Boudkkazi et al., 2011). Furthermore, spatiotemporal aspects of analog-digital integration in axonal signals can be investigated (Alle and Geiger, 2006; Shu et al., 2006).

#### REFERENCES

Akemann, W., Mutoh, H., Perron, A., Park, Y. K., Iwamoto, Y., and Knöpfel, T. (2012). Imaging neural circuit dynamics with a voltage-sensitive fluorescent protein. J. Neurophysiol. 108, 2323–2337. doi: 10.1152/jn.00452.2012

HD-MEAs can be arranged in a multi-well-plate format to realize high-throughput as required, e.g., for large-scale genomic interventions (RNAi or CRISPR) or compound screenings, using human iPSC-derived neurons to model neurological diseases. HD-MEAs enable access to a variety of electrophysiological parameters, including axonal properties, which can be used for characterizing functional phenotypes of neurological disease models. Therefore, HD-MEAs can be used as a platform for drug screening, pre-clinical diagnostics and will find applications in the evolving landscape of precision medicine.

From a technological perspective, it is conceivable that only the combination of different recording modalities will substantially increase the number of applications. Extracellular, intracellular and optical readouts can be combined to determine how they can complement each other. For example, subthreshold voltage distributions can be optically visualized while simultaneously measuring axonal signals throughout the axonal arbors using HD-MEAs. Such an approach will allow for deciphering effects of axonal and synaptic plasticity in neuronal networks and provide functional insights into axon physiology and, possibly, pathophysiology. In particular, it may become possible in the future to better understand the functional underpinnings of clinically heterogeneous diseases that arise from axonal disturbances.

#### AUTHOR CONTRIBUTIONS

VE, FF, MO, and AH wrote the manuscript. VE built the figures.

#### FUNDING

This work was supported by the European Community through the European Research Council Advanced Grants 694829 "neuroXscales" (Horizon 2020) and the Swiss National Science Foundation Grant 205321\_157092/1 ("Axons"). FF received individual support by the Swiss National Science Foundation "Ambizione" Grant PZ00P3\_167989. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

#### ACKNOWLEDGMENTS

M. Emmenegger and E. J. Rushing, both at the University of Zurich, are acknowledged for their help with the manuscript and proofreading.




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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 © 2019 Emmenegger, Obien, Franke and Hierlemann. 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(s) 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.

# Thinking About the Nerve Impulse: The Prospects for the Development of a Comprehensive Account of Nerve Impulse Propagation

#### Linda Holland<sup>1</sup>† , Henk W. de Regt<sup>2</sup> and Benjamin Drukarch<sup>1</sup> \*

#### Edited by:

#### Dominique Debanne,

INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Ahmed El Hady, Princeton University, United States Guilherme Lucas, University of São Paulo, Brazil

> \*Correspondence: Benjamin Drukarch b.drukarch@vumc.nl

#### †Present address:

Linda Holland, Department of Philosophy, Faculty of Humanities, Vrije Universiteit Amsterdam, Amsterdam, Netherlands

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 13 November 2018 Accepted: 24 April 2019 Published: 15 May 2019

#### Citation:

Holland L, de Regt HW and Drukarch B (2019) Thinking About the Nerve Impulse: The Prospects for the Development of a Comprehensive Account of Nerve Impulse Propagation. Front. Cell. Neurosci. 13:208. doi: 10.3389/fncel.2019.00208 <sup>1</sup> Amsterdam Neuroscience, Department of Anatomy and Neurosciences, Vrije Universiteit Amsterdam, Amsterdam UMC, Amsterdam, Netherlands, <sup>2</sup> Department of Philosophy, Faculty of Humanities, Vrije Universiteit Amsterdam, Amsterdam, Netherlands

Currently, a scientific debate is ongoing about modeling nerve impulse propagation. One of the models discussed is the celebrated Hodgkin-Huxley model of the action potential, which is central to the electricity-centered conception of the nerve impulse that dominates contemporary neuroscience. However, this model cannot represent the nerve impulse completely, since it does not take into account non-electrical manifestations of the nerve impulse for which there is ample experimental evidence. As a result, alternative models of nerve impulse propagation have been proposed in contemporary (neuro)scientific literature. One of these models is the Heimburg-Jackson model, according to which the nerve impulse is an electromechanical density pulse in the neural membrane. This model is usually contrasted with the Hodgkin-Huxley model and is supposed to potentially be able to replace the latter. However, instead of contrasting these models of nerve impulse propagation, another approach integrates these models in a general unifying model. This general unifying model, the Engelbrecht model, is developed to unify all relevant manifestations of the nerve impulse and their interaction(s). Here, we want to contribute to the debate about modeling nerve impulse propagation by conceptually analyzing the Engelbrecht model. Combining the results of this conceptual analysis with insights from philosophy of science, we make recommendations for the study of nerve impulse propagation. The first conclusion of this analysis is that attempts to develop models that represent the nerve impulse accurately and completely appear unfeasible. Instead, models are and should be used as tools to study nerve impulse propagation for varying purposes, representing the nerve impulse accurately and completely enough to achieve the specified goals. The second conclusion is that integrating distinct models into a general unifying model that provides a consistent picture of nerve impulse propagation is impossible due to the distinct purposes for which they are developed and the conflicting assumptions these purposes often require. Instead of explaining

**58**

nerve impulse propagation with a single general unifying model, it appears advisable to explain this complex phenomenon using a 'mosaic' framework of models in which each model provides a partial explanation of nerve impulse propagation.

Keywords: nerve impulse propagation, action potential, Hodgkin-Huxley model, soliton model, comprehensive modeling, complete representation, model as tool, comprehensive framework

## INTRODUCTION

fncel-13-00208 May 13, 2019 Time: 14:57 # 2

In a celebrated paper, Hodgkin and Huxley (1952a) presented a model with which they provided a quantitative description of the electrical events underlying the generation and propagation of a nerve impulse. This model is still vitally important in the neurosciences and is the foundation for a broad area of neuroscientific research (Catterall et al., 2012). The 'Hodgkin-Huxley' (HH) model was the result of a long period of electricitycentered study in electrophysiology that had started in 1791 with the work of Galvani (Piccolino, 1998; Drukarch et al., 2018). In line with its history, the model considers the nerve impulse as a purely electrical pulse or 'action potential'. It describes the action potential as the result of ion fluxes across the neural membrane due to an ion-specific change in membrane permeability upon an alteration in the membrane potential (Hodgkin and Huxley, 1952a).

The behavior of the HH model nerve is in good agreement with several electrical properties of the (propagated) nerve impulse in experiments. However, the model cannot account for non-electrical manifestations of the nerve impulse for which there is ample experimental evidence. Changes that are found to occur in association with nerve impulse propagation include, but are not restricted to, mechanical and thermal changes (reviewed in Drukarch et al., 2018). These changes could have functional importance in nerve impulse propagation (Costa et al., 2018). However, whether they do, and, if so, how they are related to the electrical aspect of the nerve impulse, is still a matter of debate (Mueller and Tyler, 2014; El Hady and Machta, 2015).

Notwithstanding the remaining uncertainties, opinions have been voiced that the available experimental evidence asks for a more comprehensive consideration of the nerve impulse that accounts for electrical as well as non-electrical aspects of this phenomenon, rather than representing it as a solely electrical event (Andersen et al., 2009; Mueller and Tyler, 2014). Consequently, in neuroscientific literature, alternative models have appeared that attempt to take into account electrical and non-electrical changes associated with nerve impulse propagation (Heimburg and Jackson, 2005; Rvachev, 2010; El Hady and Machta, 2015). In one of the proposed models, the 'Heimburg-Jackson' model, the nerve impulse is considered to be a propagating density pulse in the neural membrane. In this model, the focus is shifted from membrane proteins, i.e., ion channels (which play an important role in nerve impulse generation and propagation according to the view that evolved after introduction of the HH model), to membrane lipids. It is usually contrasted with the HH model (Heimburg and Jackson, 2006; Andersen et al., 2009; Appali et al., 2012). Moreover, the Heimburg-Jackson model is designated as a potentially revolutionary model that challenges neuroscientific dogmas about nerve impulse propagation (Fox, 2018, reprinted in the Special Editions Volume 27 of Scientific American entitled 'Revolutions in Science'; Meissner, 2018). Currently, there is an active debate whether the Heimburg-Jackson model (which is supported by experimental measurements in (artificial lipid) membranes (Heimburg and Jackson, 2005; Wang et al., 2018) and some neuronal models (Gonzalez-Perez et al., 2014, 2016; Wang et al., 2018) but is still largely theoretical in nature) can replace the HH model, and several tests to decide between these models have been proposed (Meissner, 2018). However, although more extensive experimental validation is important, this should not be the only perspective from which alternative models are evaluated. It should be complemented with a conceptual analysis that investigates distinct models of nerve impulse propagation and discusses their role in studying this complex phenomenon. Such an analysis is needed since experimental data can always be interpreted in different ways, and additional arguments are needed to decide which interpretation of these data is superior.

In addition, instead of contrasting these different approaches to nerve impulse propagation, it is also argued in current (neuro)scientific literature that views focusing on membrane proteins and membrane lipids should be integrated in a general unifying model. Such a general unifying model is developed to incorporate, integrate and explain all relevant aspects of the nerve impulse by unifying different manifestations of the nerve impulse and the interaction(s) between them (Mueller and Tyler, 2014; Engelbrecht et al., 2018b). An important argument for developing such a general unifying model is to obtain insights in nerve impulse propagation that cannot be acquired using models that focus on only one or a few aspects of the nerve impulse without studying the interactions between them. In Mueller and Tyler's words: "To advance our understanding of how nervous systems operate it is important to develop comprehensive models where electrical, chemical, and mechanical energies are not compartmentalized from one another, but rather cooperate in a synergistic manner to regulate neuronal excitability and signaling. By starting to consider the interplay between electrical, chemical, and mechanical energy, new paradigms for understanding and studying the biophysics of neural systems will advance our comprehension of brain function" (Mueller and Tyler, 2014, p. 3).

At first sight, developing a general unifying model seems to be a promising approach for building a comprehensive framework of nerve impulse propagation. However, this proposal also raises several questions. First, is it feasible to actually construct such a model or is this mission too ambitious to accomplish? Second, if it is at least in theory possible to construct such a model, what

should the model comprise? And, third, how should we tackle its construction?

In this article, we will conceptually analyze a recently introduced general unifying model, developed by Engelbrecht et al. (2016, 2018a,b). This article builds on a previous article by us (Drukarch et al., 2018) in which we discuss the HH model and alternative models of nerve impulse propagation from a historico-scientific perspective covering the (neuro)scientific literature on the phenomenon of nerve impulse propagation. Here, we follow up on this and discuss some models of nerve impulse propagation from a conceptual point of view in order to conceptually analyze the feasibility of the idea of developing a general unifying model or comprehensive model of nerve impulse propagation, using a recently introduced general unifying model of this phenomenon as an example. Combining the results of our conceptual analysis with recent insights from philosophy of science, we will make some recommendations for the study of nerve impulse propagation. More specifically, we will evaluate in the section "The Engelbrecht Model: An Attempt at a General Unifying Model" whether the 'Engelbrecht' model provides a complete and accurate representation of the propagating nerve impulse. Before elaborating on the Engelbrecht model, however, we will examine in the section "The Hodgkin-Huxley Model" whether the standard model of the nerve impulse, the HH model, represents the nerve impulse accurately and completely. In the section "Recommendations for (Future) Approaches to Studying Nerve Impulse Propagation", we use our analysis of the Engelbrecht model and insights from philosophy of science to formulate recommendations (1) with regard to the role of models in studying nerve impulse propagation and (2) for constructing a comprehensive framework of nerve impulse propagation. Finally, in the concluding section, a possible role for a general unifying model in this comprehensive framework will be discussed. Although a very important issue, we would like to emphasize that the current study is not aimed to discuss or predict the consequences of modeling nerve impulse propagation for different types of nerve fibers using the models referred to here.

## MODELS AS COMPLETE AND ACCURATE REPRESENTATIONS OF NERVE IMPULSE PROPAGATION?

#### The Hodgkin-Huxley Model

The HH model is often considered to provide a complete and accurate representation of the (propagating) nerve impulse, which according to this model is a purely electrical pulse. In other words, the HH model is usually taken to reflect or mirror the biologically 'real' nerve impulse. In this section, we will examine whether the HH model indeed provides such an accurate and complete representation of the nerve impulse. In this discussion, 'accurate' is defined as (nearly) "free from error especially as the result of care" and 'complete' as "having all necessary parts, elements, or steps" (which is in accordance with the definition of these terms in the online Merriam-Webster dictionary in 2018). We discuss the HH model here, first of all, because it is a vitally important model in the neurosciences (e.g., Catterall et al., 2012). It is the result of a long and impressive research tradition in the neurosciences (for an elaborate review, see Drukarch et al., 2018) and is often confirmed in subsequent neuroscientific studies (e.g., Tasaki and Hagiwara, 1957; Naharashi et al., 1964). Moreover, it has now been accepted as an educational textbook-model of action potential generation and propagation (e.g., Purves et al., 2012). Secondly, because it is a well-known model among neuroscientists, which allows us to illustrate the meaning of the concepts 'accurate' and 'complete'. And, finally, because it embodies the received view to which proposed alternative models of nerve impulse propagation are and have to be related.

The propagating nerve impulse is a phenomenon that cannot be observed directly. Therefore, Hodgkin and Huxley devised experiments to obtain information about this phenomenon. In these experiments they used the voltage clamp technique. With this technique, the membrane potential of an isolated nerve fiber can be changed suddenly, after which it is held constant (clamped) using an electrical feedback circuit. The current that must be injected in the nerve fiber to keep the membrane potential constant is assumed to be similar to the current that flows through the neural membrane (Hodgkin et al., 1952).

On the basis of data that Hodgkin and Huxley gathered in their experiments (Hodgkin and Huxley, 1952b,c,d; Hodgkin et al., 1952) they developed a model (Hodgkin and Huxley, 1952a) in which the nerve impulse is described as the result of "a capacity current which involves a change in ion density at the outer and inner surfaces of the membrane, and an ionic current which depends on the movement of charged particles through the membrane" (Hodgkin et al., 1952, p. 426) upon depolarization of the membrane. The ionic current can be further divided in currents of sodium and potassium ions and a leakage current of other ions. The sodium and potassium ions travel down their electrochemical gradient across the membrane that is selectively permeable for them during different phases of the nerve impulse (Hodgkin and Huxley, 1952a). More specifically, Hodgkin and Huxley modeled the neural membrane as an electrical circuit (**Figure 1**), consisting of a capacitor representing the lipid bilayer, resistors conceptualizing the ionspecific membrane permeability, and batteries modeling the concentration gradient across the membrane that drives the flow of ionic current through the membrane. The mathematical equation that can be derived from this electrical circuit describes the total current density through the membrane quantitatively (see **Equation 1**). To model the propagating nerve impulse, this equation had to be extended in order to take into account the current flow along the nerve fiber as well (Hodgkin and Huxley, 1952a). However, we will not discuss this extended equation here to avoid unnecessary complexity.

At the time when Hodgkin and Huxley developed and introduced their model, the "thickness and composition of the excitable membrane" were unknown (Hodgkin and Huxley, 1952a, p. 501). Therefore, they did not know how sodium and potassium ions pass the nerve fiber membrane. For this reason, they tried to find equations for the sodium and potassium conductance terms in **Equation 1** "which describe the conductances with reasonable accuracy and are sufficiently simple for theoretical calculation of the action potential"

by comparing theoretical equations with experimental data (Hodgkin and Huxley, 1952a, p. 506). **Equation 1** is thus a simplified version of the equation that Hodgkin and Huxley developed to describe the total current through the membrane. In the complete equation, the terms for the potassium and sodium conductance are given by ion-specific constants and ionspecific dimensionless variables. The changes of these variables over time are described in separate differential equations. The rate constants of these differential equations are in turn given by additional equations (Hodgkin and Huxley, 1952a). For the same reason as mentioned above, these equations will not be discussed here.

Since Hodgkin and Huxley developed phenomenological equations for the sodium and potassium conductance of the membrane, these equations are "an empirical description of the time-course of the changes in permeability to sodium and potassium" (Hodgkin and Huxley, 1952a, p. 541). For this reason, it cannot be concluded that the HH model provides an accurate representation of the nerve impulse, because "[a]n equally satisfactory description of the voltage clamp data could no doubt have been achieved with equations of very different form, which would probably have been equally successful in predicting the electrical behavior of the membrane" (Hodgkin and Huxley, 1952a, p. 541). Although Hodgkin and Huxley limited the possible explanations of the conductance changes of the neural membrane considerably with their experiments and model (e.g., they excluded the possibility that the membrane breaks down in a non-specific manner allowing non-specific ion flow through the membrane), the conductance equations that Hodgkin and Huxley developed do not provide evidence in favor of a certain mechanism of membrane permeability, they could not provide "any certain information about the nature of the molecular events underlying changes in permeability" (Hodgkin and Huxley, 1952a, p. 501).

A few decades later a new technique was developed, the patch clamp (Neher and Sakmann, 1976). With the patch clamp technique, which is a refinement of the voltage clamp technique, the current flowing through small patches of the membrane can be measured. In experiments involving the patch clamp, evidence could be provided that the ion flow through the membrane is localized to ion channels embedded in the membrane (e.g., Sigworth and Neher, 1980). Thus, the HH model could be supplied with a physical interpretation of the ion conductance through the membrane, and in combination with this additional information the nerve impulse could be represented accurately with the HH model<sup>1</sup> .

However, does the HH model also represent the nerve impulse completely? Hodgkin and Huxley stood in a research tradition that had started in the 18th century, the electrophysiological research tradition. In electrophysiology, the electrical nature of the nerve impulse was (and is) generally accepted and intensively studied (for a historical overview, see Clower, 1998; Piccolino, 1998; Drukarch et al., 2018). Electrophysiologists investigated the action potential in increasing detail, providing insights in the form of the action potential, the velocity of its conduction, the importance of the neural membrane for the generation and propagation of action potentials, and the selective nature

$$\mathcal{M} = \left[\mathbb{1}\right] \mathsf{C}\_{\mathsf{M}} \frac{\mathsf{c}\mathsf{V}}{\mathsf{c}\mathsf{t}} + \left[\mathbb{2}\right] \mathsf{g} \mathsf{c}\left(\mathbb{V} - \mathsf{V}\mathsf{c}\right) + \left[\mathbb{3}\right] \mathsf{g} \mathsf{u}\_{\mathsf{H}}\left(\mathbb{V} - \mathsf{V}\mathsf{u}\right) + \left[\mathbb{4}\right] \mathsf{g} \mathsf{c}\left(\mathbb{V} - \mathsf{V}\mathsf{c}\right)$$

In this equation, term [1] describes the capacity current, which depends on the membrane capacitance (CM) and the change in the displacement of the membrane voltage from its resting value over time ( dV dt ), and the other terms describe the total ionic current, which consists of [2] a potassium ion (K) current, [3] a sodium ion (Na) current and [4] a leakage (L) current of other ions. Each ionic current is determined by the ionic permeability of the membrane which is described in terms of an ionic conductance (gion, which is the inverse of the electrical resistance) and a driving force that is the result of the difference between the displacement of the membrane potential from its resting value (V) and the equilibrium potential for the ions given as a displacement from the resting membrane potential (Vion) (Hodgkin and Huxley, 1952a).

<sup>1</sup> In the section "The Engelbrecht Model: An Attempt at a General Unifying Model" it will turn out, however, that not every (neuro)scientist agrees with this conclusion.

EQUATION 1 | Hodgkin-Huxley equation describing the total membrane current.

of membrane permeability. Hodgkin and Huxley (1952a,b,c,d) especially added insights to the last item on this list, and thereby contributed to an explanation of the time-course of the membrane voltage during the action potential.

Due to this long tradition of electrophysiological research in which electricity was the main focus for hypothesizing about, experimenting on and modeling of the nerve impulse, we understand the action potential, the electrical aspect of the nerve impulse, quite well. In fact, based on this understanding of the nerve impulse as an electrical phenomenon, it has been asserted that the electrical aspect of the nerve impulse is "the causal agent in [nerve impulse] propagation" (Hodgkin, 1964, p. 1148). However, this assertion is clearly the result of the assumption that the HH model represents the nerve impulse completely. Still, from the fact that the hypotheses that are studied (and thus the questions that are posed and answered about the nerve impulse) in electrophysiology are mainly electrical in nature, it does not follow that the nerve impulse is itself of an exclusively electrical nature. Experimental evidence has shown that the nerve impulse is not only manifested by an action potential, but also by mechanical and thermal changes, which could be of functional importance for nerve impulse initiation and/or propagation (Costa et al., 2018; Drukarch et al., 2018). Since the HH model cannot account for these non-electrical manifestations of the nerve impulse, it does not represent the nerve impulse completely. Therefore, concluding that the electrical action potential is the causal agent in nerve impulse propagation appears premature, since the fundamental cause(s) of this phenomenon might as well be of a non-electrical nature.

## The Engelbrecht Model: An Attempt at a General Unifying Model

The ample experimental evidence that the nerve impulse is accompanied by mechanical changes like axon swelling (e.g., Tasaki and Iwasa, 1982) and changes in intracellular pressure (Terakawa, 1985), and temperature changes (e.g., Howarth et al., 1968), has led to a resurgence of interest in the modeling of nerve impulse propagation in (neuro)scientific literature. Several new models have been developed that try to account for electrical, mechanical and/or thermal changes during nerve impulse propagation (Heimburg and Jackson, 2005; Rvachev, 2010; El Hady and Machta, 2015). Moreover, some (neuro)scientists have argued that all relevant aspects of the nerve impulse need to be incorporated, integrated and explained in a general model unifying different manifestations of the nerve impulse and their interaction(s) (Mueller and Tyler, 2014; Engelbrecht et al., 2018b). The idea behind the latter proposal, although not stated explicitly by the authors, seems to be that incorporating all relevant details about these manifestations and the processes underlying them enables the representation of the nerve impulse and its propagation in a complete and accurate way (something that could not be achieved by Hodgkin and Huxley (1952a) with their model). In this section, as an illustration, we will discuss a recently introduced general unifying model that is still in the process of development and refinement, the Engelbrecht model (Engelbrecht et al., 2016, 2018a,b). More specifically, we will answer the question whether this model can represent the nerve impulse and its propagation completely and accurately (without assuming that this is in fact the aim of the model).

As already mentioned above, the Engelbrecht model is neither the only model that attempts to model (non-)electrical manifestations accompanying the nerve impulse nor is it the first. However, the method for doing so distinguishes Engelbrecht and coworkers from other modelers like Heimburg and Jackson (2005); Rvachev (2010), and El Hady and Machta (2015). The latter modelers do not try to integrate existing models in a general unifying model in order to study (aspects of) nerve impulse propagation as Engelbrecht and coworkers do. This 'nonintegrating' approach becomes clear in the article of El Hady and Machta (2015), who model the mechanical aspect of the nerve impulse as driven by the electrical aspect of this phenomenon, in the following quotes: "Our model does not assume a particular mechanism underlying the electrical component of the [action potential]" (p. 2) and "Our model does not require an underlying theory of how this electrical component arises. We emphasize that any traveling electrical wave will induce a co-propagating mechanical wave . . ." (p. 5)<sup>2</sup> . In this article, we conceptually analyze the attempt to integrate different models in order to obtain a general unifying model of nerve impulse propagation, since this accords with the intuition that neuroscience strives for a complete and accurate representation of complex neuroscientific phenomena. In the following, we will focus our discussion on the Engelbrecht model as an illustration of such an attempt.

In the Engelbrecht model, three waves are described mathematically: an electrical pulse, a pressure wave in the axoplasmic fluid of the nerve fiber and a mechanical wave in the neural membrane. The equations describing these waves are coupled via so-called coupling forces. The authors assume that the process of nerve impulse propagation proceeds as follows (**Figure 2**): an electrical signal above a certain threshold induces the generation of an electrical pulse, which in turn brings about a pressure wave in the axoplasm. The electrical pulse and the pressure wave together generate a mechanical wave in the neural membrane, which has a longitudinal and a transverse component. In its turn, the mechanical wave can influence the electrical pulse via mechanical activation; e.g., the opening of ion channels via mechanical input (Engelbrecht et al., 2016, 2018a,b).

Since the Engelbrecht model is a non-statistical mathematical model, it yields exact predictions that follow with certainty from the model's starting assumptions. Thus, this model in which an ensemble of waves is described mathematically can be used to predict process characteristics of nerve impulse propagation (Engelbrecht et al., 2018b). However, the correctness of the predictions of such a model depends on the correctness of its assumptions. This means that even if the process characteristics that are predicted with the model

<sup>2</sup>Of course, El Hady and Machta (2015) have ideas about the mechanism underlying the electrical aspect of the nerve impulse. More specifically, they propose two possibilities (p. 2): "Our model does not assume a particular mechanism underlying the electrical component of the [action potential]. Indeed, we expect that the surface waves we predict would accompany the [action potential] predicted by Hodgkin and Huxley and the cable theory, even if they do not contribute to neuronal function. However, our results also allow for the possibility that the mechanical changes that accompany these surface waves feed back and influence the electrical [action potential], giving them functional importance".

are in agreement with experimental data, the value of these predictions remains relative to the following assumptions: (1) the assumption that the electrical signal triggers the described process of nerve impulse propagation, (2) the assumption that the distinct manifestations of the nerve impulse are the result of distinct processes, (3) the manifestations or processes that are assumed to be relevant for nerve impulse propagation, (4) the assumed order of the described processes, (5) the interactions between the described processes that are assumed to be relevant, and (6) the underlying assumptions about the way in which these processes interact. Although there is experimental evidence for the co-occurrence of intracellular pressure changes and mechanical displacements of the membrane during action potential propagation (Tasaki and Iwasa, 1982; Terakawa, 1985), the proposed models for the mechanisms underlying these co-occurring non-electrical waves are largely theoretical in nature (for a discussion of proposed models, see Drukarch et al., 2018). Thus, the value of the Engelbrecht model for predicting process characteristics of nerve impulse propagation depends on the correctness of assumptions that have not been experimentally tested as yet. Nevertheless, since we do not have experimental counterevidence against these assumptions or better evidence in favor of other assumptions, the choices of the modelers seem to make sense. However, these unverified assumptions have consequences for the conclusion whether the Engelbrecht model represents nerve impulse propagation accurately and completely: the agreement between the predictions of the model and experimental data does not imply a complete and accurate representation of this process as long as there is no better evidence for the assumptions made concerning completeness and accuracy (assumptions 1, 3, and 5 and assumptions 1, 2, 4, and 6, respectively). Thus, although the Engelbrecht model seems to include all relevant details about nerve impulse propagation, whether it can and does represent this complex process completely and accurately depends on the correctness of the assumptions about the initiation and the process of nerve impulse propagation.

In fact, it can be demonstrated that in its present form the Engelbrecht model does not represent the process of nerve impulse propagation accurately. To see why not, we need to zoom in on the components of the model. The model consists of existing mathematical models, which are used to describe the single processes involved in nerve impulse propagation (i.e., the electrical pulse, the axoplasmic pressure wave and the mechanical wave in the neural membrane, **Figure 2**). These models are integrated using coupling forces that are developed by the modelers themselves (Engelbrecht et al., 2016, 2018a,b).

For modeling the (propagating) electrical pulse, Engelbrecht and coworkers use the 'FitzHugh-Nagumo' model. This model is a simplification of the HH model. Instead of focusing on two ion currents (sodium and potassium), this model only describes one ion current. Both the FitzHugh-Nagumo model and the HH model can account for key characteristics of the action potential: the presence of a threshold for action potential generation, the allor-none behavior of the action potential, etc. (Engelbrecht et al., 2016, 2018a,b). However, in both these models also an important assumption is made, namely that the membrane capacitance is constant (Hodgkin and Huxley, 1952a; FitzHugh, 1961). Since this assumption entails that the capacity current (first term in **Equation 1**) depends only on the membrane capacitance and the change in membrane voltage over time, the capacity current only plays a role when the membrane potential of the isolated nerve fiber is suddenly changed in voltage clamp experiments. When, after that, the membrane potential is kept constant, the first term in **Equation 1** will become zero, and "the ionic current can be obtained directly from the experimental records" with the voltage clamp (Hodgkin et al., 1952, p. 426).

In the Engelbrecht model the (propagating) longitudinal component of the mechanical wave in the neural membrane is described using the model that Heimburg and Jackson (2005, 2006) developed. In order to explain the Heimburg-Jackson model, which is a thermodynamic model, some background information is needed. This model is based on the notion that under physiological conditions a membrane is predominantly in a fluid phase in which the lipids in the membrane are relatively disordered. Under these conditions, the membrane lipids are slightly above their melting temperature. A little below body temperature, the membrane lipids undergo a melting transition, and the fluid phase of the membrane transitions to a denser gel phase in which the lipids are more ordered. According to the Heimburg-Jackson model, the nerve impulse then is a localized electromechanical density pulse which consists of a traveling region of membrane in the gel phase in an environment of resting membrane in the fluid phase. During the density pulse, both the thickness and the area of the membrane change (compared to the resting membrane). These changes in membrane thickness and area lead to a change in the membrane capacitance during the nerve impulse (Heimburg and Jackson, 2005, 2006; Andersen et al., 2009; Appali et al., 2012; Wang et al., 2018). For a mathematical illustration of the dependence of the membrane capacitance on membrane thickness and area, see **Equation 2**.

EQUATION 2 | The membrane capacitance is a function of the membrane area and thickness.

$$\mathsf{C}\_{\mathsf{T}\heartsuit} = \mathsf{K}\_{\mathsf{T}\heartsuit} \ast \mathsf{c}\_{\mathsf{T}\heartsuit} \ast \frac{\mathsf{A}\_{\mathsf{T}\heartsuit}}{\mathsf{d}\_{\mathsf{T}\heartsuit}}$$

In this equation, C<sup>m</sup> is the membrane capacitance, K<sup>m</sup> the dielectric constant of the membrane, ε<sup>0</sup> the permittivity of free space, A<sup>m</sup> the area of the membrane, and d<sup>m</sup> the membrane thickness.

Although the assumption that the membrane capacitance is constant simplifies the study of the ionic current in voltage clamp experiments considerably and might be correct under the conditions in the voltage clamp, the result of this assumption is that the change in membrane capacitance during the nerve impulse is absent in the generally accepted explanation of the action potential (the electrical aspect of the nerve impulse) in terms of ionic currents through the membrane. However, in line with the Heimburg-Jackson model, the explanation of the action potential should at least be partly in terms of the changing membrane capacitance due to membrane area and thickness changes during the nerve impulse ("[s]ince the membrane is asymmetrically charged, these changes appear as a voltage pulse . . . and lead to a capacitive current" (Andersen et al., 2009, p. 107)) and not solely in terms of ions flowing across the membrane. Andersen et al. (2009, p. 105) phrase it even more firmly: "it seems that known changes in membrane area during the action potential are of an order of magnitude sufficient to account for the observed voltage changes during the action potential".

Thus, two of the component models that are used in the Engelbrecht model, the Hodgkin-Huxley/FitzHugh-Nagumo model and the Heimburg-Jackson model, are incompatible due to inconsistencies with regard to the membrane capacitance, resulting in a logically inconsistent general unifying model. This implies that the model cannot be a fully accurate representation of reality, since such a representation should be free of inconsistencies. More specifically, in reality the capacitance of the neural membrane cannot be constant and change during the nerve impulse at the same time. Since the Engelbrecht model integrates incompatible models, it must represent the nerve impulse and its propagation inaccurately.

#### RECOMMENDATIONS FOR (FUTURE) APPROACHES TO STUDYING NERVE IMPULSE PROPAGATION

#### Models as Tools to Study Nerve Impulse Propagation for Varying Purposes

Thus far we have seen that it is not straightforward to represent nerve impulse propagation accurately and completely using neuroscientific models. The HH model (in combination with information from subsequent studies on ion channels) does not represent the (propagating) nerve impulse completely, and whether it represents this phenomenon accurately is called into question in the Heimburg-Jackson model. Furthermore, we are not sure whether the Engelbrecht model, which unifies different manifestations of the nerve impulse and the interaction(s) between them, represents nerve impulse propagation completely. Moreover, since the Engelbrecht model attempts to integrate the incompatible HH model and Heimburg-Jackson model it does not represent this phenomenon accurately. Therefore, we want to present another perspective on the role of models in studying nerve impulse propagation by introducing two important aspects of models that have not entered the discussion yet: the (neuro)scientist that constructs and uses the model and the purpose for which the model is constructed and used.

If we look again at **Figure 1**, we see an electrical circuit. However, in and by itself this illustration does not represent the neural membrane. It is just an electrical circuit with some resistors, batteries and a capacitor. For it to become a model that represents the neural membrane, at least one scientist should intend to use this electrical circuit as such. Whether this model provides a useful representation of the neural membrane depends on the purpose for which the model is used by the scientist. For example, this model will not provide a useful representation of the neural membrane when it is used for the purpose of studying the molecular composition of the neural membrane, since an electrical circuit cannot provide information about this. On the other hand, the model of an electrical circuit does provide a useful representation of the neural membrane when it is used for studying the electrical manifestation of the nerve impulse as Hodgkin and Huxley (1952a) have shown in their work (see the section "The Hodgkin-Huxley Model") and as is confirmed by many other scientists thereafter.

Philosopher of science Giere calls the conception of representation illustrated above the 'intentional conception of scientific representation', according to which: "Agents (1) intend; (2) to use model, M; (3) to represent a part of the world, W; (4) for some purpose, P" (Giere, 2010, p. 274). This formulation shows that a model cannot represent a phenomenon by itself. In addition, an agent (e.g., a scientist) is needed who uses the model as a representation of the phenomenon for a specific purpose s/he wants to achieve. More specifically, depending on the purpose for which an agent wants to use the model, s/he should specify which similarities are intended between the model and the phenomenon modeled, and how precise the model should correspond to experimental measurements of the phenomenon (Giere, 2004, 2006, 2010). Thus, a model does not represent reality accurately and completely simpliciter, but it represents it accurately and completely enough for a scientist to achieve a certain purpose. This approach to modeling implies that we do not have to incorporate as many details as possible in a model, but only those details that are relevant for reaching the goal of the model.

As already discussed in the section "The Hodgkin-Huxley Model", the HH model does not provide an accurate representation of the action potential. It is also not meant to do so. The HH model is developed for the goal of describing the (propagating) action potential using a quantitative description of the membrane current. In the legend of **Figure 1** and the explanation of **Equation 1**, we clearly see the similarities between the electrical circuit and the neural membrane that are specified by Hodgkin and Huxley (1952a). The details in this model are restricted to those that are important for achieving the goal of the model, i.e., not all the details about the structure and function of the neural membrane are included in the model, only those that are important for describing the electrical aspect of the nerve impulse. The data that were used for the development of the HH model, **Equation 1**<sup>3</sup> , were obtained in voltage clamp experiments (in which the voltage is kept constant). Using the resulting equation, the curve for the (propagated) action potential (i.e., the voltage change that cannot be measured under a voltage clamp) can be calculated. The curve that is produced using **Equation 1** corresponds well with the (propagated) action potential measured in isolated nerve fibers, providing evidence that the action potential can indeed be described using the HH model (Hodgkin and Huxley, 1952a). However, since Hodgkin and Huxley chose to develop theoretical equations for the sodium and potassium conductance of the neural membrane which they fitted to experimental data (by lack of sufficient knowledge about the membrane), they could only speculate about the mechanism of permeability that is responsible for these changes (Hodgkin and Huxley, 1952a). Thus, Hodgkin and Huxley could not use their model for explaining the molecular mechanism underlying the permeability changes of the neural membrane during the nerve impulse. They could not specify the similarities between the (conductances/resistors of the) electrical circuit and the neural membrane accurately and/or completely enough for this purpose.

The nerve impulse can also be modeled for quite different purposes. Heimburg and Jackson, for instance, aim to develop a thermodynamic model of nerve impulse propagation (Andersen et al., 2009; Appali et al., 2012). Their model is presented in the section "The Engelbrecht Model: An Attempt at a General Unifying Model" as a model of the longitudinal component of the mechanical wave in the neural membrane, like it is used in the Engelbrecht model. However, as the goal of developing a thermodynamic model indicates and as already became clear during the discussion in the section "The Engelbrecht Model: An Attempt at a General Unifying Model", the Heimburg-Jackson model encompasses more than only the description of a mechanical wave. Rather, it aims to provide a comprehensive description of the propagating nerve impulse in terms of mechanical and electrical changes (and other changes, like thermal ones). According to this thermodynamic model, the nerve impulse is "a self-sustaining and localized density pulse with a moving segment of the nerve membrane in the gel [phase]" or 'soliton' which can propagate without loss of energy through the neural membrane (Andersen et al., 2009, p. 107). This soliton is associated with a heat release when the membrane transitions from the fluid to the gel phase and a subsequent heat reabsorption when the membrane transitions back to the fluid phase. Since no net heat is gained from or lost to the environment during soliton propagation, the soliton is classified as an adiabatic pulse (since, in thermodynamics, an adiabatic process has precisely these characteristics). Electrical, mechanical and thermal changes are all macroscopic features of a soliton in the neural membrane, which can be measured during its propagation and should be in agreement with the characteristics of an adiabatic process (Heimburg and Jackson, 2005, 2006; Andersen et al., 2009; Appali et al., 2012).

Since the Heimburg-Jackson model is a thermodynamic model, with this model "a macroscopic description" can be given of the nerve impulse in the neural membrane "in terms of [macroscopic] quantities that are detectable directly by our senses and instruments", like temperature and volume (Giancoli, 2009, p. 454). Thus, this model is not aimed at identifying the microscopic constituents involved in the process of nerve impulse propagation that are responsible for the macroscopic quantities that are experimentally measured. Instead, its goal is to describe nerve impulse propagation macroscopically in terms of these experimental measures based on thermodynamic laws. More specifically, this macroscopic description should meet the thermodynamic laws applied to an adiabatic process. Every macroscopic measurement of the propagating nerve impulse (e.g., electrical, mechanical, thermal, etc.) provides a test of the correctness of approaching the nerve impulse as an adiabatic pulse. However, whether nerve impulse propagation is an adiabatic process still needs to be proven. In particular, it has to be experimentally demonstrated that the heat production and subsequent reabsorption during propagation is exactly reversible, which is difficult due to technical limitations of the available experimental instruments (Andersen et al., 2009; Drukarch et al., 2018).

According to this approach to models, in which the purpose for which a model is developed and used is taken into account, the HH model cannot be considered superior, equivalent or inferior to the Heimburg-Jackson model. Since models should be judged based on whether they can achieve certain goals, and since these two models are not developed and used for the same goal, it does not make sense to assess them comparatively. However, this is not a problem for the progress of (neuro)science. For this, it is first and foremost important to learn lessons from these models and use insights obtained with them, e.g., for understanding the nerve impulse better, developing new models or designing new experiments.

Going back to the Engebrecht model, the general unifying model that attempts to integrate the HH model and the Heimburg-Jackson model, the question that still needs to be answered is: for which purpose is this model developed? According to Engelbrecht et al. (2018b, p. 32): "[i]n terms of complexity, the goal is to formulate a model that will be able to describe an ensemble of waves of different physical origin (electrical and mechanical)". If the aim of the model is interpreted

<sup>3</sup>Note that **Equation 1** is a simplification of the original equation developed in the HH model. Moreover, for modeling a propagating action potential **Equation 1** has to be extended. These points are also discussed in the section "The Hodgkin-Huxley Model".

in terms of coupling the phenomenological, mathematical descriptions of the measured curves of the electrical pulse and the mechanical waves independently of their physical basis, this goal can be achieved. But if these phenomenological, mathematical descriptions are interpreted in terms of their physical basis, problems arise. In the Engelbrecht model it is assumed that the different aspects of the nerve impulse are the result of distinct processes. The single processes are described in distinct component models unified in the general model. However, one of these component models, the Heimburg-Jackson model, does not describe a purely mechanical wave in the neural membrane, as is suggested in the Engelbrecht model: in fact, its description also encompasses the electrical pulse. Moreover, the Heimburg-Jackson model is not compatible with the HH model with regard to the physical basis of the electrical pulse. Of note, the Heimburg-Jackson model suggests that the different manifestations of the nerve impulse could be features of a single process instead of being the result of distinct processes, as is assumed in the Engelbrecht model (although this thermodynamic model itself does not provide insights in the molecular basis of the process of nerve impulse propagation). At the moment this remains to be elucidated experimentally. Due to these problems, the equations in the Engelbrecht model cannot be interpreted in terms of their physical basis.

Still, using the ensemble of phenomenologically described waves, the Engelbrecht model can provide insights in the mathematically possible process characteristics and, more specifically, interactions between the single waves based on (future) experimental observations of the spatiotemporal relations (or hypothetical spatiotemporal relations) between the electrical and mechanical manifestations of the nerve impulse (Engelbrecht et al., 2018a). These insights could in turn be used to guide future investigations in order to identify the actual interactions between the waves and the microscopic constituents that are responsible for them.

#### The Construction of a Comprehensive Framework of Nerve Impulse Propagation

In the section "The Engelbrecht Model: An Attempt at a General Unifying Model", we have shown that the Engelbrecht model cannot provide a consistent picture of the nerve impulse and its propagation, since it integrates component models that are incompatible due to an inconsistency regarding the membrane capacitance. Indeed, in general, if a general unifying model is built using component models of single aspects of the nerve impulse, it will be virtually impossible to construct a model that provides a consistent picture of nerve impulse propagation. The reason for this is the fact that the component models are developed for varying purposes which require different and often conflicting idealizing assumptions in order to achieve those purposes<sup>4</sup> . This suggests that a comprehensive framework of nerve impulse propagation will not be accomplished by developing a single general unifying model. An alternative approach may therefore be required to develop a comprehensive framework of nerve impulse propagation. Here, we suggest one that is based on an account of philosopher of science Hochstein (2016), who argues that a neuroscientific mechanism (e.g., nerve impulse propagation) cannot be mechanistically explained<sup>5</sup> in one model but, instead, that many (sometimes contradictory) models are needed to provide such an explanation.

Understanding a complex phenomenon like nerve impulse propagation is not easy. Models need to be developed in order to make parts of this phenomenon comprehensible to us. To achieve this, idealizing assumptions need to be made in accordance with the purpose for which the models are developed. With these models, that provide partial explanations of nerve impulse propagation, a comprehensive framework can be built in the way a mosaic is constructed using several tiles<sup>6</sup> . Thus, in the resulting framework the overall explanation of nerve impulse propagation can be inferred from a set of models like the picture represented by a mosaic can be inferred from a collection of tiles. All models in the framework put constraints on the others. More precisely formulated, the parts of the models that successfully represent a part of nerve impulse propagation put constraints on the other models within the collection. However, the resulting comprehensive framework will not look like a puzzle of which the pieces fit perfectly together. Instead, (at least at the start) the framework will have gaps due to the fact that not all aspects of the nerve impulse are or can be modeled (yet). In addition, some of the models within the framework will overlap or will be based on conflicting assumptions. As a result, the explanation of nerve impulse propagation needs to be inferred from the piecemeal and sometimes contradictory representation of this phenomenon in the distinct models that constitute the comprehensive framework. Moreover, the comprehensive framework will evolve over time, and the explanation of nerve impulse propagation can change due to the addition of the latest (neuro)scientific insights to the framework or the removal of erroneous models. In addition, the explanation that is given of nerve impulse propagation using a comprehensive framework will also depend on the purpose for which the explanation is employed, as discussed in the section "Models as Tools to Study Nerve Impulse Propagation for Varying Purposes".

The suggested (construction of a) comprehensive 'mosaic' framework of nerve impulse propagation might seem very unsatisfying compared to the ideal of a single, logically consistent general unifying model. However, our current explanation of the action potential, the electrical aspect of the nerve impulse, is already the result of a framework consisting

<sup>4</sup>This is one of the problems with regard to the neuroscientific explanation of a mechanism using a single model which is discussed by Hochstein (2016). Craver and Kaplan (2018) discuss this problem in the context of developing norms of completeness for mechanistic explanations.

<sup>5</sup> "[A] model provides [a mechanistic] explanation when it identifies four essential features of the mechanistic system [e.g., nerve impulse propagation]: (1) The parts of the system. (2) The way in which these parts are spatially and temporally organized within the system. (3) The operations that go on between the relevant component parts. (4) The resulting phenomenon produced by the system." (Hochstein, 2016, p. 1393).

<sup>6</sup>Craver (2007) introduces the metaphor of a mosaic in the context of presenting a model of the unity of neuroscience (which is aimed to reflect neuroscientific practice).

of a set of distinct models that has developed over time. In order to illustrate that the above suggested approach to develop comprehensive frameworks for explaining complex phenomena may work in neuroscientific practice, and to show how such a comprehensive framework is built, we will sketch the history of the discovery and subsequent study of the sodium channel after the introduction of the HH model and discuss this history in the context of the construction of a comprehensive framework of the action potential. The following discussion is based on reviews by Barchi (1988) and Trumpler (1997).

With the HH model the sodium conductance of the neural membrane could be modeled. However, in the time period in which this model was introduced, the physical basis underlying the sodium conductance was unknown, leaving a gap in the explanation of the action potential. It took decades before this sodium conductance could be studied in more detail using the patch clamp technique, with which sodium currents through small patches of the membrane can be measured (we already discussed this briefly in the section "The Hodgkin-Huxley Model"). However, before it could be concluded that the patch clamp measurements were related to the representation of the action potential in the HH model, the relation between the 'macroscopic' currents measured with the voltage clamp and the 'microscopic' currents measured with a patch clamp had to be established. Assuming that the microscopic currents measured in patch clamp experiments are the result of identical sodium channels that function independently, the average of the sum of many microscopic current measurements should be in accordance with the characteristics of a macroscopic sodium current measured with a voltage clamp. This was shown to be the case, thereby illustrating that the microscopic sodium conductance is responsible for the macroscopic one (Sigworth and Neher, 1980). Here, we see clearly that the characteristics of the macroscopic sodium current were used as a constraint for the microscopic sodium currents in order to determine whether the results obtained with the patch clamp could be added to the framework that explains the action potential.

However, the framework explaining the action potential did not only consist of an electrophysiological representation of sodium conductance based on electrophysiological data and models. In addition, models representing the molecular structure of the sodium channel, which was assumed to be responsible for the sodium conductance, were developed. One of the first things known about the purified sodium channel protein, which could be identified using neurotoxins like radiolabeled tetrodotoxin, was its molecular weight. The structure of this tetrodotoxin-binding protein was not established at that time, but using patch clamp recordings it was shown that the protein has biophysical properties that correspond to those expected for the "physiologically defined [sodium] channel" (Rosenberg et al., 1984, p. 5597), demonstrating that this protein fits in the framework that explains the action potential. Later, the genetic code of the protein was identified, the amino acids that correspond to this genetic code were determined, and models of the protein structure were developed (Noda et al., 1984; Guy and Seetharamulu, 1986). Thus, the molecular structure of the sodium channel was represented in models that do not represent sodium currents across the membrane. Moreover, although the models of the protein structure were based on the experimental evidence about the genetic code and the corresponding amino acids, these models were only partially overlapping (and thus at some points contradictory) due to different considerations of the scientists. Since both models were in agreement with the available experimental data, both can be considered part of the framework explaining the action potential at that time. Such models of the sodium channel structure were in turn used to suggest which structural parts of the sodium channel are involved in channel activation and inactivation (Noda et al., 1984; Guy and Seetharamulu, 1986; Stühmer et al., 1989). These suggestions could be tested experimentally by changing the molecular structure of the sodium channel (using genetic engineering) and investigating its resulting electrophysiological characteristics (using voltage- and patch clamp recording) (Stühmer et al., 1989). By exploring relationships between the molecular structure and electrophysiological characteristics of the sodium channel in this way, the framework explaining the action potential could be complemented with new pieces of experimental information about (the kinetics of) sodium channel gating. This information could then be used to limit the models of the sodium channel structure in the framework to those that are in agreement with the latest experimental data (but which still could be contradictory at other points).

Thus, the history starting with a sodium conductance in the HH model and resulting in the discovery and study of the molecular structure of the sodium channel shows how a comprehensive framework has been built from distinct models that inform and constrain each other. This set of models can be used to explain the action potential without integrating all these models into one general unifying model. Of course, the explanation of the action potential is not only based on models that represent the molecular structure or electrophysiological characteristics of sodium channels, but this example suffices to illustrate that the overall explanation is inferred from distinct models that each provide part of the explanation. In a comparable way a comprehensive framework of nerve impulse propagation can be constructed, which may or may not include the HH model, the Heimburg-Jackson model and the Engelbrecht model.

#### CONCLUSION

From a critical examination of the Engelbrecht model we have drawn two conclusions, and combining these conclusions with recent insights from philosophy of science, we have made two recommendations for the study of nerve impulse propagation. The first conclusion of our analysis is that attempts to develop models that represent nerve impulse propagation accurately and completely appear unfeasible. Instead, models are and should be used as tools to study nerve impulse propagation for selected goals, representing the nerve impulse accurately and completely enough to achieve these goals. The second conclusion is that since models of distinct aspects of the nerve

impulse, developed for selected purposes, require different and often incompatible idealizations, they cannot be integrated in a general unifying model that consistently models nerve impulse propagation in all its details. Instead of unifying such models in one general model, we suggest that a comprehensive 'mosaic' framework of nerve impulse propagation should be constructed using distinct models. From this collection of models the explanation of this complex phenomenon can be inferred based on the piecemeal and sometimes contradictory representation of it in the distinct models. This explanation of nerve impulse propagation can change over time due to the addition of models to, or the removal of models from, the comprehensive framework.

However, although a general unifying model cannot provide an all-encompassing explanation and representation of nerve impulse propagation, this does not mean that it cannot fulfill a function in a comprehensive framework of nerve impulse propagation. It can be of additional value in the framework if it serves a purpose that other models cannot. For instance, a general unifying model may provide insight in the causal relations between the different aspects of the nerve impulse, which is something that models of single aspects of the nerve impulse cannot capture. In such a general unifying model not all details regarding nerve impulse propagation need to be incorporated, but instead the incorporation of details should be limited to the ones that are relevant to the study of causal relations. However, as follows from the discussion here, there are some requirements that should be met before a general unifying model can be of value for the study of causal relations. The first requirement is that the different manifestations of the nerve impulse are actually results of separate processes and not just distinct features of a single process, since, in the latter case, a model focusing on this process can already capture the causal relations. This should be sorted out experimentally, which is not straightforward to do in the case of the nerve impulse, since it is currently not possible to study the electrical and mechanical aspects of the nerve impulse in isolation in nerves using experimental interventions. If the different manifestations of the nerve impulse turn out to be the result of distinct processes, the second requirement is that the models of the separate processes that are unified in the general unifying model should offer compatible perspectives on the causal relations that are studied, since these causal relations cannot be clarified if they are described in a logically inconsistent way in the general unifying model.

#### REFERENCES


Thus, the motivation, given in the "Introduction", to develop a general unifying model in order to obtain insights in nerve impulse propagation that cannot be acquired with models that focus only on one or a few aspects of the nerve impulse without studying the interactions between these aspects, still stands. However, in this article, we have shown that these insights are not achieved by incorporating as many details as possible about nerve impulse propagation, but by focusing on the goals that cannot be reached by compartmentalized models and by incorporating details accordingly. The Engelbrecht model provides a good example here. With this model, insights in the mathematically possible interactions between the electrical and mechanical manifestations of the nerve impulse can be provided based on spatiotemporal relations between them, which requires only the phenomenological and mathematical description of these manifestations. However, since these phenomenological descriptions cannot be interpreted in terms of their physical basis, this model cannot provide an accurate and complete representation of nerve impulse propagation.

## AUTHOR CONTRIBUTIONS

LH wrote the article. LH, HR, and BD discussed several versions of the article. In these discussions, HR and BD provided feedback and made additional contributions, both contributed equally to the article. All authors approved the manuscript for publication.

#### ACKNOWLEDGMENTS

We would like to thank Prof. Thomas Heimburg for explaining the Heimburg-Jackson model in more detail. In addition, we are greatly indebted to an insightful blog written by Dr. Shamit Shrivastava for understanding the thermodynamic principles underlying the modeling of the nerve impulse, this blog is entitled "Applying Einstein's Scientific Philosophy to Biological Physics: a revolution waiting to happen", published online on Medium on February 20, 2016, https://medium.com/@Shamits/applying-einstein-s-scientificphilosophy-to-biological-physics-a-revolution-waiting-to-



**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 © 2019 Holland, de Regt and Drukarch. 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(s) 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.

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Matthew N. Rasband, Baylor College of Medicine, United States Juan José Garrido, Spanish National Research Council (CSIC), Spain Hiroshi Kuba, Nagoya University, Japan

#### \*Correspondence:

Catherine Faivre-Sarrailh catherine.sarrailh@univ-amu.fr

#### †Present address:

Giulia Bonetto, Wellcome – MRC Cambridge Stem Cell Institute, University of Cambridge, Cambridge, United Kingdom Bruno Hivert, CNRS UMR7289, Institut de Neurosciences de la Timone, Aix-Marseille Université, Marseille, France

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 22 February 2019 Accepted: 02 May 2019 Published: 16 May 2019

#### Citation:

Bonetto G, Hivert B, Goutebroze L, Karagogeos D, Crépel V and Faivre-Sarrailh C (2019) Selective Axonal Expression of the Kv1 Channel Complex in Pre-myelinated GABAergic Hippocampal Neurons. Front. Cell. Neurosci. 13:222. doi: 10.3389/fncel.2019.00222

# Selective Axonal Expression of the Kv1 Channel Complex in Pre-myelinated GABAergic Hippocampal Neurons

Giulia Bonetto<sup>1</sup>† , Bruno Hivert<sup>1</sup>† , Laurence Goutebroze<sup>2</sup> , Domna Karagogeos<sup>3</sup> , Valérie Crépel<sup>1</sup> and Catherine Faivre-Sarrailh<sup>1</sup> \*

1 INSERM UMR1249, Institut de Neurobiologie de la Méditerranée, Aix-Marseille Université, Marseille, France, <sup>2</sup> INSERM UMR-S 1270, Institut du Fer à Moulin, Faculté des Sciences et Ingénierie, Sorbonne Université, Paris, France, <sup>3</sup> Department of Basic Sciences, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology, University of Crete Medical School – University of Crete, Heraklion, Greece

In myelinated fibers, the voltage-gated sodium channels Nav1 are concentrated at the nodal gap to ensure the saltatory propagation of action potentials. The voltage-gated potassium channels Kv1 are segregated at the juxtaparanodes under the compact myelin sheath and may stabilize axonal conduction. It has been recently reported that hippocampal GABAergic neurons display high density of Nav1 channels remarkably in clusters along the axon before myelination (Freeman et al., 2015). In inhibitory neurons, the Nav1 channels are trapped by the ankyrinG scaffold at the axon initial segment (AIS) as observed in pyramidal and granule neurons, but are also forming "pre-nodes," which may accelerate conduction velocity in pre-myelinated axons. However, the distribution of the Kv1 channels along the pre-myelinated inhibitory axons is still unknown. In the present study, we show that two subtypes of hippocampal GABAergic neurons, namely the somatostatin and parvalbumin positive cells, display a selective high expression of Kv1 channels at the AIS and all along the unmyelinated axons. These inhibitory axons are also highly enriched in molecules belonging to the juxtaparanodal Kv1 complex, including the cell adhesion molecules (CAMs) TAG-1, Caspr2, and ADAM22 and the scaffolding protein 4.1B. Here, taking advantage of hippocampal cultures from 4.1B and TAG-1 knock-out mice, we observed that 4.1B is required for the proper positioning of Caspr2 and TAG-1 along the distal axon, and that TAG-1 deficiency induces alterations in the axonal distribution of Caspr2. However, the axonal expression of Kv1 channels and clustering of ankyrinG were not modified. In conclusion, this study allowed the analysis of the hierarchy between channels, CAMs and scaffolding proteins for their expression along hippocampal inhibitory axons before myelination. The early steps of channel compartmentalization preceding myelination may be crucial for stabilizing nerve impulses switching from a continuous to saltatory conduction during network development.

Keywords: Caspr2, TAG-1, protein 4.1B, juxtaparanodes, parvalbumin, somatostatin, interneuron

## INTRODUCTION

fncel-13-00222 May 15, 2019 Time: 16:34 # 2

In myelinated fibers, ion channels are targeted to precise sub-cellular compartments at the axon initial segment (AIS) and nodes of Ranvier contributing to safe action potential propagation. At the node of Ranvier, the voltage-gated Na<sup>+</sup> (Nav) channels are enriched at the nodal gap to ensure saltatory conduction, while the K<sup>+</sup> channels are localized at nodes and juxtaparanodes to secure spike propagation (Rasband, 1998; Devaux and Gow, 2008). On both sides of the node, the paranodal junctions restrict the lateral diffusion of Na<sup>+</sup> and K<sup>+</sup> channels and preclude current leakage across the paranodes (Salzer, 2008). The segregation of ion channels at the nodes of Ranvier is induced by contacts with the myelinating glial cells (Ching et al., 1999). Moreover, the localization of the Na<sup>+</sup> and K<sup>+</sup> channels is strongly dependent on cell adhesion molecules (CAMs) at nodes, paranodes, and juxtaparanodal regions of myelinated axons (Eshed-Eisenbach and Peles, 2013). Specifically, the nodal concentration of Na<sup>+</sup> channels depends on the interactions between the axonal CAM neurofascin186 and extracellular matrix proteins (Sherman et al., 2005; Feinberg et al., 2010). Neurofascin186 clustering recruits the scaffolding proteins ankyrinG and ßIV spectrin which in turn mediate the sequestration of Nav channels. In addition, the lateral diffusion of nodal Na<sup>+</sup> channels is restricted by the axo-glial junctions at paranodes, which are formed by the axonal proteins Caspr/contactin and the glial neurofascin155 (Bhat et al., 2001; Charles et al., 2002).

The trapping of voltage-gated K<sup>+</sup> (Kv) Kv1.1/Kv1.2 channels at the juxtaparanodal regions depends on axo–glial interactions mediated by CAMs including TAG-1/contactin2/CNTN2 and Caspr2/CNTNAP2 (Poliak et al., 2001, 2003; Traka et al., 2003; Horresh et al., 2008). Within the axonal membrane, TAG-1 forms a cis-complex with Caspr2, which allows the arrangement of a ternary complex with the glial-secreted form of TAG-1 (Tzimourakas et al., 2007; Savvaki et al., 2010). Disruption of either Caspr2 or TAG-1 in knock-out (KO) mice prevents the proper clustering of Kv1 channels at juxtaparanodes (Poliak et al., 2003; Traka et al., 2003). Moreover, TAG-1-deficient animals show alteration of myelinated axon conduction in the corpus callosum (Zoupi et al., 2018), as well as behavioral deficits and defects in gating and motor coordination (Savvaki et al., 2008). Similarly, the loss of Caspr2 is associated with defects in the propagation of action potentials along myelinated axons in the corpus callosum, with a slow-down of the repolarisation phase (Scott et al., 2017).

A number of scaffolding proteins, including band 4.1B, αII, and ßII spectrin are expressed at paranodes and juxtaparanodes (Denisenko-Nehrbass et al., 2003; Ogawa et al., 2006; Zhang et al., 2013). In 4.1B-null mice the accumulation of TAG-1, Caspr2, and Kv1 at juxtaparanodes is altered, indicating the crucial role of this protein in the formation of the juxtaparanodal domain (Horresh et al., 2010; Buttermore et al., 2011; Cifuentes-Diaz et al., 2011; Einheber et al., 2013). A dynamic and precise subcompartmentalization of Kv1 channels that may help to regulate the conduction occurs in developing myelinated axons (Vabnick et al., 1999). Precisely, Kv1 channels and Caspr2 are first enriched at paranodes and progressively restricted to juxtaparanodes, while they could be seen transiently trapped between heminodes and at the newly formed nodal zone. In contrast, the distribution of the scaffolding protein 4.1B is restricted to internodes and preferentially co-localized with Caspr at paranodes (Hivert et al., 2016). The transient localization of Kv1 channels at nodes and paranodes may be directly involved in speeding repolarisation to allow trains of action potentials (Vabnick et al., 1999).

In inhibitory neurons, the myelination processes as well as the mechanisms leading to the segregation of ion channels at the nodes of Ranvier have been poorly investigated. It has been recently reported that pre-myelinated hippocampal GABAergic neurons, including parvalbumin (PV) and somatostatin (SST) cells, display high density of Nav1 channels associated with ankyrinG in clusters (the so-called "pre-nodes") along the axon (Freeman et al., 2015). Adhesive contact with ensheathing myelinating cells is a prerequisite for the nodal trapping of Na<sup>+</sup> channels in pyramidal neurons whereas pre-nodal clusters can be selectively induced in GABAergic neurons by oligodendroglial secreted factors. Interestingly, the presence of Nav1 clusters is correlated with an acceleration of conduction in pre-myelinated inhibitory axons (Freeman et al., 2015).

In the present study, we examine the distribution of the Kv1 complex in hippocampal pre-myelinated inhibitory neurons. We show that GABAergic neurons, namely the PV and SST cells, selectively display high concentration of Kv1 channels all along their axon and the associated molecules, TAG-1, Caspr2, ADAM22, and protein 4.1B. Furthermore, we demonstrate that in these pre-myelinated inhibitory neurons, TAG-1 is required for the proper distribution of Caspr2, while 4.1B is necessary for the correct localization of both Caspr2 and TAG-1. Interestingly, we found that TAG-1 expression in vivo is constrained to specific CA1 hippocampal layers; it is selective to the SST cells in the stratum oriens and the PV cells in the stratum pyramidale and may be possibly related to a pre-myelinated phenotype. The specific expression of CAMs associated with the Kv1 channels in the GABAergic neurons may help to secure conduction during network development.

## MATERIALS AND METHODS

#### Animals

The care and use of rats and mice in all experiments were carried out according to the European and Institutional guidelines for the care and use of laboratory animals and approved by the local authority (laboratory's agreement number D13-055-8, Préfecture des Bouches du Rhône). The following rat and mouse strains were used in this study: Wistar rats and C57bl/6 mice (Janvier Breeding Center), Tag-1 KO mice (Traka et al., 2003), and 4.1B KO mice (Cifuentes-Diaz et al., 2011).

## Cell Culture

Primary mixed hippocampal cell cultures were prepared from embryonic day 18 Wistar rats. Hippocampi were collected in Hanks' balanced salt solution, dissociated with trypsin and plated at a density of 1.2 10<sup>5</sup> cells/cm<sup>2</sup> on poly-L-lysine (Sigma-Aldrich,

Merck) coated coverslips. Hippocampal neurons were cultured in Neurobasal supplemented with 2% B-27, 1% penicillinstreptomycin and 0.3% glutamine in a humidified atmosphere containing 5% CO2 at 37◦C. The mixed hippocampal cultures were maintained for 3–4 weeks in vitro and contained astrocytes and oligodendrocytes. Unless specified, all culture reagents were purchased from Gibco, Thermo Fisher Scientific. Once a week half of the culture medium was replenished. Hippocampal cell cultures were prepared from embryonic day 16 wild type, Tag-1 KO (Traka et al., 2003) or 4.1B KO mice (Cifuentes-Diaz et al., 2011) using the same protocol. At least, three different hippocampal cell cultures were performed from wild type and KO mice and processed in parallel on the same days for immunofluorescence staining.

#### Antibodies and Immunofluorescence Staining

The following primary antibodies were used: rabbit antiserum against protein 4.1B (Cifuentes-Diaz et al., 2011), rabbit anti-TAG-1 TG3 (Buttiglione et al., 1998), and rabbit anti-ankyrinG, a gift from Dr. Gisèle Alcaraz. Human anti-Caspr2 antiserum was previously described (Pinatel et al., 2015). Mouse antipanNav mAb (clone K58/35) was purchased from Sigma, chicken anti-MAP2 antibody (ab5392) and rat anti-MBP mAb (ab7349) from Abcam, rabbit anti-Prox1 antibody (ab5475) from Millipore, goat anti-PV antibody (PVG-214) from Swant, goat anti-SST mAb (sc55565) from Santa-Cruz. Mouse anti-Kv1.1 (clone K20/78), anti-Kv1.2 (clone K14/16), anti-Kv1.4 (clone K13/31), anti-ADAM22 (clone N46/30), and anti-ankyrinG (clone N106/36) mAbs were obtained from NeuroMab (UC Davis/NIH NeuroMab Facility). Mouse anti-TAG-1 (1C12) and anti-GAD65 (GAD6) mAbs were from Developmental Studies Hybridoma Bank. AlexaFluor-405, -488, -568 and - 647-conjugated secondary antibodies were purchased from Molecular Probes.

Live immunostaining was performed using mouse anti-TAG-1 1C12 (1:2000), rabbit anti-TAG-1 TG3 (1:400), or human anti-Caspr2 (1:400) antibodies for 30 min and with secondary antibodies (1:800) for 30 min diluted in culture medium at room temperature. Cells were fixed with 1 or 4% paraformaldehyde in PBS for 10 min and permeabilized with 0.1% Triton-X100 for 10 min. Immunofluorescence staining on fixed neurons was performed using rabbit anti-ankyrinG (1:400), rabbit anti-4.1B (1:2000), rabbit anti-prox1 (1:2000), chicken anti-MAP2 (1:10,000) antibodies, rat anti-MBP mAb (1:200), mouse anti-panNav (1:500), anti-Kv1.1, anti-Kv1.2, anti-Kv1.4, anti-ADAM22, anti-ankyrinG (1:100) mAbs for 60 min and with AlexaFluor-conjugated secondary antibodies for 30 min diluted in PBS with 3% bovin serum albumin. Immunostaining with goat anti-PV (1:500) or mouse anti-SST (1:200) antibodies was performed overnight at 4◦C.

#### In vivo Study and Immunohistochemistry

For the in vivo study, P21 (n = 3) rats were deeply anesthetized with a mix of ketamine–xylazine (Vetoquinol) and then transcardially perfused with PBS followed by 4% paraformaldehyde in PBS. Brains were removed and placed in the same fixative for 30 min, then cryoprotected by infiltration in 30% sucrose overnight, embedded in 7.5% gelatin-15% sucrose, and immediately frozen in a dry ice-isopentane bath. Thirty micron-thick cryostat sections were mounted on SuperfrostVR Plus microscope slides (Thermo Fisher Scientific), permeabilized by immersion in ice-cold acetone at −20◦C for 10 min, blocked for 1 h in 5% bovine serum albumin containing 0.5% Triton X-100 in PBS, and incubated overnight at 4◦C with combinations of the following primary antibodies: goat anti-PV (1:500), goat anti-SST (1:500), mouse anti-TAG-1 (1C12, 1:2000), human anti-Caspr2 (1:200), mouse anti-Kv1.2 (1:100), rabbit anti-ankyrinG (1:400), rat anti-MBP (1:200). Slides were then washed and incubated with the appropriate AlexaFluor-conjugated secondary antibodies (1:800) for 2 h. Slides were covered with Vectashield mounting medium (Vector Laboratory), which contains DAPI to visualize cell nuclei.

## Image Acquisition and Statistical Analysis

Image acquisition was performed on a Zeiss laser-scanning microscope LSM780 equipped with 63× 1.32 NA oil-immersion objective for cell culture and 20× or 63× objectives for hippocampal slice imaging. Images of AlexaFluor-stained cells were obtained using the 488 nm band of an Argon laser and the 405, 568, and 647 nm bands of a solid-state laser for excitation. Fluorescence images were collected automatically with an average of two-frame scans at airy 1. Maximum intensity projection of images and plot profiles of immunofluorescence intensity (10 pixels width) were carried out using ImageJ software (NIH). Images are single confocal sections unless the number of z-steps is indicated.

The percentage of SST and PV neurons positive for TAG-1, Caspr2, and Kv1.2 was determined by examining at least 50 neurons on 2 coverslips per condition (wild type, TAG-1 KO and 4.1B KO mice). 4-z step confocal sections (410 nm) were acquired with the same settings (laser intensity and gain) and maximum intensity projections were generated before analysis. Results were expressed as mean ± SEM of at least three independent experiments. Statistical analyses were performed using the GraphPad Prism software. The data normal distribution was tested using d'Agostino and Pearson's test. The Student's paired t-test or the one-way analysis of variance (ANOVA), followed by Dunnett post hoc test was performed.

## RESULTS

### The Kv1.2 Subunits Are Highly Expressed Along Inhibitory Axons in Hippocampal Cultures

We examined the distribution of the Kv1 channels in hippocampal cell culture at Day in vitro DIV21, a representative day before myelination onset. It has been reported that Kv1.2 is concentrated at the AIS in subpopulations of hippocampal neurons after DIV10 (Ogawa et al., 2008;

Sanchez-Ponce et al., 2012). Here, we showed that Kv1.2 immunostaining was restricted at the AIS in some neurons (**Figures 1A,B**, yellow arrows). Kv1.2 was detected at the AIS of granule cells identified using immunostaining for the transcription factor prox1 (**Figure 1D**, yellow arrow). Strikingly, the Kv1.2 channels were also strongly expressed along the axon in some neurons identified as GABAergic neurons using immunostaining for GAD65 (**Figures 1A,C**, red arrows). We showed that these neurons were either PV<sup>+</sup> or SST<sup>+</sup> interneurons as illustrated for PV<sup>+</sup> neurons in **Figure 1E**. The inhibitory axons displayed distal clusters of Nav channels and ankyrinG (**Figures 1F,G**, red arrows) as it has been described specifically in pre-myelinated GABAergic neurons in hippocampal cultures (Freeman et al., 2015). We analyzed more precisely the distribution of Kv1.2 relatively to the ankyrinG clusters along the inhibitory axons at DIV21. As shown in **Figure 1G**, immunostaining for Kv1.2 after fixation and permeabilization indicated that these channels were enriched at the AIS co-localized with ankyrinG and homogenously distributed along the axon. Plot profile analysis illustrates that Kv1.2 was concentrated at the AIS together with ankyrinG and uniformly present along the axon irrespectively to peaks corresponding to ankyrinG clusters (**Figure 1H**, red arrows).

We noticed that the GABAergic neurons showing Kv1.2 distribution all along their axon also exhibited high expression of the Kv1.2 channel at the level of their soma by comparison with excitatory neurons that displayed AIS-restricted expression of Kv1.2 (**Figure 1A**). We estimated the immunofluorescence intensity of Kv1.2 in the soma of GAD65-positive neurons (n = 30) relatively to those of other neurons in the same area (n = 93) and observed that it was increased by 33 ± 4%. These data suggest that the axonal distribution of Kv1.2 channels may be correlated with the level of expression in the cell body.

Kv1 channels exist as homomeric and heteromeric complexes in neurons and distinct Kv1 channels could be selectively addressed at the axonal membrane based on their subunit composition (Jenkins et al., 2011). In addition to Kv1.2, the Kv1.1, and Kv1.4 subunits have been reported to be concentrated at the AIS of cultured hippocampal neurons (Ogawa et al., 2008). Indeed, we observed that Kv1.1 was expressed at the AIS of excitatory neurons (**Figure 2A**, yellow arrows). However, Kv1.1 was weakly expressed at the AIS and along the axons of GAD65-positive inhibitory neurons by comparison with Kv1.2 (**Figures 2A,B**) whereas it was mainly detected as vesicles in the somato-dendritic compartment of these cells (**Figure 2A**). The Kv1.4 subunit was colocalized with ankyrinG at the AIS of excitatory neurons (**Figures 2C,D**, yellow arrows), but very faintly expressed in GAD65- or SST-positive neurons (**Figures 2C,D**, red arrows). Altogether, these results suggest that Kv1 channels expressed in inhibitory axons in hippocampal cell cultures are composed mainly of Kv1.2 subunits.

Next, we asked whether the high level of Kv1.2 along inhibitory axons may be correlated with myelination or occurred before myelination onset using immunostaining for MBP as a marker of myelinating oligodendrocytes (**Figure 3A**). Mixed hippocampal cultures were performed in standard conditions but with plating at high density. These cultures contained glial cells, including few oligodendrocytes identified using immunostaining for the myelin basic protein (MBP) (**Figure 3**, red). However, at DIV 21, only very few neurons presenting high level of Kv1.2 along their axon were myelinated and in this case Kv1.2 only formed clusters along the myelinated segments (**Figure 3B**, green arrows in inset).

## TAG-1, Caspr2, ADAM22, and Protein 4.1B Are Selectively Expressed Along Inhibitory Axons in Cultured Hippocampal Neurons

We investigated whether the cell adhesion and scaffolding molecules associated with the Kv1 channels at the juxtaparanodes in myelinated fibers may be also selectively expressed by inhibitory neurons. We previously reported that Caspr2 is preferentially expressed by GABAergic neurons in hippocampal cell cultures. Using live immunostaining with anti-Caspr2 antibodies from patients affected by autoimmune encephalitis, we have shown that Caspr2 is detected all along the axolemma including at the presynaptic terminals of inhibitory neurons (Pinatel et al., 2015). Here, we investigated the cell-type specific expression of TAG-1, which interacts both in cis and in trans with Caspr2 and may be either cis-associated with Caspr2 along the inhibitory axons or trans-interacting at the postsynapse with presynaptic Caspr2 (Traka et al., 2003; Savvaki et al., 2010; Pinatel et al., 2015). Live immunostaining was performed using mouse anti-TAG-1 1C12 mAb at DIV21. As observed for Kv1.2 channels, TAG-1 was strongly expressed along the axon of some neurons, which displayed ankyrinG at the AIS as well as organized in regularly spaced clusters along the entire axonal length (**Figures 4A,B**, red arrowheads). Surface double-immunostaining was performed using anti-TAG-1 mAb and human anti-Caspr2 antibodies, and indicated that the two CAMs were co-expressed along the same axons (**Figure 4B**). We hypothesized that these axons may belong to inhibitory neurons since exhibiting axonal clusters of ankyrinG. This was confirmed using doubleimmunostaining for TAG-1 and GAD65 (**Figure 4C**). In addition, TAG-1 and Caspr2 were co-localized at the inhibitory pre-synaptic terminals surrounding the soma of pyramidal cells (**Supplementary Figure S1**). Next, using immunostaining with antibodies directed against SST and PV, we determined that both subtypes of inhibitory cells displayed high level of expression of TAG-1 along their axons (**Figures 4F,G**). As observed for Kv1.2, we noticed that the axonal distribution of TAG-1 along inhibitory axons also occurred before myelination (**Figure 3C**).

In addition to be highly expressed along inhibitory axons, TAG-1 was also expressed in a subpopulation of neurons at the AIS (approximately 30%) (**Figures 4A,D**, yellow arrows). In contrast to what has been observed for Kv1.2 (**Figure 1D**), the granule cells identified with the marker prox1 were negative for TAG-1 (**Figure 4E**).

We then investigated more precisely the relative distribution of TAG-1 and Caspr2 along inhibitory axons at DIV21 and observed that the two CAMs were strongly co-localized (**Figure 5B**). However, only TAG-1 was enriched at the AIS as

neurons (yellow arrows in panel A,B) or distributed all along the axon in a subpopulation of neurons (red arrows in panel A) identified as GABAergic neurons using GAD65 labeling (C, red). (D) Granule cells positive for prox1 (blue asterisk) display Kv1.2 localized at the AIS. (E,F) GABAergic neurons including PV<sup>+</sup> neurons (E, blue) exhibit high expression of Kv1.2 all along their axon and clusters of Na<sup>+</sup> channels labeled using anti-panNav mAb (F, red). (G,H) Fluorescence intensity profiles were generated starting from the AIS (G, white arrows) following the axon. The axonal clusters of ankyrinG are indicated with red arrows (G,H). Kv1.2 is co-localized with ankyrinG at the AIS, but do not co-cluster with ankyrinG along the axon. Note that Kv1.2 is restricted to the AIS (G, yellow arrow) in a neighboring neuron (asterisk). Scale bar: 50 µm in panel (A); 20 µm in panel (B–G).

FIGURE 2 | Expression of Kv1 subunits in cultured hippocampal neurons. Cultured hippocampal neurons at DIV21 were immunostained for Kv1.1 (A), Kv1.2 (B), or Kv1.4 (C,D). Double-staining for GAD65 (A–C, green) or SST (D, blue) and ankyrinG (A–C, blue; D, red). Kv1.1, Kv1.2, and Kv1.4 are expressed at the AIS of excitatory neurons co-localized with ankyrinG (yellow arrows) and negative for SST or GAD65. (A) Kv1.1 is faintly detected along the axon (red arrows) and is present in intracellular vesicles in inhibitory neurons. (C,D) Kv1.4 is not detected along the inhibitory axons (red arrows). The cell bodies of SST- and GAD65-positive neurons are indicated with red asterisks. Scale bar: 20 µm.

illustrated by the plot profile (**Figures 5A,B,E,F**). Since protein 4.1B is known to bind the cytoplasmic tail of Caspr2 and is required for the recruitment of the juxtaparanodal complex in myelinated fibers, we also analyzed its distribution and found that it was present along the distal axon and faintly expressed at the AIS of inhibitory neurons (**Figures 5C,G**). Similarly to TAG-1 and Caspr2, ADAM22, another CAM associated with the Kv1 complex at the AIS (Ogawa et al., 2008; Hivert et al., 2019) was found to be preferentially expressed all along inhibitory axons in mature cultured hippocampal neurons (**Figure 5D**). ADAM22 appeared to be enriched at the AIS of inhibitory neurons, in a manner similar to TAG-1 (**Figure 5D**, red arrows).

## Interdependent Expression of Caspr2, TAG-1, and Protein 4.1B in Axons of SST and PV Neurons

To determine whether the proteins of the Kv1 complex are interdependent for their enrichment along hippocampal inhibitory axons, we analyzed their expression taking advantage

FIGURE 3 | Kv1.2 and TAG-1 are highly expressed along axons before myelination. Cultured hippocampal neurons at DIV21 were immunostained for Kv1.2 (A,B, green) or TAG-1 (C, green), MBP (red) as a marker of oligodendrocytes and ankyrinG (blue). (A,C) A number of unmyelinated neurons are labeled for Kv1.2 or TAG-1 all along their axons. (B) Few neurons are myelinated and show high density of Kv1.2 close to ankyrinG clusters under myelinated segments (green arrows in the inset). Scale bar: 20 µm; 10 inset µm.

of KO mice for TAG-1 or 4.1B protein. Hippocampal cell cultures from wild type, TAG-1 KO and 4.1B KO mouse embryos were performed in parallel on the same day. As expected, we observed the absence of immunostaining for TAG-1 or 4.1B in hippocampal neurons from TAG-1 or 4.1B KO mice, respectively, confirming the specificity of immunostaining in wild type neurons (**Figures 6F,G**, **7C**). Live immunostaining at DIV21 indicated that the cell surface expression of Caspr2 was strongly altered in the inhibitory neurons from either TAG-1 or 4.1B KO mice, as shown for SST<sup>+</sup> neurons (**Figures 6A–C**). Specifically, 92% of SST<sup>+</sup> neurons were positive for Caspr2 in the wild type, whereas only 64% or 48% of them expressed Caspr2 in the TAG-1 or 4.1B KO hippocampal cultures, respectively (**Figure 6D**). Similarly, only half of the PV<sup>+</sup> neurons expressed Caspr2 in the TAG-1 and 4.1B KO (46 and 42%, respectively) by comparison with the wild type cultures (82%, **Figure 6E**). These data indicate that TAG-1 and 4.1B proteins are necessary for the proper expression of Caspr2 in inhibitory neurons, suggesting that Caspr2 may be stabilized in a preformed complex along the axonal membrane before myelination.

Next, we analyzed the axonal surface expression of TAG-1 in hippocampal cultures from 4.1B KO mice (**Figure 7**). Remarkably, we observed that in some inhibitory neurons the protein was totally missing, whereas in other cells TAG-1 expression was restricted to the AIS as shown for SST<sup>+</sup> neurons (**Figure 7B**, red arrows). Precisely, TAG-1 expression was detected only at the AIS in 16.7% of the SST<sup>+</sup> neurons in the 4.1B KO versus 6% in wild type (**Figure 7D**). Likewise, TAG-1 was restricted at the AIS in 14.6% of the PV<sup>+</sup> neurons in 4.1B KO versus 2.7% in the wild-type (**Figure 7E**). Since the axonal expression of Caspr2 is altered in the absence of protein 4.1B, altogether these data suggest that the association of TAG-1 in complex with Caspr2 and 4.1B may modulate the distal distribution of the protein along the inhibitory axons.

## Kv1.2 Distribution Is Not Altered in Knock-Out Mice for TAG-1 or Protein 4.1B

The distribution of Kv1 channels at the juxtaparanodes is strongly altered in myelinated axons of the KO mice for TAG-1 or 4.1B (Traka et al., 2003; Cifuentes-Diaz et al., 2011; Hivert et al., 2016). It was therefore important to analyze whether the expression or distribution of Kv1.2 could be impaired at an early step in pre-myelinated GABAergic axons deficient for TAG-1 or 4.1B. We did not observe any difference in the expression of Kv1.2 either in SST<sup>+</sup> or PV<sup>+</sup> neurons deficient for TAG-1 or protein 4.1B, compared to the wild type situation as illustrated for SST<sup>+</sup> neurons (**Figures 8A–C**). Kv1.2 was expressed in approximately 90% of the SST<sup>+</sup> and PV<sup>+</sup> neurons in the cultures from wild type, TAG-1 or 4.1B KO mice at DIV21 (**Figures 8D,E**). Furthermore, the high expression of Kv1.2 channels was correlated with the presence of ankyrinG clusters both in the wild type and mutant mice (**Figures 8A–C**). All together, these results point toward a mechanism for recruiting Kv1 channels along premyelinated inhibitory axons, which is independent from TAG-1 and protein 4.1B.

#### In vivo Expression of the Cell Adhesion Molecules Associated With the Kv1 Channels in the Developing Hippocampus

To evaluate the physiological relevance of our observations in vitro, we further addressed whether GABAergic neurons may also selectively express the Kv1 complex proteins in the developing hippocampus. The onset of myelination of GABAergic neurons in the hippocampus was reported from P14 (Freeman et al., 2015). Using immunostaining on hippocampal tissue sections from rats at post-natal day 21 (P21), we analyzed the expression of TAG-1 in SST<sup>+</sup> and the PV<sup>+</sup> inhibitory neurons (**Figure 9**). We observed that the SST<sup>+</sup> neurons located in the stratum oriens of the CA1 region were positive for TAG-1 (42.1 ± 4.3%, n = 3) (**Figures 9A,C**). In contrast, SST<sup>+</sup> cells in other hippocampal regions, such as the hilus of the dentate gyrus, were negative for TAG-1 (**Figures 9A,D**). The PV<sup>+</sup> neurons expressed TAG-1 within the pyramidal layer (69.9 ± 8.3%, n = 3) (**Figures 9B,E**) while they were negative in other areas, such as the stratum lacunosum moleculare (**Figure 9F**). In addition, these subtypes of inhibitory neurons were negative for TAG-1 within the other hippocampal areas i.e., the CA3 and the dentate gyrus (**Figures 9A,B**). We showed that TAG-1 was enriched at the AIS of SST<sup>+</sup> cells proximal to the myelin segment immunostained for MBP (**Figure 9G**) and also localized at the AIS of PV<sup>+</sup> cells using double-staining for ankyrinG (**Figure 9H**).

Next, we analyzed the pattern of expression of Kv1.2 in the CA1 region of the hippocampus (**Figure 10**). We found that Kv1.2 was localized at the AIS of PV<sup>+</sup> cells in the pyramidal layer (**Figures 10A,A**0) and SST<sup>+</sup> cells in the stratum

panel (C–G).

pyramidale (**Figure 10C**) and oriens (**Figure 10B**), but distally as compared to ankyrinG (**Figure 10B**0). We observed that PV<sup>+</sup> cells in the pyramidal layer (**Figure 10D**) and SST<sup>+</sup> cells located in the stratum oriens (**Figure 10E**) were positive for both Caspr2 and Kv1.2.

Our results show that the Kv1 complex proteins are enriched in the GABAergic neurons of the CA1 hippocampal region in vivo. Both PV and SST inhibitory neurons specifically express Kv1.2, TAG-1, and Caspr2, similarly to our in vitro findings. Moreover, a layer-specific expression of TAG-1 can be observed for SST and PV neurons that may indicate a specialization of these cells associated with myelination.

#### DISCUSSION

The Kv1 channels play a prominent role in repolarising the axon after action potential initiation at the AIS and

FIGURE 5 | Subcellular distribution of TAG-1, Caspr2, protein 4.1B, and ADAM22 in cultured hippocampal neurons. Hippocampal neurons at DIV21 were labeled for TAG-1 (A), TAG-1 and Caspr2 (B), 4.1B (C), or TAG-1 and ADAM22 (D). Axons exhibiting clusters of ankyrinG were identified as inhibitory axons (A–D, red arrows). Immunolabelling for TAG-1 and Caspr2 was performed on live cells. (A,B) TAG-1 is enriched at the AIS whereas Caspr2 is evenly distributed along the axon. (C) Protein 4.1B is distributed along the axon and excluded from the AIS and ankyrinG clusters. (D) ADAM22 is enriched at the AIS and colocalized with TAG-1 all along the axon in neurons that display distal clusters of ankyrinG and is also detected at the AIS of other subtypes of neurons (yellow arrow). (E–G) Fluorescence intensity profiles were generated starting from the AIS (white arrows) following the axons in panel (A–C). The axonal clusters of ankyrinG are indicated with red arrows. TAG-1 is co-localized with ankyrinG at the AIS, but do not co-cluster with ankyrinG along the axon (E). Caspr2 and protein 4.1B are not enriched at the AIS (F,G). Scale bar: 20 µm.

anti-ankyrinG (green) and goat anti-SST (blue) antibodies. Axons of SST<sup>+</sup> cells are indicated with red arrows. The AIS of one SST-negative cell is indicated with a yellow arrow in panel (A). Maximum intensity of confocal images (4-z steps of 410 nm). (D,E) Quantification of the percentage of SST<sup>+</sup> (D) or PV<sup>+</sup> (E) neurons that were labeled for Caspr2. The percentage of neurons showing Caspr2 axonal staining is significantly reduced in cells from either TAG-1 or 4.1B KO mice. Mean ± SEM of three independent experiments. For each experiment, at least 50 neurons were analyzed. For the statistics, one-way ANOVA with post hoc Dunnett test was used. Comparison with wild type group: <sup>∗</sup>p < 0.05 and ∗∗p < 0.01. (F,G) Neurons from wild type (F) or 4.1B KO (G) mice immunostained using rabbit anti-4.1B (green), chicken anti-MAP2 (blue), and mouse anti-Kv1.2 (red) antibodies. Scale bar: 20 µm.

in regulating propagation at the juxtaparanodes (Trimmer, 2015). During myelination, these channels are progressively enriched at the juxtaparanodes and at early stages, when the paranodal junctions have not yet formed or stabilized, Kv1 transiently localizes at nodes and paranodes (Vabnick et al., 1999; Hivert et al., 2016) and may be directly involved in speeding repolarisation to allow trains of action potentials. The dynamic distribution and precise sub-compartmental profile of Kv1 is thought to play an essential role in the developing axons switching from a continuous to a saltatory mode of conduction. In the present study, we show that in hippocampal cell cultures, the Kv1.2 subunits are selectively expressed all along GABAergic axons including the AIS before myelination, together with clusters of Nav1 channels and ankyrinG. Inhibitory axons are also highly enriched in molecules originally identified as part of the Kv1 complex at the juxtaparanodal regions of myelinated fibers, including the CAMs TAG-1, Caspr2, and ADAM22, as well as the scaffolding protein 4.1B. Cultures from TAG-1- or protein 4.1B-deficient mice indicate that the expression of TAG-1, Caspr2 and protein 4.1B is interdependent whereas the distal distribution of the Kv1.2 subunits is maintained in the absence of TAG-1 or protein 4.1B. In vivo, only subsets of SST and PV GABAergic neurons are positive for TAG-1 in the juvenile rat hippocampus, including the SST cells in the stratum oriens and the PV neurons in the stratum pyramidale, which also express Kv1.2 channels. This accurate distribution of ion channels and associated molecules along pre-myelinated axons may be crucial to regulate firing during development.

## Axonal Distribution of the Kv1 Complex in Inhibitory Hippocampal Neurons

In myelinated axons, the proper distribution of the Nav1 and Kv1 channels is strongly dependent on CAMs at nodal,

paranodal, and juxtaparanodal regions. Specifically, a complex of TAG-1, Caspr2, and protein 4.1B mediates axo-glial contacts at juxtaparanodes and is required for Kv1 channel clustering (Poliak et al., 2003; Traka et al., 2003). However, TAG-1 and Caspr2 are dispensable for the trapping of the Kv1 channels at the AIS (Ogawa et al., 2008; Duflocq et al., 2011). Here, we observed that TAG-1 and ADAM22 are enriched at the AIS and expressed all along pre-myelinated inhibitory axons, whereas Caspr2 and protein 4.1B display a more distal distribution. Furthermore, taking advantage of KO mouse lines, we showed that Caspr2, TAG-1, and 4.1B are interdependent for their distribution along inhibitory axons. The expression of Caspr2 was strongly reduced along the inhibitory axons from TAG-1 or 4.1B KO hippocampal cultures. TAG-1 and protein 4.1B bind the ectodomain and the cytoplasmic tail of Caspr2, respectively, and may be required for its stabilization at the axonal membrane. We hypothesize that the association of Caspr2 with protein 4.1B may stabilize Caspr2 at the axolemma by inhibiting its internalization (Bel et al., 2009; Pinatel et al., 2017). Next, we observed that in contrast to Caspr2, the distal distribution of TAG-1 in inhibitory axons was reduced only in a small percentage of 4.1B-deficient neurons. We previously reported the level of TAG-1 is not altered in the brain of 4.1B KO mice (Cifuentes-Diaz et al., 2011). TAG-1 is trapped at the AIS independently of Caspr2 which is not enriched at that site. Our data suggest that TAG-1 may be associated with ADAM22 at the AIS and also along the axon. Indeed, we recently reported that TAG-1 can be associated with ADAM22 using co-immunoprecipitation experiments and that the two CAMs are sorted together in axonal transport vesicles (Hivert et al., 2019). However, the persistence of Kv1.2 subunits along the axons in TAG-1- and protein 4.1B-deficient cells reveals that the Caspr2/TAG-1/4.1B complex may be dispensable for the distal distribution of Kv1 channels. This indicates that the Kv1.2 tetramers which are axonally transported with their Kvß2 accessory subunits (Gu and Gu, 2010) are targeted to the axon independently from their associated CAMs. In the same way, the CAM neurofascin186, which is implicated in the initial nodal clustering of Nav1 channels in myelinated axons, is targeted at the axonal membrane through distinct mechanisms than the Nav1 channels (Zhang et al., 2012). In addition, neurofascin186 is not required for the clustering of pre-nodal complexes in pre-myelinated inhibitory neurons (Dr. Nathalie Sol-Foulon, personal communication). This early clustering of Nav1 channels linked with ankyrinG appears to be mediated by extracellular matrix proteins and soluble form of CAMs secreted by oligodendrocytes and it does not require the contact with the glial membrane. Our results indicate that this is unlikely to be the case for the clustering

of the Kv1 channels at the nodes since we observed that the Kv1 channels are enriched at the AIS and thereafter uniformly distributed along the pre-myelinated axon, with the clustering of Kv1 being only detected where the myelin segments contact the axon. Interestingly, such a contact-dependent clustering of Kv1 channels has also been reported using cocultures of hippocampal neurons with TAG-1 expressing HEK cells (Gu and Gu, 2011).

We further show that both the Kv1.1 and Kv1.2 subunits are expressed in GABAergic neurons whereas the Kv1.4 subunit is only localized at the AIS of excitatory neurons in hippocampal cell culture. However, Kv1.1 is faintly expressed along the inhibitory axons while it is strongly detected as intracellular vesicles. In this context, it is interesting to note that Kv1.4, which contains an ER export signal, has been shown to induce the cell surface targeting of Kv1.1 (Manganas and Trimmer, 2000; Lai and Jan, 2006; Jenkins et al., 2011). Therefore, these results suggest that Kv1 channels in inhibitory axons in hippocampal cell culture may mainly consist of Kv1.2 subunits. Importantly, the different composition of Kv1 tetramers allows distinct thresholds of channel activation (Bagchi et al., 2014).

#### In vivo Selective Expression of TAG-1 in Subtypes of GABAergic Neurons in the Hippocampus

Recent reports have highlighted the possibility that different subtypes of GABAergic neurons could be myelinated. Longrange projecting inhibitory neurons connecting hippocampus with extra-hippocampal areas are known to be myelinated (Jinno et al., 2007; Melzer et al., 2012). This is the case of SST neurons in the stratum oriens of CA1, which project to the subiculum and to the entorhinal cortex. Surprisingly, it has been recently reported that a substantial fraction of myelin, both in mouse and human neocortex, belongs to GABAergic inhibitory neurons, in particular fast-spiking PV interneurons (Micheva et al., 2016; Stedehouder et al., 2017). The PV cells in the CA1

FIGURE 9 | TAG-1 is expressed in subtypes of PV<sup>+</sup> and SST<sup>+</sup> inhibitory neurons in the hippocampus. (A,B) Coronal hippocampal cryosections from postnatal day 21 (P21) rat at low magnification, stained for the nuclear marker DAPI, TAG-1 (green) and SST (A) or PV (B). The indicated hippocampal areas, i.e., the stratum oriens (Or), the pyramidal layer (Pyr), the stratum lacunosum-moleculare (L-M) and the hilus, are shown at high magnification in panel (C–F). (C–F) Coronal hippocampal cryosections from P21 rat labeled for TAG-1 (green), SST (red, C,D) or PV (red, E,F), and DAPI. TAG-1 is selectively expressed by SST<sup>+</sup> and PV<sup>+</sup> inhibitory neurons in specific layers of the CA1 hippocampus, the stratum oriens for SST<sup>+</sup> neurons (C and yellow arrow in panel A) and the pyramidal layer for PV<sup>+</sup> cells (E and yellow arrow in panel B). TAG-1 is not expressed in other areas of the hippocampus, such as in the SST<sup>+</sup> cells in the hilus of the dentate gyrus (D and red arrow in panel A) or the PV<sup>+</sup> cells in the stratum lacunosum-moleculare (F) or CA3 pyramidal layer (red arrow in panel B). (G,H) Sagittal hippocampal cryosections from P21 rat labeled for SST, TAG-1, and MBP as a marker of myelin (G) or PV, TAG-1, and ankyrinG (H). TAG-1 is localized at the AIS (white arrows) in both SST<sup>+</sup> and PV<sup>+</sup> inhibitory neurons in the CA1 hippocampal region. Note that the SST<sup>+</sup> neuron positive for TAG-1 is myelinated. Wide-field (A,B) and confocal (C–H) microscopy images. Maximum intensity of 6-z steps of 830 nm (C–F) or 3-z steps of 1.38 µm (G) or 1 µm (H). Scale bar: 80 µm in panel (A,B); 50 µm in panel (C–F); 15 µm in panel (G,H).

P21 rat labeled for PV (A, blue) or SST (B,C, blue), ankyrinG (red) or Caspr2 (red) and Kv1.2 (green). (A,A0) Kv1.2 is detected at the AIS of a PV<sup>+</sup> cell in the stratum pyramidale (Pyr). (B–C) Kv1.2 is localized at the AIS of SST<sup>+</sup> neurons in the stratum oriens (B,B0) and stratum pyramidale (C). AIS are indicated with arrows. Note that Kv1.2 is distributed more distally than ankyrinG along the axon (B0). (D,E) Caspr2 and Kv1.2 are co-expressed in PV<sup>+</sup> cells of the stratum pyramidale (D) and SST<sup>+</sup> cells in the stratum oriens (E). Single confocal section (A–C) and maximum intensity of 5-z steps of 1.31 µm (insets in panel A0,B0) or 4-z steps of 830 nm (D,E). Scale bar: 15 µm.

stratum pyramidale of hippocampus have been described to be frequently myelinated at 8–12 weeks of age, mainly on the proximal axonal segments, independently of their morphological subtypes (i.e., basket or bi-stratified) (Stedehouder et al., 2017). PV interneurons are high energy demanding cells, for which it is logical to think that myelin may provide axonal metabolic

support (Kann et al., 2014; Krasnow and Attwell, 2016). Our results indicate that TAG-1 is exclusively expressed by some subtypes of GABAergic neurons in the rodent hippocampus, namely the PV cells of the pyramidal layer and the SST neurons of the stratum oriens in 3-week old rats. It remains to be precisely determined whether this selective expression of TAG-1 as a juxtaparanodal component may be associated with the myelinated fate of both local PV interneurons in the stratum pyramidale and long-range projecting SST neurons of the stratum oriens. Supporting this possibility, we observed that TAG-1 is enriched at the AIS of some SST<sup>+</sup> cells of the stratum oriens, proximal to myelin segments.

The inhibitory axons of the PV and SST cells display prenodal clusters of Nav1 channels, which have been shown to promote acceleration of conduction in pre-myelinated axons as analyzed in cultured hippocampal neurons (Freeman et al., 2015). The presence of Nav1 clusters along pre-myelinated PV interneurons as observed in vitro and also in vivo (Freeman et al., 2015) may be related with the results of Hu and Jonas (2014), which showed a gradual increase of Na<sup>+</sup> conductance in the distal axon of PV interneurons. The authors suggest that a high density of Na<sup>+</sup> channels could be necessary for ensuring both speed of propagation and fast-spiking action potentials in unmyelinated axons. In addition, it has been shown that Kv1.1 channels localized at the AIS dampen excitability and prevent high frequency discharge at normal subthreshold levels in fastspiking GABAergic cortical neurons (Goldberg et al., 2008). The Kv1.1 subunit is co-localized with ankyrinG at the AIS of PV basket cells in the hippocampus in vivo (Campanac et al., 2013). Here, we observed that the Kv1.2 subunit and TAG-1 are expressed at the AIS of both in PV and SST cells in the CA1 region of the hippocampus. Our data show the expression of a high density of Kv1 channels associated with CAMs occurring along pre-myelinated axons of subtypes of PV interneurons during development. With this respect, it will be important to analyze the physiological role of the high axonal content of the Kv1 complex in PV interneurons before myelination or in demyelinated pathological conditions.

#### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and/or the **Supplementary Files**.

#### REFERENCES


#### ETHICS STATEMENT

This study was carried out in accordance with the recommendations of the European and Institutional guidelines for the care and use of laboratory animals and approved by the local authority (laboratory's agreement number D13-055-8, Préfecture des Bouches du Rhône).

#### AUTHOR CONTRIBUTIONS

GB conceived and performed the experiments, analyzed the data, and wrote the manuscript. BH conceived and performed the experiments and analyzed the data. LG and DK provided the reagents and KO mice and discussed the data. VC discussed the data and provided the financial support. CF-S conceived and performed the experiments, analyzed the data, wrote the manuscript, provided the financial support, and supervised the study.

#### FUNDING

This work was supported by the Association pour la Recherche sur la Sclérose en Plaques (ARSEP) to CF-S and DK. GB is a postdoctoral fellow with the financial support of ARSEP. The project funded was entitled "Assembly of the juxtaparanodal complex under normal and pathological conditions."

#### ACKNOWLEDGMENTS

We are grateful to Drs. Oussama El Far, Eric Di Pasquale, Nathalie Sol-Foulon, and Agnès Baude for their helpful discussions. We thank the University of California, Davis/National Institutes of Health NeuroMab Facility and Developmental Studies Hybridoma Bank of the University of Iowa.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00222/full#supplementary-material

axons requires neurexin IV/Caspr/Paranodin. Neuron 30, 369–383. doi: 10. 1016/s0896-6273(01)00294-x


balance in hippocampal circuits. Neuron 77, 712–722. doi: 10.1016/j.neuron. 2012.12.020



**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 © 2019 Bonetto, Hivert, Goutebroze, Karagogeos, Crépel and Faivre-Sarrailh. 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(s) 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.

# Modulation of Ion Channels in the Axon: Mechanisms and Function

Kenneth J. Burke Jr. and Kevin J. Bender\*

Neuroscience Graduate Program and Department of Neurology, Kavli Institute for Fundamental Neuroscience, Weill Institute for Neurosciences, University of California, San Francisco, San Francisco, CA, United States

The axon is responsible for integrating synaptic signals, generating action potentials (APs), propagating those APs to downstream synapses and converting them into patterns of neurotransmitter vesicle release. This process is mediated by a rich assortment of voltage-gated ion channels whose function can be affected on short and long time scales by activity. Moreover, neuromodulators control the activity of these proteins through G-protein coupled receptor signaling cascades. Here, we review cellular mechanisms and signaling pathways involved in axonal ion channel modulation and examine how changes to ion channel function affect AP initiation, AP propagation, and the release of neurotransmitter. We then examine how these mechanisms could modulate synaptic function by focusing on three key features of synaptic information transmission: synaptic strength, synaptic variability, and short-term plasticity. Viewing these cellular mechanisms of neuromodulation from a functional perspective may assist

#### Edited by:

Dominique Debanne, INSERM U1072 Unité de Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Maarten H. P. Kole, Netherlands Institute for Neuroscience (KNAW), Netherlands Dmitri A. Rusakov, University College London, United Kingdom

> \*Correspondence: Kevin J. Bender kevin.bender@ucsf.edu

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

> Received: 01 March 2019 Accepted: 01 May 2019 Published: 17 May 2019

#### Citation:

Burke KJ Jr and Bender KJ (2019) Modulation of Ion Channels in the Axon: Mechanisms and Function. Front. Cell. Neurosci. 13:221. doi: 10.3389/fncel.2019.00221 in extending these findings to theories of neural circuit function and its neuromodulation.

Keywords: presynaptic, action potential, GPCR, modulation, neurotransmission

## INTRODUCTION

Neuromodulators exert powerful control over both neuronal circuit activity and animal behavior throughout the brain (Marder, 2012; Nadim and Bucher, 2014). Neuromodulatory transmitters engage G-protein coupled receptors (GPCRs), activating intracellular signaling cascades that then can directly activate or modify the properties of ion channels. Neuromodulatory transmitters can bind GPCRs many microns from the site of release, regulating activity within a volume of neuropil (Agnati et al., 1995; Rice and Cragg, 2008; Liu et al., 2018), though cases of more direct synapselike transmission are also found throughout the brain (Kia et al., 1996; Sesack et al., 2003; Gantz et al., 2013; Courtney and Ford, 2016). Neuromodulatory regulation of ion channels affects how ion channels respond to voltage deflections on short and long time scales, thus affecting how certain features of synaptic input are transformed into neuronal output. This process occurs throughout neuronal arbors, including dendritic and axonal arbors (Athilingam et al., 2017; Labarrera et al., 2018; Yu et al., 2018). Here, we focus on neuromodulation of ion channels in the axon. Recent advances, including the ability to more directly interrogate ion channel function in small axonal compartments, has improved our understanding of how channel function is regulated in these compartments. These modulatory events dramatically affect how synaptic information is integrated to generate patters of action potentials (APs) as well as how those APs are transformed into transmitter release at axon terminals (**Figure 1A**).

Axonal ion channels are important for many aspects of neuronal function, from the initiation and propagation of APs to the release of neurotransmitter (**Figure 1A**). APs are initiated in the axon initial segment (AIS), a cellular compartment enriched with voltage-gated ion channels and GPCRs (**Figure 1B**). At this location, synaptic currents are converted from a graded voltage signal into a train of APs. Due in part to the AP initiation threshold, this transformation is fundamentally non-linear; as a result, the output spike pattern of a neuron is highly sensitive to the neuromodulation of the small fraction of ion channels localized to the AIS.

Neuromodulation of ion channels further down the axon also significantly affects how information is propagated to downstream synapses. Like in the AIS, modulation of ion channels at axonal boutons, the site of neurotransmitter release, also occurs through activation of GPCRs (**Figure 1C**). Known targets of neuromodulation at the axonal bouton include voltage-gated sodium (NaV), potassium (KV), and calcium (CaV) channels. In particular, modulation of CaVs can strongly impact the release of neurotransmitters because vesicle release is a direct (but probabilistic and non-linear) function of calcium concentration. Intracellular calcium also influences how the release of neurotransmitter changes with different patterns of presynaptic activity, a critical component of short-term plasticity (STP). As a result, subtle changes to ion channel function at the axonal bouton can result in large effects on synaptic strength, STP, and synaptic information transmission.

In this review, we will provide brief overviews of the biophysical processes involved in AP initiation, propagation, and neurotransmitter release, with an emphasis on how various neuromodulatory mechanisms that target axonal ion channels alter the dynamics of vesicle release and STP at the synapse. We focus primarily on studies performed in vertebrate central circuits, drawing from neuromodulatory systems like dopaminergic and GABA<sup>B</sup> receptor systems in which significant mechanistic detail has been elucidated. For a recent review of membrane excitability across axonal compartments (see Alpizar et al., 2019). We intend to provide the reader with an intuitive understanding of the connection between neuromodulatory mechanism and function; for more mathematical descriptions of presynaptic release, STP and information transfer, see these references (Tsodyks and Markram, 1997; Dayan and Abbott, 2001; Silver, 2010; Hennig, 2013). By focusing on these biophysical intervention points for neuromodulation and their functional impact, we hope to frame presynaptic neuromodulation in terms that are more easily translated to the study of neuronal circuit dynamics.

#### REGULATION OF ACTION POTENTIAL INITIATION

Action potential initiation and propagation are regulated by neuromodulators at several sites. APs are first generated in the AIS, a specialized axonal compartment adjacent to the somatodendritic compartment (Bender and Trussell, 2012; Kole and Stuart, 2012; Huang and Rasband, 2018). The AIS is enriched with sodium and potassium channels that underlie to the rising and falling phases of the AP, as well as other ion channel classes that can augment the AP initiation process, including CaVs and hyperpolarizationactivated cyclic nucleotide-gated (HCN) cation channels (Bender and Trussell, 2009; Yu et al., 2010; Martinello et al., 2015; Ko et al., 2016). The precise site of AP initiation can be regulated by activity on short time scales (Scott et al., 2014), and can be structurally modified over longer time scales (Grubb and Burrone, 2010; Kuba et al., 2010). Furthermore, activation of neuromodulatory GPCRs can either enhance or weaken the function of many of these ion channel classes.

CaV3.2 channels, which are expressed in the AIS of many neuronal classes (Bender and Trussell, 2009; Martinello et al., 2015; Clarkson et al., 2017; Dumenieu et al., 2018), are the target of neuromodulation by both dopamine and acetylcholine. These CaVs contribute to subthreshold depolarization and highfrequency AP bursts in many systems (Cain and Snutch, 2013). Dopamine, acting through D3 receptors, hyperpolarizes CaV3.2 voltage-dependent steady state inactivation (Yang et al., 2016). Because the steady-state inactivation level of CaV3.2 channels varies markedly near typical resting membrane potentials (−60 to −90 mV, Serrano et al., 1999; Yang et al., 2016), changes in voltage-dependent inactivation can affect the number of channels available during AP generation. Ultimately, the net effect of dopaminergic modulation is to reduce burstiness, which has been observed in both auditory brainstem and neocortical neurons (Bender et al., 2010, 2012; Clarkson et al., 2017). Cholinergic modulation, by contrast, hyperpolarizes voltage-dependent activation properties of AIS-localized CaV3.2 channels in hippocampal granule cells, increasing AIS calcium concentration near resting membrane potentials (Martinello et al., 2015). The predominant effect of increased basal calcium levels is to reduce calcium-sensitive KV7 potassium current, which in turn lowers the threshold for AP initiation. Thus, neuromodulation that affects different biophysical aspects of CaV3.2 function can have bidirectional effects on AP generation.

Axon initial segment HCN channels and sodium channels can also be regulated by neuromodulators, specifically serotonin 5-HT1A receptors. In auditory brainstem, serotonin suppresses HCN channels via Gi/o-mediated inhibition of cyclic AMP, leading to a hyperpolarization of resting membrane potential and AP threshold (Ko et al., 2016). In mouse cortex and frog spinal cord, serotonin instead has inhibitory effects on axonal sodium channels, reducing sodium channel current density (Cotel et al., 2013; Yin et al., 2015). In cortex, this has a preferential effect on the NaV1.2 channel subtype specifically but appears to have a more ubiquitous effect on NaVs in the spinal cord. Serotonin's effects in the spinal cord, however, appear to be due to 5-HT1A receptors expressed in the soma rather than the AIS itself (Cotel et al., 2013). This insight may help explain why physiological effects of serotonin can be observed in the AIS despite uncertainty

FIGURE 1 | Cellular mechanisms of neuromodulation of axonal ion channels. (A) Schematic of axon subcompartments. Sodium (NaV), potassium (KV), and calcium (CaV) permeable voltage-gated ion channels are shown in red, blue, and green, respectively. (B) Schematic of GPCR neuromodulation of voltage-gated ion channels in the axon initial segment. Bars or circles at end of lines indicate a net reduction or increase, respectively, in target channel ion flux as a result of neuromodulation. Note that inhibition of KV7 channels is a downstream consequence of CaV3.2 modulation due to changes in intracellular calcium concentration. (C) Schematic of GPCR neuromodulation of Ca<sup>V</sup> in the terminal bouton. Solid lines indicate direct binding of Gβγ subunits to CaVs, dashed lines indicate intermediate steps.

over the precise subcellular localization of 5-HT1A receptors (Petersen et al., 2017).

### REGULATION OF ACTION POTENTIAL PROPAGATION AND WAVEFORM

Once APs are initiated, they propagate down the axon to sites of vesicle release known as active zones (AZs). This AP propagation itself is not perfectly reliable. For example, APs may fail at axonal branch points (reviewed in Kress and Mennerick, 2009), or near nerve terminals (Kawaguchi and Sakaba, 2015). Furthermore, some spikes generated during high frequency bursts of APs can fail to propagate to release sites (Khaliq and Raman, 2005; Monsivais et al., 2005; Roberts et al., 2008), or exhibit variable conduction velocities that can be augmented in part by dopaminergic regulation of axonal HCN channels (Ballo et al., 2010, 2012). Additionally, astrocytes can regulate AP waveform through ionotropic receptor activation or buffering of extracellular potassium (Menichella et al., 2006; Perea et al., 2007; Bay and Butt, 2012; Bellot-Saez et al., 2017).

Those APs that do arrive at axonal terminals produce a local depolarization that activates CaVs. The resulting calcium influx drives transmitter release via a non-linear reaction dependent on the third- to fourth-order of the local calcium concentration (Katz and Miledi, 1970; Reid et al., 1998; Schneggenburger and Neher, 2000; Scimemi and Diamond, 2012). This nonlinear relationship between release and calcium is dependent on several factors, including the physical distance between CaVs and calcium sensors, calcium buffer dynamics and the geometry of the bouton, and the binding affinity and cooperativity requirements of these sensors for calcium (Augustine, 2001; Stanley, 2016; Brunger et al., 2018). Because of this non-linearity, small changes in AP waveform that affect calcium influx can have large effects on release.

Interestingly, however, neuromodulators that regulate AP waveform tend to also have other, more direct mechanisms for influencing Pr. For example, dopamine can broaden or narrow APs via D1- or D2-family receptors, respectively, as measured in the primary axon of cortical pyramidal cells (Yang et al., 2013). But the dominant effect of D1 receptors at release sites appears to be direct regulation of Ca<sup>V</sup> function, rather than AP waveform modulation (Burke et al., 2018). Similarly, while Gi/o-coupled receptors including the CB1 cannabinoid receptor have been shown to activate G-protein coupled inward rectifier potassium channels (GIRKs) in the axon (Alger et al., 1996; Daniel and Crepel, 2001; Diana and Marty, 2003), the dominant functional effect of Gi/o-coupled receptor activation at boutons is the direct regulation of CaVs through Gβγ-dependent signaling (Lüscher et al., 1997; Brown et al., 2004, but see Zurawski et al., 2018), as discussed below.

Action potential waveform adaptation during high-frequency activity has also been repeatedly shown to either suppress or enhance vesicle release, depending on the mechanism of adaptation. In cultured Purkinje cells, attenuation of AP height near terminals strongly suppresses transmitter release (Kawaguchi and Sakaba, 2015). Surprisingly, at hippocampal mossy fiber boutons a similar activity-dependent shortening and widening of axonal APs at high frequency leads to an increase in vesicle release probability (Geiger and Jonas, 2000). The difference between these two synapses may lie in the mechanisms that underlie spike adaptation. AP height is reduced during ongoing activity in both synapses, largely due to reductions in sodium or potassium currents in Purkinje and mossy fiber boutons, respectively. This would be predicted on its own to decrease the activation of CaVs and reduce

calcium influx. However, reductions in potassium currents lead to a larger broadening of the AP waveform in mossy fiber boutons than in Purkinje cell axons, increasing the total time the membrane is depolarized. This increased duration of membrane depolarization appears to be sufficient to counteract the reduction in AP height and ultimately increase the overall calcium influx. Indeed, in cerebellar stellate interneurons, a similar widening of presynaptic AP waveforms in response to prolonged somatic depolarization also leads to enhanced transmitter release due to the inactivation of KV3 potassium channels (Rowan et al., 2016; Rowan and Christie, 2017). Thus, a subtle mechanistic difference in spike waveform adaptation can lead to the opposite outcome for vesicle release probability.

Axon terminal voltage can also be affected by several mechanisms beyond manipulations of AP waveform, leading to alterations in transmitter release. Terminal CaVs can be sensitive to subthreshold depolarization (Awatramani et al., 2005). This subthreshold activity can be mediated by the local activity of ionotropic receptors, including GABA<sup>A</sup> receptors which may depolarize axon terminals (Price and Trussell, 2006; Christie et al., 2011), nicotinic acetylcholine receptors (McKay et al., 2007), or glutamatergic receptors (Pinheiro and Mulle, 2008). Alternatively, subthreshold activity at the soma, filtered by axonal cable properties, can propagate to and affect the terminal membrane (Alle and Geiger, 2006; Shu et al., 2006), especially in cells with high input resistance (Christie et al., 2011). This so-called "analog signaling" interacts with APs at the terminal to alter release (Rama et al., 2018). Thus, multiple mechanisms exist to regulate the excitability of the presynaptic bouton and vesicle release, including neuromodulatory GPCR signaling, activity-dependent AP waveform adaptation and subthreshold voltage fluctuations.

#### REGULATION OF ACTIVE ZONE VOLTAGE-GATED CALCIUM CHANNELS

Calcium channels localized to active zones are among the most extensively studied effector targets of neuromodulation (reviewed in: Catterall and Few, 2008; Zamponi and Currie, 2013). Typically, presynaptic terminals are enriched with the CaV2 class of calcium channels. This group is comprised of three different isoforms: CaV2.1 (P/Q-type), CaV2.2 (N-type), and CaV2.3 (R-type). Axonal expression of each of these isoforms varies by cell type, and, at times, postsynaptic target (Éltes et al., 2017). For example, some GABAergic synapses express CaV2.1 or CaV2.2 channels exclusively (Poncer et al., 1997; Li et al., 2007; Bender and Trussell, 2009; Cao and Tsien, 2010; Szabo et al., 2014). By contrast, many glutamatergic synapses express a mix of CaV2.1, CaV2.2, and CaV2.3 channels (Brown et al., 2004; Ritzau-Jost et al., 2014). Calcium influx via CaV2.1 and 2.2 channels tends to dominate AP-evoked release (Turner et al., 1992; Wheeler et al., 1994; Bucurenciu et al., 2010; Ritzau-Jost et al., 2014; Burke et al., 2018), whereas 2.3 channels have been shown to be more critical for AP-independent spontaneous release (Ermolyuk et al., 2013). These channels have different kinetics (Colecraft et al., 2001) and exhibit differential activation depending on AP duration. For example, at mossy fiber boutons, CaV2.1 channels are best recruited by fast AP waveforms whereas longer duration waveforms recruit CaV2.1, 2.2, and 2.3 channels to comparable levels (Li et al., 2007). Thus, mechanisms of AP waveform neuromodulation or adaptation discussed earlier may impact synapses differentially depending on the expression levels of different Ca<sup>V</sup> isoforms. Moreover, isoform-specific mechanisms of neuromodulation could result in synapse-specific changes to short term plasticity (Colecraft et al., 2001). Such changes have been observed with presynaptic forms of long-term potentiation where CaV2.2 channels are preferentially incorporated into synapses following plasticity induction (Ahmed and Siegelbaum, 2009).

Direct inhibition of CaV2 channels by Gβγ subunits is perhaps the most common and best understood form of G-proteinmediated neuromodulation of presynaptic calcium channels (reviewed in: Currie, 2010; Padgett and Slesinger, 2010). This form of modulation is common across presynaptically expressed Gi/o-coupled receptors, including GABA<sup>B</sup> receptors (Bean, 1989; Mintz and Bean, 1993; Otis and Trussell, 1996; Park and Dunlap, 1998; Takahashi et al., 1998; Chalifoux and Carter, 2011), CB1 cannabinoid receptors (Hoffman and Lupica, 2000; Huang et al., 2001; Kreitzer and Regehr, 2001; Wilson et al., 2001; Zhang and Linden, 2009), type 2 muscarinic acetylcholine receptors (Qin et al., 1997), D2 dopamine receptors (Pisani et al., 2000; Momiyama and Koga, 2001), opioid receptors (Endo and Yawo, 2000; Hjelmstad and Fields, 2003), metabotropic glutamate receptors (Faas et al., 2002), and adenosine receptors (Yawo and Chuhma, 1993; Lüscher et al., 1997). Direct binding of Gβγ subunits to CaV2 channels affects channel biophysics by both slowing activation kinetics and by depolarizing the voltage dependence of activation (Bean, 1989; Colecraft et al., 2000). Interestingly, Gβγ-bound CaV2.2 exhibits a greater number of "reluctant" openings than CaV2.1 channels in which channel open duration is reduced or delayed. Thus, in response to AP depolarizations, the net effect of Gβγ-mediated inhibition is to reduce calcium influx. However, these calcium currents are also modestly shorter in duration for Gβγ-bound CaV2.2 channels than CaV2.1 channels (Colecraft et al., 2001). All of these mechanisms converge on reduced calcium influx per AP, which subsequently reduces the probability of neurotransmitter release.

While Gβγ-dependent signaling is a well-understood form of GPCR-mediated CaV2 channel regulation, GPCRs can also regulate CaV2 channels through other pathways. Dopamine and nociceptin receptors have both been shown to promote channel internalization through GPCR-channel complexes (Altier et al., 2006; Kisilevsky and Zamponi, 2008; Kisilevsky et al., 2008), though whether such mechanisms occur at presynaptic terminals remains unclear (Kisilevsky et al., 2008; Murali et al., 2012). If present at presynaptic terminals, channel internalization could lead to a functional silencing of release sites, essentially reducing synapse number.

D1/D5 dopamine receptors have also been shown to regulate calcium influx through high-voltage activated (presumably CaV2) calcium channels in dissociated striatal neurons via PKAdependent signaling (Surmeier et al., 1995; Zhang et al., 2002). Similarly, D1/D5 receptors regulate CaV2.1 and CaV2.2 calcium

influx in select glutamatergic inputs to prefrontal pyramidal neurons, also via a PKA-dependent pathway (Burke et al., 2018). The precise mechanism of calcium channel modulation remains unclear, but it is clearly distinct from Gβγ-mediated effects because dopaminergic modulation did not occlude further modulation via GABA<sup>B</sup> receptors. Moreover, in contrast to Gβγ-dependent modulation, dopamine did not reduce a single channel's calcium influx per AP, but rather the probability individual channels would open in response to an AP. This small difference in mechanism resulted in differential functional effects on release; while both dopamine and GABA<sup>B</sup> reduced Pr at this synapse, only GABA<sup>B</sup> altered STP (further discussed below). This form of presynaptic regulation without marked changes in STP has also been observed for noradrenergic (Delaney et al., 2007) and kappa opioid receptor-dependent modulation (Li et al., 2012; Tejeda et al., 2017). In these cases, the mechanism of action appeared to be either Gβγ-dependent effects at sites downstream of CaVs (e.g., SNAP25, see Delaney et al., 2007; Zurawski et al., 2018), or via other signaling cascades (e.g., ERK, see Li et al., 2012).

Overall, even when focusing only on ion channel function in axons, there exist many different cellular mechanisms to modulate axon excitability and synaptic transmission. While many of these mechanisms were initially identified due to their functional consequences of regulating vesicle release, we continue to gain insight into how modulation of ion channel biophysical properties affects information transmission across synapses. Further characterization of synaptic transmission before and after neuromodulation will help in identifying the functional role that these mechanisms play in vivo.

#### FUNCTIONAL CONSEQUENCES

Neuromodulation of synaptic transmission at the presynaptic axon results in marked changes in information transfer from presynaptic to postsynaptic target. Neuromodulation can affect this process on multiple timescales, affecting three key aspects of transmission at the terminal: (1) synaptic strength, (2) synaptic variability, and (3) STP. By regulating presynaptic calcium influx and vesicle release, axonal neuromodulation can control the strength of specific subsets of synaptic inputs relative to others. But because transmitter release is probabilistic, it also regulates the extent to which individual presynaptic APs are reliably transmitted to the postsynaptic cell. Finally, regulation of STP controls a release site's strength as a dynamic function of its past activity, which can create a frequencysensitive postsynaptic signal from a sequence of all-or-none presynaptic APs. Considering synaptic neuromodulation from this functional lens can lead to insight into how cellular mechanisms in the axon might be employed in neural information processing in vivo.

#### Synaptic Strength and Variability

Neuromodulatory GPCRs can exert fast and reversible control of synaptic strength by altering the probability of neurotransmitter release, Pr. In order to focus on broader functional impacts, we will define Pr at the level of the synapse, i.e., the probability that the active zone successfully releases a vesicle of neurotransmitter in response to an AP. This quantity is the product of many complex underlying variables, including the number of vesicles available for release, their distance to sources of calcium influx, and the probability of release of that each of these vesicles as a function of intracellular calcium. Within this framework, synaptic strength is therefore defined as the product of Pr, the number of release sites N, and the quantal size q (i.e., the amount of postsynaptic current generated from one vesicle).

Changes to both presynaptic release through modification of Pr and postsynaptic sensitivity to neurotransmitter q will change synaptic strength linearly. Importantly, however, this is only true on average, because presynaptic neuromodulation also changes the variability of the synapse, whereas postsynaptic modifications of q do not (**Figure 2A**; for comprehensive review of Pr and synaptic variability, see Branco and Staras, 2009). This variability in vesicle release is a major source of overall variability in synaptic transmission, and due to the non-linear relationship between calcium influx and Pr, neuromodulators that regulate presynaptic calcium influx will strongly influence both synaptic strength and variance.

While the importance of average synaptic strength in information transmission may be intuitively clear, the role of synaptic variability may be less obvious. Naively, an increase in synaptic variability through reductions in Pr might be predicted to make the synaptic signals noisier, degrading the ability of the synapse to convey information about presynaptic AP trains to postsynaptic targets (Zador, 1998; but see Goldman, 2004). However, this may depend on how those synaptic signals are integrated in the postsynaptic cell. For example, in a cell where very few strong input synapses drive APs, reducing q below AP threshold could completely abolish postsynaptic spiking, whereas reducing Pr would simply reduce the likelihood of AP generation (**Figure 2B**). If synapses are modeled as simple binomial processes, then the result of reducing q is a sharp reduction of spiking near the AP threshold non-linearity, contrasted with a more gradual reduction in postsynaptic AP generation when Pr is reduced. In the case of strong q suppression (**Figure 2B**, bottom), the postsynaptic spike sequence then carries no information about the sequence of synaptic inputs, whereas in the latter case of modulating Pr this information transmission is merely diminished.

This generalization does not, however, extend to all circumstances. First, it ignores non-linearities in dendritic integration, where synchronized excitatory inputs can generate dendritic calcium or NMDA spikes that are either independent of or coordinated with spikes generated in the AIS (Larkum et al., 1999; Schiller et al., 2000; Branco and Häusser, 2011). Whether the neuromodulation of synaptic variability impacts dendritic spikes similarly to how it impacts AIS spikes remains unstudied. Second, for cells that receive many weak synaptic inputs with low Pr (e.g., some synapses between neocortical excitatory neurons; Markram et al., 1997), the effects of synaptic variability are more complex and depend on the voltage of the postsynaptic membrane. If the

depressing STP dynamics, respectively.

postsynaptic membrane voltage is close to AP threshold, an increase in synaptic variability can push weaker signals over the AP threshold and increase postsynaptic output that is correlated with the weak signal; conversely, if the postsynaptic cell is well above threshold, synaptic noise and increased membrane conductance can lead to reduced output (Shu et al., 2003; Azouz, 2005). In this way, a neuromodulatory weakening of Pr and increase in synaptic variability can surprisingly improve the encoding capability of a postsynaptic neuron by broadening its dynamic range (Silver, 2010). Thus, modulation of synaptic strength through modification of release probability can have many indirect effects on neuronal information processing beyond linear changes in synaptic strength.

#### Short-Term Plasticity

At many synapses throughout the brain, the strength of a single synapse strength is a function of its previous activity (**Figures 2C,D**). This process of use-dependent regulation of vesicle release, termed STP, can be altered markedly by neuromodulatory GPCRs. STP depends on many factors, including variable Pr, availability of readily releasable vesicles, and AP waveform adaptation with repeated activity. For example, short-term facilitation is mediated through specific isoforms of calcium sensing proteins including synaptotagmin 7, which increase Pr in response to relatively low levels of calcium (Jackman et al., 2016). Because the concentration of free calcium in the bouton decays on the timescale of tens of milliseconds (Brenowitz and Regehr, 2007), these proteins allow the calcium from recent APs to non-linearly boost vesicle release over physiologically relevant frequencies of APs. However, the pool of readily releasable neurotransmitter vesicles is finite and depletion of this pool can lead to activitydependent short-term depression of transmitter release when presynaptic AP rates are high (Betz, 1970; for review see Zucker and Regehr, 2002).

The interplay between these mechanisms of facilitation and depression (and many others) can lead to frequency-dependent filtering of synaptic strength (Tsodyks and Markram, 1997; Dittman et al., 2000). This transformation of presynaptic spike trains into graded, frequency-dependent postsynaptic signals has many functional use cases. For example, facilitating synapses can effectively propagate bursts and minimize low-frequency single APs, which may serve to enhance the signal-to-noise ratio of bursts of activity that encode behaviorally relevant information (Laviolette et al., 2005; Burgos-Robles et al., 2007; Holmes et al., 2012). Conversely, depressing synapses can subtract these bursts from the sequence transmitted

to the postsynaptic cell, for example as in adaptation to sensory stimuli (Chance et al., 1998; Chung et al., 2002). Depression has also been shown to implement gain control over inputs with different baseline activity levels, allowing for the postsynaptic cell to respond to relative, rather than absolute, changes in input firing rate (Abbott et al., 1997). Finally, combinations of facilitation and depression can implement band-pass filtering, where activity would be weakened both above and below a characteristic frequency band. Temporal filtering of this sort can enhance responses to transient sensory stimuli (Chance et al., 1998) and may match frequency bands of behaviorally relevant circuit oscillations (Pietersen et al., 2009).

#### Canonical Presynaptic Neuromodulation

Short-term plasticity is often regulated in parallel with synaptic strength when a neuromodulator modifies presynaptic calcium influx. For example, changes in calcium influx will affect the calcium sensors that mediate short-term facilitation, but changes in Pr will also affect the extent of depletion-mediated short-term depression. In fact, these effects can both occur simultaneously to conceal each other. For example, at high-Pr synapses short-term facilitation can be limited by vesicle depletion. At such a synapse, reductions in calcium influx can both reduce Pr and unveil underlying facilitation (Zucker and Regehr, 2002; Sakaba, 2006). Indeed, reductions in Pr with parallel increases in short-term facilitation as measured by the "paired-pulse ratio" (PPR) are so common that they are considered a hallmark of presynaptic neuromodulation of release (Dittman and Regehr, 1998).

A common example of synaptic suppression with changes in STP is activation of presynaptic GABA<sup>B</sup> receptors. As described above, GABA<sup>B</sup> receptor activation suppresses presynaptic calcium currents via Gβγ-dependent signaling (Mintz and Bean, 1993; Wu and Saggau, 1995). Alongside other calciumindependent mechanisms (Dittman and Regehr, 1996; Sakaba and Neher, 2003), this leads to a potent suppression of release probability while increasing short-term facilitation of subsequent events (Chalifoux and Carter, 2011; Burke et al., 2018). This combination of effects has been hypothesized to support faithful transmission at high frequencies in auditory brainstem (Brenowitz et al., 1998). The behavioral role that this shift in STP plays is unclear; while genetic ablation of the GABA<sup>B</sup> receptor appears to reduce both anxiety and depressive phenotypes in mice (Mombereau et al., 2004), these mutations likely silence GABA<sup>B</sup> receptor expression at all subcellular locations. Better tools to disentangle the many cellular functions of the GABA<sup>B</sup> receptor (including increasing postsynaptic conductance, hyperpolarizing postsynaptic voltage, reducing Pr, and increasing facilitation) will be required to attribute behavioral effects to these transformations of synaptic function. Furthermore, tools to precisely separate the two presynaptic effects of GABA<sup>B</sup> (reducing Pr and increasing facilitation) would allow us to better understand the function of other presynaptic neuromodulators that also employ Gβγ-dependent signaling pathways, such as the CB1 receptor. Alternatively, experiments that compare activation of presynaptic neuromodulators with different effects on synaptic transmission (e.g., two presynaptic inhibitors of Pr that differ in effects on facilitation) could more clearly tie these effects on STP to circuit activity and behavior.

#### Non-canonical Presynaptic Neuromodulation

While Gβγ-dependent signaling canonically regulates both synaptic strength and STP, which we will term temporal modulation, some presynaptic neuromodulators appear to regulate Pr in isolation, which we will term gain modulation. These latter cases violate the dogma that presynaptic modulation also regulates PPR and demonstrate that temporal and gain modulation do not map cleanly onto presynaptic and postsynaptic mechanisms, respectively. Indeed, any form of modulation that essentially silences synapses (permanently or stochastically) can functionally be characterized as gain modulation. This includes both presynaptic mechanisms (e.g., axonal AP propagation failures, removal of synapses or active zones, slowly dissociating Ca<sup>V</sup> antagonists) as well as postsynaptic mechanisms (e.g., changes in postsynaptic receptor density or ion channel amplification of synaptic potentials). Similarly, while presynaptic mechanisms to modulate facilitation and depression have been extensively documented, some postsynaptic mechanisms have also been implicated (e.g., local reduction in synaptic driving force; Abrahamsson et al., 2012). Experimental identification of presynaptic or postsynaptic mechanisms therefore require more than simply measuring changes in levels of facilitation or depression (e.g., PPR) and should include other more direct measurements of release probability, such as measurements of synaptic variance (Sigworth, 1980; Saviane and Silver, 2006; Delaney et al., 2007) or optical measurements of transmission at individual synapses (e.g., optical quantal analysis, Oertner et al., 2002; Higley et al., 2009; Little and Carter, 2012; Sylantyev et al., 2013; Boddum et al., 2016; Burke et al., 2018).

One common mechanism for observing presynaptic gain modulation is direct blockade of calcium channels using slowly dissociating antagonists such as cadmium or conotoxin-MVIIC (Hefft et al., 2002; Hjelmstad, 2004; Scimemi and Diamond, 2012). Several neuromodulatory systems have also been found to exert similar effects, including D1/D5 in prefrontal cortex (Gao et al., 2001; Seamans et al., 2001; Burke et al., 2018), D1/D5 at the perforant pathway (Behr et al., 2000), kappa-opioid receptors at amygdalar inputs to the nucleus accumbens (Tejeda et al., 2017), kappa-opioid receptors in the bed nucleus of the stria terminalis (Li et al., 2012), and noradrenergic receptors in central amygdala (Delaney et al., 2007). While these neuromodulators likely employ different signaling pathways, they share in common the regulation of Pr apparently without changing STP. Importantly, this presynaptic neuromodulation only of synaptic strength is different from temporal modulation in how it transforms information as it is transmitted across the synapse. While canonical Gβγ-dependent signaling suppresses transmission from low-frequency presynaptic APs while preserving or enhancing high-frequency transmission, these non-canonical gain neuromodulators that only regulate Pr serve to control the

average strength of the synapse while preserving the relative strength of transmitted frequencies.

Mechanisms of presynaptic gain modulation can be grouped into two major categories: first, changes in the number of vesicles available for release, and second, changes in release probability per vesicle. An example of this first category is found at the neuromuscular junction of Drosophila, where homeostatic adaptation to postsynaptic glutamate receptor blockade is achieved through an enhancement in the size of the readily releasable pool of vesicles (Weyhersmuller et al., 2011). This adaptation is best described as gain modulation because the change in short-term facilitation was significantly smaller than the change in synaptic strength. However, as noted earlier, a finite RRP can lead to vesicle depletion with activity, which leads to frequency-dependent short-term depression (Zucker and Regehr, 2002; Sakaba, 2006). Increasing RRP size could hypothetically remove this depression and unmask facilitation, thus acting as temporal modulation; therefore, increases in RRP size may only implement gain modulation if depletion is not a significant factor under baseline conditions.

An example of the second category, presynaptic gain modulation through changes in Pr, was recently observed at excitatory synapses in prefrontal cortex (Burke et al., 2018), and may underlie similar observations made with kappa opioid receptor-dependent modulation in subcortical regions (Li et al., 2012; Tejeda et al., 2017). Here, presynaptic release probability was suppressed by activation of dopaminergic D1 receptors. Unlike some other forms of presynaptic gain modulation, however, the underlying mechanism was a reduction in calcium influx. Interestingly, typical mechanisms that reduce presynaptic calcium, such as a reduction in extracellular calcium concentration, often appear as temporal modulation with strongly correlated with changes in facilitation (Zucker and Regehr, 2002). The gain modulation by the D1 receptor represents an important caveat to this common pattern; because D1 receptor activation suppressed calcium channel open probability, the functional consequence of this modulation was to reduce release probability in a nearly "all-or-none" fashion. Thus, the effect of this modulation bears more resemblance to an AP conduction failure than a "canonical" reduction in AP-evoked calcium channel currents.

### Function Following Form at Nanodomain Synapses

Why do some neuromodulators that regulate Pr also regulate STP, whereas others do not? As mentioned earlier, the size of the RRP and the extent of vesicle depletion could be one explanation. Another is the functional coupling of CaVs and vesicles at active zones (**Figure 3**). The presynaptic configuration where release of each vesicle is driven by calcium influx through many CaVs is termed a calcium microdomain; when release is driven by very few CaVs per vesicle, this is termed a calcium nanodomain (for review, see Stanley, 2016). Regulation of the probability of individual Ca<sup>V</sup> channel opening has been shown to lead to gain and temporal modulation in nanodomain and microdomain configurations, respectively; by contrast, Ca<sup>V</sup> calcium influx per AP can lead to temporal modulation under both configurations (**Figures 3B,C**; Otis and Trussell, 1996; Hefft et al., 2002; Hjelmstad, 2004; Eggermann et al., 2012; Scimemi and Diamond, 2012; Burke et al., 2018). Thus, at synapses with nanodomain coupling between CaVs and vesicles, the precise mechanism by which CaVs are modulated can dictate whether a neuromodulator causes gain or temporal modulation. In other words, any observations made where a neuromodulator employs a mix of apparent pre- and postsynaptic mechanisms (e.g., an increase in CV without an increase in PPR) should be couched aside experiments designed to assess whether the same synapses utilize nano- or microdomain release mechanisms.

The neuromodulation of synaptic strength has been understudied in the context of functional coupling between CaVs and vesicles. The aforementioned experiments examining D1 receptor modulation in PFC suggested a critical role of CaV-vesicle functional coupling in its effects on synaptic transmission (Burke et al., 2018). These synapses appear to employ a nanodomain release configuration in which differential Ca<sup>V</sup> recruitment per AP affects STP (Scimemi and Diamond, 2012). At these synapses in PFC, D1 receptor activation reduced individual Ca<sup>V</sup> channel open probability at the presynaptic axon, leading to gain modulation of synaptic transmission, whereas activation of the GABA<sup>B</sup> receptor reduced Ca<sup>V</sup> current per AP and led to temporal modulation. Taken together, these data led to the hypothesis that D1 activation would modulate postsynaptic responses to all input frequencies similarly, whereas GABA<sup>B</sup> activation would preferentially suppress responses to low-frequency inputs. Experiments quantifying postsynaptic AP generation confirmed this hypothesis. Whether this functional distinction between gain and temporal modulation extends to naturalistic patterns of activity seen in vivo, and what functional role it may play in circuit neuromodulation, has yet to be investigated.

## FUTURE DIRECTIONS

While the use of fixed frequency synaptic stimulation is both common and important in investigations of cellular mechanisms of synaptic transmission, it also likely obscures how STP and its neuromodulation affect the noisy and irregular patterns of active neurons in vivo. Similarly, many effects of neuromodulation observed in ex vivo acute slice preparations have yet to be linked to specific behavioral outcomes in vivo. Recent work has begun to investigate how different synaptic mechanisms contribute to neuronal computations in vivo (Bolding and Franks, 2018; Evans et al., 2018; Lien and Scanziani, 2018). As the experimental technology to measure neuronal activity in vivo continues to improve, it is becoming increasingly possible to bridge the gap between mechanistic studies in vitro and functional studies in vivo and better incorporate synaptic neuromodulation into theories of neuronal circuit function. The highly non-linear behavior of synapses, including their variability, short-term dynamics and complex neuromodulation, are likely to be a critical component of future research into how cellular processes impact neural circuits and behavior. It will be

critical to move from mere identification of synaptic connectivity to the identification of the neural codes employed by these connections, as well as identification of when, where, and how neuromodulators are engaged in vivo. To achieve this, new tools that can provide real-time measurements of neuromodulatory activity, including sensors for neurotransmitters (Jing et al., 2018; Marvin et al., 2018; Patriarchi et al., 2018; Sun et al., 2018) and intracellular signaling molecules (Violin et al., 2003; Jiang et al., 2017; Ma et al., 2018), will be critical. These tools can be complemented by methods to measure and manipulate activity patterns at individual neurons and even individual synapses (Lee et al., 2019), including both genetically and functionally defined neural circuits (Guenthner et al., 2013; Grewe et al., 2017; Wang et al., 2017; Parker et al., 2018). Together, these technological advances will allow us to quantify how neuromodulators regulate complex activity patterns as they propagate throughout synaptic networks. Moreover, more precise tools are needed to dissect the relative contributions of pre- and post-synaptic effects of neuromodulatory GPCRs, for example distinguishing the functional roles of GABA<sup>B</sup> activation in changing postsynaptic

conductance versus presynaptic Pr and STP (Zurawski et al., 2018). The ability to disentangle these many distinct effects will be critical in developing a quantifiable and falsifiable theory of the role neuromodulation plays in synaptic computation.

## AUTHOR CONTRIBUTIONS

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

#### REFERENCES


## FUNDING

This work was supported by grants from the NIH (DA035913, MH112117, and MH112729).

## ACKNOWLEDGMENTS

We are grateful to Anna Lipkin and other members of the Bender Lab for comments and feedback.


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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 © 2019 Burke and Bender. 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(s) 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.

# Axonal Spectrins: Nanoscale Organization, Functional Domains and Spectrinopathies

#### Cheng-Hsin Liu<sup>1</sup> and Matthew Neil Rasband1,2 \*

<sup>1</sup> Program in Developmental Biology, Baylor College of Medicine, Houston, TX, United States, <sup>2</sup> Department of Neuroscience, Baylor College of Medicine, Houston, TX, United States

Spectrin cytoskeletons are found in all metazoan cells, and their physical interactions between actin and ankyrins establish a meshwork that provides cellular structural integrity. With advanced super-resolution microscopy, the intricate spatial organization and associated functional properties of these cytoskeletons can now be analyzed with unprecedented clarity. Long neuronal processes like peripheral sensory and motor axons may be subject to intense mechanical forces including bending, stretching, and torsion. The spectrin-based cytoskeleton is essential to protect axons against these mechanical stresses. Additionally, spectrins are critical for the assembly and maintenance of axonal excitable domains including the axon initial segment and the nodes of Ranvier (NoR). These sites facilitate rapid and efficient action potential initiation and propagation in the nervous system. Recent studies revealed that pathogenic spectrin variants and diseases that protealyze and breakdown spectrins are associated with congenital neurological disorders and nervous system injury. Here, we review recent studies of spectrins in the nervous system and focus on their functions in axonal health and disease.

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Juan José Garrido, Spanish National Research Council (CSIC), Spain Matthew S. Grubb, King's College London, United Kingdom

#### \*Correspondence:

Matthew Neil Rasband rasband@bcm.edu

Received: 29 March 2019 Accepted: 09 May 2019 Published: 28 May 2019

#### Citation:

Liu C-H and Rasband MN (2019) Axonal Spectrins: Nanoscale Organization, Functional Domains and Spectrinopathies. Front. Cell. Neurosci. 13:234. doi: 10.3389/fncel.2019.00234 Keywords: spectrin, super-resolution microscopy, axonal excitable domains, axon integrity, spectrinopathy

## OVERVIEW OF SPECTRINS IN THE NERVOUS SYSTEM

Spectrins were first isolated from the membranes of red blood cell ghosts (Marchesi and Steers, 1968) – in fact, the name spectrin derives from specter. Spectrins were identified as cytoskeletal proteins that confer elasticity to erythrocytes allowing them to withstand the shear forces experienced in the circulatory system (Elgsaeter et al., 1986). Since then, the functions of spectrins in diverse cell types were expanded to include signaling transduction (Hund et al., 2010), intracellular trafficking (Ikeda et al., 2006), and cellular polarity (Galiano et al., 2012).

Spectrins are expressed in all metazoan cells, but complicated tissues may express and localize spectrins in cell and compartment-specific manners. The human genome encodes two α-spectrins (SPTA, SPTAN1; αI and αII spectrin, respectively) and five β-spectrins (SPTB, SPTBN1, SPTBN2, SPTBN4, SPTBN5; βI-βV spectrin, respectively). In the nervous system, αII-spectrin (non-erythrocytic α-spectrin) is the sole α-subunit as verified at mRNA transcript (Zhang et al., 2014) and protein levels (Huang et al., 2017a). βI-spectrin is concentrated in cortical layer 2 and 4, cerebellar granule cells, and in the soma of Purkinje cells (Stankewich et al., 2010), while βII-spectrin is widely expressed in neurons and glia (Galiano et al., 2012; Zhang et al., 2013; Susuki et al., 2018). βIII-spectrin is found in the soma and dendrites of the cerebellar molecular layer

(Stankewich et al., 2010). βIV-spectrin is concentrated at axon initial segments (AIS) and nodes of Ranvier (NoR) (Berghs et al., 2000). βV-spectrin is mainly expressed in the hair cell (Legendre et al., 2008) and photoreceptor (Papal et al., 2013). In this review, we will describe how new super-resolution microscopy techniques have facilitated a new appreciation for the function of spectrin cytoskeletons, what spectrins' functions are in the axon during development, and how dysfunction of spectrins lead to neurological disorders.

## STRUCTURE AND DOMAINS OF SPECTRINS

α-spectrins consist of a tetramerization motif at the N-terminus, followed by 21 tandem spectrin-repeats (SR), a Src homology domain 3 (SH3), a calmodulin-binding domain (only in αII-spectrin), and a calcium-binding EF-domain at the C-terminus. β spectrins consist of two actin-binding calponin homology (CH) domains (CH1-2) at the N-terminus, followed by 17 tandem SR [except for βV-spectrin, which contains 30 SR (Stabach and Morrow, 2000)], and a lipid-binding pleckstrin homology (PH) domain at the C-terminus. To mediate their interaction between membrane proteins and the actin-based cytoskeleton, SR 15 of β-spectrins binds to the ZU5 domains of ankyrins (Kennedy et al., 1991). βIV-spectrin also binds to a non-canonical phosphorylation-dependent site in ankyrinG's giant exon (Jenkins et al., 2015). A pair of α/β-spectrins bind side-by-side to form a heterodimer. This is mediated by the SR 20-21 in α-spectrin and SR 1-2 in β-spectrin, although one recent study revealed a non-canonical dimerization domain in SR14-15 of βIV-spectrin (Huang et al., 2017a). Heterodimers further assemble head-to-head as a functional heterotetramer complex; this interaction is mediated by the N-terminus of α-spectrin and SR 17 of β-spectrin (Elgsaeter et al., 1986). In Drosophila and Caenorhabditis elegans, there is only one α subunit (Dubreuil et al., 1989) and two β subunits (β and βH-spectrin in Drosophila; β<sup>G</sup> and βH-spectrin in C. elegans) (Dubreuil et al., 1987, 1990; McKeown et al., 1998; Moorthy et al., 2000). These α and β-spectrins are similar to their vertebrate homologs in structure and biophysical properties (Dubreuil et al., 1989; Moorthy et al., 2000).

### VISUALIZING THE SPECTRIN CYTOSKELETON BY SUPER-RESOLUTION MICROSCOPY

The dynamic rearrangement of the cytoskeleton accommodates morphological changes and intracellular networks necessary to maintain cellular homeostasis. Highly polarized cell types like neurons undergo extensive re-organizations of cytoskeletal architecture to differentiate into cells with distinct functional and structural compartments such as axons and dendrites. Understanding how spectrins function together with other cytoskeletal components at the single molecule level has shed light on the detailed mechanisms of neuronal development, structure, and function.

Visualizing spectrin-dependent cytoskeletons at resolutions below that achieved by conventional light microscopy was first achieved using electron microscopy (EM) of the erythrocyte membrane (Byers and Branton, 1985). The approximately 200 nm rod structure of spectrin tetramers were crosslinked with junctional complexes to form hexagonal meshworks. Since then, EM-based approaches have been performed in cultured neurons (Jones et al., 2014) and tissues including outer hair cells (Legendre et al., 2008) and brain (Stankewich et al., 2010; Efimova et al., 2017). These studies provide valuable information about subcellular localization of spectrins with high-resolution images. However, the dense and compact nature of the cytoskeletal network limits clear description of the intricate architecture of neuronal spectrins. Furthermore, the special fixation procedures for sample preparation are relatively destructive, which makes it challenging to preserve the molecular integrity. Immunofluorescence microscopy-based assays can also uncover the spatial features of spectrins and their associated proteins in a variety of cellular compartments by combining multichannel chromophores. However, the resolution using immunofluorescence microscopy is limited to the optical diffraction limit of about 250 nm. Over the last decade, these limitations were gradually overcome through the use of advanced super resolution microscopy.

Super resolution microscopy can be categorized into three major types including: single-molecule-localization microscopy (such as stochastic optical reconstruction microscopy (STORM) and photoactivated localization microscopy (PALM)), periodic light pattern based structured illumination microscopy (SIM), and scanning technique based stimulated emission depletion microscopy (STED) (Sydor et al., 2015). Depending on the type of microscopy, the resolution can be anywhere from 10 to 130 nm in the xy plane, and 300 nm in the z-direction. Furthermore, by labeling molecules with photo-switchable fluorescent probes, accurate three-dimensional information of distinct molecules can be analyzed in multicolor images (Bates et al., 2007). Some imaging modalities also allow for live imaging and the temporal resolution can range from milliseconds to minutes, which confers the ability to visualize molecular dynamics. These strengths facilitate discoveries down to single molecule and supramolecular characterizations.

By employing super resolution microscopy both in fixed (Xu et al., 2013; Leterrier et al., 2015) and live cultured neurons and brain slice (Xu et al., 2013), spectrins were found in a periodic arrangement along axon shafts with a 190 nm spacing, which matches the length of each purified spectrin tetramer as previously visualized by EM (Bennett et al., 1982). Actin and its capping protein adducin wrap around the circumference of axons as ring-like structures and connect with spectrins throughout the axon (Xu et al., 2013). This pattern is observed in both unmyelinated and myelinated axons (D'Este et al., 2016, 2017), various neuron types in vitro (He et al., 2016), and in species from C. elegans to human (He et al., 2016). Within axons, the periodicity of spectrins can also be seen at specialized excitable domains like the axon initial segment (AIS) (**Figures 1B,D,F**)

confirming that spectrins are arranged head-to-head in the spectrin tetramer. (G,I,K) Images captured by conventional fluorescent microscopy show αII-spectrin at node/paranodes, βII-spectrin at paranodes, and βIV-spectrin at nodes in myelinated axons. (H,J,L) Images captured by STORM super-resolution microscopy show a periodic lattice of αII, βII, and βIV-spectrins with spacing around 190 nm. (A–L) are adapted from Huang et al. (2017a,b). (M) Graphic illustration of the periodic spatial organization of the spectrin-based cytoskeleton and its associated proteins in axons. At axonal excitable domains including axon initial segments and nodes of Ranvier, the key molecules for membrane excitability (AnkG, Nav, Kv) in these regions show a similar periodicity. Additionally, spectrins build an intra-axonal boundary (as indicated by red arrow) to restrict excitable domain localizations. Spectrin periodicity in dendrites, however, is less prominent.

and NoR (**Figures 1H,J,L**; Zhong et al., 2014; D'Este et al., 2015; Huang et al., 2017a,b). Interestingly, the key molecules for membrane excitability in these regions show a similar periodicity, such as voltage-gated sodium channels (Xu et al., 2013; D'Este et al., 2017), KCNQ2 potassium channels (D'Este et al., 2017), ankyrinG (Leterrier et al., 2015), and the cell adhesion molecule neurofascin (D'Este et al., 2015; **Figure 1M**). These results suggest the actin-spectrin-based cytoskeleton organizes the subcellular distribution of functional units in axons. It will be interesting to determine if these spatial features participate directly in action potential properties, perhaps by modulating AIS length or position (Grubb and Burrone, 2010; Kuba et al., 2010; Arancibia-Cárcamo et al., 2017).

In contrast to axons, the periodicity of the spectrin-based cytoskeleton is less pronounced in somatodendritic domains (He et al., 2016; Han et al., 2017) and glia (D'Este et al., 2016; He et al., 2016). Spectrin's periodic pattern in axons is also distinct from the hexagonal network previously described in erythrocytes by EM (Byers and Branton, 1985) and STORM super-resolution microscopy (Pan et al., 2018). These remarkable differences raise several important questions including how is the architecture of spectrin-based cytoskeleton established, what are the key associated molecules involved in this process, how do these mechanisms work in a cell-type or compartment-specific manners, and what is the functional consequence of different spectrin architectures.

## ROLES FOR SPECTRINS IN AXON INTEGRITY

Spectrins allow erythrocytes to deform and withstand the shear forces experienced during vascular flow or as these cells move through capillaries that may be even smaller than the diameter of the erythrocytes themselves. In neurons, axons also encounter distinct types of mechanical stresses including tensile and torque forces due to the movement joints and limbs. The spectrin-based cytoskeleton also helps to maintain axonal integrity under these mechanical forces.

In C. elegans, UNC-70 βG-spectrin is highly expressed in the nervous system including the nerve rings, nerve cord and commissural axons (Moorthy et al., 2000). Although loss of βG-spectrin does not affect neurite outgrowth or integrity during embryogenesis (Hammarlund et al., 2007), after hatching, axons are progressively broken with increasing age, and these axons have aberrant morphology (Hammarlund et al., 2000, 2007; Moorthy et al., 2000). This phenotype can be mitigated by paralyzing the worms (Hammarlund et al., 2007), indicating that spectrins stabilize axons against tensile forces resulting from locomotion. Furthermore, worms lacking βG-spectrin cytoskeleton simultaneously with microtubule protein MEC-7 β-tubulin or microtubule-associated protein PTL-1 tau showed large coils and kinks in their axons (Krieg et al., 2017), suggesting these cytoskeletal components are essential to withstand tension and torque forces. In sensory neurons, which experience forces due to touch and movement, the pre-stressed βG-spectrin is also required for mechanosensation (Krieg et al., 2014).

In mice, disrupting axonal β-spectrins including βII or βIV-spectrin showed no or only minor axon degeneration (Yang et al., 2004; Zhang et al., 2013). It is possible that loss of these spectrins can be partially compensated as other β-spectrins substitute for and replace those that are lost (Ho et al., 2014). Therefore, to determine the role of axonal spectrins, Huang et al. (2017a) abolished αII-spectrin, the only α-subunit in the nervous system, so that the entire spectrin cytoskeleton is compromised due to the loss of all α/β-spectrin heterotetramers. Mice lacking αII-spectrin in the central nervous system showed widespread axon degeneration (Huang et al., 2017a). Interestingly, loss of αII-spectrin from peripheral sensory neurons also caused axon degeneration, but mostly in large diameter myelinated axons; large diameter axons also show aberrant innervation of proprioceptor and mechanoreceptor nerve endings, while small diameter axons (mainly non-myelinated axons) remained intact (Huang et al., 2017b). The difference between central and peripheral sensory neurons may result from the contribution of the AIS to axon integrity: αII-spectrin is highly clustered at the AIS, a region crucial for maintenance of neuronal polarity in CNS neurons (Huang et al., 2017a), but pseudo-unipolar sensory neurons do not have AIS (Gumy et al., 2017). The vulnerability of large diameter axons to degeneration may also reflect disruption of NoR in αII-spectrin deficient nerves. Huang et al. (2017b) reported that nodes of large diameter axons have more αII-spectrin than small diameter non-myelinated axons. Together these observations suggest that spectrins located at axonal excitable domains may be important for axon survival and integrity. Future studies that abolish spectrin cytoskeletons specifically at the AIS or nodes may help test these ideas.

## ROLES FOR SPECTRIN AT AXONAL EXCITABLE DOMAINS

### Axon Initial Segments

Neuronal action potentials are generated at a specialized axonal region proximal to the soma called the axon initial segment (AIS). These regions are 20–40 µm in length and consist of highly concentrated voltage-gated sodium (Nav) and potassium (Kv) channels, which allow highly localized and transient changes in membrane properties to initiate action potentials (**Figure 1M**). AIS cytoskeletal proteins, especially AnkyrinG (AnkG) and βIV-spectrin, play critical roles in AIS formation and maintenance (Zhang and Bennett, 1998; Komada and Soriano, 2002; Lacas-Gervais et al., 2004; Yang et al., 2007; Hedstrom et al., 2008; Galiano et al., 2012).

How do AIS form and what causes AnkG and βIV-spectrin to become enriched at these sites? Studies in cortical and hippocampal neurons showed that newly differentiated neurons, where axon polarity is defined but AIS are not yet present, αII/βII-spectrin form a complex with AnkyrinB (AnkB) at the distal tip of the axon. As neurons mature, the AnkB/αII/βII-spectrin submembranous cytoskeleton progressively backfills the axon. As this occurs, AnkG, αII/βIV-spectrin begin to be expressed and are targeted to the axon. These cytoskeletal proteins are unable to occupy

the same domains as AnkB and αII/βII-spectrin and thus are effectively excluded from the distal axon. Instead, the only place they can form a submembranous cytoskeleton is at the proximal axon where AnkB and αII/βII-spectrin are not located. Thus, this distal cytoskeleton functions like an intra-axonal boundary to restrict AnkG and αII/βIV-spectrin to the proximal axon (Galiano et al., 2012; **Figure 1M**). Loss of αII- or βII-spectrin disrupted AIS integrity (Galiano et al., 2012; Huang et al., 2017a; Wang et al., 2018b), and manipulating the formation of AnkB/αII/βII-spectrin complexes by gain-of-function approaches both in vitro and in vivo further determined the role of the complexes as intra-axonal barriers that restrict the length and location of AIS (Galiano et al., 2012). Another study in motor neurons showed that during early development, AnkG is ubiquitously expressed throughout the axon along with AnkB/αII/βII-spectrin. Later on, AnkG is more enriched at the proximal axon, whereas AnkB/αII/βII-spectrin is relatively restricted at the distal domain (Le Bras et al., 2014). The differences of AIS assembly between hippocampal neurons and motor neurons could result from the distinct temporal expression of these key components, myelination, and unique protein interacting partners that occur in a context-dependent manner.

After the AIS is established, βIV-spectrin functions as the major β-spectrin subunit enriched in this domain (**Figures 1C,D**). Six βIV-spectrin splice variants (βIV61-66) have been identified (Berghs et al., 2000; Tse et al., 2001; Komada and Soriano, 2002), although βIV61 and βIV66 are the two major isoforms expressed in neurons (Komada and Soriano, 2002; Lacas-Gervais et al., 2004; Uemoto et al., 2007). βIV61 is a 280 kDa full-length isoform, whereas the 140 kDa βIV66 is much shorter and with a start site midway through spectrin repeat 10. The temporal expression of these two isoforms is different, as βIV61 is found at developing AIS, while βIV66 expression increases and it becomes the dominant isoform after AIS are established (Berghs et al., 2000; Yoshimura et al., 2016). This observation suggests the AIS spectrin tetramers may be assembled from two different βIV-spectrin isoforms with splice variant switching occurring between early and late developmental stages. Intriguingly, although these spectrins are different lengths, the apparent spacing of actin remains unchanged (Leterrier et al., 2015; Yoshimura et al., 2016). Furthermore, since βIV66 spectrin lacks the CH domain, a non-canonical actin binding motif must exist within βIV66, or there may be other proteins that mediate interactions between spectrin and the actin cytoskeleton.

The roles of βIV-spectrin at the AIS have begun to be determined using a series of transgenic and spontaneous βIV-spectrin mutant mice. βIV-spectrin null mice generated using a gene-trap approach still form AIS in neurons, but the immunoreactivity of Nav and AnkG are dramatically decreased, suggesting that βIV-spectrin is dispensable for AIS formation, but is required to stabilize AIS structure (Komada and Soriano, 2002). This result was also shown in mice lacking only βIV61 (Lacas-Gervais et al., 2004; Uemoto et al., 2007) and in βIV-spectrin mutant mice (qv3J mice have a frameshift mutation in the C-terminal SD domain of both βIV61 and 66) (Yang et al., 2007). These studies confirmed the necessity of the βIV61 variant and βIV spectrin's C-terminus for AIS integrity. All βIV-spectrin transgenic and mutant mice have tremors, ataxia, and auditory defects, which likely result from the abnormal action potential firing due to AIS disruption.

In addition to its excitable properties, the AIS also functions as a filter to regulate the differential trafficking of somatodendritic and axonal molecules. Previous studies revealed that AnkG-deficient axons lack an AIS, and that in the absence of an AIS axons acquire dendritic features including the entry of dendritic proteins (e.g., MAP2) into axons (Hedstrom et al., 2008).

AnkG and βIV-spectrin may directly function as a diffusion barrier or intracellular "filter" regulating the differential localization of membrane proteins, organelles, vesicles, and even lipids (Leterrier and Dargent, 2014). How do ankyrins and spectrins regulate these functions? One possibility is that spectrins may participate in assembly of a stable platform or scaffold that in turn regulates dynamic actin patches thought to regulate the entry of vesicles and other proteins into the axon (Watanabe et al., 2012; Balasanyan et al., 2017). Although previous studies showed the periodic spacing of spectrins is similar between proximal (βIV-spectrin) and distal axon (βII-spectrin) spectrin cytoskeletons (Xu et al., 2013), whether dynamic changes in cytoskeleton structure occur during protein trafficking through the AIS remains to be determined. We speculate that many other factors including as yet unidentified AIS proteins that interact with βIV-spectrin or AnkG, post-translational modifications, and the splicing variants of βIV-spectrin also contribute to how AIS maintain neuronal polarity.

Despite the very stable nature of the AIS and the common βIV-spectrin and AnkG-based AIS cytoskeleton, AIS morphology, protein composition, and even location can differ among the various types of neurons (Kole and Stuart, 2012; Höfflin et al., 2017); additionally, these features may change in response to external stimuli. Dynamic changes in AIS structure can alter neuronal excitability (Grubb and Burrone, 2010; Kuba et al., 2010). Several mechanisms, including increased intracellular calcium, altering activity and the surface expression of membrane receptors and ion channels, and axo-axonic synapse interaction have been proposed to mediate AIS plasticity (as reviewed in Yamada and Kuba, 2016; Jamann et al., 2018). Nevertheless, the process whereby the underlying cytoskeleton is reorganized remains unknown. Future studies to analyze spectrins using real-time imaging to capture these dynamic changes, super-resolution microscopy, and comparison among different neuron subtypes, may help to uncover how spectrins play roles in AIS heterogeneity and plasticity.

#### Nodes of Ranvier

After an action potential is initiated at the AIS, the membrane depolarization propagates along the axon to downstream nerve endings to connect to the next cell in the circuit. In myelinated axons, voltage-gated ion channels are highly enriched at NoR to facilitate saltatory action potential conduction. Nodes are short gaps in the myelin sheath where the action potential

is regenerated through the clustered ion channels. Multiple neuron-glia interactions are responsible for the assembly and maintenance of nodes, and impairment of these processes has been linked to disorders including multiple sclerosis (Craner et al., 2004; Howell et al., 2006), Charcot–Marie–Tooth (CMT) disease (Devaux and Scherer, 2005; Saporta et al., 2009), Guillain-Barré syndrome (Yuki and Hartung, 2012), and spinal cord and traumatic brain injuries (Reeves et al., 2010). Nodal spectrin-based cytoskeletons are critical in both health and disease.

Nodes of Ranvier can be divided into three distinct domains: (1) node, where Nav channels are clustered, (2) paranodes, which flank nodes and are the sites where each successive layer of the myelin sheath attaches to the axon, and (3) juxtaparanodes, which are highly enriched in Kv1 K+ channels, immediately adjacent to the paranode, and covered by the myelin sheath. In zebrafish, αII-spectrin is found throughout axons, but can also be found enriched at nodes and paranodes during early development (**Figures 1G,H**). Mutant zebrafish with an αII-spectrin nonsense mutation at spectrin repeat 13 had diffuse Nav channel intensity, a longer node length, and disrupted paranodal structure, indicating αII-spectrin is required for the proper formation of NoR (Voas et al., 2007). Consistent with this interpretation, mice lacking αII-spectrin in peripheral sensory neurons had ataxia and impaired action potential conduction, disrupted NoR, and axon degeneration (Huang et al., 2017b). Together, these results confirm that αII-spectrin is necessary for node of Ranvier formation across species. However, determining the function of αII-spectrin specifically at nodes or paranodes is challenging due to its presence in both domains. Therefore, studies depleting domain-specific spectrins to disassemble αII/β-spectrin complexes is necessary to understand spectrin's location-specific functions.

Like at the AIS, nodal βIV-spectrin interacts with AnkG and actin to form a submembranous cytoskeleton (**Figures 1K,L**). Furthermore, this spectrin cytoskeleton includes both βIV61 and βIV66 (Berghs et al., 2000; Komada and Soriano, 2002; Lacas-Gervais et al., 2004; Uemoto et al., 2007). Mice lacking βIV61 alone had weaker Nav channel intensity at nodes, along with wider and swollen nodal ultrastructure (Lacas-Gervais et al., 2004; Uemoto et al., 2007); these phenotypes were more prominent in βIV-spectrin null mice (Komada and Soriano, 2002; Uemoto et al., 2007) and in the qv3J βIV-spectrin mutant mice (Yang et al., 2004), confirming the necessity of both isoforms to maintain nodal integrity. Remarkably, restoring the expression of βIV-spectrin in adult βIV-knockout mice mitigates nodal disruption, although the timing is critical (Saifetiarova et al., 2018). Intriguingly, despite weaker Nav channel intensity, compound action potential conduction velocities are intact in βIV-spectrin deficient mice (Yang et al., 2004), suggesting the ataxic phenotypes and early lethality observed in many βIVspectrin mutant mice may reflect impaired AIS function rather than nodal dysfunction. Consistent with this idea, the percentage of nodes with Nav channels in βIV spectrin mutant mice is not different from controls (Susuki et al., 2013; Ho et al., 2014), suggesting that βIV-spectrin is dispensable for Nav channel clustering, or there are compensatory mechanisms that help to clustering and stabilize nodal Nav channels. For example, βI-spectrin, the major β-spectrin in erythrocytes, is enriched at nodes in the qv3JβIV spectrin mutant mice (Ho et al., 2014). Interestingly, the expression of βI-spectrin in the dorsal roots of qv3J mice was comparable to the wild type, indicating there is a pre-existing pool of βI-spectrin in the axons that is not normally found at nodes. Subsequent studies using AnkG knockouts revealed that whether βI or βIV spectrin is found at nodes depends on the type of Ankyrin found at nodes. Although AnkG is the usual nodal Ankyrin, removing AnkG by conditional knockout can be rescued by AnkyrinR (AnkR). Thus, AnkR preferentially interacts with βI spectrin and can rescue Nav channel clustering in the absence of AnkG (Ho et al., 2014). If βI spectrin is normally found in axons but is not located at nodes, what is it doing in axons? Furthermore, since βI-spectrin can compensate for loss of βIV-spectrin to rescue node function, the importance of a nodal spectrin cytoskeleton remains unknown. Future studies that eliminate both βI and βIV-spectrin from the nodes will help to answer this question.

In contrast to βIV-spectrin's nodal localization, βII-spectrin is found throughout the axon and is enriched at paranodes where it interacts with protein 4.1B (Ogawa et al., 2006; Zhang et al., 2013; **Figures 1I,J**). Mice lacking βII-spectrin in peripheral sensory neurons have motor dysfunction due to disrupted proprioception, longer nodal length, and juxtaparanodal Kv1 K<sup>+</sup> channels that are mislocalized into paranodes (Zhang et al., 2013). However, the axoglial junction itself was unaffected. These results showed that paranodal axonal spectrins are the molecular basis of diffusion barriers flanking NoR (**Figure 1M**). This function is reminiscent of the intra-axonal boundary that restricts AnkG to the AIS. However, in contrast to AIS (Galiano et al., 2012), loss of the axonal paranodal spectrins did not disrupt the clustering of nodal AnkG or Nav channels (Zhang et al., 2013). This difference from AIS indicates that although some mechanisms are shared between the two, additional clustering mechanisms exist at nodes. At AIS an intra-axonal cytoskeletal barrier clusters AnkG and βIV spectrin, while at NoR two glia-dependent mechanisms recruit AnkG and converge on axonal spectrins (Susuki et al., 2013; Amor et al., 2017).

βII-spectrin is also found in Schwann cells at paranodes, and mice lacking βII-spectrin in myelinating glial cells have disrupted paranodal axoglial junctions in young mice. These defects eventually resolve, but then re-appear as mice age, suggesting that glial βII-spectrin is required for the timely formation and long-term maintenance of paranodal junctions (Susuki et al., 2018).

#### SPECTRINS IN NEUROLOGICAL DISEASE AND INJURY

#### Pathogenic Spectrin Variants

Heterozygous mutations in SPTAN1 lead to early infantile epileptic encephalopathy-5 (EIEE5, OMIM# 613477) (**Table 1**), which is characterized by seizures with hypsarrhythmia, intellectual disability and delayed development. Several mutations have been identified near spectrin repeat 20-21



(Saitsu et al., 2010; Hamdan et al., 2012), which mediates α/β-spectrin dimerization. Biochemical analyses showed that complexes formed between mutant αII-spectrin and βII or βIII-spectrins are less thermostable. Furthermore, the mutant αII-spectrin also causes spectrin aggregation, disruption of AIS structure including reduced Nav channel clustering, and impaired action potential firing (Saitsu et al., 2010; Hamdan et al., 2012). Mice expressing human pathogenic SPTAN1 variants have shortened or no dendrites and a smaller cell soma. Neurons induced from patient-derived iPSC also have less complex neuronal processes and spectrin aggregations (Wang et al., 2018b). These phenotypes were highly similar to SPTAN1 null animals (Huang et al., 2017a; Wang et al., 2018b), indicating that pathogenic SPTAN1 variants may behave in a dominant negative manner.

Mutations in SPTBN2 give rise to spinocerebellar ataxia type 5 (SCA5, OMIM# 600224) (**Table 1**), which is characterized by adult-onset and progressive motor incoordination, postural abnormalities and swallowing difficulties. Autopsy tissue from heterozygotic patients with an in-frame deletion at spectrin repeat 3 showed significant loss of Purkinje cells and a thinner molecular layer in the cerebellum. This mutant βIII-spectrin allele also impaired the synaptosomal localization of the glutamate transporter EAAT4 in Purkinje neurons, which may be an underlying cause of the neurodegeneration (Ikeda et al., 2006). Another nonsense recessive allele in SPTBN2 caused developmental cerebellar ataxia and cognitive impairments during childhood. These phenotypes are distinct from SCA5, and this developmental disorder is called spectrin-associated autosomal recessive cerebellar ataxia type 1 (SPARCA1) (Lise et al., 2012; **Table 1**). Nevertheless, how these pathogenic variants give rise to different neurological signatures remains poorly understood. Additional studies are required to reveal the functions, expression profiles and associated proteins of βIII-spectrin in the nervous system; these studies may reveal how these different SPTBN2 variants give rise to distinct disorders.

Several different pathogenic variants in SPTBN4 were recently described (Knierim et al., 2017; Wang et al., 2018a). These patients all have a remarkably similar disease including congenital hypotonia, developmental delay and intellectual disability from early childhood; some patients also have seizures and central deafness (OMIM# 606214) (Wang et al., 2018a; **Table 1**). Wang et al. (2018a) investigated the consequences of these mutations and found that for many, their capacity to interact with AnkG and to be clustered at the AIS was compromised. For other mutations near the C-terminus, the mutant βIV-spectrin protein was unable to bind to phosphoinositides. These properties are essential to stabilize the cytoskeletal architecture of the AIS and to cluster ion channels at AIS and NoR. Future studies to determine the impact of spectrin pathogenic variants on other AIS functions, such as regulating polarity through control of intracellular trafficking, may help determine the cause of pathological phenotypes in these patients.

#### Proteolysis of Spectrins After Injury

Spectrin breakdown products (SBP) have been widely used as biomarkers for central nervous system injury for three main reasons. First, the Ca2+-dependent cysteine protease calpain is activated after CNS injury and cleaves full length αII-spectrin (280 kDa) into 150 and 145 kDa fragments (Pike et al., 2001). These SBP can be isolated from cerebrospinal fluid, allowing clinical evaluation. Second, the quantitative and temporal expression of SBP are highly correlated with the severity of injury and affected regions as evidenced by multiple injury models in rodents, which renders SBP as useful indicators to evaluate the degree of trauma. Finally and most importantly, the breakdown of spectrin-based cytoskeleton faithfully reflects axonal damage, as shown by the disruption of AIS (Schafer et al., 2009) and axon degeneration (Yang et al., 2013). These strengths render SBP as powerful indicators of axon injury and degeneration.

How is the cleavage of αII-spectrin regulated? There are at least two known mechanisms. First, Src-kinase phosphorylates αII-spectrin at Tyr1176 (adjacent to the SH3 domain and cleavage site) which reduces the susceptibility to proteolysis by calpain (Nicolas et al., 2002; Nedrelow et al., 2003). Second, binding between calpain and its endogenous inhibitor

calpastatin maintains homeostatic enzymatic activity. However, after injury, increased intracellular [Ca2+] tips the balance toward activated calpain which degrades the calpastatin. This exacerbates calpain-mediated proteolysis of αII-spectrin (Yang et al., 2013). Transgenic mice that constitutively overexpress human calpastatin (hCAST) in neurons have reduced levels of αII-spectrin SBP and improved motor performance after injury (Schoch et al., 2012). Exogenous delivery of calpastatin into injured neurons also mitigates axon degeneration (Yang et al., 2013). Many calpain inhibitors have now been developed for therapeutic purposes, although improvements in efficacy and safety are still needed [for review see (Ono et al., 2016)]. It is also important to emphasize that αII-spectrin is but one of calpain's many targets and functional deficits in neurons are not due solely to disruption of the spectrin cytoskeleton.

Increased levels of SBP have been reported in many neurological disorders other than CNS injury, including amyotrophic lateral sclerosis (Yamashita et al., 2012), Guillain-Barré syndrome (McGonigal et al., 2010), Parkinson's disease (Diepenbroek et al., 2014) and acute inflammatory autoimmune demyelinating models (Guyton et al., 2010; Das et al., 2013). Inhibition of calpain activity in these studies generally reduced SBP levels. Future studies that examine not only the integrity of axons, but also the structures whose function depends on specialized spectrin-based cytoskeletons (e.g., AIS and NoR), may help to define the pathophysiology of these diseases and injuries. Additionally, it will be important to

#### REFERENCES


determine whether the protective effects of calpain inhibitors is due to their protection of glial or axonal spectrins.

#### CONCLUSION

Since their original description in erythrocytes, our understanding of spectrins has dramatically increased and these important cytoskeletal proteins are recognized as being essential to the functions of diverse cell types in the nervous system. With the advent of advanced microscopy techniques and genetically modified mice, the roles of spectrins are now becoming much clearer. This knowledge will not only help to define the basic function of the nervous system, but it may also suggest therapeutic strategies for nervous system disorders and injuries that include altered or disrupted spectrin cytoskeletons.

#### AUTHOR CONTRIBUTIONS

Both authors wrote the manuscript.

## FUNDING

This study was funded by the Dr. Miriam and Sheldon G. Adelson Medical Research Foundation (Grant Nos. NIH R01 NS044916 and NIH R01 NS069688).




**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 © 2019 Liu and Rasband. 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(s) 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.

# Glutamate Imaging Reveals Multiple Sites of Stochastic Release in the CA3 Giant Mossy Fiber Boutons

Sylvain Rama\*, Thomas P. Jensen and Dmitri A. Rusakov\*

UCL Queen Square Institute of Neurology, University College London, London, United Kingdom

One of the most studied central synapses which have provided fundamental insights into cellular mechanisms of neural connectivity is the "giant" excitatory connection between hippocampal mossy fibers (MFs) and CA3 pyramidal cells. Its large presynaptic bouton features multiple release sites and is densely packed with thousands of synaptic vesicles, to sustain a highly facilitating "detonator" transmission. However, whether glutamate release sites at this synapse act independently, in a stochastic manner, or rather synchronously, remains poorly understood. This knowledge is critical for a better understanding of mechanisms underpinning presynaptic plasticity and postsynaptic signal integration rules. Here, we use the optical glutamate sensor SF-iGluSnFR and the intracellular Ca2<sup>+</sup> indicator Cal-590 to monitor spike-evoked glutamate release and presynaptic calcium entry in MF boutons. Multiplexed imaging reveals that distinct sites in individual MF giant boutons release glutamate in a probabilistic fashion, also showing use-dependent short-term facilitation. The present approach provides novel insights into the basic mechanisms of neurotransmitter release at excitatory synapses.

#### Edited by:

Haruyuki Kamiya, Hokkaido University, Japan

#### Reviewed by:

Jon Storm-Mathisen, University of Oslo, Norway Marco Fuenzalida, University of Valparaíso, Chile

#### \*Correspondence:

Sylvain Rama s.rama@ucl.ac.uk; rama.sylvain@gmail.com Dmitri A. Rusakov d.rusakov@ucl.ac.uk

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

> Received: 26 February 2019 Accepted: 16 May 2019 Published: 04 June 2019

#### Citation:

Rama S, Jensen TP and Rusakov DA (2019) Glutamate Imaging Reveals Multiple Sites of Stochastic Release in the CA3 Giant Mossy Fiber Boutons. Front. Cell. Neurosci. 13:243. doi: 10.3389/fncel.2019.00243 Keywords: dentate gyrus, CA3 pyramidal cell, short-term plasticity, glutamate release, giant mossy fiber bouton, action potential

## INTRODUCTION

The dentate gyrus is the entry into the hippocampus, with the mossy fibers (axons of granule cells) innervating both CA3 pyramidal cells and stratum-lacunosum interneurons (Acsády et al., 1998). These distinct postsynaptic cell populations are connected through distinct presynaptic elements: "giant" mossy fiber boutons (gMFBs, 4–10 µm) across and their smaller (2–3 µm) variant synapsing onto the thorny excrescences of CA3 pyramidal cells, and relatively small (0.5–2 µm) en-passant boutons and the filopodial extensions emerging from gMFBs both connecting to interneurons (Chicurel and Harris, 1992; Acsády et al., 1998; Rollenhagen et al., 2007). Hippocampal MFB connections show prominent facilitation during repetitive activity and are considered strong "detonating" synapses, generating large postsynaptic responses in CA3 pyramidal cells (Vyleta et al., 2016). This function is sustained by specific morphology, as they show multiple active zones per MFB, and thousands of synaptic vesicles densely packed inside (Acsády et al., 1998; Rollenhagen et al., 2007). They have been widely studied because MF synapses play a key role in processing spatial information such as pattern completion, pattern separation and storage of sequences of events (Kobayashi and Poo, 2004; Bischofberger et al., 2006). Moreover, these synapses provide a key experimental model for analog-digital control of synaptic transmission, linking presynaptic voltage, presynaptic calcium entry, and glutamate release (Geiger and Jonas, 2000;

Alle and Geiger, 2008; Scott et al., 2008). Finally, changes in MF transmission have been a major pathophysiological indicator in epilepsy (Ben-Ari and Represa, 1990; Morimoto et al., 2004) and Down syndrome (Witton et al., 2015). Therefore, an inquisitive exploration of MF synapses helps to understand the fundamentals of synaptic transmission and hippocampal network function in a wide context.

#### RESULTS

### Simultaneous Imaging of Presynaptic Calcium Entry and Glutamate Release at Presynaptic MF Boutons

To directly monitor glutamate release by MFBs, we turned to organotypic slices which we biolistically transfected with the SFiGluSnFR A184V construct (termed iGluSnFR thereafter; see section "Methods"), as detailed earlier (Jensen et al., 2019). With the sparse expression among cells, the iGluSnFR basal fluorescence was sufficient to reveal cell morphology and to track the cell axon. We thus patch-loaded dentate granule cells with the red-shifted calcium-sensitive dye Cal-590 (Tischbirek et al., 2015; Jensen et al., 2019) and followed their axon up to at least 100 µm from the cell soma, toward the CA3 area (**Figures 1A,B**).

In individual cells, we evoked 5 action potentials (APs) at 20 Hz, a bursting pattern similar to that in vivo (Pernía-Andrade and Jonas, 2014; Vyleta et al., 2016; Chamberland et al., 2018). Once we focused on the MF bouton of interest, either of the two imaging protocols was employed: (i) for boutons smaller than 4 µm, a fast "tornado" scanning mode covering the bouton profile (Jensen et al., 2017, 2019), and (ii) for boutons above 4 µm, a straight line-scan along the longest axis of the bouton. In either case, we scanned at 500 Hz and collected both iGluSnFR and Cal-590 fluorescence. Signals were converted as 1F/F values, and the Cal-590 signal was used to confirm AP arrival to the bouton (**Figure 1C**). The iGluSnFR signal revealed glutamate release sites in the bouton, showing release successes and failures (**Figure 1D**). At each individual site, release probability (calculated as the release success rate over all the trials) increased progressively with the AP number in the train, showing classical facilitation (**Figure 1E**). The initial release probability (first AP) at individual release sites was 0.37 ± 0.07 (mean ± SEM, n = 11 boutons), consistent with previous observations (Lawrence et al., 2004).

## Distinct Release Sites Display Stochastic Release

In 6 out of 11 recorded boutons, we could clearly distinguish at least two active release sites, providing rapid glutamate discharges, which did not appear synchronized. We recorded between 3 and 14 consecutive trials (1 min apart) per bouton. Glutamate releases from spatially separate areas were detected in 80 ± 12% trials per bouton (mean ± SEM, a total of n = 43 trials). They were either synchronized or independent (**Figure 2A**). In 25 ± 8% of the recordings (n = 43), we could observe spontaneous (or possibly asynchronous, postburst) release by some release sites (asterisks in **Figure 2** traces). In one gMFB, there were up to four distinct release sites with the first AP inducing glutamate release in only 2 of them and spontaneous release in one of them, independent from the other 3 (**Figure 2B**).

## DISCUSSION

In this brief report, we expressed the SF-iGluSnFR reporter dye in dentate granule cells and monitored glutamate release in gMFBs during brief trains of evoked APs. We detected multiple release sites in individual boutons displaying non-synchronized release activity. This appears in contrast to CA3-CA1 synapses, the majority of which displayed only one detectable glutamate release hotspot (20 out of 23; organotypic slices) whereas the two-hotspot boutons (3 out of 23) showed no detectable asynchrony (Jensen et al., 2019). At the same time, EM data report dual active zones in 38% of CA3-CA1 connections (Shepherd and Harris, 1998), suggesting that super-resolution approaches, such as stochastic localization, once combined with the present technique, might help to better resolve individual release hotspots. Indeed, optical diffraction limit, stereological bias, and limitation of 3D volume scanning should underestimate the occurrence of release sites and therefore their release asynchrony. In some cases, the distinction between en-passant boutons [which are not supposed to have multiple active zones (Acsády et al., 1998)] and the small subtype of giant MF boutons could also be less than clear-cut. Despite of these limitations, the present approach enables us to detect and explore glutamate release and its stochastic features in a direct manner, the task that has hitherto been difficult to achieve.

## Maintenance of High Frequency Transmission by Cross-Talk?

At many synapses, the rates of vesicle fusion exceed the rates of their replenishment leading to vesicle depletion during highfrequency activity (Zucker and Regehr, 2002). However, gMFBs could have formed in a similar way to the Purkinje terminals or the neuro-muscular junction (Telgkamp et al., 2004; Knodel et al., 2014), with large boutons with multiple active zones and densely packed with synaptic vesicles (Rollenhagen and Lübke, 2010). At gMFB synapses, large areas of the opposing pre- and postsynaptic membranes are separated by a narrow cleft. This extracellular space geometry provides, at least in theory, favorable conditions for neurotransmitter spill-over among multiple postsynaptic densities, thus achieving high-fidelity transmission even at low release probabilities and low rates of vesicle replenishment (Vergnano et al., 2014; Zheng et al., 2017). However, our glutamate imaging data suggest that this may not be the case for the MF-CA3 transmission, as the majority of individual glutamate release hotspots in presynaptic boutons do not seem to overlap, at least during first spikes. Indeed, if Purkinje cells do fire at high rates (Telgkamp et al., 2004), it is rarely the case for granule cells of the dentate gyrus (Pernía-Andrade and Jonas, 2014). Moreover, lower release probabilities and readily releasable vesicle pools make hippocampal mossy fiber boutons

en-passant bouton. The fast "Tornado" (spiral) line-scan was set-up to cover most of the bouton visible area. (C) Typical imaging protocol. Traces: Five APs initiated by brief (5 ms) current pulses at 20 Hz (holding voltage −80 mV); Image panels: Tornado line-scans recorded in the Cal-590 (upper) and SF-iGluSnFR (lower) emission channels. (D) Same recordings as in panel (C), but pixel values were averaged over the length of the tornado line-scan and converted as 1F/F. Note that for the Cal-590 signal, each AP induced a calcium entry in the presynaptic bouton (middle) whereas APs 2 and 5 failed to induce a glutamate release (bottom, black arrows). (E) Average release probability (mean ± SEM) for the AP train (n = 11 boutons). Note the increasing probability with the AP number, reflecting presynaptic facilitation.

more suitable for presynaptic facilitation than high-frequency transmission (Delvendahl et al., 2013).

## Implications for Postsynaptic Signal Integration and Presynaptic Machinery

Morphological studies employing 3D electron microscopy have shown that individual giant MF boutons tend to form synaptic connections on more than one postsynaptic CA3 pyramidal cell (Acsády et al., 1998; Rollenhagen and Lübke, 2010). The present finding that individual release sites in such boutons can discharge glutamate relatively independently in a stochastic fashion, suggests that postsynaptic responses in their distinct cell targets could be similarly de-synchronized. It has been previously reported that in juvenile rats, gMFBs may co-release GABA and glutamate (Walker et al., 2001; Ruiz et al., 2003; Beltrán and Gutiérrez, 2012; Münster-Wandowski et al., 2013). The present results thus suggest that GABA and glutamate release from the same gMFB could be, in principle, stochastically separated. Finally, gMFBs show significant structural plasticity in the pilocarpine and kindling models of epilepsy (Danzer et al., 2010; McAuliffe et al., 2011), which could directly affect functional interaction between their individual release sites. What molecular mechanisms underpin such structural and functional changes remains an intriguing and important question.

## METHODS

## Organotypic Cultures of Rat Hippocampus

Hippocampal slice cultures were prepared as described previously (Bialowas et al., 2014). All experiments were carried out according in accordance with the European Commission Directive (86/609/EEC) and the United Kingdom Home Office (Scientific Procedures) Act (1986). Briefly, postnatal day 7–8 Wistar rats were briefly anesthetized by isoflurane inhalation, the brain removed and each hippocampus individually dissected in ice-cold sterile slicing solution consisting (in mM) of Sucrose 105, NaCl 50, KCl 2.5, NaH2PO4 1.25, MgCl2 7, CaCl2 0.5, Ascorbic acid 1.3, Sodium pyruvate 3, NaHCO3 26 and Glucose 10. Hippocampal slices (350 µm) were placed on 20-mm latex membranes (Millicell-CM, Millipore, United Kingdom) inserted

into 35-mm Petri dishes containing 1 ml of culture medium and maintained for up to 30 days in an incubator at 34◦C, 95% O2–5% CO2. The culture medium contained (in ml) 25 minimal essential medium, 12.5 Hanks' balanced saline solution, 12.5 horse serum, 0.5 penicillin/streptomycin, 0.8 glucose (1 M), 0.1 ascorbic acid (1 mg/ml), 0.4 HEPES (1 M), 0.5 B27, and 8.95 sterile H2O. To limit glial proliferation, 5 mM cytosinearabinoside (Ara-C) was added to the culture medium at 4 days in vitro (DIV) for one night.

#### Biolistic Transfection of iGluSnFR Variants

Second generation iGluSnFR variant SF-iGluSnFR.A184V was expressed under a synapsin promoter in dentate gyrus granule cells in organotypic slice cultures using biolistic transfection techniques adapted from manufacturer's instructions. In brief, 6.25 mg of 1.6 micron Gold micro-carriers were coated with 30 µg of SF-iGluSnFR plasmid. Organotypic slice cultures at 8 DIV were shot using the Helios gene-gun system (Bio-Rad) at 120 psi. The slices were then returned to standard culture media the next day and remained for 3–7 days before experiments were carried out.

#### Axon Tracing and Imaging of Pre-synaptic Boutons

We used a Femtonics Femto2D-FLIM imaging system, integrated with patch-clamp electrophysiology (Femtonics, Budapest) and linked on the same light path to two femtosecond pulse lasers MaiTai (SpectraPhysics-Newport) with independent shutter and intensity control. Patch pipettes were prepared with thin walled borosilicate glass capillaries (GC150-TF, Harvard apparatus) with open tip resistances 2.5–3.5 M. Internal solution contained (in mM) 135 potassium methanesulfonate, 10 HEPES, 10 di-Tris-Phosphocreatine, 4 MgCl2, 4 Na2-ATP, 0.4 Na-GTP (pH adjusted to 7.2 using KOH, osmolarity 290–295), and supplemented with Cal-590 (300 µM; AAT Bioquest).

Pre-synaptic imaging was carried out using an adaptation of pre-synaptic glutamate and Ca2<sup>+</sup> imaging methods previously described (Jensen et al., 2017, 2019). Cells were first identified as iGluSnFR expressing using two-photon imaging at 910 nm and patched in whole cell mode as above. Following break-in, 10–15 min were allowed for Cal-590 to equilibrate across the axonal arbor. Axons, identified by their smooth morphology and often tortuous trajectory, were followed in frame scan mode to their targets. Putative Giant Boutons were identified as varicosities on axon collaterals with a minimum diameter and length of ∼2–3 µm (Acsády et al., 1998; Rusakov and Fine, 2003; Rama et al., 2015).

#### REFERENCES


For fast imaging of action-potential mediated iGluSnFR and Cal-590 fluorescence transients at single boutons a spiral shaped ("tornado") scan line was placed over the bouton of interest (described further in the text), which was then scanned at a sampling frequency of ∼500 Hz with excitation at 910 nm. APs were typically induced by trains (20 Hz) of 5 short (5 ms) pulses of depolarizing current (900–1400 pA) in current clamp mode and synchronized with biphoton fluorescent imaging. Ten to fifteen acquisitions were made per boutons, recordings showing APs failures were discarded.

### Data Analysis

After acquisition, iGluSnFr or Cal-590 fluorescence was converted to 1F/F values. Region of Interest (ROIs) were defined by fitting the fluorescence profile with Gaussian equation and extracting the Full Width at Half Maximum (FWHM) of this Gaussian. All of this was calculated by custom-written analysis programs written in Labview (National Instruments) and Matlab (MathWorks).

## DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and/or the supplementary files.

## ETHICS STATEMENT

All experiments were carried out according in accordance with the European Commission Directive (86/609/EEC) and the United Kingdom Home Office (Scientific Procedures) Act (1986).

## AUTHOR CONTRIBUTIONS

SR, TJ, and DR designed the experiments. SR and TJ carried out the patch-clamp and imaging experiments in neurons. SR carried out the analysis. SR and DR wrote the manuscript. All authors contributed to manuscript writing.

## FUNDING

This work was funded by Marie-Curie Fellowship IF-746247 Astromodulation, by the Wellcome Trust Principal Fellowship (212251/Z/18/Z), and by the ERC Proof of Principle grant (767372 – NEUROCLOUD).



**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 © 2019 Rama, Jensen and Rusakov. 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(s) 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.

# Dynamic Regulation of Synaptopodin and the Axon Initial Segment in Retinal Ganglion Cells During Postnatal Development

, Dominik Dannehl<sup>1</sup>

,

Annabelle Schlüter1,2, Sabrina Rossberger<sup>3</sup>†

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Juan José Garrido, Spanish National Research Council (CSIC), Spain Hiroshi Kuba, Nagoya University, Japan

\*Correspondence:

Maren Engelhardt maren.engelhardt@ medma.uni-heidelberg.de

†Present address: Sabrina Rossberger, DELMIC B.V., Delft, Netherlands

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

> Received: 20 April 2019 Accepted: 28 June 2019 Published: 30 July 2019

#### Citation:

Schlüter A, Rossberger S, Dannehl D, Janssen JM, Vorwald S, Hanne J, Schultz C, Mauceri D and Engelhardt M (2019) Dynamic Regulation of Synaptopodin and the Axon Initial Segment in Retinal Ganglion Cells During Postnatal Development. Front. Cell. Neurosci. 13:318. doi: 10.3389/fncel.2019.00318 Jan Maximilian Janssen<sup>1</sup> , Silke Vorwald<sup>1</sup> , Janina Hanne<sup>4</sup> , Christian Schultz<sup>1</sup> , Daniela Mauceri<sup>2</sup> and Maren Engelhardt<sup>1</sup> \*

1 Institute of Neuroanatomy, Center for Biomedical Research and Medical Technology, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, <sup>2</sup> Department of Neurobiology, Interdisciplinary Center for Neurosciences, Heidelberg University, Heidelberg, Germany, <sup>3</sup> Kirchhoff-Institute for Physics, Applied Optics, Heidelberg University, Heidelberg Germany, <sup>4</sup> Abberior Instruments GmbH, Heidelberg, Germany

A key component allowing a neuron to function properly within its dynamic environment is the axon initial segment (AIS), the site of action potential generation. In visual cortex, AIS of pyramidal neurons undergo periods of activity-dependent structural plasticity during development. However, it remains unknown how AIS morphology is organized during development for downstream cells in the visual pathway (retinal ganglion cells; RGCs) and whether AIS retain the ability to dynamically adjust to changes in network state. Here, we investigated the maturation of AIS in RGCs during mouse retinal development, and tested putative activity-dependent mechanisms by applying visual deprivation with a focus on the AIS-specific cisternal organelle (CO), a presumed Ca2+-store. Whole-mount retinae from wildtype and Thy1-GFP transgenic mice were processed for multi-channel immunofluorescence using antibodies against AIS scaffolding proteins ankyrin-G, βIV-spectrin and the CO marker synaptopodin (synpo). Confocal microscopy in combination with morphometrical analysis of AIS length and position as well as synpo cluster size was performed. Data indicated that a subset of RGC AIS contains synpo clusters and that these show significant dynamic regulation in size during development as well as after visual deprivation. Using super resolution microscopy, we addressed the subcellular localization of synpo in RGC axons. Similar to cortical neurons, RGCs show a periodic distribution of AIS scaffolding proteins. A previously reported scaffold-deficient nanodomain correlating with synpo localization is not evident in all RGC AIS. In summary, our work demonstrates a dynamic regulation of both the AIS and synpo in RGCs during retinal development and after visual deprivation, providing first evidence that the AIS and CO in RGCs can undergo structural plasticity in response to changes in network activity.

Keywords: axon initial segment, cisternal organelle, synaptopodin, retinal ganglion cell, visual deprivation

## INTRODUCTION

fncel-13-00318 July 27, 2019 Time: 14:57 # 2

In the retina, visual processing relies on a chain of neurons that transmit information from the outmost photoreceptor layer to the innermost retinal ganglion cell (RGC) layer (Masland, 2012). RGCs convey information via higher order nuclei in the visual pathway to the primary visual cortex (V1) and associated regions. During development, V1 undergoes defined critical periods of cortical plasticity, which shape and refine the mature visual map (reviewed in Hensch, 2004). These critical periods are defined by activity patterns across the visual pathway, and lack of neuronal activity and visual input leads to significant alterations of the final network configuration in V1 (reviewed in Hensch, 2005). While the role of somatodendritic plasticity in this context has been studied extensively (Levelt and Hubener, 2012), it has only recently been acknowledged that axonal plasticity may play an equally important role for the development of sensory cortices (reviewed in Jamann et al., 2017).

The axon initial segment (AIS) is a structurally and molecularly unique axonal domain (Huang and Rasband, 2018; Leterrier, 2018) and is the site of action potential initiation (Kole and Stuart, 2012). Recent work has suggested that it is linked to regulating neuronal excitability on a single cell level, most likely via homeostatic mechanisms (reviewed in Wefelmeyer et al., 2016; Engelhardt et al., 2019). This concept is based on a growing body of evidence from in vitro and in vivo studies and across multiple species showing that the AIS contributes to cellular excitability by increasing or decreasing its length or distance to the soma in response to changes in network activity (reviewed in Yamada and Kuba, 2016; Jamann et al., 2018). These events are thought to be a direct result of changes in synaptic drive either during development or in the mature network: Longer AIS reflect a decrease in synaptic drive, for example after sensory deprivation, and facilitate action potential generation, whereas shorter or distally relocated AIS result from an increase in synaptic drive and are correlated with decreased excitability (reviewed in Jamann et al., 2018).

In work leading to the present study, we described the activitydependent structural maturation of the AIS in V1 pyramidal neurons, which undergo distinct periods of length maturation during the postnatal phase until closure of the critical period of cortical plasticity in mice around P35 (Gutzmann et al., 2014). Visual deprivation led to a significant modulation of this maturation period; in fact, V1 pyramidal neurons were no longer able to reach mature AIS lengths (Gutzmann et al., 2014). The underlying mechanisms that regulate AIS plasticity, in particular length and location changes, remain largely unknown. Recent evidence indicates that intraaxonal Ca2<sup>+</sup> levels may play an important role for AIS plasticity and considering the importance of Ca2<sup>+</sup> currents for the generation and timing of action potentials (Bender and Trussell, 2009), this seems intuitive. Our previous work highlighted a role for the cisternal organelle (CO) in AIS plasticity in V1 pyramidal neurons (Schlüter et al., 2017). The CO consists of stacks of smooth endoplasmic reticulum and is a putative regulator of Ca2+ storage and release in the AIS (Benedeczky et al., 1994; Bas Orth et al., 2007). The structural integrity of the CO is organized by the actin-binding protein synaptopodin (synpo; Bas Orth et al., 2007), which therefore is an excellent molecular marker of this intraaxonal compartment (Sanchez-Ponce et al., 2011; Schlüter et al., 2017).

Currently, it is unclear whether RGC AIS constitute a group of neurons similar to cortical pyramidal cells in terms of AIS morphology, maturation and plasticity, and whether putative AIS plasticity in RGCs could be partially regulated by the dynamic remodeling of the CO. In the present study, we therefore investigated the structural maturation of AIS length and synpo expression in RGCs during retinal development and in dark-reared mice, utilizing a combination of multichannel immunofluorescence, confocal and super resolution microscopy as well as morphometrical analysis. Our data indicate that RGC AIS share a common nanostructure with other excitatory neurons of the visual pathway. Furthermore, RGC AIS develop with similar activity-dependent profiles as shown for V1: Both the AIS and synpo in RGCs undergo periods of dynamic remodeling during retinal development and after visual deprivation, indicating that organelles in the AIS of RGCs can undergo structural plasticity in response to changes in network activity and might therefore impact cellular function during visual processing.

## MATERIALS AND METHODS

#### Animals

The following mouse and rat strains were used: wildtype C57BL/6JRj mice (Janvier Labs, France), B6.Cg-Tg(Thy1- EGFP)MJrs/J mice (own colony at Heidelberg University), and wildtype RjHan:SD rats (Janvier Labs, France). Animals of mixed gender from C57BL/6JRj strain, Tg(Thy1-EGFP)MJrs/J strain, and RjHan:SD strain were maintained with food and water ad libitum on a regular 12 h light/dark cycle. C57BL/6JRj wildtype mice were used for deprivation studies, reared on a 24 h dark cycle as described below, and for the postnatal development study (ages P10 to P > 55). For morphometrical studies of AIS and synpo cluster localization, adult (P > 55) wildtype mice and rats as well as Thy1-EGFP mice were used.

### Developmental Study

For the analysis of AIS length and synpo expression in RGC AIS during retinal development, a total of 6 wildtype mice were analyzed in each of the following age groups: P10, P15, P21, P28, P35, P > 55 (two retinae per mouse, at least 100 AIS per animal <sup>1</sup>= at least 600 AIS/group). For the analysis of AIS in Thy1-EGFP mice, a total of 5 adult (P > 55) mice and a total of 5 control (P > 28) mice were used. For super resolution imaging of the AIS scaffold and synpo clusters in AIS of RGCs, a total of 5 adult (P > 55) wildtype rats and mice were analyzed. Thirty AIS were examined in total. A summary of all experimental groups is given in **Table 1**.

TABLE 1 | Experimental and control groups used in the current study with indication of age of animal, mouse strain, period of visual deprivation, and treatment of tissue for immunofluorescence.


#### Visual Deprivation

Wildtype and Thy1-EGFP mice were kept in completely dark cages with food and water ad libitum. Total absence of light was controlled by exposure of photographic paper located in the cages. Groups of 6 (wildtype) and 11 (Thy1-EGFP) mice each were reared in complete darkness from P0–28 and P0– 35, respectively. Analyses then proceeded immediately after the period of visual deprivation. Data from the developmental study (P28 and 35, wildtype; P > 28, Thy1-EGFP) served as controls for deprivation experiments. All experimental groups are summarized in **Table 1**.

#### Tissue Preparation

Mice were exsanguinated with 0.9% saline under deep anesthesia with ketamin (120 mg/kg BW)/xylazine (16 mg/kg BW). Animals were then perfused transcardially with ice-cold 4% paraformaldehyde (PFA) in 1x PBS. Whole retinas were extracted and processed as follows: Eyes were enucleated with fine curved forceps and were transferred into a 5 cm culture dish containing ice-cold 1x PBS. Retinae were dissected under a stereomicroscope with an internal light source. A hole was cut into the eye at the corneal limbus by using a pair of fine spring scissors. After a circumferential incision along the limbus, the cornea, iris, vitreous body, and lens were removed in toto. The retina was extracted from the eye cup. Retinae were fixed in 4% PFA for 10 min and were washed three times in 1x PBS before further processing.

#### Immunofluorescence

Double and triple immunofluorescence was performed on freefloating whole retinae as described previously (Schlüter et al., 2019). Retinae were blocked for 4-5 h (in 0.5% Triton X-100, 0.2% bovine serum albumin and 0.02% sodium azide in 1x PBS) at 4◦C. Primary antibodies were diluted in dilution buffer (1% Triton X-100, 10% fetal calf serum and 0.02% sodium azide in 1x PBS) according to previously validated concentrations (Gutzmann et al., 2014; Schlüter et al., 2017). Retinae were incubated with primary antibodies for 24 h at 4◦C. Afterward, tissue was washed three times in 1x PBS for 15 min each. Retinae were then incubated with fluorophore-conjugated secondary antibodies diluted in dilution buffer for 24 h at 4◦C, followed by additional washing steps (3x in 1x PBS, 15 min each). Prior to mounting, retinae were fixed for 10 min in 4% PFA and washed in 1x PBS (2x for 5 min). Tissue was then cut from the rim to 1/3 of the radial length and was flat-mounted on slides. All performed stainings were accompanied by negative controls, in which omitting the primary antibody completely abolished all stainings. For confocal and STED microscopy, retinae were embedded in Roti <sup>R</sup> -Mount FluorCare mounting medium or Mowiol (Carl Roth, Karlsruhe, Germany). For SIM and SMLM, retinae were embedded in ProLong <sup>R</sup> Gold mounting medium (Thermo Fisher Scientific, Waltham, MA, United States) or switching buffer [10% dd H2O, 10% 1x PBS, 80% glycerol, 0.1M cysteamine, 100u glucose oxidase (Type VII from Aspergillus niger), 800u catalase (from Bovine liver), 0.1M D-(+)-Glucose]. For shift corrections (SIM and SMLM), 1 µl of FluoSpheres <sup>R</sup> (FluoSpheres <sup>R</sup> Fluorescent Color Kit, Carboxylate-Modified Microspheres, 0.04 µm, four colors; Thermo Fisher Scientific, Rockford, IL, United States) was transferred near the edge of the slide. Coverslips were sealed onto slides using transparent nail polish. All antibodies used in this study are summarized in **Supplementary Table 1**.

#### Confocal Microscopy

Conventional laser scanning confocal microscopy was carried out using a C2 confocal microscope (Nikon, Alzenau, Germany; laser lines: 642, 543, and 488 nm), with a 60x objective (oil immersion, NA 1.4) and a SP5 confocal microscope Leica, Mannheim, Germany; Laser lines: 633, 561, 514, and 488 nm) with a 63x objective (oil immersion, NA 1.4), respectively. To increase the number of in-focus immunoreactive structures, stacks of images were merged into a maximum intensity projection and saved as jpeg and tif format. Thickness of single optical sections was 0.2 µm in stacks of 3–5 µm total depth. Confocal x-y-resolution was constantly kept at 0.21 µm per pixel. Images for qualitative analysis were evaluated and enhanced for contrast in Fiji (Image J) and Photoshop C5 (Adobe Systems, United States).

#### Super Resolution Microscopy

Three different super resolution methods were applied to obtain a comprehensive understanding of the RGC AIS nanostructure.

Stimulated Emission Depletion (STED) imaging was performed using a STEDYCON (Abberior Instruments GmbH, Göttingen) with excitation lasers at 488, 561, and 640 nm, and a STED laser at 775 nm (maximum intensity 1.25 W; all lasers are pulsed with 40 MHz repetition rate). The STEDYCON was mounted on the camera port of an AxioImager.Z2 upright microscope (Zeiss, Jena, Germany), equipped with a 100x objective (alpha Plan-Apochromat, Oil, DIC, Vis, NA 1.46; Zeiss). The pinhole was set to 1.1 Airy units for 650 nm emission. Fluorescence was detected on avalanche photo diodes, with emission bands between 650–700 nm, 578–627 nm, and 505–545 nm, respectively. Data was stored in .obf format and exported as tif files for further analysis.

Correlative Structured Illumination Microscopy (SIM) and Single Molecule Localization Microscopy (SMLM) were performed using a custom-built microscope, which is described in detail in Rossberger et al. (2013). For acquisition, a high

numerical objective (Leica HCX PL APO 100x/1.4 oil CS), a charge-coupled device-camera (Sensicam QE, PCO, Kelheim, Germany) and the following laser lines were used: 568 nm laser line (Coherent Sapphire 568 HP, 200 mW, Coherent, Dieburg, Germany) and 671 nm (VA-I-300-671, 300 mW, Beijing Viasho Technoloy Co. Ltd., Beijing, China). For each laser line, excitation and emission light were separated using an appropriate dichroic mirror (Di02-R568 and Q680LP, both Semrock, Rochester, NY, United States) and emission filter combination (BLP01-561, Semrock and LP XF 3104, Omega Optical, Olching, Germany).

Prior to SIM and SMLM acquisition, sections were scanned for correlated AIS-(568 nm) and Synpo-(647 nm) signal using the widefield mode of the microscope. For this purpose, the 568 nm excitation laser line was used in combination with an edge basic longpass emission-filter (BLP01-568R-25, Semrock, Rochester, NY, United States). The resulting widefield image (pixel size of 64.5 nm) shows an overlay of both color channels within one image and was used for shift corrections of the two color channels recorded separately in super resolution mode. Details of SIM and SMLM image acquisition are outlined in the **Supplementary Methods**.

#### Morphometrical Analysis

We classified RGCs in Thy1-GFP mice where the entire cell could be visualized and measured soma size, dendritic tree diameter and stratification of dendrites into the inner plexiform layer (IPL) according to previously published guidelines (Sun et al., 2002b). We used parameters of soma and dendritic field size to classify RGCs into the different classes (A1–A2, B1– B4, C1–C6, D1–D2; O'Brien et al., 2014) as well as dendritic stratification into the IPL to further isolate A RGCs (RGCA) into ON- and OFF-ganglion cells (Anderson et al., 2016; Saha et al., 2016). Confocal z-stack images of entire RGCs were projected using AutoQuant X3 software (Media Cybernetics). The obtained three-dimensional images were turned 90 degrees to visualize the stratification of the dendritic tree of RGCs within the IPL (**Supplementary Figure S1A**). ON-ganglion cells were identified based on the ramification of their dendritic processes in sublamina b of the IPL whereas OFF-ganglion cells ramify in sublamina a of the IPL. In order to confine our data analysis to the RGC layer specifically and avoid any potential cross-contamination with cells or AIS from other retinal layers, confocal stacks were acquired exclusively within the ganglion cell layer (GCL) of the retina. The GCL could be identified clearly by NeuN immunostaining, nuclei labeling (TOPRO), and its location within 5–10 µm underneath the nerve fiber layer of the mouse retina. Thus, AIS of other retinal layers, such as AIS-like processes from AII amacrine cells located in the inner nuclear layer (Wu et al., 2011) were not included in our analysis. AIS in the GCL were selected only after clear identification of proximal and distal endpoints of immunoreaction to ankyrin-G (ankG) or βIV-spectrin could be traced across optical sections of a stack without any discontinuation or broad stratification into other layers, based on the 3D-projections created for the RGC classification (**Supplementary Figure S1B**). Overlapping AIS were not included in the analysis to avoid any potential interference of immunofluorescent signal with length and distance analysis.

AIS length and distance from the soma were obtained using a self-written program in Python (AISuite et al., unpublished; Hoefflin et al., 2017; Ernst et al., 2018). Briefly, in this application, the AIS is traced manually, beginning with the axon hillock and ending with the axon past visible AIS staining to exclude personal bias. The cut-off threshold for AIS length identification was set to 30% of the individual maximum intensity. Triplets of AIS signal values were analyzed to reduce the influence of upward outliers. The proximal and distal borders of the AIS were determined as the first, respectively the last triplet of signal values which were higher than the defined cut-off. The pixel difference between the proximal and distal end of the AIS was calculated and converted into length in µm taking the microscope's calibration into account. AIS distance to the soma was determined by calculating the distance between the onset of the individual region of interest at the axon hillock and the estimated beginning of the AIS, using the same cut-off. All data were exported as HDF5 and Excel files for statistical analysis.

Periodicity of the AIS scaffold was analyzed similar to previously published methods (D'Este et al., 2015). Briefly, brightness and contrast were adjusted linearly for each STED and SMLM image. Fluorescence intensity plot profiles were measured using ImageJ along a 5 pixel wide line drawn along the AIS. For each AIS, a minimum of 3 regions were measured. The distances between interpeaks were determined using the peak analyze function in OriginPro software (Additive Friedrichsdorf, Germany).

#### Synpo Expression Analysis

Number and size of synpo clusters were measured using a self-written macro in ImageJ as previously published (Schlüter et al., 2017). AIS containing synpo-positive immunofluorescence signals were manually outlined. Background signals beyond the AIS were eliminated. For cluster analysis, the "Color Threshold" option was used. Threshold level was set to 55 and minimum size of pixels was 5. Both values were kept constant during measurements. Synpo-positive clusters per AIS were defined by these parameters and were measured automatically for mean number and size (in pixels). For cluster sizes, mean pixel values were translated into µm<sup>2</sup> (area [µm<sup>2</sup> ] = area [pixels] × (microscope resolution)<sup>2</sup> ).

#### Image Analysis

For analysis of SIM data, nine images of conventional resolution for each z layer and each color channel were recorded. These images were reconstructed and deconvolved using custom developed software written in Matlab (Best et al., 2011). Image reconstruction resulted in one image for each layer within the z-stack and each color channel. For reconstruction of synpo clusters within RGC AIS, 3D SIM images were processed first by blind iterative deconvolution (theoretical PSF based on the optical properties of the microscope and the sample, 10x iteration) according to standard procedures in AutoQuant X3 (Media Cybernetics). Subsequently, to visualize x-y-z information about synpo cluster localization within the AIS,

deconvolved files were reconstructed (surface) using Imaris 9.0 (Bitplane, Zurich) according to previously published protocols (Schlüter et al., 2017).

For analysis of SMLM data, single molecule positions of optically isolated molecules were determined by using custom software written in Python. Briefly, a Gaussian function was fitted to each single molecule signal and its center of mass was calculated. Center coordinates evaluated from all images of the sequence were transferred into one image, marking the position of one fluorophore. The mean position or localization accuracy was 1x = 10.6 nm, resulting in a position image. Images were rendered using a triangulation algorithm as previously published (Baddeley et al., 2010). The area spanned by three next neighbor fluorophore positions (triangle) was translated inversely into intensity values depending on the size of the area. High intensity values were translated into small distances between fluorophore positions and vice versa. Pixel size for visualization was either 5, 32.25, or 64.5 nm. Single molecule positions were randomly jittered to generate 100 slightly different images, which were overlaid afterward to smooth structure edges. Thus, single molecule positions within the images were transferred into an image showing structures in a more conventional sense.

#### Statistical Analysis

Mean values of AIS length and position as well as size and number of synpo clusters per AIS were calculated in Excel (Microsoft). Standard deviation (SD) were calculated and mean values were plotted and analyzed in GraphPad Prism 7 software (GraphPad Software, San Diego, CA, United States). Values were tested for normal distribution by performing Shapiro–Wilk normality test (for testing mean values, n = 6) or D'Agostino and Pearson normality test (for testing single values, n > 600). Unpaired t-test or Mann–Whitney t-test was carried out for statistical comparison of two groups. One-way ANOVA, Kruskal–Wallis or two-way ANOVA test was applied for comparing three or more groups. Post hoc correction was performed by Tukeys or Sidak post test. Boxes extend from the 25th to 75th percentile. Error bars are drawn down to the minimum and up to the maximum value. Asterisks indicate significant differences (∗p ≤ 0.05). For frequency distribution, bin centers were classified by dividing the entire range of values into a series of intervals. Values were then counted and assigned to each interval. For frequency distribution of ankG/β-spectrin periodicity, the entire range was 0–0.4 µm. Bin center steps were 0.02 µm. For frequency distribution of AIS length, the entire range was 10–55 µm. Bin center steps were 2 µm.

#### RESULTS

#### AIS of Mature RGCs Are Characterized by a Distal Localization and a Defined Nanoscale Scaffold

The morphology of RGC AIS in adult mouse retinae was characterized by immunofluorescence against typical AIS scaffolding proteins such as ankyrin-G (ankG) and βIVspectrin, followed by confocal and super resolution microscopic qualitative analysis (**Figures 1**, **2**). We found that both scaffolding proteins are expressed abundantly across all unmyelinated fiber tracts traversing the retina toward the optic disk and colocalize with neurofilament 200 kDa (**Figure 1A**). Individual RGC AIS are clearly distinguishable from the thicker fiber tracts based on their thin structure, increased ankG/βIV-spectrin expression, and decreased neurofilament 200kDa-immunoreaction (**Figure 1A**, magenta arrows). Using the transgenic Thy1 M-GFP mouse line, which sparsely labels RGCs under control of the Thy1 promoter in the retina (Feng et al., 2000), we observed a significant distance between the soma and proximal beginning of the AIS in most RGCs (20 ± 7.1 µm SD; **Figures 1B,D**). This highlights a significant difference to pyramidal neurons in V1, which in mice almost never showed a gap between proximal AIS and soma, but if a gap was detectable, the distance was significantly smaller (P28 visual cortex 2.3 ± 1.5 µm SD; **Figures 1C,D**).

To investigate the nanoscale architecture of the AIS in RGCs, we utilized STED microscopy and Single Molecule Localization Microscopy (SMLM). Analysis revealed that the ankG and βIV-spectrin scaffold is periodically spaced with distances of approximately 181 ± 26.08 nm SD between single fluorescent signal peaks (STED, **Figures 2A–D**; For SMLM: 205.6 nm ± 42.22 nm SD **Supplementary Figures S2A,B,C**). These findings confirm that RGC AIS are of similar nanostructure as other neuron populations, for which a scaffold with ∼190 nm spacing has been reported (D'Este et al., 2015; Leterrier et al., 2015). STED microscopy also revealed a striking deviation in AIS architecture compared to other neuron populations. RGC AIS often appear 'looped' or arranged in a corkscrew manner almost reminiscent of a double-helix structure (**Figures 2A,B**), with large 'gaps' between two single strands of axonal scaffold (**Figure 2A**).

#### AIS of RGCs Undergo Dynamic Length Maturation During Postnatal Development

The structural maturation of RGC AIS during the postnatal retinal development was investigated by immunofluorescence and confocal microscopy combined with AIS length analysis as previously published (Gutzmann et al., 2014; Schlüter et al., 2017). AIS length development was analyzed from P10 until adulthood (P > 55; **Figure 3**). AIS were the longest during the early postnatal period until eye-opening around P15 (P10: 24.45 ± 0.42 µm SD, P15: 24.11 ± 0.28 µm SD; **Figures 3A,D**). From P21 onward, AIS length significantly decreased, reaching stable length from P28 until adulthood (P21: 20.68 ± 0.36 µm SD, P28: 16.92 ± 0.28 µm SD, P > 55: 16.82 ± 0.25 µm SD; **Figures 3B,D**). In parallel, the cumulative length distribution of retinal AIS significantly shifted from a heterogeneous distribution to a homogenous length distribution at P21 (**Supplementary Figures S3A–H**). Across the three adult stages analyzed, RGC AIS length averaged at 16.9 µm ± 0.6 µm SD (P28, P35, and P > 55; **Figure 3D**), indicating that RGC AIS are shorter than AIS of other cell populations in adult wildtype

Insert: magnification of boxed region in (B), indicating the gap between proximal AIS onset and the soma (upper panel, white arrows) and the length of the entire AIS (lower panel, magenta arrows). (C) Image of V1 cortical pyramidal neurons from adult mouse stained for NeuN (green) and βIV-spectrin (magenta), with only a small distance between soma and proximal AIS indicated by white arrows. (D) Quantification of the soma to AIS distance from V1 cortical neurons and RGCs. Unpaired t-test. <sup>∗</sup>p ≤ 0.05, n = 5 animals (at least 100 AIS per animal). Scale bar in (A) = 20 µm, (A1) = 10 µm, (B) = 30 µm, (B1) = 10 µm, (C) = 20 µm.

mice, such as the visual cortex (average approximately 33 µm; Gutzmann et al., 2014), hippocampus (average approximately 29 µm; Kaphzan et al., 2011), or substantia nigra (average approximately 26 µm; Gonzalez-Cabrera et al., 2017).

## Synaptopodin Is Expressed in AIS of RGCs During Retinal Development

A subset of AIS of hippocampal and cortical neurons express the Ca2+-storing CO (Bas Orth et al., 2007; Sanchez-Ponce et al., 2012a; Schlüter et al., 2017). Considering the difference in morphology and function between RGCs and upstream neurons of the visual pathway, we asked whether RGC AIS also contain such intraaxonal Ca2+-stores. We applied immunofluorescence in retinal whole mounts to test whether synaptopodin (synpo), a core structural component of the CO, is expressed in RGC AIS (**Figure 4**). Interestingly, we found robust synpo expression in a subset of AIS of Thy1-positive RGCs and always confined to the borders of the AIS (**Figures 4A–D**).

A previous study using super resolution microscopy in cortical neurons proposed that synpo-positive COs are clustered at ankG-deficient sites in the AIS (King et al., 2014). We addressed the question whether these clusters appear at sites of ankG-deficiency in RGC AIS. Indeed, occasionally we found synpo clusters in the vicinity of gaps in the axonal scaffold (**Figures 4B,C** and **Supplementary Figure S4B**). However, by applying super resolution microscopy, we found that synpopositive clusters are often located between rings of βIV-spectrin within the AIS (**Supplementary Figure S4A**). Occasionally, synpo clusters appeared as if they were located outside of the AIS (**Figure 4C**, arrowhead).

## The Size, but Not the Number of Synpo Clusters in AIS of RGCs Undergoes Changes During Retinal Development

In visual cortex neurons, synpo clusters undergo a dynamic regulation in both size and number during development (Schlüter et al., 2017). Here, we investigated synpo expression in RGC AIS during postnatal retinal development. Synpo expression in AIS was first observed at P10 in 26.5 ± 6.54% SD of RGC AIS (**Figures 5A,C**). During further postnatal development, the percentage of synpo-positive AIS in the retina remained stable and did not undergo any significant changes (i.e., P28: 28.17 ± 5.78% SD; **Figures 5B,C**). These data suggest that the presence of synpo in RGC AIS is not influenced by visual input mediated by the eye-opening phase around P13,14.

However, it remained an open question whether synpo clusters undergo similar dynamic changes during development as in V1 (Schlüter et al., 2017). Therefore, we examined the developmental changes of synpo expression in RGC AIS and quantified the number (**Figures 5D,E**) and size (**Figures 5F,G**) of synpo-positive clusters per AIS. At P10, the average number of synpo clusters per AIS was 1.6 ± 0.05 SD (**Figure 5E**). During further retinal development, the number of synpo clusters remained stable (i.e., P35: 1.53 ± 0.03 SD; **Figure 5E**), recapitulating the finding regarding the percentage of synpoexpressing AIS during retinal development (**Figure 5C**). The size of synpo-positive clusters in RGC AIS was 0.53 ± 0.01 µm<sup>2</sup> SD at P10 and remained stable until P21 (0.59 ± 0.01 µm<sup>2</sup> SD; **Figure 5G**). In comparison to the stable development of number of synpo-positive clusters per AIS, the size significantly decreased from P21 to P28 and P35, respectively (P28: 0.50 ± 0.02 µm<sup>2</sup> SD, P35: 0.52 ± 0.004 µm<sup>2</sup> SD; **Figure 5G**). During further postnatal development, synpo cluster sizes reached a plateau, which was maintained throughout adulthood (P > 55: 0.53 ± 0.02 µm<sup>2</sup> SD; **Figure 5G**).

### Synpo Expression in RGC AIS Seems to Reduce and Stabilize AIS Length During Retinal Development

Since synpo-positive AIS display shorter AIS length and reduced dynamic length maturation during visual cortex development (Schlüter et al., 2017), we analyzed the developmental changes of length in the subset of synpo-expressing RGC AIS (**Figure 6**), and compared it to the length maturation of the entire

AIS population in the retina (**Figure 3**). At P10, synpopositive AIS have an average length of 15.48 ± 0.35 µm SD (**Figures 6A,C**). During further postnatal development, AIS length continuously decreased (i.e., P28: 14.60 ± 0.25 µm SD; **Figures 6B,C**) and reached a plateau in adulthood (P > 55: 13.91 ± 0.12 µm SD; **Figure 6C**), at which time AIS length is significantly reduced compared to the early postnatal period at P10. In parallel, the cumulative length distribution of

bar (A) = 30 µm, (B,C) = 5 µm.

ANOVA. <sup>∗</sup>p ≤ 0.05, n = 6 animals (at least 100 AIS per animal). Scale bar (A,B) = 20 µm, (C,D) = 5 µm.

RGC AIS was significantly homogeneous already early in development (**Supplementary Figures S5A–H**). Further, the average length of synpo-positive AIS was significantly shorter during retinal development as compared to the entire AIS population [**Figure 6C**, compare to **Figure 3D**; i.e., P21 (all AIS) vs. P21 (synpo<sup>+</sup> AIS: 20.68 ± 0.88 µm SD vs. 14.75 ± 1.02 µm SD)]. These findings suggest that similar to the AIS of pyramidal neurons in the visual cortex (Schlüter et al., 2017), the presence of synpo-positive clusters within the AIS might reduce and possibly stabilize AIS length in RGCs during postnatal retinal development.

### Visual Deprivation During Retinal Development Impairs AIS Length Maturation in the Retina

Recent studies have demonstrated that sensory deprivation prevents the structural maturation of the AIS in auditory, visual

and somatosensory system neurons during development (Kuba et al., 2010; Gutzmann et al., 2014; Schlüter et al., 2017; Jamann and Engelhardt, unpublished). In fact, AIS maturation seems to be an activity-dependent process during which network activity contributes to the final mature length of AIS in cortical principal neurons (reviewed in Jamann et al., 2018). Considering the significant AIS length reduction we observed after eye-opening around P15 in RGC AIS (**Figure 3**), we hypothesized that a similar effect also contributes to AIS length maturation in the retina. To test this, we used visual deprivation protocols and reared mice in complete darkness from birth until P28 and P35, respectively. We measured AIS length in these animals and compared it to that of control animals kept under normal light/dark conditions (**Figure 7**). Similar to the observations during visual cortex development (Gutzmann et al., 2014), darkrearing led to a significant increase in AIS length at P28 and P35 (P28 control vs. dark: 16.90 ± 0.28 µm SD vs. 25.69 ± 0.39 µm SD, **Figures 7A–C**; P35 control vs. dark: 16.92 ± 0.18 µm SD vs. 25.62 ± 0.31 µm SD, **Figure 7C**).

Of note, RGCs are heterogeneous regarding their morphology, firing properties and function. We therefore used data obtained from Thy1-GFP mice to further classify the different RGCs in our dataset as outlined in the methods. We found that most Thy1 positive RGCs belong to class A1 and A2, whereas other classes were represented only by up to ca. 10% of cells (**Supplementary Figure S1C**). Due to the low number of RGCB, RGCC, and RGC<sup>D</sup> cells, sufficient detection of reliable numbers of cells and related AIS in these classes was not pursued.

Selecting only RGC<sup>A</sup> neurons for analysis, we found similar AIS elongation after dark rearing in this subtype [**Figures 7D– F**; control (P > 28) vs. dark (P28): 24.29 ± 1.95 µm SD vs. 28.33 ± 2.22 µm SD]. In these same cells, no significant difference in the gap between proximal AIS and soma was observed [**Supplementary Table 2**; control (P > 28) vs. dark (P28): 22.70 ± 3.44 µm SD vs. 22.80 ± 4.06 µm SD]. Size frequency histograms of AIS length in all RGC classes further highlighted that dark-rearing until P28 and P35 led to an AIS length distribution similar to that found in young animals, suggesting that neurons maintain a juvenile AIS length (**Supplementary Figures S3A–H**). Thus, visual deprivation seems to prevent the structural maturation and developmental shortening of AIS length in RGCs during postnatal periods.

## Visual Deprivation During Retinal Development Increases Synpo Expression and Length of Synpo-Positive RGC AIS

We next hypothesized that visual input influences not only AIS length maturation, but also the development of synpo clusters in AIS of RGCs. Thus, we compared changes in synpo protein expression in RGC AIS in control animals with animals subjected to dark-rearing for 28 and 35 days (**Figures 8A–G**). We quantified the percentage of synpo-expressing AIS as well as the number and size of synpo-positive clusters per AIS. Regarding the percentage of synpo-expressing AIS, we found that the subset of AIS that contain synpo-positive clusters increased after dark-rearing for 28 and 35 days, which was significant in P35 animals (P28 control vs. dark: 28.17 ± 2.36% SD vs. 36.83 ± 3.50% SD, **Figure 8D**; P35 control vs. dark: 24.0 ± 2.41% SD vs. 32.8 ± 1.2% SD; **Figure 8D**). Further, dark-rearing for 28 days resulted in a significant increase in the average number of synpo clusters per AIS (P28 control vs. dark: 1.53 ± 0.03 SD vs. 1.71 ± 0.04 SD; **Figures 8A,B,E**) as well as significant increase of synpo cluster size per AIS (P28 control vs. dark: 0.50 ± 0.02 µm<sup>2</sup> SD vs. 0.58 ± 0.01 µm<sup>2</sup> SD; **Figures 8A,C,F**). Longer periods of visual deprivation until P35 resulted in an unchanged number of synpo-positive clusters per AIS as compared to the control conditions (P35 control vs. dark: 1.53 ± 0.03 SD vs. 1.46 ± 0.07 SD; **Figure 8E**). Instead, an increase of the size of synpo-positive clusters in AIS of P35 darkreared mice was found when comparing them to P35 control mice and visually deprived P28 mice, respectively (P35 control vs. dark: 0.53 ± 0.004 µm<sup>2</sup> SD vs. 0.65 ± 0.04 µm<sup>2</sup> SD, **Figure 8F**; P28 dark: 0.58 ± 0.01 µm<sup>2</sup> ; **Figure 8F**). These data suggest that visual

input can influence number and size of synpo-positive clusters in AIS of RGCs during postnatal development. Moreover, synpo clusters might fuse within the AIS by further increasing in size when visual input is lacking for periods longer than P28 days. Interestingly, sensory deprivation led to an increase in RGCs that express synpo in their AIS; in other words, RGCs that normally would not express synpo, seemed to initiate expression after the lack of visual input during postnatal development.

Our findings indicate a potential AIS length-stabilizing effect of synpo in RGCs during postnatal development (**Figure 6**). Consequently, we questioned whether synpo-positive AIS still retained their ability to adapt their length to changes in visual input as seen for the entire retinal AIS population (**Figure 7**). Therefore, we quantified the length of AIS in the subset of synpo-expressing RGCs in mice that were dark-reared for 28 and 35 days and compared them to control mice raised under normal light/dark conditions (**Figure 8G**). Under all dark-rearing conditions, a significant increase in the length of synpo-positive AIS was observed (P28 control vs. dark: 14.60 ± 0.25 µm SD vs. 16.96 ± 0.28 µm SD, **Figure 8G**; P35 control vs. dark: 14.16 ± 0.27 µm SD vs. 15.68 ± 0.40 µm SD; **Figure 8G**). Further, length distribution histograms of synpo-positive AIS highlighted that visual deprivation led to a significant shift from homogenous to heterogeneous length distributions (**Supplementary Figures 5A–H**). In conclusion, even though the presence of synpo in AIS of RGCs seems to stabilize AIS length during postnatal development under physiological conditions, synpo-positive AIS maintain the ability to dynamically adjustment their length after loss of visual input.

#### DISCUSSION

In V1, where visual input is processed, the AIS of pyramidal neurons is highly plastic during development and after sensory deprivation (Gutzmann et al., 2014). For RGCs, which constitute a downstream neuron population in the visual pathway, the precise morphology as well as putative plasticity of AIS has not been studied in detail so far. In the present work, we investigated the structural maturation of AIS and the CO in

RGCs during retinal development and after sensory deprivation. Our work highlights that (1) RGC AIS have a periodically spaced scaffold of ankG/βIV-spectrin rings; (2) AIS length in RGCs changes with the maturation of the retina during postnatal development; (3) RGC AIS express the specific CO marker synpo, which is located within the ankG/βIV-spectrin scaffold occasionally in close proximity to ankG/βIV-spectrin deficient sites; (4) the percentage of synpo-positive AIS is stable during development, but synpo cluster sizes change with AIS maturation; and (5) visual deprivation prevents the maturation of AIS shortening in RGCs and increases synpo expression in AIS during postnatal development.

Taken together, our data indicate that the presence of synpo could provide structural stability to RGC AIS during periods of refinement of retinal circuits. Further, loss of visually driven synaptic input prevents the structural maturation of AIS length shortening as well as increases synpo expression in RGCs.

## AIS of RGCs Have Similar Architectural Features as Principal Cortical Neurons

Here, we analyzed AIS positions along the axon by measuring the distance of the AIS to the RGC soma in adult animals.

We found that RGC AIS appear with a significant distance to the soma compared to pyramidal neurons in V1. AIS length and/or AIS position along the axon is proposed to impact neuronal excitability depending largely on the corresponding somatodendritic morphology of neurons (Gulledge and Bravo, 2016; Hamada et al., 2016; Kole and Brette, 2018). Thus, it is likely that the observed diversity in AIS position along the axon of RGCs in our study is linked to the variability of somatodendritic morphology within the different rodent RGC classes (Sun et al., 2002a,b; Sanes and Masland, 2015). As a result, optimal neuronal excitability could be adjusted by changing AIS length/position to individually limit or promote action potential generation.

By applying super resolution microscopy in neurons in vitro, the robust nanoscale organization along the AIS submembrane scaffold has been identified as a ∼190 nm periodic ring-like architecture formed by submembrane actin bands connected by longitudinal head-to-head βIV-spectrin subunits, which extend throughout the axon (Xu et al., 2013; D'Este et al., 2015; Leterrier et al., 2015). Despite the diverse AIS morphology in RGCs, our super resolution imaging data revealed a consistent nanoscale architecture along the AIS of RGCs. As seen in neurons in vitro, we observed a periodic arrangement of βIVspectrin with distances of ∼180 nm in RGC AIS. Within the AIS, we identified synpo-positive structures, corresponding to COs, localized underneath the membrane scaffold. Recently, it has been speculated that synpo-positive clusters within the AIS of cortical neurons in vitro and in vivo are localized at gaps in the AIS scaffold, which are deficient of ankyrin-G expression (King et al., 2014). These ankG and βIV-spectrin deficient sites are apparent in images acquired by super resolution imaging (STORM and STED) in AIS of neurons in vitro (D'Este et al., 2015; Leterrier et al., 2015). By applying SIM and SMLM, we observed such gaps in the RGC AIS scaffold, which were deficient of βIV-spectrin or ankG expression. However, these gaps were only occasionally filled with synpo-positive clusters and these clusters were often detected at sites in the AIS where no obvious gaps were visible. It is important to keep in mind that the super resolution methods applied here and in other studies have limitations. For example when using SMLM, the lack of threedimensional information might impact the interpretation of data. Moreover, a high density fluorescence labeling is required for SMLM to allow detection of positions of individual molecules for reconstructing a high resolution image (Klein et al., 2014). This could also impact the accuracy of measurements of positions of single molecules as we observed for measurements of distances between single ankG/βIV-spectrin signals (∼180 nm by STED vs. ∼200 nm by SMLM). A combination of methods should help to address the still unresolved question about 'gaps' in the AIS scaffold and possible colocalization of synpo clusters in these domains. Intriguingly, King and others speculated that gaps in the ankG/βIV-spectrin-actin scaffold are required to accommodate high density protein complexes that might be crucial for the assembly and functioning of axo-axonic GABAergic synapses at the AIS (Kosaka, 1980; Benedeczky et al., 1994; King et al., 2014). So far, the presence of such GABAergic synapses at RGC AIS is supported by an early electron microscopy study of the macaque monkey retina (Koontz, 1993). However, work supporting these findings in rodent RGCs is currently lacking. Furthermore, occasionally we observed synpo clusters that appeared as if they were partially located outside of the AIS. This phenomenon could have a technical explanation. Considering that ankG immunoreaction does not highlight the outside of the axonal membrane, but rather the underlying scaffold of the axon and hence, spans less axonal diameter, the actual complete axonal diameter may be underestimated. In addition, it is intriguing to speculate that the observation is further indication of a synpo/CO-subdomain in the AIS. There is evidence from hippocampal pyramidal neuron AIS that the synpo-positive clusters may represent 'spine-like' protrusions in the vicinity of – or as a direct contact site for – GABAergic synapses (Somogyi et al., 1983).

## Length of RGC AIS Correlates With Retinal Maturation During Postnatal Development

The AIS of RGCs is located proximally in the unmyelinated part of the axon and therefore, is separated spatially from the distal myelinated part (Hildebrand and Waxman, 1983; Koontz, 1993). The molecular composition of RGC AIS is comparable to that of other neurons across different species, and has been demonstrated by several studies (Hildebrand and Waxman, 1983; Carras et al., 1992; Koontz, 1993; Boiko et al., 2003; Van Wart et al., 2007; Zhang et al., 2015). Yet, the developmental maturation of AIS length in retinal neurons remained unexplored.

AIS length and location has been linked to the excitability of neurons (Grubb and Burrone, 2010; Kuba et al., 2010; Hamada et al., 2016; Jamann et al., 2018). Data support the hypothesis that longer AIS facilitate action potential generation and thus contribute to increased neuronal excitability. Interestingly, neuronal activity and excitability are inversely related, i.e., higher activity results in AIS shortening and lower activity leads to AIS elongation, a mechanism reminiscent of homeostatic plasticity (reviewed in Adachi et al., 2015; Wefelmeyer et al., 2016).

During cortical development, AIS undergo structural length maturation from increased AIS length at embryonic and early postnatal ages to a shortening at later postnatal stages and in adulthood (Cruz et al., 2009; Galiano et al., 2012; Fish et al., 2013; Gutzmann et al., 2014; Jamann et al., 2018). Here, we addressed the question whether similar developmental profiles apply for RGCs. Indeed, at postnatal ages around eye-opening (P10/15), AIS were longest with heterogeneous length distributions indicative of 'juvenile' AIS in V1 (Gutzmann et al., 2014). A characteristic feature of the developing retina is spontaneous periodic activity (reviewed in Firth et al., 2005). Spontaneous retinal waves emerge around E16.5, undergo different stages, and last until eye-opening (reviewed in Huberman et al., 2008). Vision in mice begins around P11 through naturally closed eye lids (Krug et al., 2001). The simultaneous presence of both spontaneous retinal activity and visually driven activity might provoke the increase in AIS length of RGCs in young animals. In turn, increased excitability is proposed to be acquired for early development in sensory cortices (Oswald and Reyes,

2008; Frangeul et al., 2017). It is conceivable that increased AIS length during retinal development leads to increased RGC excitability, which contributes to the refinement of axonal projections from the retina to the visual centers of the brain. Indeed, glutamate release from bipolar cells during spontaneous retinal waves from P10–12 regulates circuit development in the retina, and patterns of RGC activity propagating forward shape the wiring of circuits in the lateral geniculate nucleus, superior colliculus and in V1 (reviewed in Kerschensteiner, 2016). Interestingly, RGC activity is fundamental not only for proper development. Abnormalities in RGC activity were observed during development of pathologies and increased activity is discussed to decelerate the degenerative progression of retinal disease (Risner et al., 2018).

Around eye-opening (P13,14), spontaneous retinal activity begins to disappear and is finally absent around P21 (Demas et al., 2003). The complete replacement of spontaneous activity with visually driven activity possibly triggered the decrease in AIS length in RGCs at P21, accompanied by a parallel homogenous AIS length distribution, which is characteristic for mature AIS in adult animals (Gutzmann et al., 2014). With proceeding development, AIS of RGCs decreased further in length, underlined by progressively more homogeneous AIS length distributions. Our findings indicate that AIS begin to mature when spontaneous retinal activity ends, suggesting that visual experience is important for the maturation of RGC AIS.

## Synpo Expression in RGC AIS Changes During Retinal Development and Stabilizes AIS Length Maturation

In rodent V1, synpo expression in the AIS begins postnatally and is most prominent in structurally mature AIS of pyramidal neurons during early critical periods of cortical development (Schlüter et al., 2017). In the present study, the first synpopositive clusters appeared in RGC AIS in P10 mice. Of note, maturation changed the size of synpo-positive clusters in RGC AIS, but the number of clusters per AIS was unaltered. In comparison to our study in the developing V1 (Schlüter et al., 2017), synpo expression was more constant during retinal development. The subset of AIS, which express synpo, amounted to ∼24 – 28% between the different ages and taking all RGC types into account. It should be pointed out that synpo clusters may possibly be associated with specific RGC classes, however, due to the overall scarcity of RGC<sup>A</sup> cells in our study, we cannot provide more detailed data at this point. The question whether synpo/CO segregates into specific RGC classes will have to be addressed in future studies. Interestingly, synpo-positive clusters within AIS were significantly different in size between P21 and P28 as well as P21 and P35. What could trigger the size reduction of synpo clusters during late postnatal development? One of the most important messengers for the induction of neuronal signaling during retinal development is Ca2<sup>+</sup> (Firth et al., 2005; Kerschensteiner, 2016). The CO and synpo have been implied in regulating local AIS Ca2<sup>+</sup> trafficking (Benedeczky et al., 1994; Sanchez-Ponce et al., 2012b; King et al., 2014). Ca2<sup>+</sup> sensitive channels (Inositol 1,4,5-trisphosphate receptors, ryanodine receptors) and Ca2<sup>+</sup> pumps (i.e., sarco/endoplasmic reticulum Ca2+-ATPase) associated with the CO are discussed to boost local cytosolic Ca2<sup>+</sup> transients during action potential firing through Ca2+-induced Ca2<sup>+</sup> release from internal Ca2<sup>+</sup> stores (Berridge, 1998; Segal, 2018). This Ca2<sup>+</sup> signaling amplification in turn could impact axonal membrane potential properties and neuronal excitability (Berridge, 1998; Segal, 2018), and thus AIS length.

In the developing retina, RGCs spontaneously fire periodic bursts of action potentials with accompanying large increases of intracellular Ca2<sup>+</sup> levels (reviewed in Firth et al., 2005). In mice, stage III – glutamatergic activity emerges from P10-14 (reviewed in Huberman et al., 2008; Kerschensteiner, 2016), declines around the time of eye opening as light-evoked signals begin to drive retinal activity, and are finally absent around P21 (Demas et al., 2003). The initial expression of synpo in RGC AIS at P10 may be linked to the appearance of stage III retinal glutamatergic waves and the imminent onset of vision. Early visual, experience along with the replacement of glutamatergic waves with light-evoked, signals may trigger a later decrease of sizes of synpo-positive clusters along with AIS length maturation of RGCs. Further, the density of synapses in the outer and IPL peaks around P21 (Xu and Tian, 2004). From P22 until P27, an increase of spontaneous excitatory and inhibitory postsynaptic currents emerges, which enhances RGC synaptic input more than fourfold (Tian and Copenhagen, 2001). This increase of synaptic input may change the firing properties of RGCs, which in turn might lead to the observed remodeling of synpo and the CO in retinal AIS.

In parallel with the emergence of synpo clusters in RGC AIS at P10, we observed a homogenous AIS length distribution compared to the entire AIS population in the retina at this age reflecting mature AIS (Gutzmann et al., 2014; Schlüter et al., 2017). The maturation of synpo-positive AIS early in development suggests that synpo presence in the AIS is a sign of structural maturity. Similar findings have been described for synpo expression in the AIS of pyramidal neurons during V1 development (Schlüter et al., 2017) or in dendritic spines (Mundel et al., 1997; Czarnecki et al., 2005).

#### Dark-Rearing Prevents Structural AIS Maturation and Remodels COs Within RGC AIS

Decreased neuronal activity caused by sensory deprivation during early postnatal development results in significant elongation of AIS, displaying characteristics observed in immature AIS. These findings suggest that increased sensory input and network activity leads to a structural maturation highlighted by AIS shortening during critical periods of development (reviewed in Jamann et al., 2018). To test whether this maturation is also a common developmental mechanism in RGCs, we investigated the structural length maturation of RGC AIS in dark-reared animals. Of note, AIS of dark-reared mice were ∼150% longer than AIS in control animals. The

average length as well as cumulative length distribution of AIS in dark-reared animals corresponded to that of juvenile AIS in young controls. These findings suggest that lack of visual input and decreased network activity in the retina leads to the prevention of structural AIS maturation in RGCs after eye-opening. Elongated AIS could maintain neuronal excitability at basal levels when sensory input is absent, which might reflect a homeostatic reaction for AIS under deprivation conditions.

Of note, the subset of RGCs that express synpo in their AIS, whose percentage was small throughout retinal development, were ∼120% higher in dark-reared animals. In all deprivation conditions, synpo-positive AIS were ∼110% longer than AIS in control animals of the same age and reached AIS length comparable to those observed in younger control animals. Further, sizes of synpo-positive clusters within RGC AIS were increased after dark-rearing. This could indicate that existing synpo-positive clusters fuse within the AIS after loss of visually driven synaptic input. The expansion of the ER most likely regulates the capacity of internal Ca2<sup>+</sup> stores (Sammels et al., 2010). Likewise, the formation of increased synpo-positive clusters is proposed to enhance Ca2<sup>+</sup> storage capacity in the spine apparatus in dendrites (Vlachos et al., 2013; Verbich et al., 2016) as well as in the CO in AIS (Schlüter et al., 2017) as a homeostatic response to loss of synaptic input. We speculate that both elongated AIS and expanded synpo-positive clusters within the AIS increase the excitability of RGCs as well as Ca2<sup>+</sup> currents in their AIS to compensate for the visual deprivation-triggered reduction in retinal network activity.

Finally, considering the significant heterogeneity of RGC classes, we would like to point out that further classification of RGC<sup>A</sup> into ON and OFF cells might be of interest since dark rearing might have differential effects on ON and OFF cells; it should silence ON cells and activate OFF cells, with presumably opposite AIS plasticity. Future studies in animal models more suited to discern a larger number of RGC classes will be able to shed light on this interesting question.

#### CONCLUSION

Our findings suggest that changes in synpo expression are linked to different stages of activity-driven processes in the developing retina. Moreover, we identified a possible role for both AIS and synpo/CO plasticity during homeostatic responses of visual input-deprived RGCs to reduced retinal network activity. Future studies could therefore focus on the subtypes of synpo-expressing RGCs, their intrinsic AIS plasticity and how it pertains to the development and maturation of functional visual circuits.

#### DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

## ETHICS STATEMENT

All animal protocols were approved by the Medical Faculty Mannheim Animal Research Board, Heidelberg University, as well as the State of Baden-Württemberg, Germany, and were conducted in accordance with Heidelberg University Guidelines on the Care of Laboratory Animals.

#### AUTHOR CONTRIBUTIONS

AS, SR, and ME conceptualized and designed the study. AS, SR, DD, JMJ, SV, and JH contributed to data acquisition and programming. AS, SR, DD, JMJ, and ME analyzed the data. AS, SR, CS, and ME interpreted the data. AS, DM, and ME prepared the manuscript. All authors approved the final version to be published.

#### FUNDING

This work was supported by the ProRetina Foundation (Pro-Re/KP/Engelhardt.1-2014/2016 to ME) and the Deutsche Forschungsgemeinschaft (SFB1134/A03 to CS and ME; SFB1158/A08 and FOR2325 to DM). DM is a member of CellNetworks. DD was funded by the MD Fellowship program of the Medical Faculty Mannheim, Heidelberg University. This work was supported by the Core Facility Life Cell Imaging Mannheim (LIMA) at the CBTM (DFG-INST 91027/10-1 FUGG). We acknowledge financial support by the Deutsche Forschungsgemeinschaft within the funding program Open Access Publishing, by the Baden-Württemberg Ministry of Science, Research and the Arts and by the Ruprecht-Karls-University Heidelberg.

#### ACKNOWLEDGMENTS

We thank Prof. C. Cremer at the Kirchhoff Institute, Heidelberg University for usage of the SIM/SMLM setup, Dr. Sidney Cambridge, Department of Anatomy, Heidelberg University, for breeding pairs of the Thy1-EGFP mouse line, and Elisabeth Mertens for her technical support. We are indebted to Dr. Elisa D'Este, Max Planck Institute of Medical Research, Heidelberg for sharing her expertise in STED microscopy and to Johannes Roos, Institute of Neuroanatomy, Medical Faculty Mannheim, for providing the AISuite software for morphometrical analysis.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00318/full#supplementary-material

#### REFERENCES

fncel-13-00318 July 27, 2019 Time: 14:57 # 17



**Conflict of Interest Statement:** SR joined DELMIC B.V. in the Netherlands, a company producing solutions for correlative light and electron microscopy, after completion of all work relating to the current study. Therefore SR declares no conflict of interest. JH works for Abberior Instruments GmbH, a company producing STED microscopes. DM is cofounder and shareholder of FundaMental Pharma GmbH, which has no conflict of interest with the present work.

The remaining 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 © 2019 Schlüter, Rossberger, Dannehl, Janssen, Vorwald, Hanne, Schultz, Mauceri and Engelhardt. 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(s) 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.

fncel-13-00407 September 4, 2019 Time: 17:3 # 1

# Excitability Tuning of Axons by Afterdepolarization

#### Haruyuki Kamiya\*

Department of Neurobiology, Hokkaido University Graduate School of Medicine, Sapporo, Japan

The axon provides a sole output of the neuron which propagates action potentials reliably to the axon terminal and transmits neuronal information to the postsynaptic neuron across the synapse. A classical view of neuronal signaling is based on these two processes, namely binary (all or none) signaling along the axon and graded (tunable) signaling at the synapse. Recent studies, however, have revealed that the excitability of the axon is subject to dynamic tuning for a short period after axonal action potentials. This was first described as post-spike hyperexcitability, as measured by the changes in stimulus threshold for a short period after an action potential. Later on, direct recordings from central nervous system (CNS) axons or axon terminals using subcellular patchclamp recording showed that axonal spikes are often followed by afterdepolarization (ADP) lasting for several tens of milliseconds and has been suggested to mediate postspike hyperexcitability. In this review article, I focused on the mechanisms as well as the functional significance of ADP in fine-scale modulation of axonal spike signaling in the CNS, with special reference to hippocampal mossy fibers, one of the best-studied CNS axons. As a common basic mechanism underlying axonal ADP, passive propagation by the capacitive discharge of the axonal membrane as well as voltage-dependent K <sup>+</sup> conductance underlies the generation of ADP. Small but prolonged axonal ADP lasting for several tens of milliseconds may influence the subsequent action potential and transmitter release from the axon terminals. Both duration and amplitude of axonal spike are subject to such modulation by preceding action potential-ADP sequence, deviating from the conventional assumption of digital nature of axonal spike signaling. Impact on the transmitter release is also discussed in the context of axonal spike plasticity. Axonal spike is subject to dynamic control on a fine-scale and thereby contributes to the short-term plasticity at the synapse.

Keywords: axon, action potential, afterdepolarization, propagation, short-term plasticity

## DYNAMIC TUNING OF AXON EXCITABILITY BY ADP

The axon carries neuronal information as a form of action potentials which reliably propagate for a long distance without attenuation (Debanne et al., 2011). A regenerative nature of spike generation provides digital property beneficial to reliable and ultrafast axonal signaling in the nervous system (Bean, 2007). Recent studies however, updated the classical view of digital axonal signaling to

Edited by:

Josef Bischofberger, University of Basel, Switzerland

#### Reviewed by:

Stefan Hallermann, Leipzig University, Germany Henrique Prado von Gersdorff, Oregon Health & Science University, United States Dmitri A. Rusakov, University College London, United Kingdom

\*Correspondence:

Haruyuki Kamiya kamiya@med.hokudai.ac.jp

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 27 May 2019 Accepted: 26 August 2019 Published: 06 September 2019

#### Citation:

Kamiya H (2019) Excitability Tuning of Axons by Afterdepolarization. Front. Cell. Neurosci. 13:407. doi: 10.3389/fncel.2019.00407

**135**

fncel-13-00407 September 4, 2019 Time: 17:3 # 2

impart analog modification by the preceding neuronal activity (Zbili and Debanne, 2019). Such a use-dependent analog modification of axonal spike is possibly due to dynamic control of excitability of axon by the preceding neuronal activity for a short period up to tens to hundreds of milliseconds after generation of action potential (Gardner-Medwin, 1972; Zucker, 1974; Bucher and Goaillard, 2011). This post-stimulus change in the excitability of axon was mediated by ADP following action potential (**Figure 1A**), which may be important for temporal integration of axonal excitability and short-term plasticity of presynaptic transmitter release (Barrett and Barrett, 1982; Ohura and Kamiya, 2016). In this review, I focused on the recent progress in understanding the mechanisms as well as the functional significance of axonal afterdepolarization (ADP) in paired-pulse modulation and short-term synaptic plasticity.

#### COMPONENTS OF AXONAL ADP

ADP following action potentials is common process observed in the nervous systems in both vertebrate and invertebrate axons (Barrett and Barrett, 1982; Borst et al., 1995; Geiger and Jonas, 2000). A small but prolonged depolarization during ADP may important factor for activity tuning of axonal excitability as well as presynaptic transmitter release. **Figure 1A** shows the typical time course of ADP in hippocampal mossy fiber model (Engel and Jonas, 2005) calculated at negative membrane potentials (−100 mV) which shows similar time course with those recorded from mossy fiber boutons experimentally (Geiger and Jonas, 2000; Ohura and Kamiya, 2018b). This model assumes a Hodgkin Huxley-type gating adapted to channels those recorded in mossy fiber terminals and implemented with K<sup>+</sup> channel inactivation. There is a considerable number of studies addressing the mechanisms underlying ADP, and it seems to be reasonable to comprehend that axonal ADP consists of common basic mechanisms and of additional specific mechanisms to particular axons.

As a common mechanism underlying axonal ADP, passive propagation of upstream action potential via axon cable has been shown to consist of a basic component of ADP (Barrett and Barrett, 1982; Borst et al., 1995; David et al., 1995). Additional contribution of several specific mechanisms, e.g., activation of slow sodium current like resurgent or persistent sodium current (Kim et al., 2010; Ohura and Kamiya, 2018b), accumulation of potassium ions surrounding axons (Malenka et al., 1981; Kocsis et al., 1983; Meeks and Mennerick, 2004), or activation of autoreceptors of glutamate and GABA (Kamiya et al., 2002; Ruiz et al., 2003; Stell et al., 2007; Zorrilla de San Martin et al., 2017), have been also suggested.

#### PASSIVE PROPAGATION VIA AXON CABLE

Cable property of axon confers a delayed depolarization due to capacitive discharge from the upstream action potential. Such a passive propagating component consists of axonal ADP at

FIGURE 1 | Components of axonal ADP. (A) Basic components constituting axonal action potential-ADP sequence. Action potentials recorded from axon or the terminal are typically followed by prolonged ADP lasting for several tens of milliseconds. The left trace represents the time course of ADP in the hippocampal mossy fiber model calculated at negative membrane potentials of –100 mV. The right traces shows ionic components due to activation of voltage-dependent Na<sup>+</sup> (VNa, blue) and K<sup>+</sup> conductance (VK, green), the electrical component due to capacitive discharge (VCap, red) also substantially contribute to the prolonged ADP. VNa, VK, and VCap were calculated by subtraction of membrane potentials calculated by removal of Na<sup>+</sup> and/or K<sup>+</sup> conductance from the terminals. Sum of VNa, VK, and VCap, therefore, was identical with action potential-ADP sequence shown in the left trace. The inset represents the time-expanded traces showing timing and sequence of the onset of VNa, VK, and VCap. The electrical component (VCap) precedes the ionic components (VNa and VK) to trigger action potential at the downstream axons. (B) Passive propagation of upstream action potential. Using a model simulation of en passant axon (10 boutons spaced every 100 µm) mimicking the structure of hippocampal mossy fibers, the relative contribution of passive propagation to the downstream ADP was evaluated by removing voltage-dependent ionic conductance (gNa and gK) from 8th–10th boutons (Continued)

#### FIGURE 1 | Continued

fncel-13-00407 September 4, 2019 Time: 17:3 # 3

and axon, as shown in red. Brief current injection into the soma elicited action potential which propagates faithfully to the 7th bouton without attenuation. The amplitude of depolarization decreased successively from the 8th bouton, and the time course was slowed down along the distance due to filtering by axon cable. The decay of the peak amplitude along the distance was fitted by a single exponential curve with 53 µm for the distance with a reduction to 1/e (37%). (C) Boosting axonal ADP by slow Na<sup>+</sup> channels. In direct whole-cell recording experiment from hippocampal mossy fiber terminals, ADP is partly mediated by tetrodotoxin (TTX)-sensitive slow activating Na<sup>+</sup> channels. In the presence of TTX, action potentials and ADP were abolished, but brief current pulse injection restored sharp depolarization followed by slow relaxation (blue). Veratridine, an inhibitor of inactivation of Na<sup>+</sup> channels, enhanced the ADP and sometimes overlaid by multiple spiking elicited by a single stimulus in mossy fiber axons (red). Modified with permission from Ohura and Kamiya (2018b) and Kamiya (2019).

least in part. Consistent with this notion, ADP recorded from a calyx of Held axon terminals was shown to be unaffected by tetrodotoxin focally applied to the axon terminals (Borst et al., 1995), suggesting the possible axonal origin of ADP. Passive nature of ADP has also supported the finding that ADP and passive electrotonic response to step hyperpolarizing current injection showed similar time courses in motor axons (Barrett and Barrett, 1982) or in hippocampal mossy fiber axons (Ohura and Kamiya, 2018b).

To evaluate quantitative contribution of passive propagation in action potential-ADP sequence, time courses of the ionic components due to activation of voltage-dependent Na<sup>+</sup> and K<sup>+</sup> channels (VNa and VK) as well as electrical components due to capacitive discharge (VCap) are compared (**Figure 1A**) in the hippocampal mossy fiber model used in our recent simulation study (Kamiya, 2019). The amplitude of VCap is more than onethird of VNa, suggesting a substantial contribution of passive electrical components in ADP, in agreement with the experiment of brief current injection in the presence of tetrodotoxin, a blocker of voltage-dependent Na<sup>+</sup> channels (Ohura and Kamiya, 2018b). The onset of VCap preceded VNa to trigger action potentials as shown in the inset with an expanded time scale.

It should be noted that passive propagation may distribute over a relatively long distance. The length constant of the axon was estimated as 455 µm in layer V pyramidal neurons in ferret cortex (Shu et al., 2006), 450 µm in rat hippocampal granule cell (Alle and Geiger, 2006), and 121 µm in cultured rat Purkinje cell (Zorrilla de San Martin et al., 2017). Although the length constant evaluated by long current pulse injection was estimated as 171 µm in our model of hippocampal mossy fibers (Kamiya, 2019), action potentials decline with shorter space constant of 53 µm for decay to 1/e (**Figure 1B**) possibly reflecting steeper filtering of fast voltage transient during action potentials. Passive propagation filtered by axon cable may thereby substantially impact the time course of action potential-ADP sequence recorded from the downstream axon.

It is worth considering whether subthreshold fluctuation of somatic membrane potentials occurring in vivo may also passively propagate to the axon. Long-range propagation of somatic depolarization into the axon has been demonstrated for hippocampal mossy fibers (Alle and Geiger, 2006) and for cortical pyramidal cell axons (Shu et al., 2006). In both studies, axonal depolarization enhanced transmitter release from the axon terminals, while the effect was limited to the proximal portion of the axons (see also Scott et al., 2008) due to passive attenuation of depolarization with the distance from the soma. On the contrary, ADP following action potentials is expected to equally distribute along the course of the axon, since action potentials propagate without attenuation. Therefore passive propagating components of axonal ADP is not depending on the distance from the soma and differed from the subthreshold somatic depolarization in this point.

Contribution of passive propagation is important for transmitter release not only from en passant boutons like the hippocampal mossy fibers, but also from bouton terminaux like calyx of Held, since it has been shown that Na<sup>+</sup> channels are excluded from the terminals but are expressed only in the axonal heminode in the distal axon (Leão et al., 2005). The depolarization at the active zone, which is directly related to Ca2<sup>+</sup> entry responsible for transmitter release, is therefore mostly reflecting passive propagation from the heminode region to the terminal boutons.

## VOLTAGE-DEPENDENCY OF AXONAL ADP

Quite puzzling observations are ADP recorded from axons or the terminals showed clear voltage-dependency. The size of ADP decreased upon depolarization of the initial membrane potentials (Begum et al., 2016; Sierksma and Borst, 2017; Ohura and Kamiya, 2018b), and sometimes reversed in polarity at more positive membrane potentials. It was also demonstrated that hyperpolarizing current injection decreased ADP (Kim et al., 2010). These findings are difficult to interpret with the passive nature of capacitive discharge of the axonal membrane, which is fundamentally voltage-independent. Therefore, the additional contribution of voltage-gated conductance which provides voltage-dependency to axonal ADP (Kamiya, 2019) must be taken into consideration.

#### K <sup>+</sup> CHANNELS SHAPE THE INITIAL PHASE OF AXONAL ADP

As additional conductance that potentially confers voltagedependency to axonal ADP, the contribution of voltagedependent K<sup>+</sup> conductance, which predominantly mediates fast repolarization of action potential (Storm, 1987; Dodson et al., 2003; Wissmann et al., 2003), was suggested. The time course of K<sup>+</sup> conductance somewhat outlasts the duration of action potentials and necessarily contributes to the subsequent ADP time course. Consistent with this notion, voltage-dependent K<sup>+</sup> conductance shapes a characteristic breakpoint at the initial phase of axonal ADP, possibly due to superimposed hyperpolarizing K <sup>+</sup> conductance on the passive depolarizing component. Sum of voltage-independent passive component and voltagedependent K<sup>+</sup> channel component with the various combination fncel-13-00407 September 4, 2019 Time: 17:3 # 4

in hippocampal mossy fiber model nicely reconstruct the characteristic time course as well as typical voltage-dependency of action potential-ADP sequence (Kamiya, 2019). It seems to be reasonable to speculate that various reported values of apparent reversal potential of axonal ADP (Begum et al., 2016; Sierksma and Borst, 2017; Ohura and Kamiya, 2018b) reflect the various contribution of passive propagation and voltage-dependent K+ channel components.

## SLOW Na<sup>+</sup> CURRENT BOOSTS ADP IN SOME AXONS

In addition to the common basic mechanisms of passive propagation and voltage-dependent K<sup>+</sup> conductance, the contribution of slow Na<sup>+</sup> current at a certain type of axon has been suggested. ADP recorded from soma sometimes are mediated by slow voltage-dependent Na<sup>+</sup> currents such as persistent-type INaP or resurgent-type INaR (Raman and Bean, 1997; Yue and Yaari, 2004; Yue et al., 2005; D'Ascenzo et al., 2009). Using direct recording from the calyx of Held axon terminals, thereafter, it has been shown that the resurgent-type Na<sup>+</sup> current INaR shapes slow time course of axonal ADP (Kim et al., 2010). In contrast, it was reported that ADP was unaffected by local application of tetrodotoxin surrounding the recorded terminals at the same axon terminals (Borst et al., 1995), although the reason of the different results in these studies is unclear. This discrepancy may be explained by the finding that Na<sup>+</sup> channels are not located in the calyx terminal but in the distal heminode region of the axon (Leão et al., 2005). Recently we also have reported that ADP at hippocampal mossy fiber terminals is also partially mediated by voltage-dependent Na<sup>+</sup> current (Ohura and Kamiya, 2018b) since it was suppressed by a Na<sup>+</sup> channel blocker tetrodotoxin and was enhanced by an inhibitor of inactivation of Na<sup>+</sup> channel veratridine (**Figure 1C**), as shown for ADP at the calyx of Held terminals (Kim et al., 2010). These slow Na<sup>+</sup> channels raise axonal excitability for a while and help to support faithful spiking of axons during repetitive stimuli. Their molecular identity, as well as the precise subcellular localization of the axonal slow Na<sup>+</sup> channels, remain to be determined. It is also uncertain whether this mechanism is generally applicable to other types of axons in different brain regions.

## ACCUMULATION OF K<sup>+</sup> SURROUNDING AXONS

It was reported that stimulation of parallel fiber axons in rat cerebellum cause elevation of extracellular K<sup>+</sup> concentration surrounding axons and caused prolonged depolarization and hyperexcitable period lasting for a hundred of milliseconds (Malenka et al., 1981; Kocsis et al., 1983). It is intriguing to speculate that action potential in axon or EPSPs in postsynaptic neurons caused elevation of extracellular K<sup>+</sup> concentration in the extracellular space and axon to depolarize by elevated K<sup>+</sup> concentration surrounding axons. It will be worth testing the possible contribution of astroglia in shaping axonal ADP since local extracellular K<sup>+</sup> buffering depends mainly on astroglia. It is also intriguing to test the roles of gliotransmitters in shaping axonal ADP, since glutamate released from astroglia was shown to broaden action potentials locally (Sasaki et al., 2011). However, the increase in elevated levels of K<sup>+</sup> was observed only when strong and repetitive stimuli were given. The single shock-induced K<sup>+</sup> increase was detectable only when a K<sup>+</sup> channel blocker 4-AP was applied. Therefore, it seems to be that this mechanism may not contribute to the generation of ADP physiologically by single action potential at single axon.

## CONTRIBUTION OF AUTORECEPTOR ACTIVATION IN AXONAL ADP

In some specific axons, it has been shown that activation of autoreceptors of GABA (Pouzat and Marty, 1999; Zorrilla de San Martin et al., 2017) participates in axonal ADP. Activation of axonal GABAA-autoreceptors at cerebellar interneuron axons causes excitatory GABAergic autoreceptor currents (Pouzat and Marty, 1999), possibly due to higher chloride concentration in axoplasm, and facilitate transmitter release and increase neuronal firing rate (Mejia-Gervacio and Marty, 2006). Similar depolarizing autoreceptor current was also reported for cultured Purkinje cell axons (Zorrilla de San Martin et al., 2017). It was also suggested that kainate-type glutamate receptors may assist ADP in hippocampal mossy fiber axons recorded optically using voltage-sensitive dye (Kamiya et al., 2002). It should be noted that autoreceptor activation surely contributes to a certain subset of axons in the nervous system, this is not a common mechanism for all types of the axon, but a relatively rare and specific contribution to axonal ADP.

### IMPACT OF AXONAL ADP ON SUBSEQUENT ACTION POTENTIAL AND TRANSMITTER RELEASE

Slow time course of axonal ADP implies that the excitability of the axon is modulated cumulatively during repetitive stimuli at short intervals. The small and slow depolarization of ADP may affect the states of the voltage-dependent Na<sup>+</sup> and K<sup>+</sup> channels and thereby potentially modify the subsequent action potentials. Using whole-bouton recording from mossy fiber terminals, we recently have reported (Ohura and Kamiya, 2018b) that the peak height of the action potentials was almost unchanged, although the amplitudes of the action potentials measured from the elevated initial membrane potential were reduced in paired-pulse stimuli at short intervals (**Figure 2A**). Elevated membrane potentials by ADP may facilitate steadystate inactivation of voltage-dependent Na<sup>+</sup> channels (Engel and Jonas, 2005; Rama et al., 2015), and thereby may slow the rising phase of action potentials. Consistent with this, axonal spike recorded extracellularly from single mossy fiber terminal, which is expected to reflect the first derivative of action potential recorded intracellularly (Meeks et al., 2005), displayed short-term depression of the amplitude at short fncel-13-00407 September 4, 2019 Time: 17:3 # 5

intervals (Ohura and Kamiya, 2018a) as shown in **Figure 2B**. Inactivation of Na<sup>+</sup> channels was also suggested for mediating adaptive broadening of spike initiation site during somatic depolarization, as demonstrated by simultaneous soma and axon recordings from hippocampal mossy fibers (Scott et al., 2014). It was also demonstrated that the preceding ADP also enhanced inactivation of K<sup>+</sup> channels, leading to a usedependent broadening of action potentials (Geiger and Jonas, 2000; Kole et al., 2007).

Voltage-dependent Ca2<sup>+</sup> channels are also affected by the preceding ADP. Modulation of presynaptic Ca2<sup>+</sup> current would be expected to modulate transmitter release and short-term synaptic plasticity (Bischofberger et al., 2002; Li et al., 2007; Zorrilla de San Martin et al., 2017). Although the detailed biophysical mechanism remains to be clarified, facilitation of Ca2<sup>+</sup> current consequently enhances the subsequent transmitter release from the axon terminals at the culture Purkinje cell axon terminals (Zorrilla de San Martin et al., 2017) and hippocampal mossy fiber terminals (Ohura and Kamiya, 2018b). Impacts on the downstream synaptic transmission is a small but non-negligible role of axonal ADP since the amount of transmitter release is steeply dependent on the amount of Ca2<sup>+</sup> entry during an action potential supralinearly (Zucker and Regehr, 2002). In fact, it has been shown that subthreshold depolarization of the calyx of Held raised the Ca2<sup>+</sup> levels by weak activation of P/Q-type Ca2<sup>+</sup> channels and enhanced transmitter release from the terminals (Awatramani et al., 2005).

by the paired stimuli at short intervals. (B) Paired-pulse depression of axonal spikes recorded from single mossy fiber boutons by loose-patch clamp recordings. The

amplitude of the second spike was slightly reduced than the first spike at short intervals. Modified with permission from Ohura and Kamiya (2018a,b).

## CONCLUSION

fncel-13-00407 September 4, 2019 Time: 17:3 # 6

Recent studies using the direct electrophysiological recordings from axons or axon terminals in the central nervous system have revealed that the excitability of axons is regulated more dynamically than previously thought. In this review article, advances in the understanding of the mechanisms and the functional significance of ADP following axonal action potentials were summarized. It has been demonstrated that electrical signals passively propagate for hundreds of micrometers, and consequently, the passive propagating component due to the capacitive discharge of axons substantially contributes to the propagating action potential-ADP sequence. The changes in the excitability by axonal ADP last for tens or hundreds of milliseconds and therefore may play an important role in temporal integration of neuronal activity and short-term synaptic

### REFERENCES


plasticity. Such a fine-scale dynamics of axonal excitability play pivotal roles in fine-tuning and temporal integration of neuronal network functions.

#### AUTHOR CONTRIBUTIONS

HK conceptualized and designed the study and drafted the manuscript.

## FUNDING

This study was supported by Grant-in-Aid for Scientific Research (KAKENHI) from the Japan Society for the Promotion of Science (18K06514 to HK).


fncel-13-00407 September 4, 2019 Time: 17:3 # 7


**Conflict of Interest Statement:** The author declares 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 © 2019 Kamiya. 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(s) 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.

# Large-Scale Mapping of Axonal Arbors Using High-Density Microelectrode Arrays

Torsten Bullmann1,2,3, Milos Radivojevic<sup>4</sup> , Stefan T. Huber <sup>1</sup> , Kosmas Deligkaris 1,5 , Andreas Hierlemann<sup>4</sup> \* and Urs Frey 1,4,6

 *RIKEN Quantitative Biology Center, RIKEN, Kobe, Japan, <sup>2</sup> Graduate School of Informatics, Kyoto University, Kyoto, Japan, Carl Ludwig Institute for Physiology, University of Leipzig, Leipzig, Germany, <sup>4</sup> Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland, <sup>5</sup> Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan, MaxWell Biosystems AG, Basel, Switzerland*

Understanding the role of axons in neuronal information processing is a fundamental task in neuroscience. Over the last years, sophisticated patch-clamp investigations have provided unexpected and exciting data on axonal phenomena and functioning, but there is still a need for methods to investigate full axonal arbors at sufficient throughput. Here, we present a new method for the simultaneous mapping of the axonal arbors of a large number of individual neurons, which relies on their extracellular signals that have been recorded with high-density microelectrode arrays (HD-MEAs). The segmentation of axons was performed based on the local correlation of extracellular signals. Comparison of the results with both, ground truth and receiver operator characteristics, shows that the new segmentation method outperforms previously used methods. Using a standard HD-MEA, we mapped the axonal arbors of 68 neurons in <6 h. The fully automated method can be extended to new generations of HD-MEAs with larger data output and is estimated to provide data of axonal arbors of thousands of neurons within recording sessions of a few hours.

Keywords: axons, high-density microelectrode array, extracellular electrical field, action potential, axonal arborizations, action potential propagation, high-throughput screening

#### INTRODUCTION

The classical view of axons is that of mere transmission cables (Hodgkin and Huxley, 1952), while dendrites integrate distinct synaptic inputs (Spruston, 2008), and learning and memory are perceived to be a consequence of synaptic plasticity (Redondo and Morris, 2011). Recent data, however, indicate that the functional capacity of axons may be much more complex (Debanne, 2004; Ohura and Kamiya, 2016; Rama et al., 2018).

According to the classical theory describing giant squid axons (Hodgkin and Huxley, 1952), voltage-gated sodium and potassium channels support self-sustained action potentials that propagate along the axon. That is also true for mammalian axons, but at least two additional types of cationic channels have been described. These channels are activated by G-protein dependent receptors or hyperpolarization and modify the shape and propagation of the action potentials (Elgueta et al., 2015; Ko et al., 2016).

Axons can be surrounded by a myelin sheet that leads to saltatory conduction of action potentials (Tasaki, 1939), instead of the continuous conduction that has been observed in nonmyelinated axons, such as the giant squid axons (Hodgkin and Huxley, 1952). Mammalian axons

#### Edited by:

*Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France*

#### Reviewed by:

*Adelaide Fernandes, University of Lisbon, Portugal Valentina Carabelli, University of Turin, Italy*

#### \*Correspondence:

*Andreas Hierlemann andreas.hierlemann@bsse.ethz.ch*

#### Specialty section:

*This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience*

Received: *23 May 2019* Accepted: *20 August 2019* Published: *06 September 2019*

#### Citation:

*Bullmann T, Radivojevic M, Huber ST, Deligkaris K, Hierlemann A and Frey U (2019) Large-Scale Mapping of Axonal Arbors Using High-Density Microelectrode Arrays. Front. Cell. Neurosci. 13:404. doi: 10.3389/fncel.2019.00404* also show considerable variations in their diameter (Gaussian distribution around a peak at 200 nm diameter) and their number of branch points and varicosities, which affect the conduction velocity of action potentials. Differences in axon lengths have been found to produce defined temporal delays for spike trains for coincidence detection in the auditory system (Seidl et al., 2010; Stange-Marten et al., 2017). Furthermore, axonal delays in the neocortex show sub-millisecond precision (Swadlow, 1994), which is compatible with mechanisms of spike-timing-dependent synaptic plasticity (Dan and Poo, 2004). These characteristics lead, according to computational studies (Izhikevich, 2006), to the emergence of precisely timed firing patterns.

Early computational studies have suggested that some axonal arbors can act as filters for spike patterns by the selective failure of action potential propagation (Lüscher and Shiner, 1990). Whereas cerebellar mossy fibers in the cerebellum can reliably transmit spike trains up to 1.6 kHz (Ritzau-Jost et al., 2014), occasional failures have been observed in the axons of CA3 pyramidal neuron at firing frequencies of 30–40 Hz (Meeks and Mennerick, 2007). Failure depends on the diameter and the branching morphology as well as on the activation of presynaptic A-type potassium channels. The morphology and molecular composition of the individual axonal arbors has been found to influence the timing and shape of the action potential (Bischofberger et al., 2002; Alle and Geiger, 2006; Cho et al., 2017) arriving at the presynapse, which affects synaptic transmission and plasticity. For example, broadening of action potentials due to slow inactivation of voltage-gated potassium channels during high-frequency spike trains was found to facilitate synaptic release (Geiger and Jonas, 2000). Furthermore, axonal signaling and synaptic connectivity have been found to constitute important parameters in induced-pluripotent-stem-cell (iPSC) models of Parkinson's (Kouroupi et al., 2017) and amyotrophic lateral sclerosis (Wainger et al., 2014).

The understanding of information processing in axons is a fundamental question in neuroscience; however, the availability of experimental data is severely limited due to the small axon diameter. Most data sets have been gathered by performing patch clamp recordings of axonal membranes, at axon terminals and boutons, at the intact axon shaft or at the axonal bleb that is formed upon cutting axons (Ohura and Kamiya, 2016). However, these patch-based methods are not very well-suited to track the propagation of action potentials at more than two sites or even across the full axonal arbor. Moreover, the patch recording time is limited to a few hours while axonal recording is a serial process and has to be done axon after axon. Finally, patchbased methods constitute endpoint measurements and following the development of axonal arbors over extended periods is not possible. Another possibility to study axons includes the use of imaging tools and optogenetics (Chen et al., 2013), and it has been shown that imaging of single axon terminals is possible (Hoppa et al., 2014). However these methods are still limited in signal-to-noise ratio as well as in temporal resolution (Emmenegger et al., 2019).

A viable alternative to the methods described above includes the use of high-density microelectrode arrays (HD-MEAs), based on complementary-metal-oxide-semiconductor (CMOS) technology (Eversmann et al., 2003; Berdondini et al., 2009; Frey et al., 2010; Ballini et al., 2014; Bertotti et al., 2014; Viswam et al., 2016; Tsai et al., 2017). HD-MEAs can be used to capture neuronal activity at high temporal resolution across spatial scales, including networks, dendrites and most importantly, axons (Obien et al., 2015). CMOS-based HD-MEAs have been used to study the action potential propagation along axonal arbors (Bakkum et al., 2013) and the initiation of action potentials at the axon initial segment (Bakkum et al., 2019), as well as to track single action potentials along axons (Radivojevic et al., 2017) and stimulate single axon initial segments (Ronchi et al., 2019). Furthermore, HD-MEA recordings can be combined with classical patch clamp recording to study postsynaptic currents in response to pre-synaptic stimulation (Jäckel et al., 2017).

The objective of this work was to provide a method for highthroughput scanning of axonal arbors and mapping their axonal delays with minimal or no need to adjust parameters for the detection of axonal signals. Using a standard HD-MEA (Frey et al., 2010), we mapped the axonal arbors of more than 68 neurons in <6 h.

## MATERIALS AND METHODS

#### Animal Use

Timed pregnant rats (Wistar) were obtained from a commercial vendor (Nihon SLC, Japan). Animals were sacrificed on the day of arrival to obtain embryos for primary neuron cultures. All experimental procedures on animals were carried out in accordance with the European Council Directive of 22 of September 2010 (2010/63/EU) and have been approved by the local authorities in Japan (Animal Care and Use Committee of RIKEN; QAH24-01).

## High-Density Microelectrode Array (HD-MEA)

Sub-cellular resolution extracellular recordings were obtained using a CMOS-based HD-MEA (Frey et al., 2010) with 11,011 electrodes, arranged in a hexagonal pattern and featuring an electrode density of 3,150 electrodes/mm<sup>2</sup> . The culture chamber of the HD-MEA was prepared as described before (Heer et al., 2007) with minor modifications: after attaching the chamber ring (polycarbonate, 19 mm inner diameter, 8 mm high) using epoxy resin (EPO-TEK 301-2, Epoxy Technology Inc.), GlobTop (G8345D-37, Namics Inc.) was used to cover the bond wires while keeping the electrode area clean, and the remaining area was covered by a thin film of PDMS (Sylgard 184, Dow Corning). Platinum black was electrochemically deposited (Marrese, 1987) [with modifications of the original procedure (Heer et al., 2007)] on the electrodes to decrease their impedance in order to improve signal-to-noise characteristics (Viswam et al., 2014). Before plating, the surface of the HD-MEAs was rendered hydrophilic by oxygen-plasma treatment (40 s, 20 W), incubated for 4 h with of 50µg/ml Poly-D-Lysine (Sigma-Aldrich, P7280) in PBS, washed twice with aqua dest and air-dried for 1 h.

#### Primary Neuron Cultures

Adult rats were anesthetized with isofluorane and killed using a guillotine. The embryos were removed from the uterus and decapitated. Their neocortex was dissected in ice-cold dissection medium (HBSS without Ca2<sup>+</sup> and Mg2+; Gibco, NO.14175) and incubated for 20 min at 37◦C in Trypsin/EDTA (Sigma-Aldrich). After washing twice with plating medium (Neurobasal A, supplemented with 10% Fetal bovine serum, 2% B27 Supplement, 1:100 GlutaMax, all from Gibco, Japan, and 10µg/ml Gentamicin, Sigma-Aldrich, Japan), the tissue was mechanically dissociated, passed through a 40µm nylon mesh, and centrifuged 6 min at 200 g. The supernatant was removed; the cells were suspended and counted. A 20 µl drop containing 10,000 cells was placed on the electrode area of the HD-MEA in the middle of the culture chamber. The cultures were covered with a membrane, permeable to gas but not to water vapor, and placed in a standard incubator (37◦C, 5% CO2, 80% relative humidity). The neurons were allowed to settle and attach to the surface during 30 min. Thereafter, the culture chamber was filled with 600 µl serumfree, astrocyte-conditioned DMEM/Hams's F12 medium (Nerve Culture Medium, Sumitomo, Japan, #MB-X9501). Medium was completely exchanged with 600 µl conditioned medium after 4 days and then every 7 days until day 17 in vitro.

#### Recordings and Spike Event Detection

For recording, HD-MEAs were placed in a bench-top incubator (TOKAI HIT, Japan, INU-OTOR-RE) with temperature control, and 5% CO<sup>2</sup> was supplied by a gas-mixer and humidified by a water bath. In order to avoid the evaporation of medium during prolonged recording intervals, the water bath and the lid temperature set point was set 1K and 3K above the sample temperature set point, which was 35◦C. The HD-MEA recordings were performed using custom scripts, written in LabView (National Instruments, US), Matlab (Mathworks, US), C++ and Python running on a standard PC with a Linux operating system. Data underwent lossless data compression and were directly stored on a server on the local LAN.

Offline analysis of the recordings included filtering, event detection and averaging. First, a band-pass filter (2nd order Butterworth filter, 100–3,500 Hz) was used to remove slowly changing field potentials as well as high frequency noise. The remaining (background) noise was characterized by the median absolute deviation (MAD), which is resilient to outliers in the data but represents a consistent estimator of the standard deviation, <sup>s</sup><sup>V</sup> <sup>=</sup> 1.4826 MAD Vsig . Using a voltage-threshold method for event detection (Lewicki, 1998), negative signal peaks below a threshold of Vthr = 5s<sup>V</sup> (Vthr > 50 µV in all cases) were identified (**Figure 1C**). To avoid multiple detection of the same spike, successive events within <0.5 ms were discarded.

#### Mapping of Axonal Initial Segments

To initially identify the location of axonal initial segments (AISs), the whole array was scanned using configurations in which non-overlapping blocks of 6 × 17 electrodes (**Figure 1D**) were connected to the amplifiers through the switch matrix (Frey et al., 2010) (schematic in **Figure 1B**). After recording for 30 s from every electrode in the array, spike detection was performed for each electrode and taking the median value summarized the amplitude of the negative peaks. The median of the negative peak for each electrode was plotted as a map showing some areas with large negative peaks (**Figure 2A**). Such local minima were assumed to indicate the putative (proximal) AIS locations (Bakkum et al., 2019). We did not distinguish between inhibitory and excitatory neurons according to the AIS waveform (Mita et al., 2019).

#### Mapping of Electrical "Footprints"

To map the electrical "footprint" (spatial distribution of extracellularly measured electrical potentials obtained with the densely packed electrodes) of neuronal units and their axonal arbors over the entire array, we used a series of configurations in which so called "fixed electrodes" were always connected to the amplifiers through the switch matrix (Frey et al., 2010), whereas the remaining "variable electrodes" were connected in sequential configurations (schematic in **Figure 1E**). After recording the spontaneous activity for 115 s for each of these configurations, spike sorting was performed and the electrical "footprint" was calculated using the spike-triggered average as previously described Bakkum et al., 2013; Müller et al., 2015; Deligkaris et al., 2016; Radivojevic et al., 2016, 2017; Jäckel et al., 2017.

To perform spike-triggered averaging we need to reliably record spiking activity of the neurons. Therefore, we selected the fixed electrodes at the putative locations of the AISs but imposed a spatial restriction in order to not record the same neuron twice. For selection of fixed electrodes, all electrodes were ranked according to their median negative peak amplitude (see previous section). The electrode with the highest rank was selected, afterwards all electrodes in its proximity (within 100µm distance) were discarded from the list, and the procedure was repeated.

## Spike Sorting

Even in sparse cultures some electrodes will pick up spikes from multiple neurons in their vicinity. Therefore, spike sorting was performed for each fixed electrode after recording. Waveforms were extracted for a period of 1.5 ms before to 1.5 ms after the negative peak of each event comprising 61 samples for each event. In order to extract those features that best separate the different clusters of spikes, we performed a principal component analysis. We choose the first 10 principal components as spike features (Abeles and Goldstein, 1977), containing more than 85% of the energy of the signal. KlustaKwik (Kadir et al., 2014) was used to fit a mixture of Gaussians with unconstrained covariance matrices and automatically selected the number of mixture components. Clusters containing more than 2,500 spiking events in total were assigned to distinct neurons. This number corresponds to an average of 14 spikes in each of the 179 recording configurations. With 14 samples the spike triggered averaging reduces the noise by approximately a factor <sup>√</sup> 1 14 = 0.27. This procedure omits neurons with a firing rate below 14 spikes/115 s ≈ 7 spikes/min for which we could not compute

(A). The HD-MEA has a high number and density of electrodes in the recording area and a limited number of low-noise on-chip amplifiers placed at the periphery. A switch matrix allows for using different recording configurations by selecting recording electrodes and connecting them to the amplifiers (B). Extracellular recordings enabled the detection of spiking events by a simple thresholding procedure (C). The amplitude of the negative peak of these spikes was mapped across the entire HD-MEA by recording from all electrodes using non-overlapping block configurations (D). This map reveals the location of individual neurons, as neuronal axon initial segments (AISs) are strong contributors to a neuron's local extracellular field potential. Neuronal footprints (see, e.g., Figure 2B) were obtained by recording with multiple configurations consisting of both, fixed electrodes, as well as randomly selected electrodes (E). The fixed electrodes (indicated in black) were located near the AIS of the neuron and did not change between the configurations. The remaining electrodes of the HDMEA where sequentially recorded in batches (indicated by the same color) consisting of electrodes at randomly selected locations. Spike sorting of the spike events on the fixed electrodes was performed to obtain the activity of single neurons. Spike-triggered averages from all configurations were then combined into a single footprint for each neuron revealing the axonal delays (E). (B) was adapted with permission from Obien et al. (2015).

a reliable footprint. The uniqueness of the detected neurons was confirmed by assessing their different footprints (**Figure 6**). Clusters leading to identical footprints were manually merged to single neurons, and the footprints of the merged neurons were re-calculated.

## Optimal Recording Configurations for High-Throughput Scanning of Electrical Footprints

The extracellular signals originating from axons and dendrites are very small with respect to the background electrical activity

FIGURE 2 | Activity map and footprint of an example neuron. The marker in the activity map reveals the location of the AIS of the example neuron (A). The circle size indicates the square-root-scaled count of spiking events per electrode. The median negative amplitude of the spikes is color-coded with a cut-off at −200 µV. Spike triggered averaging shows the axonal footprint (B). The circle diameter indicates the square-root-scaled amplitudes of the average APs. The axonal delay is color-coded. Close-ups of 3 regions (labeled I, II, III), showing the average AP waveforms, are presented in the lower panels. Gray axonal contours serve as guide to the eye and are estimated by observing the spatial movement of signal peaks in consecutive movie frames (Radivojevic et al., 2017). The asterisc (\*) indicates an artifact probably from a large spike at the AIS of a presynaptic neuron.

and noise, so that spike-triggered averaging was applied. We developed a set of recording configurations to map the electrical footprint of several neurons in parallel by utilizing the switch matrix of our HD-MEA. The switch matrix can be dynamically configured to connect a large number, e, of electrodes to a smaller number, a, of amplifiers. In a first-order approach, one could use one electrode as trigger and the remaining electrodes to scan the neuronal footprint, which would result in a large number of configurations, cw, needed to scan the whole array, c<sup>w</sup> = e/a. For recording axonal arbors of n neurons, electrodes near the AISs of these n neurons have to be always connected to amplifiers (n fixed electrodes). The remaining amplifiers can then be connected to the remaining electrodes in several successive configurations (variable electrodes). Following this procedure, the whole array can be scanned with

$$c\left(n\right) = \frac{e-n}{a-n}$$

configurations. For n neurons we need c(n) configurations, which means on average C (n) = c(n) /n configurations for one neuron. An optimal strategy means to choose n in such a way that C (n) → min for 0 < n < a. With n < a ≪ e, the number of neurons being much smaller than the number of electrodes, we can approximate:

$$C\left(n\right) = \frac{e - n}{\left(a - n\right)n} \approx \frac{e}{\left(a - n\right)n}$$

The right-hand side has a minimum for n = a/2. Therefore, approximately half of the amplifiers should be connected to fixed electrodes. The other half of the amplifiers can then be used to scan the whole array in 2c<sup>w</sup> configurations, or on average C<sup>a</sup> = C (a/2) = 4e/a 2 configurations per neuron. The axonal arbors of a single neuron may extend over the whole array, but by scanning the axonal arbors of many neurons in parallel, the average number of configurations, Ca, per neuron is much less than the number of configurations, cw, required for scanning the whole array for large a :

$$C\_a = \frac{4e}{a^2} \ll \frac{e}{a} = c\_w$$

This is due to the fact that increasing the number of amplifiers quadratically decreases the average time to scan a single neuron, which allows for high-throughput acquisition of axonal delay maps.

#### Live Imaging

Live-cell visualization of whole neurons was performed by transfection (Bakkum et al., 2013; Radivojevic et al., 2016). Transfection was performed using a pLV-hSyn-RFP plasmid from Edward Callaway (The Salk Institute, US; Addgene, #22909) and Lipofectamine 2000 (Life Technologies) in accordance with the manufacturer's protocol. A Leica DM6000 FS microscope, a Leica DFC 345 FX camera, and the Leica Application Suite software were used to produce the micrographs.

#### RESULTS

To initially identify the location of axonal initial segments (AISs), the whole array was scanned by using configurations in which non-overlapping blocks (**Figure 1D**). The median of the negative peak for each electrode was plotted as a map showing some areas with large negative peaks (**Figure 2A**). Such local minima were assumed to indicate the putative (proximal) AIS locations (Bakkum et al., 2019). In low-density cultures, several AISs could be distinguished (**Figure 1A**). So called "fixed electrodes" were then selected as trigger electrodes at the putative locations of the AISs, while the remaining "variable electrodes" were selected in sequential configurations to map the electrical footprint of neuronal units and their axonal arbors (Bakkum et al., 2013; Müller et al., 2015; Deligkaris et al., 2016; Radivojevic et al., 2016, 2017; Jäckel et al., 2017) over the entire array (**Figure 1E**). After spike-triggered averaging, the amplitude and delay of axonal signals could be mapped across the whole recording area for each individual neuron (**Figure 2B**).

#### High-Throughput Scanning of Electrical "Footprints"

We used HD-MEA with 11,011 electrodes and 126 amplifiers (Frey et al., 2010). We connected 62 amplifiers to fixed electrodes and used the remaining amplifiers to scan the whole array selecting 64 electrodes at random positions, which would yield a total of c(n) = e−n <sup>a</sup>−<sup>n</sup> = 11011−62 <sup>126</sup>−<sup>62</sup> = 10949 <sup>64</sup> = 172 configurations (see section Spike Sorting). However, due to the design of the switch matrix in our HD-MEA, some electrodes cannot be selected in the same configuration, which increased the number of recording configurations to 175 (see **Table 1**).

In our culture, 53 of the 62 fixed electrodes recorded singleunit activity. However, only 28 axonal arbors could be identified, because 25 electrodes did not record enough spikes to reliably determine arbor structures (see Methods). The remaining 9 fixed electrodes recorded multi-unit activity, so that spike sorting was used to identify single-neuron activity and to obtain additional 40 axonal arbors. In total, we mapped the axonal arbors of 68 neurons. For further analysis we only used the n = 46 neurons with axonal arbors extending over more than 50 electrodes (**Figure 6**).

#### Identification of Axonal Arbors

Previously (see Figure 6 in Bakkum et al., 2013), axonal arbors were traced according to the occurrence of negative peaks in signal amplitudes in the spike-triggered averages of extracellularly recorded electrical signals that exceeded 5 times the background noise (sV). This method (hereafter termed "method I") evaluates the spike-triggered averages for each electrode separately, without considering their spatial arrangement and signal correlations between neighboring electrodes. We used another method (hereafter termed "method II") to benefit from the fact that the delay of the negative signal amplitude peak in the extracellularly measured potential originating from a single axon is very similar at neighboring electrodes it passes by. When we mapped the delay of these negative signal peaks in the spike-triggered averages (**Figure 3A**), the resulting map showed a distinct region of similar delays against a background of random delays (**Figure 3B**). This finding is due to the fact that signals originating from a common source, e.g., from an axon of the same neuron, are very similar across neighboring electrodes, whereas in the case of random signals the negative peak could occur anywhere in the



*AP band* = *300 Hz*−*10 kHz. SM, switch matrix; APS, active pixel sensor. The expected number of neurons which can be mapped simultaneously in a single recording session are highlighted in boldface.*

*<sup>a</sup>Assuming one neuron per fixed electrode. Note that spike sorting should be used in dense cultures to identify single-neuron activity, which would increase this number.*

*<sup>b</sup>Total (RMS) noise consists of circuit noise, noise from dendritic Pt black electrodes (1.8* µ*V) (Viswam et al., 2019) as well as from background neuronal activity (4* µ*V). These noise sources are uncorrelated and they add up to 3.1* µ*V in saline (Frey et al., 2010) and to about 5* µ*V in the neuronal cultures cultured on our HD-MEA. From these values, we can estimate the total noise while recording from such cultures on other HD-MEA with similar electrodes.*

*<sup>c</sup>Factor by which the recording time per configuration increases to obtain a similar noise reduction after spike-triggered averaging. This factor is the square of the ratio between the total noises for each HD-MEA.*

*<sup>d</sup>Full-frame readout does not require selection configuration with different electrodes.*

*<sup>e</sup>Number of neurons was fixed at 1,000 for comparison with HD-MEAs with larger number of electrodes and switch-matrix design.*

interval [1tpre, 1tpost] for which the spike triggered averaging was performed (see histogram in **Figure 3C**). 1tpre and 1tpost represent the boundaries relative to the spike triggering, so that the total spike-triggered average has the length T = 1tpost − 1tpre. To quantify the smoothness of the delay map, the delay was sampled in a neighborhood (compare **Figure 4H**) of hexagonal shape around each electrode, and the sample standard deviation Sτ<sup>n</sup> was calculated. Note, that in the case of a uniform distribution over the interval [0, 1], the standard deviation of a sample is bounded by 0 ≤ s ≤ 0.5 and shows a characteristic distribution, depending on the number of observations, N, in each sample.

This distribution shows a sharp peak around the mean standard deviation:

$$\overline{s\_{random}} = \frac{1}{\sqrt{12}}.$$

There is no analytical expression for this distribution, but after a coordinate transformation of the interval, it can be approximated by a beta distribution B(α, β).

In case that axonal signals are present, the delays in the neighborhood of an electrode with a negative peak at t are distributed in the interval [t − r c ;t + r c ], depending on the velocity, c, of the action potential and the distance, r, between the electrodes. Therefore, the mean of the sample standard deviation for axonal delays is:

$$
\overline{s\_{\text{axon}}} = \frac{2r}{c\sqrt{12}} = \frac{r}{c\sqrt{3}}.
$$

For an HD-MEA with r = 18 µm and a typical conduction velocity for short-range-projecting axons in the rat neocortex of 0.3−0.44 m/s (Lohmann and Rörig, 1994; Telfeian and Connors, 2003), a standard deviation of around 30 µs can be expected (compare with **Figure 3E**). At the boundary, more and more neighboring electrodes will no more pick up the axonal signal, so that the sample standard deviation shifts toward:

$$\overline{s\_{random}} = \frac{T}{\sqrt{12}}\text{-} $$

In our case, with T = 8 ms, a standard deviation of 2.3 ms for background signals would be expected (compare with **Figure 3D**). Empirically, the distribution of saxon can be approximated by an (truncated) exponential distribution E(λ) (see below). Therefore, axons have a distribution of sτ<sup>n</sup> with a peak close to zero, which is clearly distinguishable from the distribution for the background. A threshold smin, placed at the local minimum in the sτ<sup>n</sup> distribution (**Figure 3G**), can be used to separate both populations. The electrodes with a sτ<sup>n</sup> below this threshold represent negative peaks that are consistent across neighboring electrodes (**Figure 3I**). If these peaks appear after the negative peak at the AIS (**Figure 3H**), they are assumed to originate from the axonal arbor of the neuron (**Figure 3J**).

For a limited number of neurons, the ground truth in the form of fluorescence images was available, so that we could compare the performance of the new method (method II; **Figure 4B**) with the old method (method I; **Figure 4A**) employing a fixed threshold at 5s<sup>V</sup> (Bakkum et al., 2013).

electrodes located close to the (proximal) AIS (red trace), close to axons (black) and for electrodes recording background activity and noise (gray). The negative peak at the AIS appears slightly earlier than at the trigger electrode. Mapping (B) and histogram (C) of the delay of the negative peak, τ , showing an irregularly shaped area with a "smooth" gray value outlining the axonal arbor, which is surrounded by a "salt-and-pepper" patterned background area. Axonal signals appear at 0 *ms* < τ < 2 *ms*. Spike-triggered averages for *N* = 7 neighboring electrodes, located in the "salt-and-pepper" region (D), feature a large sample standard deviation for the delays, *s*τ*<sup>n</sup>* , as compared to those located in the "smooth" region (E). Mapping (F) and histogram (G) of *s*τ*<sup>n</sup>* . The small irregularly shaped area outlining the axonal arbor is dark, whereas the surrounding area is displayed in lighter tones. Segmentation is done by placing the threshold *sthr* ≈ 0.5 *ms* in the valley between the sharper peak (black), close to 0 *ms*, and the broad peak (gray) around the expected *sbackground* = 8/ √ 12*ms* (open triangle) for random delays. Mapping of electrodes, where the negative peak appears after the negative peak of the AIS (H), with *s*τ*<sup>n</sup>* < *s*min (I), which record presumably axonal signals (J). The crosshair symbol shows the location of the (proximal) AIS, the green and blue dots represent a patch of 7 neighboring electrodes located in the "salt-and-pepper" and "smooth" areas, respectively. Corresponding negative peaks are indicated by triangles of the same color.

An example of a transfected neuron is shown in **Figure 4C**. More electrodes were selected by method II than by method I, which could be compensated for by lowering the threshold, e.g., to 3s<sup>V</sup> (**Figure 4D**). In order to compare the electrode selection (a set of electrode coordinates, E) with the groundtruth axon information (a set of pixels in the image, A), we

(G) with respect to an increased electrode distance (H): increasing the distance from *<sup>r</sup>* <sup>≈</sup> <sup>18</sup> <sup>µ</sup><sup>m</sup> (B) to *<sup>r</sup>* <sup>≈</sup> <sup>36</sup> <sup>µ</sup><sup>m</sup> (E) yields a higher true positive rate and <sup>H</sup> <sup>≈</sup> <sup>200</sup>

µm. Axons were manually traced from fluorescence images (DsRed fluorescence displayed using an inverted grayscale) (C).

used the Haussdorff distance H(A, E), which is commonly used in computer vision to measure how strongly two shapes differ from each other. After registering the fluorescence image to the electrode coordinate system, we calculated

$$H = \max\left\{\sup\_{a \in A} \inf\_{e \in E} d(a, e), \sup\_{e \in E} \inf\_{a \in A} d(a, e)\right\}$$

using the Euclidean distance d(a, e) between the coordinate e = xe, y<sup>e</sup> T of an electrode recording an axonal signal and the coordinate a = xa, y<sup>a</sup> T of the pixel representing an axon in the fluorescence image. For smaller threshold for method I lead to a larger deviation from the ground truth than method II. This was mainly due to the fact that, more electrodes far away from the axonal arbors were selected. The new method inherently relies on adjacency and rejected these "outliers" and produced more compact maps that more closely followed the ground truth. In other words, the distributions of the feature

used to classify the electrical activity as either axonal signals or as background, showed a larger overlap for method I than method II. We tested the robustness of method II against the spatial distance of the electrodes by increasing the spatial extension of the neighborhood while keeping the number of electrodes in each neighborhood constant (N = 7). When hexagonal patterns with r = 2 × 18 µm (**Figure 4E**) or r = 3 × 18 µm distance between electrodes were selected, the distance to the ground truth only slightly increased (**Figure 4G**). However, it seemed that for a carefully chosen threshold (e.g., around 4.5sV, H ≈ 100 µm, **Figure 4F**), the original method performed as well as the new method.

Due to the limits of the Haussdorff distance in estimating the quality of the extracted mappings, we also calculated the receiveroperator characteristics (ROC) (Fawcett, 2006), which is possible, as both segmentation methods are binary classifiers. We fitted the respective empirical distributions of their scores with a mixture of two partially overlapping distributions representing axonal

segmentation of an individual neuron, segmented by methods I (A,D) and II (B,E). The empirical distribution (NP) of amplitudes *Vn* (log normalized by signal noise, σ*V* ) and the sample standard deviations of the delays, *s*τ*<sup>n</sup>* (normalized by *T*/2) of the negative peaks were fitted (fit NP) to obtain the distributions of axonal signals (positive class, P) and background activity (negative class, N). The corresponding true-positive rate (TPR) and false-positive rate (FPR) were calculated for each possible threshold and plotted as ROC curve (C). The cross depicts the position of the (fixed) threshold of method I (FPR = 0.00009, TPR = 0.7), whereas the circle indicates the (adaptive) threshold of method II (FPR = 0.011, TPR = 0.85). Method II (gray shading) performs better than method I (blue shading) as shown by the larger area under the curve (AUC). This held true for all *n* = 46 neurons (F), and, although method I has a lower FPR (H), its TPR (G) was much lower than that of method II, as it missed out on more than 50% of the axonal signals.

signals ("positive" class, P) and background activity ("negative" class, N) with:

1. two normal distributions N (**Figure 5A**) for the segmentation with method I (**Figure 5D**)

<sup>P</sup>(x) <sup>≈</sup> <sup>p</sup>N<sup>N</sup> (x;µN, <sup>σ</sup> 2 N ) <sup>+</sup> <sup>p</sup>P<sup>N</sup> (x;µP, <sup>σ</sup> 2 P ) with <sup>x</sup> <sup>=</sup> log <sup>V</sup><sup>n</sup> sn , µ<sup>N</sup> < µ<sup>P</sup>

2. a beta distribution B and a truncated exponential distribution E (**Figure 5B**) for the segmentation with method II (**Figure 5E**):

 $P(\mathbf{x}) \approx p\_N \mathcal{B}(\mathbf{x}; \alpha\_N, \beta\_N) + p\_P \mathcal{E}(\mathbf{x}; \lambda\_P) \text{ with } \mathbf{x} = \frac{s\_{r\_0}}{T/2}, \mathcal{E}(\mathbf{x}; \lambda) = 1$   $\frac{\lambda \varepsilon^{-\lambda x}}{1 - \varepsilon^{-\lambda x}}$  for  $0 \le x \le 1$ 

For both methods, we used the fitted distributions to estimate the probability observing axonal signals (P +) or background activity (P −).


We then numerically calculated the cumulative distributions in order to calculate the true positive rate (TPR) and false positive rate (FPR) for each threshold, x, and plotted them as an ROC curve (**Figure 5C**). The area under the curve (AUC) showed

square-root-scaled count of spiking events per electrode. The median negative amplitude of the spikes is color-coded with a cut-off at −200 µV. Spike-triggered averaging shows the axonal footprint of 46 neurons (C). Only neurons with axonal arbors extending over more than 50 electrodes are shown.

*(Continued)*

FIGURE 6 | The circle size indicates the square-root-scaled amplitudes of the average APs. The axonal delay is color-coded. Gray axonal contours serve as guide to the eye and have been estimated by observing the spatial movement of signal peaks in consecutive movie frames. The axonal contours of all neurons were color-coded and combined, showing the axonal arbors in the recorded neuronal network (B).

that the new method consistently had a better performance than the original method for a total of n = 46 neurons (**Figure 5F**). Furthermore, the automatic threshold procedure yielded a much better TPR (**Figure 5G**) at the expense of a slightly increased false-positive rate FPR in comparison to the original method (**Figure 5H**).

## DISCUSSION

HD-MEAs with more than 3,000 electrodes per square millimeter and dedicated low-noise on-chip amplifiers are suitable tools to record the electrical activity of individual axonal arbors. We first optimized a recording scheme for the switch matrix HD-MEA that relied on combinations of fixed and variable recording sites for high-throughput parallel mapping of as many neurons as possible per total recording time. The method described here shows a promising way to obtain axonal arbors at large scale from potentially all neurons during a single recording session. As an example, 68 neurons were mapped in parallel, 48 neurons of which featured large axonal arbors (**Figure 6**). This yield can be further improved using an HD-MEA design with an increased number of simultaneously active recording channels, decreasing the number of necessary measurement configurations and, hence, the on average the required measurement time per neuron to a few seconds (**Table 1**).

We then developed a method to distinguish axonal signals from the background noise. Axonal arbors reveal themselves by typical waveforms of the extracellular electric field potentials (Bakkum et al., 2013, 2014; Petersen et al., 2015; Deligkaris et al., 2016). Previously (Bakkum et al., 2013), axonal arbors were traced according to the occurrence of negative peaks in signal amplitudes in the spike-triggered averages of extracellularly recorded electrical signals that exceeded 5 times the background noise. With this threshold more than 50% of the smaller axonal signals are lost (**Figure 5G**). Lowering the threshold can alleviate this problem, however, the likelihood that background signals are falsely assigned to axonal arbors also increases. Some electrodes measuring spurious signals can easily be detected, if they are located at comparably large distance from electrodes that record genuine axonal signals. Typically, these false positives are removed manually after visual inspection of the recorded waveforms and their isolated location in the recording area. However, this procedure is not possible for more than a few recorded axonal arbors. Therefore, we developed a new method that compares the axonal delays on neighboring electrodes. If these delays are similar, the corresponding signals most likely originated from the same axon. If there are large differences in the delay, the corresponding signals may represent background noise. Both methods, amplitude thresholding (Bakkum et al., 2013) and the new method, worked well when we validated them by comparing their results with the morphologies of axonal arbors obtained by sparse transfection (Bakkum et al., 2013; Radivojevic et al., 2016). Upon comparing both methods according to their ROCs on a larger data set of 46 axonal arbors, the new method based on local correlations outperformed the classic amplitude thresholding. Furthermore, the new method does not require manual intervention, e.g., for setting a threshold.

The example workflow demonstrated here enables highthroughput scanning of axonal arbors and mapping of their axonal delays without the need to adjust parameters for the detection of axonal signals. This method can be extended to new generations of HD-MEAs (Ballini et al., 2014; Viswam et al., 2016; Yuan et al., 2018) and can be used to obtain data from axonal arbors of thousands of neurons within a recording session of a few hours (**Table 1**). Our example workflow yielded axonal arbors of 68 neurons, 46 of which featured axonal arbors extending over more than 50 electrodes (**Figure 6C**). These axonal arbors showed considerable variation in total length, but also in local branching patterns and axonal delays (**Supplemental Figure 1**). Interestingly, some neurons featured footprints in the form of disconnected patches, which could be the signature of saltatory conduction of action potentials. This observation is consistent with the reported formation of nodal components in neuronal cultures (Freeman et al., 2015), but requires further experimental validation.

Our method can be used for automated selection of neurons with suitable axonal arbors for stimulation experiments (Jäckel et al., 2017), single action potential tracking (Radivojevic et al., 2017), automated patching (Obien et al., 2019), for mapping of ion receptors by local drug application (Sasaki et al., 2011) and even for automated single-cell phenotyping of axonal conduction in human iPSC-derived neuronal cultures.

#### DATA AVAILABILITY

The Hana (high density microelectrode array recording analysis) analysis pipeline is open source. All source code as well as example data to replicate the figures are available at: http://github.com/tbullmann/hdmea\_axon. The example data consists of spike triggered-averages that were extracted from the raw recordings.

## ETHICS STATEMENT

All experimental procedures on animals were carried out in accordance with the European Council Directive of 22 September 2010 (2010/63/EU) and had been approved by the local authorities (Animal Care and Use Committee of RIKEN; QAH24-01).

## AUTHOR CONTRIBUTIONS

TB designed the study, performed experiments, wrote the software, analyzed data, assembled figures, interpreted the results, prepared, and revised the manuscript. MR performed recording and imaging experiments. SH implemented and tested analysis algorithms. KD performed cell culture experiments. AH interpreted the results, prepared, and revised the manuscript. UF planned the study, supported the experiments, interpreted the results, and revised the manuscript.

#### FUNDING

The HD-MEA work at ETH Zurich was financially supported by the European Community through the European Research Council Advanced Grant 694829 neuroXscales (Horizon 2020) and the Swiss National Science Foundation Grant

#### REFERENCES


205321\_157092/1 (Axons). Financial support through the Swiss Commission for Technology and Innovation project 25933.2 PFLS-LS is also acknowledged.

#### ACKNOWLEDGMENTS

We thank Alexander Stettler and Peter Rimpf for post-processing CMOS chips as well as Manuel Schröter, Roland Diggelmann and Felix Franke for helpful discussions about spike sorting.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00404/full#supplementary-material

Supplementary Figure 1 | Sholl analysis for number of electrodes (A) and axonal delay (B) for *n* = 46 neurons shown in Figure 6.


**Conflict of Interest Statement:** UF is a co-founder of MaxWell Biosystems AG, Mattenstrasse 26, Basel, Switzerland.

The remaining 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 © 2019 Bullmann, Radivojevic, Huber, Deligkaris, Hierlemann and Frey. 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(s) 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.

# Axonal Computations

#### Pepe Alcami 1,2 \* and Ahmed El Hady 3,4 \*

*<sup>1</sup> Division of Neurobiology, Department of Biology II, Ludwig-Maximilians-Universitaet Muenchen, Martinsried, Germany, <sup>2</sup> Department of Behavioural Neurobiology, Max Planck Institute for Ornithology, Seewiesen, Germany, <sup>3</sup> Princeton Neuroscience Institute, Princeton University, Princeton, NJ, United States, <sup>4</sup> Howard Hughes Medical Institute, Princeton University, Princeton, NJ, United States*

Axons functionally link the somato-dendritic compartment to synaptic terminals. Structurally and functionally diverse, they accomplish a central role in determining the delays and reliability with which neuronal ensembles communicate. By combining their active and passive biophysical properties, they ensure a plethora of physiological computations. In this review, we revisit the biophysics of generation and propagation of electrical signals in the axon and their dynamics. We further place the computational abilities of axons in the context of intracellular and intercellular coupling. We discuss how, by means of sophisticated biophysical mechanisms, axons expand the repertoire of axonal computation, and thereby, of neural computation.

#### Edited by:

*Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France*

#### Reviewed by:

*Mickael Zbili, INSERM U1028 Centre de Recherche en Neurosciences de Lyon, France Alon Korngreen, Bar-Ilan University, Israel*

> \*Correspondence: *Pepe Alcami alcami@bio.lmu.de Ahmed El Hady ahady@princeton.edu*

#### Specialty section:

*This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience*

Received: *03 May 2019* Accepted: *27 August 2019* Published: *18 September 2019*

#### Citation:

*Alcami P and El Hady A (2019) Axonal Computations. Front. Cell. Neurosci. 13:413. doi: 10.3389/fncel.2019.00413* Keywords: analog-digital signaling, action potential generation, propagation, resistance, capacitance, myelin, axo-axonal coupling

## 1. INTRODUCTION

Neurons are compartmentalized into input compartments formed by dendrites and somas, and an output compartment, the axon. However, in the current era, there is a widespread tendency to consider that the biophysics of single neurons do not matter to understand neuronal dynamics and behavior. Neurons are often treated as point processes with disregard of the complex biophysical machinery that they have evolved. Moreover, neuronal computations are assumed to be mostly performed by dendrites or at synapses (Südhof and Malenka, 2008; Stuart et al., 2016), and axons are reduced to simple, static, and reliable devices. However, a wealth of literature supports that this is not the case: axons form complex structures that ensure a variety of sophisticated functions and they are highly dynamic. Here, we aim to review evidence that axons perform complex computations which depend on a myriad of biophysical details and ensure the generation and propagation of neuronal outputs. We will not discuss biophysics of synaptic release, reviewed elsewhere (Südhof and Malenka, 2008).

More than six decades after seminal discoveries in experimentally accessible invertebrate axons (Hodgkin and Huxley, 1952), axonal research has unraveled previously-unsuspected, rich and dynamical electrical signaling in axons, which consists of a hybrid of analog and digital signaling. Contrary to the giant invertebrate axons studied in the early days (Hodgkin and Huxley, 1952; Furshpan and Potter, 1959), most invertebrate and vertebrate axons are thin and present complex extended arborizations (e.g., **Figure 1**), making it difficult to record from them. However, successful electrophysiological recordings from axons and terminals have been performed (Hu and Jonas, 2014; Kawaguchi and Sakaba, 2015) and electron and optical microscopy have made it possible to deepen our understanding of fine axonal structures (Rash et al., 2016; D'Este et al., 2017). Moreover, the combination of new structural imaging techniques with electrophysiology has made it possible to study how structural changes at the sub-micrometer scale impact function (Chéreau et al., 2017).

We will first illustrate general signaling principles in axons, before delving into the generation and propagation of action potentials (APs) and their dynamical regulation. We will comment on the computational abilities enabled by different mechanisms throughout the article. Finally, we will position axons in the context of their interactions with other compartments and with each other, by virtue of axo-axonal coupling (Katz and Schmitt, 1940; Furshpan and Potter, 1959) and finally, indirectly via glial cells.

#### 2. REVIEW OF AXONAL COMPUTATIONS

#### 2.1. General Principles: Signaling in Axons 2.1.1. Of Axons and Brains

The propagation of electrical signals along axons controls the reliability and the timing with which neural networks communicate. The spatial extent of axonal trees introduces delays between the generation of an AP in a neuron and its arrival to the presynaptic site, where information is relayed to a postsynaptic cell. Thereby, the axonal propagation delay influences the temporal relationship of presynaptic and postsynaptic activity (Izhikevich et al., 2004).

The delays in AP propagation encode information (Seidl et al., 2010) and contribute to re-configuring neural circuits through plastic mechanisms such as spike timing dependent plasticity (Bi and Poo, 1998; Izhikevich et al., 2004). Each synapse is characterized by its own "critical window," given by the delay between presynaptic and postsynaptic activity, to induce synaptic plasticity. The speed at which signals travel along axons can vary over four orders of magnitude, from tens of centimeters per second in thin unmyelinated axons to 100 m/s in giant myelinated fibers (Xu and Terakawa, 1999; Schmidt-Hieber et al., 2008); highlighting the ability of biophysical specializations of different axons to conduct APs at different speeds. In computational terms these specializations allow signals to travel at different speeds in neural circuits, diversifying and expanding the timescales at which neural computations take place. Moreover, they modulate the speed of information processing in neural circuits.

Axons have evolved different intricate geometries (**Figure 1**), revealing specific structure-function specializations. Constraints to axonal morphology include (1) spatial constraints: axons occupy large volumes of nervous systems, yet they require internal components necessary to their function such as mitochondria, which constrain their minimal functional size; (2) energetic requirements may have evolutionary exerted a selection pressure on axonal properties (Perge et al., 2009; Harris and Attwell, 2012); (3) efficiency of electrical information processing in relation to structure-function specializations. The last point on electrical information processing will be the main focus of the current review.

One first needs to define what a computation is in the context of neuronal information processing. We can state that the role of a neuron is to generate and transmit electrical signals. Ultimately, subthreshold signals and spikes propagate in axons, conveying a combined functional output message to the synaptic terminals (reviewed in Zbili and Debanne, 2019). These output signals need to first be generated by integrating input information received by soma and dendrites. Any modification of the input/output relation is to be considered a computation (Silver, 2010) since it contributes to the transformations that ultimately generate the functional message carried by axons. It is important to note that these modifications are inherently non-linear as they deviate from computations by a linear and static cable.

#### 2.1.2. Propagation of Electrical Signals in the Axon

Propagation of electrical signals in the axon results from a combination of specialized active and passive mechanisms. Active properties are shaped by neuronal voltage-gated ion channels recruited as a function of the dynamics of the membrane potential whereas passive properties are determined by the axonal membrane at rest and by axonal geometry.

As increasingly appreciated, APs are not just an on/off switch, and electrical signaling in the axon should be regarded as a hybridization of analog and digital signaling (Shu et al., 2006) (**Figure 2**). Furthermore, APs are strongly regulated by the background analog activity provided by subthreshold postsynaptic events. For example, the inactivation of potassium Kv1 channels in the axon initial segment broadens the axonal AP waveform and increases unitary excitatory postsynaptic potentials (EPSP) amplitude in layer V pyramidal neurons (Kole

et al., 2007). Interestingly, Na<sup>v</sup> channels have also been implicated in analog-digital signaling. The recovery from inactivation of axonal Na<sup>v</sup> channels can increase AP amplitude, enhancing synaptic transmission (Rama et al., 2015). Note that some neurons do not encode information with APs but only with graded signals (graded potential neurons; Borst and Haag, 1996).

#### 2.1.3. Non-electrical Changes

Signaling in axons and neurons is usually regarded as purely electrical. However, electrical signals are accompanied by other biophysical changes in the neuronal membrane, some of which may further contribute to signaling. The AP is accompanied by changes in many biophysical properties such as temperature, mechanical membrane properties, and optical birefringence (Abbott et al., 1965; Cohen et al., 1970; Howarth, 1975; Howarth et al., 1975; Tasaki and Iwasa, 1982b; Tasaki and Byrne, 1992). For example the changes in the optical properties of the axon during propagation have been at the basis of the label free interferometric imaging of APs in in-vitro systems (Akkin et al., 2007; Oh et al., 2012; Batabyal et al., 2017).

Mechanical displacements associated with the AP have been measured in many experimental contexts (Hill et al., 1977; Iwasa and Tasaki, 1980; Tasaki and Iwasa, 1982a,b). These mechanical displacements can be regarded as propagating surface modes that are elicited via the large electrostatic force produced by the AP. In this regard, the AP is an electro-mechanical pulse (El Hady and Machta, 2015). Interestingly, converging evidence suggests that mechanics play a role in electrical signaling (Tyler, 2012). Moreover, there is mounting evidence that some voltage sensitive channels such as sodium and potassium channels are mechanically modulated locally and that many neurons express mechanically-activated channels (Schmidt and MacKinnon, 2008; Schmidt et al., 2012; Ranade et al., 2015). Interestingly, mechanically sensitive ion channels are present in the internodes of myelinated axons (Brohawn et al., 2019). Future research is needed to establish the functional relevance of nonelectrical changes that accompany action potentials, including in particular the relevance of mechanical displacements.

## 2.2. Biophysics of Action Potential Generation

#### 2.2.1. A Brief Historical Perspective on the Action Potential

At the resting, non-excited state, mostly potassium channels are open and the resting potential is, as a consequence, close to the reversal potential for potassium, maintained around −70 mV. In 1939, Hodgkin and Huxley published the first trace of an AP recorded from the squid axon using an intracellular electrode where one can see a very clear overshoot. Following this in 1949, the proposal that sodium ions are the main mediator of AP generation was put forward by Hodgkin and Katz (1949). They studied the effect of systematically varying the concentration of sodium ions and measured its impact on the amplitude of the AP recorded. Subsequently, Keynes managed to show that nerve excitation leads to an increase in the transmembrane flow of sodium ions by tracing the movement of the radioactive isotope Na<sup>24</sup> in repeatedly stimulated squid axons (Keynes, 1951). These seminal findings confirmed that sodium ions are the main contributors to AP generation.

#### 2.2.2. Variations of Action Potentials

APs are characterized by a width, a height and an overshoot magnitude (i.e., referring to the AP height beyond 0 mV). Despite sharing a general biophysical mechanism for initiation, the shape of APs varies in different types of neurons. For example, there are cells that exhibit very narrow APs of a few hundreds of microseconds in width, reflecting a fast spiking behavior, such as some GABAergic interneurons, Purkinje neurons which are GABAergic projection neurons, glutamatergic neurons of the subthalamic nucleus, and Medial nucleus of the trapezoid body (MNTB) cells in the superior olivary complex. CA1 pyramidal neurons in the hippocampus have, in contrast, a relatively wide AP and dopaminergic neurons have an even wider AP of up to 4 ms (reviewed in Bean, 2007).

Apart from the shape of the single spike, neurons can exhibit a diversity of firing patterns. For example, they can be bursting or non-bursting on one hand and they can be adapting or non-adapting on the other hand. Adaptation during a train of APs refers to the process by which AP properties, typically rate and amplitude, decrease within the spike train. There are many biophysical mechanisms by which spike frequency adaptation can happen. The most prominent mechanisms are an increase in outward current flowing through calcium-activated potassium channels and an increasing outward current produced by the electrogenic sodium-potassium pump (Powers et al., 1999). Moreover, there is also a substantial sodium channel inactivation induced by a long lasting depolarization (Sawczuk et al., 1997).

The diversity of AP shapes along with the firing patterns are a result of the different combinations of ion channels that the neuron expresses (reviewed in Marder and Goaillard, 2006). The expression of ion channels impacts the computational abilities of neurons (e.g., narrow action potentials and short after-hyperpolarizations allow cells to generate high firing rates). Narrow action potentials allow neurons to follow high frequency inputs with higher fidelity than cells with wide action potentials and long refractory periods. Remarkably, in addition to constraining bandwidth of information processing, different AP widths may convey different information content (Borst and Sakmann, 1999).

#### 2.2.3. The Axon Initial Segment

Before delving into the mechanistic details of AP generation, it is crucial to appreciate the complex anatomy of the Axon Initial Segment (AIS), the site of AP initiation (**Figure 3A**). The AIS is the main computational unit in axons, allowing them to integrate input signals and generate outputs (APs). Its distance from the soma can vary from 20–60 µm (Somogyu and Hamori, 1976; Sloper and Powell, 1979; Duflocq et al., 2011) to 120 µm (dopaminergic cells; Moubarak et al., 2019). The specific length of the AIS is variable across neurons as it has to adapt it to its own excitability properties. The excitability of the AIS is modulated by varying compositions of sodium and potassium channels clustered at the AIS.

The AIS contains a highly-specialized protein machinery that gives it a distinct character (reviewed in Leterrier, 2016). One such protein is Ankyrin G, a scaffolding protein that is also present at the nodes of Ranvier (Kordeli et al., 1995). Ankyrin

FIGURE 3 | Action potential generation. (A) Ultrastructure of the axon initial segment. A highly-structured spatial organization characterizes proteins at the AIS. (B) Action potential of a stellate cell from the cochlear nucleus with two components: a fast rising phase of the action potential contributed by the AIS and a second phase contributed by the somatodendritic (SD) compartment. Right, phase plane plot of this cell. Modified from Yang et al. (2016) (CC-BY).

G anchors voltage-gated channels such as voltage-gated sodium (Nav) and potassium channels (Kv) to the membrane along with other adhesion molecules (Davis et al., 1996). Beta IV spectrin is another protein expressed in the axon initial segment. Beta IV spectrin's main function is to cluster sodium channels at the axon initial segment while simultaneously binding to the actin cytoskeleton (reviewed in Rasband, 2010; **Figure 3A**).

The AIS in mammalian neurons has been established as the site of the AP initiation following a series of seminal studies that began in the mid 1950s (Araki and Otani, 1955; Coombs et al., 1957; Fatt, 1957). The location of AP initiation has been further confirmed by combining precise electrophysiological measurements and imaging technologies. These allow to precisely identify the locus of AP initiation which was established to be in the distal part of the AIS, 20–40 µm from the soma (Palmer and Stuart, 2006; Kole et al., 2007; Meeks and Mennerick, 2007; Atherton et al., 2008; Foust et al., 2010; Palmer et al., 2010). The AIS is considered to be the site of AP initiation also because of several key properties. It contains a high sodium channel density. Furthermore, AIS sodium channels show a voltage dependence shifted to lower voltages, favoring their activation at less depolarized voltages than at the soma (Hu et al., 2009). Finally, the relatively large electrotonic distance of the AIS from the soma renders distal sodium influx more efficient in evoking a local membrane depolarization, compared to an AIS that would start at the soma. Note that electrophysiological recordings from invertebrates have shown that the initiation of the AP can happen at multiple locations acting in an independent manner (Calabrese and Kennedy, 1974; Meyrand et al., 1992; Maratou and Theophilidis, 2000), as will be discussed below. Along with its specialized protein machinery and acting as the site of AP initiation, the AIS also acts as a diffusion barrier between the somatodendritic and axonal compartments, filtering transport materials passing from soma to axon (Song et al., 2009; Brachet et al., 2010). Note however that the AIS length and its distance from the soma can be regulated in an activity-dependent manner (Grubb and Burrone, 2010; Kuba et al., 2014) and that in some neurons, AP initiation has been reported to occur at the first node of Ranvier (Clark et al., 2005; Lehnert et al., 2014), as will be developed later.

#### 2.2.4. The Sodium Ionic Dynamics and Action Potential Initiation

The extent to which the density of sodium channels is higher in the AIS and the contribution of this high density of sodium channels to AP initiation is a matter of active investigation. There is a consensus that sodium channel density is higher in the AIS but the order of magnitude is still unclear. Immunostaining of sodium channels consistently indicates that there is a higher channel density in the AIS of various neuron types (Wollner and Catterall, 1986; Boiko et al., 2003; Meeks and Mennerick, 2007). Lorincz and Nusser (2010) counted around 200 Na<sup>v</sup> 1.6 sodium channels per square micrometer in the AIS of hippocampal pyramidal cells using electron microscopy. Given that the conductance of a single sodium channel is around 15 pS (Colbert and Johnston, 1996), one would expect a conductance density of about 3,000 pS per square micrometer. On the contrary, electrophysiological measurements from membrane patches pinpoint that sodium channel density is about 3–4 channels per square micrometer in the AIS, which is the same as the somatic density (Colbert and Johnston, 1996; Colbert and Pan, 2002). A similar conclusion was reached on the basis of recordings from blebs that form when cortical axons are cut in in vitro preparations. This might be due to the inability to draw AIS Na+ channels into the patch-clamp recording pipette due to their tight coupling to the actin cytoskeleton (Kole et al., 2008). In this article, the authors record a much larger sodium current after disruption of the actin cytoskeleton (Kole et al., 2008).

Kinetics of sodium currents underlying AP generation have been extensively studied. Hodgkin and Huxley have proposed that the activity of sodium channels can be fitted by m<sup>3</sup> activation kinetics. Baranauskas and Martina (2006) found that sodium currents in three types of central neurons (prefrontal cortical cells, dentate gyrus granule cells and CA1 pyramidal cells) activate faster than predicted by Hodgkin-Huxley type kinetics following m<sup>2</sup> activation kinetics. Moreover, it was found that the half activation voltage of voltage-gated sodium channels in layer 5 pyramidal neurons is 7–14 mV lower in the distal AIS compared to the soma and decreases further with increasing distance from the soma (Colbert and Pan, 2002; Hu et al., 2009). Nav1.6 channels, which are predominantly expressed in the axon initial segment and have a lower half activation voltage (Rush et al., 2005), are proposed to be primarily responsible for the initial slope of the AP. Furthermore, sodium channels at the AIS are more capable of producing a persistent sodium current (Stuart and Sakmann, 1995; Astman et al., 2006). The persistent sodium current has a significant influence on the AP threshold (Kole et al., 2008). Moreover, it is implicated in the generation of the AP afterdepolarization and it therefore contributes directly to the generation of high frequency AP bursts (Azouz et al., 1996).

Using sodium imaging to follow sodium influx in axon, soma and basal dendrites (Fleidervish et al., 2010), the authors suggest that the ratios of Na<sup>v</sup> channel densities in these regions are approximately 3:1:0.3. Interestingly in another study by Lazarov et al. (2018), APs were initiated in the AIS, even when axonal Na<sup>v</sup> channel density was reduced to about 10% in a beta IV spectrin mutant mouse. This experimental finding indicates to a great extent that AP initiation in the AIS does not require such a high local channel density. However in that study, the precision of AP timing was substantially compromised when axonal channel density was reduced. Likewise, the temporal accuracy of AP generation from MNTB cells decreases in a beta IV spectrin mutant mouse (Kopp-Scheinpflug and Tempel, 2015).

The aforementioned section highlights the complexity of sodium ion dynamics and begs for novel imaging modalities that allow tying ultra-fast dynamics with the axonal ultrastructures in order to get insights into the intricate biophysical mechanisms underlying the very first microseconds of AP initiation. The kinetics of sodium channel activation contribute to the speed at which neurons can generate action potentials. Thereby, they constitute a crucial factor in setting the computational speed of neural circuits. The existence of a diversity of sodium kinetics in different cell types likely allows neurons to be recruited at different speeds in different circuits.

#### 2.2.5. The Action Potential Rapidness

A simple but very informative way to study the properties of APs is to plot the time derivative of the voltage (dV/dt) versus the voltage. This is called "phase-plane plot." The spike threshold can be easily visualized in such a representation, where it corresponds to the voltage at which dV/dt rises abruptly. Coombs et al. (1957) noticed that the main spike is preceded by a smaller earlier component (referred to as a "kink"). This component is interpreted as reflecting initiation of the spike in the initial segment of the axon. One can record such a component in somatic spikes in many central neurons, including neocortical pyramidal neurons which we will focus our discussion on here. As mentioned above, one of the most striking features of the AP recorded from cortical neurons has been the existence of a "kink" at the initiation of the AP. One can define the rapidness of AP onset in this cell as the slope of the phase-plane plot at dV/dt = 10 mV /ms. The AP rapidness can also be referred to as rate of voltage change. In Naundorf et al. (2006), the AP rapidness was measured from the cat visual cortical cells. AP rapidness varied between around 20–60 ms−<sup>1</sup> . It is important to mention that sharp, step-like onsets of APs have been recorded in vivo in many preparations (cat visual cortex: Azouz and Gray, 1999, and cat somatosensory cortex: in Yamamoto et al., 1990).

Several hypothesis have been proposed to explain the origin of the AP kink: (1) the backpropagation to the soma of a smoother AP generated at the AIS; (2) an abrupt opening of sodium channels due to the biophysics of neuronal compartmentalization; (3) a decreased membrane time constant due to the loading of the dendritic compartment; and (4) the cooperativity of sodium channels at the AIS.

The "lateral current hypothesis" states that the "kink" at spike onset reflects lateral current coming from the axon which becomes sharper through backpropagation from the initiation site to the soma while initiation is smooth at the initiation site (McCormick et al., 2007; Yu et al., 2008). In Yu et al. (2008), authors perform simultaneous recordings from axon blebs and soma, finding a smoother AP onset in the axon, additionally reproducing these results in a model. It is important to note that this study supporting the lateral current hypothesis was done in bleb recordings which are injured axons that may have undergone severe cytoskeletal reorganization (Spira et al., 2003) affecting sodium channels dynamics. This reorganization might alter the true dynamics of AP initiation.

Although the kink indeed might reflect the lateral current coming from the axon (Milescu et al., 2010), this hypothesis fails to account for the ability of neurons to follow 200–300 Hz frequency inputs. In order to account for this discrepancy, Brette (2013) proposed that the compartmentalization and the distance between the soma and the AIS leads to spike initiation sharpness. In his proposal, Brette suggests that the rapidness arises from the geometrical discontinuity between the soma and the AIS, rather than from the backpropagation of axonal APs. When sodium channels are placed in a thin axon, they open abruptly rather than gradually as a function of somatic voltage, as an all-or-none phenomenon.

Another proposal that takes into account the geometry of neurons is Eyal et al. (2014), in which the authors propose that increasing the dendritic membrane surface area (the dendritic impedance load) both enhances the AP onset in the axon and also shifts the cutoff frequency of the modulated membrane potential to higher frequencies. This "dendritic size effect" is the consequence of the decrease in the effective time constants of the neuron with increasing dendritic impedance load. The authors have shown this in a computational model of reconstructed layer 2/3 pyramidal neurons of humans and rats. The firing pattern at the axon is strongly shaped by the size of the dendritic tree. Authors predict that neurons with larger dendritic trees have a faster AP onset.

A last proposal to interpret AP onset rapidness is that sodium channels, which are assumed to be opening independently within the Hodgkin-Huxley framework, are gated cooperatively. The cooperativity model proposed that the half-activation voltage of the channels becomes dependent on the probability of the opening of the neighboring channels. These cooperative effects might happen mechanistically on very fast timescales either through a purely electrical, mechanical, or electro-mechanical coupling. Though there is no direct experimental test of the cooperativity of neuronal sodium channels at the AIS, it can theoretically account for the observed discrepancy between the sodium channel density and the very rapid rise of the AP at the site of initiation in the initial segment (Naundorf et al., 2006). It is important to note that cooperative gating has been previously observed in calcium, potassium, and HCN channels (Marx et al., 2001; Dekker and Yellen, 2006; Kim et al., 2014).

Apart from its mechanistic underpinnings, the fast rise of APs has attracted both experimental and theoretical approaches to study its functional implications on the biophysics of neuronal populations. Before detailing those functional implications, it is important here to go through a useful theoretical abstraction: a typical cortical neuron, embedded in a cortical network in vivo, receives about 10,000 synaptic inputs. Assuming that each of these synaptic inputs is active with a rate on the order of 1– 10 Hz, incoming signals arrive at a rate of 10 kHz. As a result, the membrane voltage exhibits strong, temporally irregular fluctuations. To understand the computational capabilities of e.g., cortical circuits, it is essential to characterize single neuron computation under such realistic operating conditions. To control the activity of entire neuronal circuits while preserving their natural firing characteristics, it would be advantageous to introduce artificial input components mimicking intrinsically generated synaptic input under precise experimental control. In order to study the dynamical properties of cortical neurons, experimenters have mimicked synaptic bombardment in vitro by injecting stochastic inputs modeled as an Ornstein-Uhlenbeck process in which sinusoidal inputs are embedded (Destexhe et al., 2001; Tchumatchenko et al., 2010; Neef et al., 2013). This experimental setting has allowed the measurement of the dynamic gain of neurons, which means how much neurons attenuate their input in the frequency domain and how fast they are able to follow a rapidly-fluctuating input. This has led to the establishment of the ability of cortical neurons to follow high frequency inputs up to 200–300 Hz (Higgs et al., 2006; Higgs and Spain, 2009; Tchumatchenko et al., 2011). Moreover, there has been a series of theoretical studies exploring the dependence of encoding capacity on the active properties of the AP initiation (Fourcaud-Trocmé et al., 2003; Wei and Wolf, 2011; Huang et al., 2012).

#### 2.2.6. AP Trajectories Beyond the Rapidness of Initiation

Although we have mostly concentrated on the initial spike rapidness, note that the phase plot can display a variety of trajectories after the onset of the AP (**Figure 3**). These trajectories are determined by additional ion channels in conjunction with sodium channels. Potassium channels are typically responsible for the repolarizing phase of the AP. The relative temporal profiles of activation of sodium and potassium channels and their subunit composition determine the width of the AP (Lien and Jonas, 2003). Furthermore, the spatial location of ion channels also contributes to the shape of AP trajectories (Yang et al., 2016; **Figure 3B**). Interestingly, Kole et al. (2007) showed that APs become thinner during axonal propagation due to the specific expression of Kv1 channels in the axons of layer 5 pyramidal neurons. It has also been shown that the AP shape affects calcium currents and transmitter release [calix of Held: (Borst and Sakmann, 1999); dentate gyrus granule cells: (Geiger and Jonas, 2000); layer 5 pyramidal neurons: (Shu et al., 2006; Kole et al., 2007); CA3 pyramidal neurons (Bialowas et al., 2015; Rama et al., 2015); cerebellar interneurons: (Rowan et al., 2016); cerebellar Purkinje cells: (Kawaguchi and Sakaba, 2015)]. Therefore, the AP shape beyond the initial spike rapidness provides an extra dimension for information encoding on a variety of timescales.

#### 2.2.7. The Action Potential at Nodes of Ranvier

Although the AP is generated at the AIS, the nodes of Ranvier contain a machinery to regenerate the AP. It is important to note that there are striking similarities between axon initial segment and nodes of Ranvier. A great deal of the protein machinery in the axon initial segment is also present in the nodes of Ranvier where the regeneration of the AP is performed. Ankyrin G, the major scaffolding protein in the AIS and the ring-like arrangement of actin and beta IV spectrin are also found in the nodes of Ranvier (D'Este et al., 2017). Nodes of Ranvier are distributed spatially along the axon to guarantee the faithful propagation of the AP. In addition, the first node of Ranvier was found to be crucial for high bandwidth bursting activity in neocortical layer 5 pyramidal neurons (Kole, 2011). In that study, the author shows that nodal persistent sodium currents at the first node of Ranvier hyperpolarize AP threshold and amplify the afterdepolarization. The study opens up the space for a computational role of the first node of Ranvier beyond the regeneration of the propagating AP. The first node faithfully follows spike frequencies with a approximately 100 µs delay (Khaliq and Raman, 2006; Palmer and Stuart, 2006; Foust et al., 2010; Palmer et al., 2010). This had led to the speculation that the nodes of Ranvier, and in particular the first node, may have an active computational role in modulating the AP initiation itself.

It is worth noting that nodes of Ranvier also express Na<sup>V</sup> 1.6, the same sodium channel subtype that is expressed in the AIS. It is even more striking that the sodium channels at the nodes also undergo the developmental changes from Na<sup>V</sup> 1.2 to Na<sup>V</sup> 1.6 during postnatal development, following a similar developmental trajectory as those found in the AIS (Rios et al., 2003). Na<sup>V</sup> is highly clustered at the nodes of Ranvier in the order of 1,200 channels per micrometers square (Rosenbluth, 1976), while internodes contain 20–25 channels per micrometers square (Ritchie and Rogart, 1977). This very high density ensures highfidelity regeneration of the AP. Given the close proximity of the first node to the cell body and high density of Na<sup>V</sup> channels, it has been postulated that, in addition to securing propagation, it could potentially generate the AP (Colbert and Pan, 2002; Clark et al., 2005; Lehnert et al., 2014). Although this might be happening, the overwhelming evidence favors that the AP initiation is happening at the AIS.

#### 2.2.8. Ectopic Spiking

AP initiation at the AIS and its subsequent orthodromic propagation have been extensively investigated. However, a number of studies demonstrates that distally generated spikes or "ectopic" APs co-exist in invertebrate and vertebrate neurons (Mulloney and Selverston, 1972; Maranto and Calabrese, 1984; Meyrand et al., 1992; Sheffield et al., 2010; Dugladze et al., 2012; Lehnert et al., 2014). Marked differences in somatic AP recordings are observed when APs are generated at the AIS or in a distal part of the axon. In particular, APs have more negative thresholds when APs are generated in distal parts of the axon. This is likely due to the fact that they do not show the strong coupling of soma to AIS which is responsible for the inactivation of sodium channels at the AIS and for a more depolarized AP generation threshold. Interestingly, given the different potential at which ectopic spikes are generated, the conductances activated during AP generation may differ between distal and proximal APs (Meyrand et al., 1992).

In invertebrates, numerous examples of ectopic spikes and of their functional relevance have been described (Mulloney and Selverston, 1972; Maranto and Calabrese, 1984; Meyrand et al., 1992). Ectopic spikes in neurons that target the hearts of the leech have been proposed to control the heart firing frequency (Maranto and Calabrese, 1984). In the somatogastric ganglion of the crab, ectopic spikes are typically observed in the lateral gastric motor neuron only when the muscles remain attached to the preparation, ectopic spikes being induced by motor contraction (Meyrand et al., 1992). Remarkably, ectopic spikes in Meyrand et al. (1992) fail to depolarize terminals onto interneurons located close to the soma, whereas they efficiently excite a distal postsynaptic target, the muscle. Thus, orthodromically-propagating spikes generated close to the soma and antidromically-propagating spikes generated distally co-exist and they can reach synapses that target different postsynaptic neurons.

Ectopic spikes have also been observed in vertebrates. In principal cells from CA3 area in the hippocampus during rhythmic activity in the gamma range (Dugladze et al., 2012), axons fire APs at five times the firing frequency detected at the soma. This is due to the activity of a specific interneuron, the axo-axonic cell, that inhibits the initial segment, thereby avoiding the backpropagation of axonal spikes to the soma. Another noteworthy case of co-ocurrence of AIS and ectopic spikes has been reported in Lehnert et al. (2014) in auditory medial superior olive (MSO) neurons. A realistic model of MSO neurons which takes into account their axonal structure and ion channel composition generates APs at both the AIS and the first node of Ranvier. Additionally, under certain pathological conditions, e.g., in epilepsy, hyperexcitable axons have been reported to generate ectopic spikes in the hippocampus (Stasheff et al., 1993). To conclude, we would like to emphasize that ectopic spikes occur in some neurons because of their multiple action potential generation sites, that is, specialized regions that act as action—potential generating computational units.

We would like to make at this point a clarification: although "action potential" and "spike" are two terms used to refer to the sodium AP generated at the axon initial segment, the term spike seems preferentially used in the literature to refer to spikes that can differ in their location (dendritic or ectopic spikes) and in their underlying ionic mechanism (e.g., calcium spike, see below).

#### 2.2.9. Beyond the Sodium Spike

The spike initiated through sodium influx is not the only spike that can propagate in the axon. In some axons, there are spikes that are generated through the influx of calcium. In the giant axon of the jellyfish Aglantha digitale (order Hydromedusae), both sodium and calcium spikes propagate in the axon (Mackie and Meech, 1985). Sodium-dependent spikes are responsible for fast swimming and calcium spikes mediate slow swimming.

In vertebrates, calcium spikes are typically restricted to the dendritic compartment where there is a calcium spike generation mechanism. The biophysical mechanisms contributing to the dendritic spikes initiation in the distal apical trunk and proximal tuft of hippocampal CA1 pyramidal neurons (Gasparini et al., 2004) are dendritic sodium and potassium channels that set AP shape and propagation properties, the highly synchronized inputs, their spatial clustering and the activation of NMDA receptors. In the olfactory bulb mitral cells and in hippocampal and cortical pyramidal cells, dendritic spikes can trigger one or more axonal APs (Stuart et al., 1997; Golding and Spruston, 1998; Larkum et al., 1999, 2001; Chen et al., 2002; Ariav et al., 2003). In addition, backpropagating axonal APs can themselves promote dendritic spikes, a reciprocal interaction that can lead to a burst of axonal APs (Pinsky and Rinzel, 1994; Mainen and Sejnowski, 1996; Larkum et al., 1999, 2001; Doiron et al., 2002).

## 2.3. Biophysics of Action Potential Propagation

#### 2.3.1. An Equivalent Electrical Circuit for Axons

The passive properties of axons can be modeled by an equivalent electrical circuit (**Figure 4A**). The axonal membrane can be reduced to two circuit elements: the lipid bilayer, modeled by a capacitor and ion channels, by a resistor. The resistance to axial current flow can be modeled by an additional resistance.

How fast signals propagate is critically controlled by the capacitance. Electrical currents need to first charge the membrane capacitance, that opposes the flow of electric current, before electrically-charged membranes can undergo voltage changes. Capacitances are proportional to the membrane

capacity (capacitance per surface area) and to the membrane surface area. The capacity of neuronal membranes is in the order of 1 µF per cm<sup>2</sup> (Gentet et al., 2000). Capacitance measurements from small axons are in the range of tens of picoFahrads (pF) (Mejia-Gervacio et al., 2007). Capacitances of larger neurons (i.e., strongly-ramifying interneurons and projection neurons) are therefore expected to be in the range of hundreds of pF to nF. Remarkably, dynamic changes in membrane capacitance are suggested by activity-dependent changes in the size of axons (e.g., Chéreau et al., 2017). However, little is known about dynamical changes in capacitance due to temperature, lipid composition, and whether these may significantly impact the propagation of electrical signals along the axon.

The membrane resistance plays a major role in controlling how far signals spread in space along the axon before membrane potential changes become imperceptible. This is typically measured by the space constant, defined as the distance over which the membrane potential decays to 37% of its initial value. The more open channels are available at the membrane, the more the axial current is attenuated in space along the axon due to current leakage through membrane channels. Remarkably, the membrane resistance can change (reviewed in Debanne et al., 2019), providing a potential source of variation in the conduction of electrical signals along axons.

The axonal axial resistance to current flow results from the combination of the resistivity of the axoplasm (that is, the cytoplasm of the axon), given in Ohms\*cm, and the diameter of the cylinder. Axial resistivity values are in the range of approximately 100 .cm (Carpenter et al., 1975; Cole, 1975). Computational models of the calyx of Held suggest that the latency and amplitude of signals propagating between release sites is highly sensitive to changes in axial resistivity, and that these changes may have a large impact on synaptic release (Spirou et al., 2008). However, changes in resistivity have not been reported so far experimentally. The axon diameter can vary in three orders of magnitude, from hundred nanometers to hundreds of micrometers in diameter. Giant fibers found in invertebrates are an example of specialized large-diameter structures that propagate electrical signals with high speed over long distances (in Hodgkin and Huxley, 1952; Xu and Terakawa, 1999; **Figure 4B**). The larger the diameter of the axon, the faster the electrical signal propagates. Taking into account cable theoretic considerations, the propagation speed increases with the square root of the diameter. Remarkably, the axon diameter, as well as the diameter of synaptic boutons, are not static properties of axons. In fact, axon diameter has been shown to be regulated in hippocampal principal cells in an activitydependent manner. Plasticity protocols induced changes in axonal diameter which were accompanied by significant changes in AP conduction velocity along CA3 pyramidal cell axons (Chéreau et al., 2017; **Figure 5A**).

#### 2.3.2. Propagation of Subthreshold Signals

Subthreshold signals propagate passively in axons, reaching synaptic terminals, where they influence spike-evoked synaptic release (Alle and Geiger, 2006). Subthreshold membrane fluctuations consist of synaptic events, typically in the range of 100 s of µVs to mVs, which in cortical neurons approximate highly stochastic background dynamics in vivo (Rudolph and Destexhe, 2003). Their propagation, referred to as analog, in comparison to the digital nature of the AP, modulates the efficiency of APs to induce neurotransmitter release in synaptic terminals (Shu et al., 2006). Given that subthreshold signals are not regenerated along the axon, analog signaling is more prominent in proximal portions of the axon. The presence of combined analog and digital signals in axons has been termed hybrid analog-digital signaling (reviewed in Zbili and Debanne, 2019).

Of particular interest is that the propagation of slow analog subthreshold signals does not only reach chemical synapses. Subthreshold signals also reach axonal electrical synapses, at which the signal is expected to be conveyed with high efficiency to the postsynaptic site due to the continuous and lowpass filtering properties of electrical transmission (reviewed in Alcami and Pereda, 2019).

The co-existence of subthreshold signals and suprathreshold signals (APs) illustrate two co-existing signaling modalities and computations in axons (reviewed in Zbili and Debanne, 2019).

#### 2.3.3. Reliability of Propagation and Action Potential Failures

Before we consider how signals propagate along axons, let us discuss the reliability of propagation. In small axons, modeling shows that APs can propagate with a large variability in their kinetics and amplitude due to channel noise (Neishabouri and Faisal, 2014). Furthermore, APs do not always efficiently propagate. In fact, failures in AP propagation are observed in many neuron types at high firing frequencies (Krnjevic and Miledi, 1959; Grossman et al., 1979; Monsivais et al., 2005).

Although geometry can generate failures (e.g., at branch points, see next section), failures typically involve active mechanisms during repetitive activation of axons as observed in a number of vertebrate and invertebrate preparations (Krnjevic and Miledi, 1959; Mar and Drapeau, 1996; Monsivais et al., 2005). Repetitive activity typically leads to extracellular potassium accumulation and subsequently to the depolarization of the axon, inducing failures of conduction by inactivating sodium channels (Grossman et al., 1979). In other cases however, repetitive activation induces AP propagation failures via hyperpolarization of the membrane (Mar and Drapeau, 1996). Additionally, computational modeling suggests that axonal gap junctions, by leaking current to coupled axons, may induce propagation failures in thin axons (Hull et al., 2015).

Note that propagation failures likely affect only a fraction of APs at physiological firing rates, and that most APs succeed in propagating. Remarkably, auditory axons are able to transmit action potentials at very high firing rates up to 1 kHz without failures (Kim et al., 2013).

Interestingly, changes in AP failure can also occur in response to membrane fluctuations, e.g., in response to synaptic inputs. Indeed, specific potassium channels of the type I<sup>A</sup> underlie a hyperpolarization-mediated conduction block in hippocampal pyramidal cells (Debanne et al., 1997). Remarkably, the activation

and de-inactivation kinetics of I<sup>A</sup> allow for a history-dependent conduction block of APs.

Propagation failures, that occur under specific conditions or under high frequency firing, induce a mismatch between action potentials at the AIS and at more distal portions of the axon where synapses are located. Interestingly, this mismatch may impact the ability of neurons to drive synapses at high frequencies, even when AIS spiking could be driven at such high frequencies. Thereby, propagation failures represent under specific conditions, a limitation to the reliable propagation of action potentials.

#### 2.3.4. More Than Linear Cables: Impact of Axonal Branching and Inhomogeneities

Axons are typically formed by complex trees and spatial heterogeneities. These include branching points, varicosities (local enlargements of the axon containing the release machinery of chemical presynaptic sites) and large structures specialized in the interaction with other cells. Examples of such structures are the "basket" formed by a specific type of interneuron, basket cells, around principal cells in many brain regions; the glomerular collateral of the climbing fiber in the cerebellum; the "pinceau" structure surrounding cerebellar Purkinje cells (Palay and Chan-Palay, 2012) or the calyx of Held in the auditory system.

Changes in axon diameter at varicosities or branching points are characterized by an impedance mismatch, that is, a need of a larger current to flow in one of the two directions to electrically load axonal branches, provoking changes in AP propagation speed (Goldstein and Rall, 1974; Manor et al., 1991). Due to this impedance mismatch, when APs need to load a larger impedance as they propagate from one mother branch into two daughter branches, their propagation will be delayed relative to the speed that they would have had if no branching was present.

In the most extreme case, the electrical signal fails to load one or two of the branches, resulting in AP propagation failure. Propagation failures have been shown to occur in branches of a number of neurons (Yau, 1976; Grossman et al., 1979; Gu et al., 1991). An interesting example is provided by the medial pressure sensory neuron in the leech, where the failure of APs to propagate can differentially affect postsynaptic cells contacted by distinct presynaptic branches (Gu et al., 1991).

Finally, branching points can also provoke a surprising effect: APs can be slowed down in the ms range, up to a level that allows the mother branch to overcome the refractory period for AP generation. As a consequence, the AP can "reflect" (that is, travel backwards), increasing synaptic release at synapses present in the branch where the AP reflects (Baccus, 1998; Baccus et al., 2000).

The impact of axonal morphologies on AP propagation is likely to be relevant in the complex axonal ramification patterns of many neurons, including vertebrate interneurons (Ofer et al., 2019). The usage of voltage sensitive-dyes that track membrane voltage with sub-millisecond precision (Palmer and Stuart, 2006) should allow following large portions of axons both in vitro and in vivo, and characterize the propagation of APs along complex axonal structures.

At this point, we would like to comment on the relevance of the physiological phenomena constrained by the morphology of axons discussed above to non-linear processing by neurons, and therefore on their computational abilities. They introduce nonlinear transformations in specific axonal compartments. Thereby, they allow for a differential encoding in different regions of the axonal tree, modulating the functional impact of APs onto different post-synaptic targets. In other words, there is not one axon, but multiple compartments in one axon. The details of AP propagation in these compartments have been explored by computational modeling, creating a detailed knowledge of how electrical activity flows in single cells (Peterson et al., 2011; Xylouris et al., 2011; Agudelo-Toro and Neef, 2013)

#### 2.3.5. Biophysical Properties of Myelinated Fibers

Many vertebrate and some invertebrate fibers are myelinated, a specialization endowed by the glial ensheathment of axons that appeared several times during evolution (Castelfranco and Hartline, 2015). Myelin, formed by compact lipidic layers produced by the membranes of glial cells (oligodendrocytes in the central nervous system and Schwann cells in the peripheral nervous system), strongly impacts the propagation of electrical signals.

In his seminal study, Lillie (1925) wrapped an iron wire placed in an acidic solution with an insulating glass cylinder. This increased the speed of propagation of electrical signals along the wire, which he postulated to occur in myelinated fibers. His prediction was confirmed decades later in axons by recording electrical signals at nodes, leading to the concept of the "saltatory" nature of transmission of electrical signals in myelinated fibers (Huxley and Stämpfli, 1949). Saltatory comes from the latin verb "saltare" (to jump), an analogy describing the very fast propagation of electrical signals between nodes of Ranvier.

Myelin modifies the electrical circuit that models the passive properties of axons described above by adding compact membrane layers in series with the axonal membrane. As a consequence, myelin increases the effective radial resistance and decreases the effective capacitance of the axon (**Figure 4C**). These two effects are due to the different properties of series resistors and series capacitors added to the circuit: series resistors sum their resistances whereas the inverse of capacitances from capacitors in series sums. The increase in effective membrane resistance (Bakiri et al., 2011) and the decrease in effective membrane capacitance by myelin have two major consequences. On the one hand, the increase in the effective axonal resistance by myelin increases the length constant. On the other hand, as a consequence of the decrease in the effective axonal capacitance, the time required to effectively load axons decreases, dramatically accelerating the propagation of electrical signals. This speeding of electrical propagation by a reduced effective capacitance underlies saltatory conduction between nodes of Ranvier (Huxley and Stämpfli, 1949; Castelfranco and Hartline, 2015). Therefore, adding myelin to an axon allows it to overcome the passive constraints that limit its computational abilities, including the speed of propagation and the distance of effective propagation of electrical signals. It additionally impacts the reliability and the jitter at which APs propagate, as will be discussed below.

#### 2.3.6. Geometry of Axons and Myelin

Theoretical studies have shown that specific myelination parameters maximize the space constant and the conduction velocity of electrical signals in axons. In particular, the ratio of the axonal diameter d to the fiber diameter D (the summed diameter of axon and myelin sheath), defined as the "g-ratio," controls the conduction of electrical signals. Rushton (1951) developed a biophysical formalism to model current flow in a myelinated axon. He deduced the relation between the ratio l/D (internode length l over D) and the g-ratio. He further demonstrated that the ratio l/D is maximal when g = 0.6, a value also found analytically to maximize the space constant. In an independent approach, Deutsch (1969) mathematically derived the geometry of axonal and myelin properties that maximize, this time, conduction velocity. He deduced that the propagation velocity is inversely proportional to the RC time constant given by the internal resistance of the axon R and the capacitance of the membrane C. Maximizing conduction speed requires minimizing the time constant of the circuit. This resulted in the same geometrical properties as those derived by Rushton: a g-ratio of 0.6. Additional modeling studies including a more complete description of myelinated fibers converged to similar conclusions (Goldman and Albus, 1968). Therefore, due to the biophysical constraints posed by the thickness of myelin and axonal size, both conduction speed and efficient spatial propagation of electrical signals are maximized by specific axonal and myelin geometries. It is noteworthy that the geometry of axons and myelin does not only control AP propagation speed (Rushton, 1951; Deutsch, 1969) but also AP temporal jitter (Kim et al., 2013).

It seems difficult to imagine that neurons have fine-tuned their dendritic computations in a cell-type specific manner (Stuart et al., 2016), but that axons would, on the contrary, be invariant and homogeneously optimizing speed by their geometry. Additionally, we know that nervous systems adapt and fine tune a plethora of properties to accomplish specific functions (Marder and Taylor, 2011). Axons indeed adjust different parameters which impact the speed of propagation of electrical signals (Seidl et al., 2010; Ford et al., 2015; Arancibia-Carcamo et al., 2017) to obtain different speeds of computation.

An illustrative example of how the geometry of axons and myelin is tuned to adjust AP propagation speed, deviating from a g-ratio of 0.6, is provided by the axon properties which encode spatial location in the avian brain (Seidl et al., 2010). The longer contralateral fibers have larger-diameter axons and longer internodal distances, compensating in this manner for an otherwise larger conduction delay relative to the shorter fibers on the ipsilateral side. In this manner, axons ensure a coincident arrival of contralateral and ipsilateral signals to the synaptic terminals. As a consequence, post-synaptic cells can act as coincidence detectors, a key computational feature that allows neural circuits to locate sounds. Another interesting example is provided by fibers specialized in carrying information for low-frequency sounds, which show larger diameters than those carrying high-frequency sounds, but also shorter internodes. In doing so, these fibers deviate from the classical dependence of both variables established by Rushton. This specialization is proposed to ensure a proper function of the circuit (Ford et al., 2015). Moreover, internode length and node diameter show graded properties as they approach the terminal in the auditory granular bushy cell axon, implementing an efficient invasion of the axon terminal by APs (Ford et al., 2015).

We have seen that a large number of structural myelination parameters act in concert to control the speed of AP propagation (Goldman and Albus, 1968). It is noteworthy to mention that myelin has introduced new degrees of freedom in the regulation of AP speed: speed depends on distance between nodes of Ranvier, on node length, node composition, and thickness of myelin (Rushton, 1951; Wu et al., 2012; Ford et al., 2015; Arancibia-Carcamo et al., 2017). These parameters can be modulated independently or in combination, thereby increasing the number of available mechanisms by which nervous systems tune the axonal propagation of electrical signals. Furthermore, dynamical changes in axons and myelin (Sampaio-Baptista et al., 2013; McKenzie et al., 2014; Fields, 2015; Sinclair et al., 2017) suggest that nervous systems dynamically adjust the properties of their fibers to achieve the specific behaviors that they control. Adding myelin has allowed axonal conduction speed to be regulated by additional mechanisms other than their diameter. Indeed new adjustable parameters appeared evolutionary with myelination (e.g., myelin thickness, node length, etc.) to dynamically fine tune the computational speed of neural circuits.

#### 2.3.7. Active Contributions to Variations of Action Potentials Along the Axon

Each active AP regeneration site along the axon can potentially generate AP variants due to their specific state and composition of ion channels and membrane potential. In particular, myelinated fibers are characterized by the presence of nonmyelinated sections, which concentrate the machinery to generate APs. These include nodes, the heminode (last unmyelinated portion before the terminal) and synaptic terminals. Remarkably, AP shape can be modified along the axon by the active channels present in these locations.

An example of local variations in AP shape through active mechanisms is found at presynaptic mossy fiber terminals (present in the axon of dentate gyrus granule cells), where local potassium channels modulate spike shape (Alle et al., 2011). Another example is provided by the exclusion of sodium channels from the terminals in the calix of Held, while being concentrated at the heminode. Such compartmental specialization has been suggested to produce APs with a shorter width in the calix (Leão et al., 2005). At the Purkinje cell nodes of Ranvier, the activation of calcium-dependent potassium channels repolarizes membranes, de-inactivating sodium channels which can then generate fast frequency spikes, and in this manner prevent AP failure at high frequencies (Gründemann and Clark, 2015). Additionally, changes in membrane voltage in the axon induced by active mechanisms can impact the efficiency of AP propagation. For example, in the leech touch cells, adaptation in response to repetitive AP firing consists of a hyperpolarization, resulting in the blockade of AP propagation (Van Essen, 1973).

We previously described how actively-generated signals can differently be passed on by two bifurcating branches, illustrating how passive properties can filter actively-generated signals (Gu et al., 1991). Remarkably, active properties of axonal branches can prevent failures by potentiating signals in specific branches in cultured hippocampal neurons (Cho et al., 2017). Failures that would occur as a consequence of the passive filtering of electrical signals can be prevented in a branch-specific manner by the presence of the sodium channel subunit NavβII, which potentiates AP propagation. Thus, the combination of passive and active properties fine tunes the computational properties of axonal branches.

#### 2.3.8. The Geometries of Axons and Myelin Are Plastic

Geometrical properties of both axons and myelin have been shown to be highly plastic. Indeed, the diameter of axons can change as a function of neuronal activity (Chéreau et al., 2017; Sinclair et al., 2017). Furthermore, the understanding of the mechanisms of myelination has revealed that properties of nodes and internodes are subject to plasticity (Young et al., 2013; reviewed in Kaller et al., 2017). Interestingly, major macroscopic changes in myelination occur in response to training paradigms in mice, allowing the acquisition of motor skills (Sampaio-Baptista et al., 2013; McKenzie et al., 2014; Xiao et al., 2016), and models of injury induce strong remodeling of myelination patterns in the auditory brainstem (Sinclair et al., 2017). Changes in myelination can involve several mechanisms: changes in internode length (Etxeberria et al., 2016), in myelin thickness (Sinclair et al., 2017) and in node length (suggested in Arancibia-Carcamo et al., 2017; **Figure 5B**). Remarkably, plasticity of myelination allows circuits to adjust their speed of computation, adding computational flexibility to neural networks.

#### 2.3.9. Nanostructures With Unknown Function

The evolutionary appearance of myelin has led to new specialized microstructures or microdomains (namely nodes, paranodes, juxtaparanodes, heminodes). Electron microscopy and recently superresolution imaging have revealed additional structures whose contribution to axonal computation remains mysterious. These structures can be observed at the nanometer scale in a highly regular spatial organization (D'Este et al., 2017), rising the question of the function of these periodic structures. For example, d'Este et al. show that the voltage-dependent potassium channel subunit Kv1.2 channels, found at the juxtaparanodes, correlates in space with the underlying actin cytoskeleton. An additional structure is the Schmidt-Lanterman incisure, a spiral cytoplasmic expansion from the outer tongue of myelin to the inner tongue. Incisures express gap junctions and their contribution to the electrical properties of myelin remain mysterious (Kamasawa et al., 2005). Likewise, exquisite arrangements of structures apposing glial and neuronal membranes and also with other glial membranes in the form of "rosettes" formed by ion channels at the paranode are still poorly understood (Rash et al., 2016).

These findings open up the following question: how do these nanostructures impact function? One would expect that further perturbing and studying those nanoscale structures in the future will further our understanding of how they contribute to axonal computations.

#### 2.4. Axons Are Not Alone: Intracellular and Intercellular Coupling

#### 2.4.1. Crosstalk of Axons With Other Compartments

Although we have done a treatment of the axon as an isolated cable as has classically been performed in the early days (Lillie, 1925; Huxley and Stämpfli, 1949; Hodgkin and Huxley, 1952), the axonal cable is coupled to the somatic and dendritic compartment at one end and, additionally, directly or indirectly to electrically-coupled cells, which also functionally act like an electrical compartment (Furshpan and Potter, 1959; Alcami and Marty, 2013; Eyal et al., 2014). Electrical coupling between the axon and the soma, and indirectly to dendrites and electricallycoupled cells, influences AP generation in the axon (Bekkers and Häusser, 2007; Eyal et al., 2014; Amsalem et al., 2016; Alcami, 2018; Goldwyn et al., 2019). Loading of these nonaxonal compartments was shown to impact AP threshold and speed (Bekkers and Häusser, 2007; Eyal et al., 2014; Amsalem et al., 2016). Their contribution to the effective membrane time constant is substantial. The somato-dendritic compartment has been shown to, by this mechanism, modify both the threshold and the initial rise of the AP (Eyal et al., 2014).

It is further interesting to consider the axon in the context of synaptic integration, that is, the computation of information received at synapses. Similar to the somato-dendritic and junctional compartments, which act as current sinks, influencing the effective kinetics and strength of excitatory inputs recorded at the soma, before they reach the AIS (Nörenberg et al., 2010; Alcami, 2018), the axonal membrane also behaves as a current sink, leaking current generated at synapses in the somatic and dendritic compartments. This phenomenon has been shown to, through a passive mechanism, accelerate the time-course of somatically-recorded excitatory synaptic events (Mejia-Gervacio et al., 2007). It has additionally been suggested to also accelerate the time-course of spikelets generated by electrically-coupled cells (Alcami and Marty, 2013). Mejia-Gervacio and collaborators (Mejia-Gervacio et al., 2007) show that the capacitive loading of axons introduces in cerebellar molecular layer interneurons a computational time constant of about 3 ms, which is one order of magnitude slower than the faster time constant to load the somatodendritic compartment. This relatively slowlycharging process of the axonal membrane accelerates the decay of excitatory postsynaptic potentials, reducing the time window for AP generation. Therefore, electrical signals that arrive to the axon are not only passively influenced by other compartments, but they also influence passive computation by the non-axonal compartments, as part of a system formed by coupled compartments.

Let us now turn our attention onto the signals propagating in axons as cells receive synaptic events in their somas and dendrites, which is a consequence of the current flow in the axon evoked by synaptic events received in dendrites and somas. These signals propagate at long distances before their complete attenuation (contributing to the analog signaling in the axon that was previously introduced). The space constant at the hippocampal unmyelinated granule cell axon is in the range of hundreds of micrometers (Alle and Geiger, 2006) and the subthreshold propagation of voltage depolarizations has been shown to increase AP evoked release (Shu et al., 2006). Interestingly, subthreshold signals do not only travel orthodromically toward the terminals, but signals generated in the axon, e.g., by synaptic receptors present on the presynaptic membrane, also travel antidromically to the soma (Trigo et al., 2010). As a consequence, these axonal events depolarize the soma and influence AP generation (de San Martin et al., 2015). In summary, intracellular and intercellular coupling render the computations of all compartments inter-dependent: axons don't carry out their computations independently from other compartments of the same cell or from other cells, and non-axonal compartments don't carry their computations independently of axons.

#### 2.4.2. Direct Coupling Between Axons

Direct coupling between axons was suggested in early work, bringing up the concept that networks of axons may directly interact with each other (Katz and Schmitt, 1940). These interactions can be explained by two forms of electrical transmission (**Figure 6A**): ephaptic transmission due to the generation of an electric field by an axon, affecting the excitability of a neighboring axon (Katz and Schmitt, 1940; Blot and Barbour, 2014; Han et al., 2018), and transmission mediated by gap junction-mediated electrical synapses (Furshpan and Potter, 1959; Watanabe and Grundfest, 1961; Bennett et al., 1963; Robertson et al., 1963; Schmitz et al., 2001). As a matter of fact, electrical synapses were first discovered in axons in a variety of preparations (Furshpan and Potter, 1959; Watanabe and Grundfest, 1961; Bennett et al., 1963; Robertson et al., 1963).

Axonal electrical synapses are expected to strongly affect electrical signals by adding a conductance pathway directly in the axon. Remarkably, axonal gap junctions allow inputs to arrive at the axon directly, blurring the pure "output" role of axons: an AP in a presynaptic axon induces a spikelet (a low-pass filtered version of the presynaptic AP) in the postsynaptic axon. Spikelets excite distal parts of the axon where the gap junctions are located. When the spikelet depolarizes the membrane potential sufficiently, they are able to evoke APs (Chorev and Brecht, 2012). Interestingly, in vivo recordings from hippocampal principal cells in CA regions from rodents revealed two types of APs: one type was preceded by a "shoulder" which was identical to the rising phase of the spikelet, and the other was a full-blown AP lacking the shoulder (Epsztein et al., 2010). Spikelets correlate with AP firing from nearby cells, confirming that they are generated by electrically-coupled cells, and not by spontaneous AP firing of distal axons (Chorev and Brecht, 2012). Altogether, these studies suggest that hippocampal pyramidal cell axons are excited through electrical synapses under physiological conditions in behaving animals, as it had been previously shown in slices (Schmitz et al., 2001).

Axonal gap junctions have additionally been proposed to underlie fast synchronization of neuronal ensembles in both physiological and pathophysiological conditions (Schmitz et al., 2001; Roopun et al., 2010). Interestingly, axo-axonal gap junctions can have a strong impact on spike coordination and coding efficiency (Wang et al., 2017). They may additionally induce AP propagation failures in thin axons as shown in a model of a brainstem networks in frog tadpoles (Hull et al., 2015). In this model, gap junction-mediated failures can be prevented by increasing gap junction resistance or membrane excitability.

Last but not least, direct axo-axonal coupling can be mediated by chemical synapses onto axons (**Figure 6A**) which are typically performed by a specific type of interneuron targeting the AIS of principal cells (chandelier cells in the neocortex; Somogyi et al., 1985). GABAergic terminals made onto neocortical and hippocampal pyramidal cells axons exert inhibitory control over AP initiation (Dugladze et al., 2012).

Owing to axo-axonal coupling, populations of axons can be regarded as a computational unit.

#### 2.4.3. Axons Interact Indirectly via Glial Cells

Finally, let us consider the contribution of glial cells to axonal function as an indirect coupling pathway between axons (**Figure 6B**). The biophysical properties of myelin are achieved by glial cells that produce myelin. Since several axons are typically contacted by a myelinating oligodendrocyte, this introduces de facto an indirect coupling pathway between axons. A number of transmission mechanisms has been described between axons and myelin (reviewed in Micu et al., 2017), whose dynamic properties depend on signaling from neurons (Hines et al., 2015). A better understanding of axo-axonal coupling mediated by glial cells will in the long run help us understand the computations of populations of axons regulated by glial cells in health and disease.

## 3. OVERVIEW OF AXONAL COMPUTATIONS

Let us at this point recall the definition of computation stated beforehand. We defined computations as modifications in the input/output transformations performed by axons. In this section, we will summarize the diverse axonal computations afforded by the various physiological processes discussed throughout the article beside the well established canonical computation of action potential generation at the AIS.


## 4. CONCLUSION

Here, we have reviewed the biophysical nature of computations performed by the axon. We have shown that the axon is not just a cable on which electrical pulses propagate but rather a computational device that modulates signaling and adds to the complexity of information processing in the brain. It should be appreciated that these computations are sophisticated enough to contribute to network level phenomena up to behavior in vivo. Relating axonal computation to behavioral phenomenology is still a nascent area which will complement studies that have focused almost exclusively on somas, dendrites or a coarse grained view of neurons. The study of axonal computation is hurdled by technical challenges, but there is already an emerging interest in developing technologies that will allow to electrophysiologically and structurally study axonal processes. Further complication arises when one realizes that axons do not act alone but in concert, exhibiting collective modes of computation conveyed by inter-axonal signaling. We propose that axonal biophysics are of vital importance for understanding not only how single neurons process information but also how neural networks coordinate their activity.

#### AUTHOR CONTRIBUTIONS

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

#### FUNDING

PA was funded by the Munich Center for Neurosciences. AE was funded by the Howard Hughes Medical Institute.

#### ACKNOWLEDGMENTS

We are grateful to Emily Jane Dennis for the drawing of the neuron in **Figure 2** and the AIS in **Figure 3**. We are grateful to Conny Kopp-Scheinflug and Henrique von Gersdorff for their feedback on previous versions of this manuscript. We are thankful to the reviewers for their insightful comments.

#### REFERENCES


channel density in the axon initial segment. Nat. Neurosci. 11, 178–186. doi: 10.1038/nn2040


mechanism for ultrafast neuronal communication. Neuron 31, 831–840. doi: 10.1016/S0896-6273(01)00410-X


**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 © 2019 Alcami and El Hady. 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(s) 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.

# Unique Axon-to-Soma Signaling Pathways Mediate Dendritic Spine Loss and Hyper-Excitability Post-axotomy

#### Tharkika Nagendran1,2 and Anne Marion Taylor1,2,3 \*

<sup>1</sup> UNC/NC State Joint Department of Biomedical Engineering, The University of North Carolina at Chapel Hill, Chapel Hill, NC, United States, <sup>2</sup> UNC Neuroscience Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC, United States, <sup>3</sup> Xona Microfluidics, LLC, Research Triangle Park, NC, United States

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Juan José Garrido, Spanish National Research Council (CSIC), Spain Haruyuki Kamiya, Hokkaido University, Japan Fengquan Zhou, Johns Hopkins University, United States

#### \*Correspondence:

Anne Marion Taylor ataylor@xona.us

#### Specialty section:

This article was submitted to Cellular Neuropathology, a section of the journal Frontiers in Cellular Neuroscience

Received: 15 May 2019 Accepted: 09 September 2019 Published: 24 September 2019

#### Citation:

Nagendran T and Taylor AM (2019) Unique Axon-to-Soma Signaling Pathways Mediate Dendritic Spine Loss and Hyper-Excitability Post-axotomy. Front. Cell. Neurosci. 13:431. doi: 10.3389/fncel.2019.00431 Axon damage may cause axon regeneration, retrograde synapse loss, and hyperexcitability, all of which affect recovery following acquired brain injury. While axon regeneration is studied extensively, less is known about signaling mediating retrograde synapse loss and hyper-excitability, especially in long projection pyramidal neurons. To investigate intrinsic injury signaling within neurons, we used an in vitro microfluidic platform that models dendritic spine loss and delayed hyper-excitability following remote axon injury. Our data show that sodium influx and reversal of sodium calcium exchangers (NCXs) at the site of axotomy, mediate dendritic spine loss following axotomy. In contrast, sodium influx and NCX reversal alone are insufficient to cause retrograde hyper-excitability. We found that calcium release from axonal ER is critical for the induction of hyper-excitability and inhibition loss. These data suggest that synapse loss and hyper-excitability are uncoupled responses following axon injury. Further, axonal ER may play a critical and underappreciated role in mediating retrograde hyper-excitability within the CNS.

#### Keywords: retrograde signaling, axon-to-soma, injury model, axotomy, dendritic spine loss, hyper-excitability

#### INTRODUCTION

Acute neural injuries (e.g., stroke, traumatic brain injury, and spinal cord injury) cause profound axon damage. Axon damage triggers an intra-cellular signaling cascade to effect neuronal injury responses, including axon regeneration, retrograde synapse loss, and hyper-excitability. These downstream responses are critical for recovery following injury. Yet, the intrinsic neuronal signaling mechanisms mediating retrograde synapse loss and hyper-excitability, in particular, remain poorly understood.

Axon injury induces differential gene expression and transcription within the soma, requiring long range signaling from the site of injury to the nucleus (Rishal and Fainzilber, 2014; Nagendran et al., 2017). Breach of the axonal membrane following axon injury causes an influx of ions, including calcium and sodium, into the intra-axonal space. The increase in sodium ions through voltage-gated sodium channels causes reversal of sodium-calcium exchangers (NCXs) located on the plasma membrane, mitochondria and ER, thus enhancing local intra-axonal calcium levels (Persson et al., 2013). Calcium release from smooth ER within the axon may also potentiate axonto-soma signaling (Cho et al., 2013; Sun et al., 2014). Axon damage of mouse peripheral sensory

neurons was reduced with blockade of both sodium channels and the reverse mode of NCX (Persson et al., 2013), supporting the critical role of NCXs in retrograde injury signaling. Whether local sodium influx and reversal of NCX during axon damage are needed to transmit signals to the soma to cause dendritic spine loss and hyper-excitability remains unknown.

Hippocampal cultures grown within a compartmentalized microfluidic platform provide an injury model system to investigate intrinsic neuronal injury response. These devices guide axonal growth of pyramidal cells, through a microgrooveembedded barrier region of almost 1 mm into an isolated axonal compartment. Because of this barrier region, axons can be injured precisely without mechanically disrupting somatodendritic regions and soluble microenvironments can be established for experimental purposes. Axotomy performed within compartmentalized platforms produced several characteristic injury responses well described in vivo, including rapid expression of the immediate early gene c-fos (Taylor et al., 2005) and reduced expression of netrin-1 one day following axon damage. Evidence of ER changes within the soma, called chromatolysis, occurs in axotomized neurons in vitro (McIlwain and Hoke, 2005; Nagendran et al., 2017). Axotomized neurons within microfluidic chambers also showed that dendritic spine loss (Gao et al., 2011; Ghosh et al., 2012; Nagendran et al., 2017) and hyper-excitability (Frost et al., 2015; Nagendran et al., 2017) occur, providing an experimentally tractable model to study initiation and progression of these neuronal injury responses. Axotomy within these platforms produced a delayed enhancement in neuronal hyper-excitability, 1 day following dendritic spine loss. The extent to which both dendritic spine loss and hyper-excitability use the same retrograde signaling mechanisms is unclear.

## RESULTS

## Sodium Influx and Reversal of Sodium Calcium Exchangers Induce Retrograde Spine Loss

To selectively injure axons of hippocampal neurons >900 µm from somata, we used compartmentalized microfluidic devices (**Figure 1A**). Primarily axons of pyramidal neurons are guided via microgrooves into a separated axon compartment where they are injured and various pharmacological treatments can be restricted to isolated axons. We previously found that blocking local activity at the site of injury using this method prevented dendritic spine loss 24 h post-axotomy (Nagendran et al., 2017), suggesting calcium and sodium influx at the site of injury are key mediators of this neuronal injury response. Reversal of NCX at the site of injury may play a key role, causing a massive local influx of calcium. To determine whether local NCX activation is required to trigger retrograde synapse loss, we performed axotomy within microfluidic devices but in the presence of the reversible NCX blocker applied specifically to the axonal compartment where axotomy was performed (**Figure 1B**). We quantified spine density using repeated live imaging and found that in the presence of

(C,D) Quantification of dendritic spine density before and 24 h after axotomy with application of either vehicle or KBR or TTX (1 µM) that was applied only to the axonal compartment for 1 h during injury. (E) Quantification of spine density before and 24 h after treatment of axonal compartment with either vehicle or sodium channel activator (veratridine, 10 µM) for 10 min in the absence of injury. n = 15 dendrites for each condition over 2 independent experiments. Paired two-tailed t-test, <sup>∗</sup>p ≤ 0.05. Error bars, s.e.m.

the NCX blocker, KB-R7943, spine loss was completely prevented (**Figures 1B,C**). Controls treated with vehicle had significantly fewer spines following axotomy (**Figures 1B,C**).

Sodium influx at the site of injury may trigger reversal of NCX needed for dendritic spine loss. Thus, we blocked sodium channels using tetrodotoxin (TTX) at the site of injury and quantified dendritic spine density changes. As expected, blocking sodium channels prevented a significant reduction in dendritic spine density (**Figure 1D**). Further, application of a potent activator of voltage gated sodium channels, veratridine, at distal axons and in the absence of injury led to a significant decrease in retrograde spine density 24 h post treatment. Together, these results show that sodium influx and reversal of NCXs at the site of injury trigger retrograde spine loss.

### Calcium Influx via Reversal of NCX Is Not Required to Induce Retrograde Hyper-Excitability Post-axotomy

We next tested whether retrograde hyper-excitability is triggered via reversal of NCXs. To examine retrograde hyper-excitability,

we used FM dyes to quantify synaptic vesicle release dynamics as performed previously (Nagendran et al., 2017). This is an unbiased approach to measure synaptic vesicle release in response to field stimulation. FM dye is first loaded into recycling synaptic vesicles in response to KCl depolarization and then FM dye unloading is optically recorded in response to field stimulation to characterize the dynamics of synaptic vesicle release. Most, if not all, presynaptic terminals that formed onto injured neurons originate from uninjured neurons, as there was no detectable retrograde labeling of these presynaptic terminals (data not shown). Previously published data showed that synaptic vesicle release increases significantly 48 h post axotomy, analyzed via FM release curves and frequency of miniature excitatory postsynaptic currents (Nagendran et al., 2017). An advantage of this method is the ability to spatially observe release events localized to labeled and/or injured neurons. As a control we repeated these experiments and also tested whether blocking NCX reversal at the site of injury prevents the increase in hyper-excitability (**Figures 2A,B**). Surprisingly, we found that blocking NCX reversal at the site of injury did not prevent the increase in release rate due to axotomy. In fact, the KBRtreated cultures were indistinguishable from the vehicle controls. We performed a similar experiment using TTX (**Figure 2C**). Again, this did not prevent axotomy-induced hyper-excitability. In fact, the increase in release rate was exacerbated with the TTX treatment. We next tested whether veratridine in the absence of injury would cause hyper-excitability (**Figure 2D**). Consistent with our preceding data, the FM release curves were indistinguishable from vehicle controls. These results suggest that retrograde hyper-excitability involves a unique triggering mechanism independent from retrograde spine loss signaling following axotomy.

## Retrograde Hyper-Excitability Post-axotomy Requires Calcium Release From ER Intracellular Stores

Calcium-mediated signaling is expected to be a critical factor in triggering retrograde hyper-excitability following injury. To further investigate the role of calcium, we applied low calcium and TTX solution within the axonal compartment at the time of injury. Surprisingly, this treatment did not alter the axotomy induced FM release kinetics compared with injured vehicle control (**Figures 3A–C**). Intracellular calcium stores may also play a critical role in axon-to-soma injury signaling, thus we next applied the low calcium/TTX solution together with blockers of ER calcium release from ryanodine (Dantrolene) and IP3 receptors (Xestospongin C). Blocking calcium release from ER normalized the synaptic vesicle release rate to uninjured control levels (**Figures 3A,D,E**).

We previously found that the increase in FM release rate following injury coincided with loss of inhibitory terminals onto injured neurons. Loss of inhibition is a cause of hyper-excitability. As confirmation that low calcium/TTX did not substantially influence axotomy-induced disinhibition, we quantified the number of vGAT immunolabeled puncta colocalized with the dendritic arbor of labeled axotomized neurons in the presence

FIGURE 2 | Calcium influx via reversal of NCX is not required to induce retrograde hyper-excitability post-axotomy. (A) Representative images of presynaptic terminals labeled with FM5-95 (FM puncta) before and after field stimulation within the somatodendritic compartment of microfluidic chambers. Color look up table 'Fire'. Scale bars, 10 µm. (B,C) FM unloading curves at 48 h following application of KBR (B) or TTX (C) to axonal compartment for 1 h during axotomy. Uninjured control: n = 782 puncta; axotomy: n = 1037 puncta; Axot. KBR: n = 1012 puncta; Axot. TTX: 1415 puncta. (D) FM unloading curves at 48 h following 10 min application of veratridine to axonal compartment without injury. Control (DMSO): n = 711 puncta; veratridine: n = 1273 puncta. Two-way ANOVA, Bonferroni post hoc test. Inset in B–D shows FM decay time constant (τ ) for puncta with τ < 360s (control: n = 654; Axot. Veh.: n = 977; Axot. KBR: n = 945 puncta; Axot. TTX: 1321 puncta). (D) control, n = 634; veratridine, n = 1177. Unpaired two-tailed t-test. 5–6 chambers for each condition over 3 independent experiments. ∗∗p < 0.001. Error bars, s.e.m.

of low calcium/TTX solution (**Figures 4A,B**). Application of this solution did not prevent the loss of inhibitory terminals. In contrast application of this solution with Dantrolene and Xestospongin C caused injured neurons to retain inhibitory terminals (**Figure 4C**).

We next investigated the specificity of whether ryanodine or IP3 receptors may regulate retrograde presynaptic excitability changes without contributions from extracellular Ca2+. Ryanodine receptors, in particular, localize to hippocampal axons (Sharp et al., 1993). Using Dantrolene to block ryanodine receptors at the site of injury, we found that this alone was sufficient to block the retrograde presynaptic release rate enhancement (**Figures 5A,B**). We next tested the effect of axotomy when Xestospongin C is applied alone to the site of injury, and found that this also blocked the presynaptic release rate enhancement. Because ryanodine receptors are critical for Ca2<sup>+</sup> induced Ca2<sup>+</sup> release (CICR), it is possible that IP3 receptor activation may induce subsequent Ca2<sup>+</sup> release via ryanodine receptors that are required for axon-to-soma signaling, thus explaining the dependence of both receptors on the retrograde enhancement in release rate (see section "Discussion"). Together, these data show that ER provides a

FIGURE 3 | ER calcium channel activation at the site of injury is required for retrograde presynaptic hyper-excitability. (A) Experimental timeline for treatment and imaging within microfluidic chambers. (B) FM unloading curves at 48 h following application of vehicle or local activity blockade solution (ABS) to axons for 1 h during axotomy. Uninjured control: n = 1135 puncta; Axot. + Veh.: n = 1834 puncta; Axot. + ABS: n = 1590 puncta; 8 chambers per condition over 4 experiments. Two-way ANOVA, Bonferroni post hoc test. (C) FM decay time constant (τ) for puncta with τ < 360 s (Uninj. control: n = 1044; Axot. + Veh: n = 1686; Axot. + ABS: n = 1478). Unpaired two-tailed t-test. Each condition includes 8 chambers over 4 experiments. (D) FM unloading 48 h after application of vehicle or ABS supplemented with ryanodine receptor blocker (Dantrolene, 20 µM) and IP3 receptor blocker (Xestospongin C, 1 µM) to the axonal compartment. Uninjured control: n = 974 puncta; Axot. + Veh: n = 1239 puncta; Axot. ABS + Dan + Xes: 1124 puncta; 5 to 6 chambers per condition over 3 experiments. Two-way ANOVA, Bonferroni post hoc test. (E) FM decay time constant (τ) for puncta (Uninj. control: n = 892; Axot. + Veh: n = 1128; Axot. ABS + Dan + Xes: n = 1025). Unpaired two-tailed t-test. Each condition includes 5–6 chambers over 3 experiments. ∗∗p < 0.001. Error bars, s.e.m.

critical source of Ca2<sup>+</sup> needed to propagate the trans-synaptic change of altering synaptic vesicle release.

#### ER-Dependent Changes Following Axotomy

Our data suggests that ER plays a critical role in transsynaptic injury signaling following axotomy. To determine whether somatodendritic ER changes following axotomy, we measured the changes in the Ca2<sup>+</sup> binding protein and ER stress marker, BiP, in the somata of injured neurons using immunolabeling (**Figures 6A,B**). Significant BiP accumulation occurred within the soma at 12 and 24 h post-axotomy. We also found significant upregulation of the ER Ca2<sup>+</sup> pump, SERCA2, within the somatodendritic compartment following axotomy (**Figures 6A,C**). These data support ER-dependent changes in Ca2<sup>+</sup> homeostasis in somata following axotomy.

## MATERIALS AND METHODS

#### Microfluidic Chambers

Poly (dimethylsiloxane) (PDMS) was molded onto a SU-8 master with 900 µm long, 3–4 µm tall and 7.5–8 µm wide microgrooves as previously described (Taylor et al., 2003, 2005). Chambers were sterilized in 70% ethanol and placed onto 500– 550 kDa Poly-D-Lysine (BD Biosciences) coated sterile German glass coverslips.

#### Hippocampal Cultures

Animal procedures were approved by the University of North Carolina at Chapel Hill Institutional Animal Care and Use Committee (IACUC). Sprague Dawley rat embryos (E18-E19) were used to prepare dissociated hippocampal cultures as previously described (Nagendran et al., 2017). Hippocampal cells were dissociated in neuron culture media i.e., neurobasal media (Invitrogen) supplemented with 1 X B27 (Invitrogen), 1 X Antibiotic-antimycotic (Invitrogen), and 1 X Glutamax (Invitrogen). Approximately ∼90,000 cells were plated into the somatodendritic compartment of the chamber. After 5–7 days of culture in microfluidic chambers, axons extended into the adjacent axonal compartment.

## Dendritic Spine and Retrograde Neuron Labeling

Dendritic spines of injured neurons were identified using G-deleted Rabies-mCherry or eGFP virus (Nagendran et al., 2017). Neurons were infected between 11 and 13 days in vitro (Wickersham et al., 2007) (Salk Institute; 1 × 10<sup>5</sup> viral units) as previously described (Nagendran et al., 2017). G-deleted RabiesmCherry or eGFP virus diluted in 200 µl neuron culture media was added to the axonal compartment of each chamber. After 2 h incubation with virus at 37◦C remove virus containing media from the axonal compartment. Saved conditioned media was added back to the axonal compartments following two washes with fresh culture media. Chambers were maintained in 37◦C incubator for ∼48 h until fluorescence expression was visible. Axotomy was performed between 13 and 15 days in vitro (DIV) as previously described (Nagendran et al., 2017).

#### Immunocytochemistry

Neuronal cultures were fixed with 4% PFA and permeabilized in 0.25% Triton X-100. Coverslips were blocked in 10% normal goat serum for 15 min each and incubated with anti-vGLUT1 (1:100; NeuroMab, clone N28/9, #75-066), anti-vGAT (1:1000; Synaptic Systems #131 003), anti-SERCA (1:500; Abcam # ab2817), and

anti-GRP78 Bip (1:200; Abcam # ab21685) primary antibodies in 1% blocking solution for overnight at 4◦C. Coverslips were then incubated with goat anti-rabbit or goat anti-mouse secondary antibodies conjugated to Alexa-fluorophores (1:500; Invitrogen) for 1 h at RT.

#### FM Dye Experiments and Analysis

Recycling synaptic vesicles of 48 h (15 DIV) postaxotomy hippocampal cultures were loaded with lipophilic dye N-(3-trimethylammoniumpropyl)-4-(6-(4-(diethylamino) phenyl) hexatrienyl)pyridinium dibromide (FM 5–95; Invitrogen) using KCl mediated depolarization as described

FIGURE 5 | Dantrolene or Xestospongin C applied at the time and location of axotomy prevent retrograde enhancement of presynaptic release rate. (A) FM unloading curves at 48 h following application of vehicle or Dantrolene (20 µM) or Xestospongin C (1 µM) to axons for 1 h during axotomy. Uninjured control: n = 1076 puncta; Axot. + Veh: n = 893 puncta; Axot. + Dan: n = 1136 puncta; Axot. + Xes: n = 2234; 5 chambers per condition over two experiments. Two-way ANOVA, Bonferroni post hoc test. (B) FM decay time constant (τ) for puncta with τ < 360 s (Uninj. control: n = 1045; Axot. + Veh: n = 857; Axot. + Dan: n = 1058; Axot. + Xes: n = 2139). Unpaired two-tailed t-test. Each condition includes 5 chambers combined over 2 independent experiments. Error bars, SEM. ∗∗p < 0.005.

previously (Taylor et al., 2013). For FM unloading, microfluidic chambers were stimulated using extracellular electrodes by placing a positive and negative electrode in each well of the somatodendritic compartment. Electrical stimulation was provided by an AD Instruments 2 Channel Stimulus Generator (STG4002) in current mode with an asymmetric waveform (−480 µA for 1 ms and + 1600 µA for 0.3 ms) for ∼1 min at 20 hz for 600 pulses. The FM 5–95 imaging was performed using a spinning disk confocal imaging system as previously described in Taylor et al. (2013). Z-stacks (31 slices) were captured every 15 s during the baseline (1 min), stimulation (1 min), and after stimulation (2 min) periods. At least 3 baseline images were acquired before electrical stimulation. Sum projected confocal z-stack were converted to 8-bit images and registered using TurboReg, an Image J plugin. We background subtracted the image stack using the image 3 min after stimulation began as described in Nagendran et al. (2017). Briefly, image stacks were thresholded to a pixel value of 15. FM puncta between 0.4 to 10 µm<sup>2</sup> were analyzed. We measured the intensity of each punctum in the whole field throughout all time series. We normalized fluorescence intensity of each puncta to the frame before stimulation. Puncta with >5% unloading after 1 min were used in the analysis as unloaded puncta. Time constants were estimated by curve fitting unloading kinetics to a single exponential decay function (Taylor et al., 2013). Curve fitting was done in MATLAB and FM puncta with time constants longer than 3 min were excluded from the analysis.

#### Drug Treatments

KB-R7943 (Tocris Bioscience # 1244) was suspended in DMSO and applied to the axonal compartment at a final concentration of 10 µM for 1 h during axotomy (including 15 min preincubation before axotomy). Tetrodotoxin citrate (TTX; Tocris Bioscience #1078) was suspended in HBS and applied to the axonal compartment at a final concentration of 1 µM for 1 h during axotomy (beginning 15 min prior to axotomy).

Veratridine (Tocris Bioscience #2918) was suspended in DMSO and applied to the axonal compartment at a final concentration of 10 µM for 10 min in the absence of axotomy/injury. Local ABS, which includes low-Ca2+, high-Mg2+, and TTX (0.5 mM CaCl2, 10 mM MgCl2, 1 µM TTX) was applied solely to the axonal compartment for 1 h during axotomy (15 min prior and 45 min after axotomy). Dantrolene (Tocris Bioscience #0507) and (-)- Xestospongin C (Tocris Bioscience #1280), stock concentrations prepared in DMSO, were diluted in HBS or ABS solution and added to axonal compartment at a final concentration of 20 and 1 µM respectively for 1 h during axotomy (with 15 min pre-treatment and 45 min treatment post-axotomy). DMSO or HBS was used as vehicles. Media stored from the axonal compartment prior to treatment was added back to the axonal compartment after treatment and washes with pre-warmed fresh neuron culture media.

### Microscopy and Image Analysis

FM and fixed imaging was performed using CSU-X1 (Yokogawa) spinning disk confocal imaging unit configured for an Olympus IX81 microscope (Andor Revolution XD). Excitation for the spinning disk confocal imaging system was provided by 405 nm, 488 nm, 561 nm, and/or 640 nm lasers. The following bandpass emission filters (BrightLine, Semrock) were used for the spinning disk: 447/60 nm (TRF447-060), 525/30 nm (TRF525-030), 607/36 nm (TR-F607-036), and 685/40 nm (TR-F685-040). Zeiss LSM 780 (63 × 1.4 NA or 40 × 1.4 NA oil immersion objective) or the spinning disk system above (60 × 1.3 NA silicon oil immersion objective) was used to capture high-resolution images of mCherry or eGFP labeled live neurons as previously described (Nagendran et al., 2017).

For FM imaging, the spinning disk confocal imaging system was used with excitation at 561 nm and the 685/40 nm emission filter. We used 2 × 2 binning to reduce the laser intensity and acquisition time for each frame; each z-stack was obtained in ∼5 s. For dendritic spine analysis, before and 24 h post-axotomy confocal z-stack images of live G-deleted Rabies-mCherry or eGFP virus labeled neurons were captured to create montages of neurons extending axons into the axonal compartment. Fluorescent protein labels the entire neuron including small protrusions like dendritic spines. Calibrated z-stack montages were analyzed for all dendrite and spine parameters. Primary dendrites were traced using the semiautomatic neurite tracing tool, Neuron J (Meijering et al., 2004). Dendritic spines were quantified based on their size and shape. The number of spines on all primary dendrites of each neuron was manually counted and spine density was calculated for 10 µm length of dendrite as [(# of spines/dendrite length) × 10] (Nagendran et al., 2017).

#### Statistical Analysis

Statistical analyses were performed using GraphPad Prism 6. Spine density before and after treatment or injury was analyzed using paired two-tailed t-test. FM unloading curves were analyzed by two-way ANOVA, using a Bonferroni post hoc test. FM decay time constants were analyzed using either unpaired two-tailed t-test. vGat puncta per area were analyzed by unpaired two-tailed t-test. For sample size, p-value, and statistical test, refer to the figure legends.

## DISCUSSION

Hyper-excitability following acquired brain injury leads to longterm effects, such as persistent seizures, chronic pain, and spasticity. Intrinsic injury signaling within damaged neurons likely plays a key role in induced hyper-excitability.

The main conclusion of our results is that axonal ER signaling plays a critical role in regulating axotomy-induced retrograde presynaptic release in hippocampal neurons. Using our in vitro microfluidic model, our data show that while NCXs at the site of injury mediate retrograde dendritic spine loss, they do not mediate the delayed retrograde changes in presynaptic release rate. Rather than influx of extracellular calcium into the cytosol, release from internal ER stores within the axon at the site of injury appears to be a critical signaling component that triggers changes in retrograde presynaptic neurotransmitter release rate.

Dantrolene or Xestospongin C applied at the time and location of axotomy, both prevented the injury-induced retrograde release

changes. Both receptors are localized to hippocampal neurons. RyRs are predominant in hippocampal CA3 and DG with less expression in CA1 (Sharp et al., 1993). IP3Rs show the opposite trend, though there is evidence of immunoreactivity of both receptors in the same neuron. Interestingly, RyRs are more prominently seen in hippocampal axons than IP3Rs (Sharp et al., 1993).

RyRs play a critical role in injury-dependent neuronal signaling. Inhibiting RyRs with Dantrolene reduced neuronal injury in an ischemic gerbil model (Wei and Perry, 1996). RyR are also necessary for CICR, suggesting the involvement of this mechanism in presynaptic release changes following axotomy (Verkhratsky, 2005). Ca2<sup>+</sup> release from IP3Rs may induce RyRmediated Ca2<sup>+</sup> release. Xestospongin C blocks SERCA pumps in addition to IP3R, preventing Ca2<sup>+</sup> uptake into the ER (Smet et al., 1999; Castonguay and Robitaille, 2002; Solovyova et al., 2002). Thus, it is also possible that the non-specific effect of this drug may alter ER calcium availability via mechanisms not involving IP3Rs and may explain why the retrograde release changes were prevented with local application of this drug. Nonetheless, a major conclusion of this data is the dependence of Ca2<sup>+</sup> release from ER, and not extracellular Ca2<sup>+</sup> influx, for the axotomyinduced enhancement in retrograde presynaptic release rate.

Our previously published data support that both axotomyinduced dendritic spine loss and presynaptic release changes are mediated by rapid transcription (Nagendran et al., 2017). Our data show that ER changes in Ca2<sup>+</sup> buffering and sequestration are observed in the soma following axotomy (**Figure 6**), supporting axon-to-soma ER-dependent Ca2<sup>+</sup> signaling. In peripheral neurons, locally initiated calcium waves can propagate to the nucleus to induce a transcriptional response (Cho et al., 2013). Other studies suggest that local influx of calcium may be a priming effect for retrograde microtubule-based transport of signaling complexes required to initiate transcription (Rishal and Fainzilber, 2014). We previously identified netrin-1, a known synaptogenic cue, as downregulated within the somatodendritic compartment both in vivo and in vitro following axon damage (Nagendran et al., 2017). Further application of exogenous netrin-1 after axotomy normalized both dendritic spine density and inhibitory terminals, suggesting netrin-1 signaling may regulate axotomy-induced synapse loss. Interestingly, ER stress activates IRE1, a sensor that activates UPR, to degrade netrin-1 mRNA (Binet et al., 2013).

Critical involvement in ER signaling is not only implicated in acute neural injuries, but also in multiple neurological

#### REFERENCES


disorders (Ozcan and Tabas, 2012), including Alzheimer's disease, Parkinson's disease, multiple sclerosis, amyotrophic lateral sclerosis, and prion diseases. In these diseases, axon damage is a first site of pathology, suggesting signaling from the axon may be a key early event and clear target for future therapeutics.

#### DATA AVAILABILITY STATEMENT

The datasets generated for this study are available on request to the corresponding author.

#### ETHICS STATEMENT

The animal study was reviewed and approved by The University of North Carolina at Chapel Hill Institutional Animal Care and Use Committee (IACUC).

#### AUTHOR CONTRIBUTIONS

TN designed the experiments, acquired the data, analyzed the data, and wrote the manuscript. AT designed the experiments and wrote the manuscript.

## FUNDING

The authors received financial support from the National Institute of Mental Health (R42 MH097377), the National Institute of Neurological Disorders and Stroke (R41 NS108895), the American Heart Association (17GRNT33700108), and Xona Microfluidics, LLC. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Viral resources were supported by the GT3 Core Facility of the Salk Institute with funding from NIH-NCI CCSG: P30 014195, an NINDS R24 Core Grant and funding from NEI. Imaging was partially performed at the Neuroscience Center Microscopy Core Facility, supported, in part, by funding from the NIH-NINDS Neuroscience Center Support Grant P30 NS045892 and the NIH-NICHD Intellectual and Developmental Disabilities Research Center Support Grant U54 D079124.


axotomized spinal motor neurons. BMC Neurosci. 6:19. doi: 10.1186/1471- 2202-6-19


**Conflict of Interest:** AT is an inventor of the multi-compartment microfluidic device (US 7419822 B2, EPO 1581612, and EPO 2719756), and is Chief Scientist and a Member of Xona Microfluidics, LLC.

The remaining author declares 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 © 2019 Nagendran and Taylor. 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(s) 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.

# Scaling of the AIS and Somatodendritic Compartments in α S RGCs

#### Vineeth Raghuram1,2,3† , Paul Werginz2,4† and Shelley I. Fried1,2 \*

<sup>1</sup> Rehabilitation Research & Development Service, Boston VA Healthcare System, Boston, MA, United States, <sup>2</sup> Department of Neurosurgery, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States, <sup>3</sup> Department of Biomedical Engineering, Tufts University, Medford, MA, United States, <sup>4</sup> Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

The anatomical properties of the axon initial segment (AIS) are tailored in certain types of CNS neurons to help optimize different aspects of neuronal function. Here, we questioned whether the AISs of retinal ganglion cells (RGC) were similarly customized, and if so, whether they supported specific RGC functions. To explore this, we measured the AIS properties in alpha sustained RGCs (α S RGCs) of mouse; α S RGCs sizes vary systematically along the nasal temporal axis of the retina, making these cells an attractive population with which to study potential correlations between AIS properties and cell size. Measurements of AIS length as well as distance from the soma revealed that both were scaled to cell size, i.e., cells with large dendritic fields had long AISs that were relatively far from the soma. Within the AIS, the percentage of Nav1.6 voltagegated sodium channels remained highly consistent, regardless of cell size or other AIS properties. Although ON RGCs were slightly larger than OFF cells at any given location of the retina, the level of scaling and relative distribution of voltage-gated sodium channels were highly similar. Computational modeling revealed that AIS scaling influenced spiking thresholds, spike rate as well as the kinetics of individual action potentials, Interestingly, the effect of individual features of the AIS varied for different neuronal functions, e.g., AIS length had a larger effect on the efficacy by which the AIS initiated spike triggered the somatic spike than it did on repetitive spiking. The polarity of the effect varied for different properties, i.e., increases to soma size increased spike threshold while increases to AIS length decreased threshold. Thus, variations in the relative level of scaling for individual components could fine tune threshold or other neuronal functions. Light responses were highly consistent across the full range of cell sizes suggesting that scaling may post-synaptically shape response stability, e.g., in addition to several well-known pre-synaptic contributors.

Keywords: axon initial segment, retinal ganglion cells, morphological scaling, axonal geometry, action potential

## INTRODUCTION

The axon initial segment (AIS) is a specialized portion of the proximal axon that mediates the initiation and propagation of action potentials in CNS neurons. Structurally, the AIS is comprised of densely packed voltage-gated sodium (Nav) and potassium channels (Kv) that are held in place by a complex network of structural proteins and tethering molecules. Much recent evidence suggests

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Matthew s Grubb, King's College London, United Kingdom Bela Volgyi, University of Pécs, Hungary

\*Correspondence:

Shelley I. Fried fried.shelley@mgh.harvard.edu

†These authors have contributed equally to this work

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 25 July 2019 Accepted: 13 September 2019 Published: 27 September 2019

#### Citation:

Raghuram V, Werginz P and Fried SI (2019) Scaling of the AIS and Somatodendritic Compartments in α S RGCs. Front. Cell. Neurosci. 13:436. doi: 10.3389/fncel.2019.00436

**183**

that AISs are tailored to help optimize specific elements of neuronal function. For example, neurons of the chick nucleus laminaris that are sensitive to low auditory frequencies have AISs that are shorter and further from the soma than the AISs of high-frequency neurons; the differences in the length and location are thought to help maximize the sensitivity to the interaural time differences (ITD) associated with each frequency range (Kuba et al., 2006). In contrast, the length of the AIS does not vary systematically in thick-tufted pyramidal neurons of the somatosensory cortex but instead, the distance between the AIS and the soma is inversely correlated to the size of the apical dendrite; this arrangement helps maintain consistency in the amplitude of the back-propagated action potential across a wide range of cellular morphologies (Hamada et al., 2016).

Within the AIS, two spatially and functionally distinct subtypes of voltage-gated sodium channels are thought to play complementary roles in the generation and back-propagation of spiking (Boiko et al., 2003; Van Wart et al., 2007; Hu et al., 2009). Nav1.6 channels are confined to the distal portion of the AIS and activate at lower levels of membrane depolarization; consistent with their higher sensitivity and greater separation from the soma (i.e., more decoupled), spikes are initiated in this portion of the AIS. In contrast, Nav1.2 channels are confined to the proximal portion of the AIS and have higher activation thresholds; these channels remain largely unactivated by the initial depolarization of the soma and thus are well-suited to effectively facilitate penetration of the AIS-initiated spike into the soma. In a previous study in rat retinal ganglion cells (RGCs) (Van Wart et al., 2007) the Nav1.6 portion was reported to comprise ∼2/3 of the total AIS length although details were not provided as to whether the ratio was for a single cell type or an average across the population of all RGCs tested. Given the specificity of the AIS in different cell types, it seems likely that the composition of the AIS, e.g., the distribution of Na<sup>v</sup> channels may also be tailored for individual cells or cell types.

Somewhat surprisingly, neither the structure nor the function of the AIS has been well studied in retinal neurons. Most mammalian retinas contain over 30 different types of ganglion cells (retinal output neurons); each type extracts different features of the visual world and uses distinct patterns of spiking to convey information to higher visual centers (Devries and Baylor, 1997; Roska and Werblin, 2001; Baden et al., 2016). Given the functional specificity of the AIS in other types of CNS neurons, it seems reasonable to question whether the AISs of individual RGC types are also customized to meet specific functional requirements. For example, the AISs of cell types that generate long-duration, high-frequency bursts of spikes may be different from the AISs of types that generate short-duration, low-frequency spike trains. Potential support for AIS specificity in RGCs comes from an earlier study that found longer AISs in brisk-transient (BT) vs. directionally selective (DS) RGCs of the rabbit retina (Fried et al., 2009). Surprisingly however, there was a great deal of overlap between the two populations with the result that the length of the AIS in many BT cells was actually shorter than that of some DS cells. This variability is somewhat curious and raises the possibility that the absolute length of the AIS may be less critical than its length relative to other cellular features.

The alpha Sustained (α S) RGCs of the mouse retina is a particularly attractive population with which to study AIS structure and function because the size of these cells varies systematically across the retina (Bleckert et al., 2014), i.e., the relationship between AIS properties and cell size can be directly evaluated. Further, because RGCs remain intact in the flatmount preparation, AIS properties can be directly correlated to a wide range of other cellular features. The fact that α S RGCs consist of both ON and OFF sub-types (Pang et al., 2003) is also attractive because AIS properties can be compared across two, functionally similar populations. Finally, the light responses of α S RGCs provide a measure of neuronal function, allowing correlations between AIS structure and cellular function to be explored. Much previous work with the α S population has led to well characterized neuronal features that facilitate the rapid and unequivocal identification of targeted cells.

Here, we measured the anatomical properties of the AIS and of other cellular features in a large number of ON- and OFF-α S RGCs that spanned the full extent of the mouse retina. We found that many cellular features, including AIS length and location, varied systematically across the retina and were generally scaled to one another. The observed scaling was similar in both ONand OFF-α S RGCs although ON cells were generally larger at any given retinal location. Unlike other cellular properties, the composition of the AIS was highly consistent across all cells but differed from previously reported values. The functional role(s) of the anatomical variations were explored using a series of morphologically- and biophysically realistic computational models; scaling was shown to influence neuronal sensitivity, spike rate and the effectiveness with which AIS initiated spikes trigger somatic spikes. Scaling may also help to stabilize responses across the population.

## MATERIALS AND METHODS

#### Immunohistochemistry

GFP line M (Thy-1 promoter) mice were chosen for anatomical experiments due to the sparse fluorescent labeling of individual RGC cell bodies as well as their complete dendritic trees (Feng et al., 2000), which enabled the ability to perform detailed morphological analyses (see below). Retinal whole-mounts were surgically isolated from Thy-1 GFP line M mice (Jackson Laboratory), fixed in 4% paraformaldehyde (w/v) solution for 30 min, washed in PBS, pH 7.4, for 1 h, and subsequently placed into 12-well clear multiwell plates (Corning Falcon) for processing through free-floating immunochemistry. Retinas were then blocked with 5% normal donkey serum (NDS) in 0.3% PBTX (10x PBS + Triton X) solution for 2 h, and then incubated with chicken anti-GFP (1/200; Abcam), mouse anti-AnkyrinG (1/200; NeuroMab clone N 106-36), rabbit anti-Nav1.6 (1/200; Millipore Sigma), and goat anti-ChAT (1/200; Millipore Sigma) in 1% NDS with 0.3% PBTX solution for 5 overnights. Following incubation in primaries, samples were washed in PBS for 2 h (4 × 30 min), and placed in Alexa Fluor 488-conjugated donkey anti-chicken (1:200; Jackson Immuno), Cy5-conjugated donkey anti-mouse

(1:200; Jackson ImmunoResearch), Alexa Fluor 405-conjugated donkey anti-rabbit (1:200; Abcam), and Alexa Fluor 594 conjugated donkey anti-goat (1:200; Invitrogen) secondary antibodies in 0.3% PBTX solution for 1 overnight. Finally, samples were washed in PBS for 1 h (2 × 30 min), mounted with Prolong gold anti-fade mounting medium (Invitrogen), cover-slipped, and placed in 4◦C refrigeration until further confocal imaging.

#### Image Acquisition and Analysis

Fluorescence imaging was performed with a laser scanning confocal microscope (Zeiss LSM 880 with Airyscan) using Zeiss Efficient Navigation (ZEN Pro) software to acquire and export images. Images of the full RGC dendritic field morphology were acquired with 20x magnification at a x/y/z resolution of 0.15 × 0.15 × 0.40 µm, while images of the soma, as well as proximal axon with AIS labeling were acquired with a 63x oil immersion objective (NA = 1.4) at a x/y/z resolution of 0.09 × 0.09 × 0.40 µm. The use of a higher magnification (63x) as well as the Thy-1 line M GFP mouse (Feng et al., 2000), which provides complete labeling of RGC morphologies, allowed for the ability to perform precise tracing around the cell body and dendritic tree. Anatomical measurements and image post-processing of confocal scans were performed in NIH Image J/FIJI package (Schindelin et al., 2012). Calculation of cell volume was performed in NIH Image J/FIJI by first converting the raw image stack into a binary image (63x magnification) using median filters and local auto thresholding via the Bernsen method (**Figure 1C**) (Bernsen, 1986); additional image processing was performed using the NIH Image J/FIJI binary processing toolbox. Separately, a region of interest (ROI) is determined by creating a maximum intensity projection of the cell in the z-dimension and then manually tracing a contour around the cell body. The ROI is then applied to the processed binary image file, and the area outside the cell body is cleared to isolate the soma. This cropped binary image of the soma is then displayed in the 3D viewer (Schmid et al., 2010) where the cell volume is calculated using the voxel counter plugin.

Confirmation of cell type was obtained using choline acetyltransferase (ChAT), an immunochemical marker which labels the processes of ON and OFF starburst amacrine cells (Baughman and Bader, 1977). These are otherwise referred to as (ONand OFF-) ChAT bands and can be used to delineate the specific sublamina in which the terminal dendrites of tentatively identified RGCs stratified (Jeon et al., 1998). Consistent with previous reports, the terminal dendrites of putative ON and OFFα S RGCs stratified above and below the ON- and OFF-ChAT bands (van Wyk et al., 2009).

The anatomical properties (e.g., start and end position, distance from the soma, length) of the AIS in confocal image stacks (63x magnification) were measured by manually identifying and precisely tracing along the region of colocalization between AnkyrinG/Nav1.6 and the green fluorescent signal of the native GFP expressed within the axons of labeled RGCs using NIH Image J/FIJI package. Measurements of AIS length and distance were performed independently from calculations of cell size (dendritic field diameter, soma diameter, soma volume). Measurements were reliable between 3 independent experimenters. In a few cases (<10), AISs were obscured, either because they overlapped with other AISs or because of interfering axon bundles, making it difficult to obtain an accurate measurement and to get agreement between examiners. In these cases, the AIS measurements were excluded from further analysis.

Simple 3-d tracing of dendritic architecture and Sholl analysis was performed in NIH ImageJ/FIJI toolbox Simple Neurite Tracer (Longair et al., 2011). Full tracing, including compartment diameters of dendritic arbors, was performed in NeuronStudio (20x magnification) (Wearne et al., 2005). Tracing of diameters of the proximal axon was performed at higher magnification (63x).

#### Electrophysiology

The care and use of animals followed all federal and institutional guidelines and all protocols were approved by the Institutional Animal Care and Use Committee (IACUC) of the Massachusetts General Hospital. Wild type (C57BL/6J) mice (Charles River Laboratories) were anesthetized with isofluorane (Henry Schein) and subsequently euthanized by cervical dislocation. Eyeballs were harvested, retinas were dissected from the eyecup and mounted, photoreceptor side down, onto a recording chamber. The retina was subsequently perfused with oxygenated Ames medium (Sigma-Aldrich) buffered to pH 7.4 at a flow rate of 2– 3 ml/min for the duration of the experiment. Temperature was maintained at ∼34◦C. Small holes were made in the inner limiting membrane in order to obtain access to RGC somata. Spiking responses were obtained using loose or whole cell patch recordings. Intracellular solution consisted of (in mM, all Sigma-Aldrich): 125 K-gluconate, 10 KCl, 10 Hepes, 10 EGTA, 4 Mg-ATP, 1 Na-GTP. Morphological analysis was allowed by adding Neurobiotin (0.25 mM, Vector Laboratories) and Alexa 488 (0.5%, Invitrogen) to the intracellular solution. Further processing of filled RGCs was performed as described above (Immunohistochemistry), but primary/secondary incubation to recover cell morphology was done with Alexa Fluor 488-conjugated streptavidin (1:200; Invitrogen).

Visual stimulation consisted of bright spots on neutral (gray) background with diameters ranging from 100–1500 µm and presented for 1 s. ON-α S cells were targeted by their large somata (diameter > 15 µm) and identified by their strong sustained light responses (Pang et al., 2003; van Wyk et al., 2009; Krieger et al., 2017).

Stimulus control and data acquisition were performed with custom software written in LabView (National Instruments) and Matlab (Mathworks). Data were recorded using an Axopatch 700B amplifier (Molecular Devices) and digitized by a data acquisition card (PCI-MIO-16E-4, National Instruments). The timing of individual spikes was detected as the depolarization (loose patch = negative; whole cell patch = positive) peak of each spike in the raw trace. Firing rate was computed by pooling

from flat mount preparations of different Thy-1 GFP-M mice. Polygons drawn around the periphery of the ON cell's terminal dendrites (dotted line) and the soma of the OFF cell (inset) were used to estimate the size of each (see text). Scale bars: 100 µm. (Bottom) Cross-sectional views of the confocal image stack reveal the stratification level of the terminal dendrites (green) relative to that of the ON and OFF ChAT bands (red). (B) Each point is a plot of soma diameter vs. dendritic field diameter for an individual ON- (unfilled) or OFF-α S RGC (filled). Blue triangles (n = 7) are from ON-α S cells for which light responses were also obtained; blue traces on the top left are representative light responses from 3 of the cells (Scale bar: 200 ms/20 mV). Gray and black lines are the best-fit linear regressions for ON- (p = 2 × 10-8) and OFF- (p = 5 × 10-6) α S cell populations, respectively. Box plots (right and top) reveal statistically significant differences in soma diameter (p = 2 × 10-4), and dendritic field diameter (p = 0. 0164) between ON- vs. OFF-α S RGCs. (C) The volume of the soma was calculated by (1,2) obtaining the raw image stack, (3) converting it into a binary image file, (4) using the maximum intensity projection to create a region of interest (ROI) around the cell body, (5) clearing the area outside of the ROI, (6) displaying the result in the NIH Image J/FIJI 3D viewer and using the voxel counter plugin. (D) Each point (n = 12) is a plot of the volume-based soma diameters were plotted vs. dendritic field diameter. The solid gray line is the best-fit linear regression (p = 0.0014). (E) Similar to D, each point is a plot of soma volume calculated from 2-d measurements vs. soma volume measured from 3-d reconstructions (see text). The solid grey line is the best-fit linear regression (p = 0.0016). (F) Expanded view of the soma and proximal axon region from two ON-α S RGCs reveals that axons (arrows) can emerge from the soma (left) or from a primary dendrite (right). Scale bars: 20 µm. (G) Box plots reveal statistically significant differences in soma diameter (p = 3 × 10-5), and dendritic field diameter (p = 8 × 10-5) for axo-somatic vs. axo-dendritic cells.

responses from multiple trials (≥3) and subsequent convolution with a 50 ms sliding window.

#### Computational Modeling

fncel-13-00436 September 26, 2019 Time: 18:4 # 5

To simulate the response of model RGCs to somatic current injection we used the approach of compartment modeling, similar to much previous work from our group (Jeng et al., 2011; Werginz et al., 2014). Thereby, current flow along the stimulated fiber as well as current flow across the neuronal membrane is simulated by a network of compartments with given electrical (membrane) properties. We used membrane dynamics from Fohlmeister (Fohlmeister et al., 2010) and ion channel densities for the five different sections along the neuron [dendrites, soma, axon hillock (soma to AIS), AIS, axon] can be found in **Supplementary Table S1**. Consistent with previous work in the retina (Jeng et al., 2011; Guo et al., 2013), the levels of voltage-gated sodium and potassium ion channels in the proximal axon were approximately 7x greater than those in the soma. Intracellular (axial) resistivity was set to 143.2 ·cm (Fohlmeister et al., 2010), specific membrane capacitance 1 µF/cm<sup>2</sup> and model temperature was set to 35◦C similar to experimental conditions. The model was solved in Matlab (Mathworks) using a custom written implicit (backward) Euler solver. Time step was set to 0.005 ms. Cell morphologies of traced cells consisted of 1388–2455 compartments depending on cell size; compartment length ranged from 3 to 5 µm. Axonal geometries were reconstructed based on trendlines derived from anatomical measurements (**Figure 2D**).

Single-spike thresholds were determined as the current amplitude necessary to elicit an action potential by a 1 ms rectangular current injection. Action potentials were detected within 3 ms after pulse offset. Spike trains were generated by constant current injections (100 pA) 400 ms in length.

#### Statistical Analysis

We measured linear correlation between two variables using Pearson's correlation coefficient. For comparison of means, we used a two-sample t-test. Significance levels were set as follows: n.s. p ≥ 0.05, <sup>∗</sup>p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001. Numerical values are presented as mean ± standard deviation of mean (SD). Boxplots use standard notation (1st Quartile, Median, 3rd Quartile); outliers are indicated outside 1.5x the inter-quartile range (3rd Quartile - 1st Quartile). All statistical analysis was performed in Matlab (Mathworks).

#### RESULTS

#### α S RGCs Have Readily Identifiable Anatomical Properties

The sparse labeling of the GFP M mouse model (Feng et al., 2000) allowed us to tentatively identify α S RGCs based on previously described morphological features (Völgyi et al., 2009; Baden et al., 2016; Bae et al., 2018) such as soma size >15 µm and dendritic field diameter >200 µm (**Figure 1A**, top panels). Total dendritic length, computation of mean segment length

FIGURE 2 | AIS features scale with cell size in α S RGCs. (A) Expanded view of the soma and proximal axon region from two typical ON-α S RGC; a small RGC with a soma diameter of ∼17 µm (top) and a large RGC with a soma diameter of ∼24 µm (bottom). Staining for Ankyrin<sup>G</sup> (blue) was used as a marker for the AIS and allowed both length (AIS L, distance between the middle and right vertical lines), as well as distance from the soma (AIS D, distance between the left and middle lines) to be determined. Scale bars: 20 µm. (B) Each point is a plot of soma diameter vs. AIS distance (left) or soma diameter vs. AIS length (right), for individual ON- (unfilled) or OFF-α S RGCs (filled). Gray and black lines are the best-fit linear regressions for ON (AIS D: p = 0.0045, AIS L: p = 0.0015) and OFF (AIS D: p = 0.0043,

#### FIGURE 2 | Continued

fncel-13-00436 September 26, 2019 Time: 18:4 # 6

AIS L: p = 0.0220) α S cell populations, respectively. Box plots (right) reveal statistically significant differences in AIS D (left, p = 0.0078), and AIS L (right, p = 7 × 10-4) for ON vs. OFF cells. (C) The diameter of the proximal axon was measured at the soma-axon border [red vertical line in (D)], the proximal edge of the AIS (blue vertical line) and the distal edge of the AIS (green vertical line) in 39 α S RGCs. Dashed lines indicate best fit linear regressions. The diameter of the axon varied with cell size at the soma-axon border (red, p = 0.0001) but not at the other two locations (p = 0.5012 and p = 0.0541, respectively). (D) Schematic representation of the soma and proximal axon of an α S RGC depicting the relationship between AIS properties and soma diameter; equations at top were derived from the best-fit plots in (B).

and Sholl analysis (Sholl, 1953) in presumed α S RGCs were also highly similar to previous reports (Bleckert et al., 2014) (**Supplementary Figure S1**), providing additional confirmation of cell type. Final verification was obtained from the stratification level of terminal dendrites (van Wyk et al., 2009): ON-α S RGCs stratified just below the ON-ChAT band (**Figure 1A** bottom, left) while OFF cells stratified just above the OFF-ChAT band (**Figure 1A** bottom, right). Using this approach, we identified a total of 47 ON-α S and 27 OFF-α S RGCs obtained from 11 different mice. Light responses were measured in seven additional putative ON-α S RGCs (**Figure 1B**, top left, blue traces) and found to be highly similar to those described previously (Pang et al., 2003; van Wyk et al., 2009; Krieger et al., 2017). Subsequent morphological analysis of these seven additional cells, using the approach described above, were consistent with the findings from the original 47 ON cells, adding additional support to the notion that the cells studied here were indeed the same population of ON-α S RGCs described in previous anatomical and physiological studies (Pang et al., 2003; van Wyk et al., 2009; Krieger et al., 2017).

Consistent with earlier studies (Bleckert et al., 2014), the spatial extent of the dendritic field was quantified by drawing a polygon around the edges of the cell's terminal dendrites (**Figure 1A**, left) and then calculating the diameter of the circle whose area matched that of the drawn polygon. A similar approach was also used to calculate the diameter of the soma (**Figure 1A**, inset), but unlike prior studies (Bleckert et al., 2014) which used maximum intensity projections at low magnification (20x) to estimate the perimeter of the soma, we were able to more clearly delineate the boundaries by manually tracing the cell body along the entire z-dimension using high (63x) magnification (see section Materials and Methods). We plotted soma size vs. dendritic field diameter for all ON- and OFF-α S cells (**Figure 1B**), unfilled (n = 47) and filled (n = 27), respectively; blue triangles represent the 7 ON cells for which light responses were also obtained). Calculating the best-fit linear regressions for the ON and OFF populations (gray and black lines, respectively) revealed a highly significant positive correlation in both populations (ON: p = 2 × 10-8; OFF: p = 5 × 10-6), suggesting that the size of the dendritic field scales with the size of the soma. This correlation differs from the findings of an earlier study with this same RGC population in which the size of the soma did not vary systematically with the size of the dendritic field (Bleckert et al., 2014). While the difference in methodology is likely to contribute to the discrepancy, we nevertheless sought to more precisely estimate the soma size of each cell using numerical integration. Briefly, we determined the somatic voxel contribution from each individual confocal slice and then summed the contribution from all slices to estimate the total somatic '3-d' volume (**Figure 1C**, see section Materials and Methods). The calculated diameter of the soma from the 3-d cell volume (n = 12) was highly correlated to its dendritic field size (**Figure 1D**), providing additional support that soma size does indeed scale with cell size. Comparison of the soma diameter calculated using the 3-d volume to the soma diameter estimated from the 2-d projection across the z-stack (**Figure 1E**) suggested the 2-d approach overestimates the somatic volume and is consistent with our observation that most α S somas appeared 'flattened,' i.e., not perfectly spherical (Bae et al., 2018). The linear correlation between the two estimates (**Figure 1E**) nevertheless suggests that soma size does increase with dendritic field size across the entire population of α S RGCs, i.e., not just the 12 cells for which were able to perform the full 3-d estimates.

The finding that soma size is correlated to dendritic field size in α S RGCs of mouse is consistent with previous reports in other types of RGCs, including α RGCs of rabbit retina (Peichl et al., 1987) as well as midget and parasol RGCs of the primate retina (Watanabe and Rodieck, 1989). This type of scaling may be cell type specific as there were significant variations in dendritic field diameter but not soma diameter in dorsal vs. ventral OFFalpha transient (α T) RGCs of the mouse (Warwick et al., 2018). Both the size of the soma as well as the size of the dendritic field were smaller in OFF-α S RGCs than in neighboring ON cells (**Supplementary Figure S2** and **Figure 1B**, box plots at right and top, respectively), consistent with previous reports in both human and primate RGCs (Dacey and Petersen, 1992; Chichilnisky and Kalmar, 2002).

We also measured the diameters of the dendritic sections from the 7 filled ON-α S RGCs to see if they too were correlated to cell size (see section Materials and Methods). A histogram of the dendritic diameters (**Supplementary Figure S3A**) revealed that 95% were between 0.36 µm and 1.48 µm (mean of 0.92 µm). A probability distribution function (PDF) was fit to each histogram (red trace) and then PDFs from all cells were overlaid (**Supplementary Figure S3B**, red lines); the distribution of dendritic diameters was similar for all cells, i.e., it was not dependent on cell size. Consequently, total dendritic surface area was found to scale linearly with dendritic field diameter (**Supplementary Figure S3C**, p = 0.0028).

In most α S RGCs (n = 50/74) the axon emerged directly from the soma, but in other cells, it emerged instead from a primary dendrite (**Figure 1F**, compare left and right panels). This arrangement is similar to that reported in other types of CNS neurons (Hamada et al., 2016; Höfflin et al., 2017) although in some of these other types, axons can emerge from secondary or even tertiary dendritic processes while here, axo-dendritic axons emerged only from primary dendrites. α S RGCs with axo-somatic axons tended to be smaller than RGCs with axodendritic axons (mean soma diameters of 19.1 vs. 21.6 µm,

p = 3 × 10-5, and mean dendritic field diameter of 287 vs. 354 µm, p = 8 × 10-5) (**Figure 1G**). Most axo-dendritic α S RGCs were ON cells (n = 21/24).

#### AIS Properties Also Scale With Cell Size

The AIS is typically the site of spike initiation in CNS neurons (Stuart et al., 1997). The high density of voltage-gated sodium channels in this region (Kole et al., 2008) combined with its much smaller surface area (vs. that of the soma) leads to more rapid depolarization of membrane voltage with a corresponding earlier onset of spiking, even though excitatory synaptic inputs typically result in a slightly stronger initial depolarization at the soma. Both the size as well as the location of the AIS can influence neuronal function (Kuba et al., 2006; Evans et al., 2015; Hamada et al., 2016) although interestingly, AIS properties mediate distinct functions in different types of neurons. For example, the length and location of the AIS is customized in individual neurons of the nucleus laminaris to help optimize sensitivity to specific auditory frequencies (Kuba et al., 2006) while the location of the AIS is tailored in thick-tufted L5 pyramidal neurons to help normalize spike amplitude across a wide range of cell sizes (Hamada et al., 2016).

Given the importance of AIS properties in shaping neuronal output in other types of CNS neurons, we questioned whether AIS properties might similarly influence neuronal function in RGCs. If so, we hypothesized that similar to other CNS neurons, one or more features of the AIS would be correlated to other morphological features of the cell; the systematic variations in cell size across the α S population (**Figure 1** and **Supplementary Figure S2**) provide an ideal substrate from which to explore this hypothesis. Variability in both the length and the location of the AIS has been reported previously in two types of rabbit RGCs (Fried et al., 2009) although any correlation between AIS properties and other RGC features was not reported in this earlier work.

Similar to previous approaches (Boiko et al., 2003; Van Wart et al., 2007; Fried et al., 2009) we used immunochemical labeling of AnkyrinG, a cytoskeletal anchoring protein (Kordeli et al., 1995) that enables dense packing of voltage-gated sodium channels in the AIS (Zhou et al., 1998), as a marker for the size and location of the AIS. The length of Ankyrin<sup>G</sup> staining (**Figure 2A**, distance between middle and right vertical lines), hereafter referred to as AIS length or AIS L, did indeed vary considerably across the population of α S RGCs (**Figure 2B**, right). Further, the length of the AIS displayed a highly significant positive correlation to soma diameter (**Figure 2B**, right, unfilled and filled circles for ON and OFF RGCs, respectively; p = 1 × 10- 6). The distance from the soma to the AIS, hereafter referred to as AIS distance or AIS D (**Figure 2A**, distance between left and middle lines), also varied across the population of α S RGCs with a similarly strong correlation to soma size (**Figure 2B**, left, p = 2 × 10-6). A comparison between the slopes of the best fit lines suggested that AIS length increases with soma size at a slightly faster rate (1.38 µm for every 1 µm increase in soma diameter) than does AIS distance (1.22 µm for every 1 µm increase in soma diameter); the equations describing the rates of increase are indicated above the schematic in **Figure 2D**.

In addition to the systematic scaling of AIS size and location, careful observation revealed variability in the diameter of the proximal edge of the axon. To quantify this, we measured the diameter of the proximal axon at three locations (**Figures 2C,D**, see section Materials and Methods): (1) the border between the soma and axon (**Figure 2D**, bottom, red vertical line), (2) the proximal edge of the AIS (blue line) and (3) the distal edge of the AIS (green line). Linear regressions of the measured points (n = 39) revealed that the diameter at the start of the axon was indeed correlated to soma size (**Figure 2C**, left, red, p = 0.0001) while the diameter at the proximal and distal ends of the AIS were not (**Figure 2C**, middle, blue, p = 0.5012; **Figure 2C**, right, green, p = 0.0541); diameters at these two locations were ∼0.6 and 1.0 µm, respectively. At locations >100 µm from the soma, the diameter of the distal axon remained largely constant at ∼1 µm, consistent with previous results in amphibian retina (Carras et al., 1992). Thus, consistent with the scaling of other neuronal features found earlier, the diameter of the proximalmost portion of the axon is also wider in larger AIS α S RGCs. Further, because the diameter of more distal portions of the axon does not scale with cell size, the angular taper between the AIS and the soma is also wider in large cells. Previous modeling work in neocortical pyramidal neurons found that the degree of angular taper in this region can influence the efficacy with which the AIS-initiated spike invades the soma (Mainen et al., 1995), suggesting a functional role for this variability (see below).

## The Ratio of Na<sup>v</sup> Channel Sub-Components Remains Constant in α S RGCs

The AIS is comprised of two distinct sodium channel sub-types (Boiko et al., 2003; Van Wart et al., 2007; Hu et al., 2009): Nav1.6 channels cluster at the distal end of the AIS and have a relatively low activation threshold while Nav1.2 channels cluster at the proximal end and have a higher activation threshold (Hu et al., 2009). Note that in the retina, Nav1.1 channels are found in the proximal axon (Van Wart et al., 2007). Action potential initiation occurs in the Nav1.6 (low threshold) portion of the AIS (Hu et al., 2009; Kole and Stuart, 2012) while the lower sensitivity of the Nav1.2 portion is thought to facilitate the effectiveness with which the AIS-initiated spike triggers a somatic spike and may also regulate the amplitude of the back-propagated (somatic) spike (Hu et al., 2009). Given the distinct functional role of each sodium channel sub-type, we questioned whether their relative distribution within the AIS might also vary across the population of α S RGCs. Antibodies specific to Nav1.6 channels have been characterized previously in unclassified rodent RGCs (Van Wart et al., 2007; Damiani et al., 2012) as well as in other types of CNS neurons (Boiko et al., 2003; Hu et al., 2009), and were used here to selectively stain this portion of the AIS in α S RGCs (**Figure 3A**, see section Materials and Methods). Although we could not selectively stain the Nav1.1 component directly (but see Van Wart et al., 2007), the Nav1.1 and Nav1.6 components do not overlap (Boiko et al., 2003; Van Wart et al., 2007) and thus the length of the non-Nav1.6 + (presumed to be Nav1.1) component could be estimated by subtracting the Nav1.6 component from

vertical lines); staining for Nav1.6 (red) was used to determine the length of the Nav1.6 component (distance between the rightmost solid and dashed vertical lines). Scale bar: 20 µm. (B) Each row corresponds to a single ON- or OFF-α S cell and depicts the composition of the AIS. The length of the red portion of the line corresponds to the length of the Nav1.6 component. The length of the blue portion (non-Nav1.6+) corresponds to the portion stained by Ankyrin<sup>G</sup> but not by Nav1.6 and therefore likely to be the Nav1.1 component (see text). The shading of the circle to the left of each line corresponds to the size of the soma diameter for that cell (scale at left). (C) The calculated ratio of Nav1.6 length to total AIS (AnkyrinG) length for each cell (scale at bottom); the shading of filled circles is the same as in (B). (D) Scatterplot of soma size vs. Nav1.6/AIS ratio (p = 0.0817). The gray arrow/data point indicates an outlier which was not used in correlation analysis. (E) Box plot reveals no statistically significant differences in soma diameter (p = 0.9366).

the length of the entire AIS. **Figure 3B** shows the distribution of each of the two sub-types of sodium channels across the population of all α S RGCs tested (n = 29). The red portion of each horizontal line corresponds to the measured length of the Nav1.6 component while the blue portion corresponds to the calculated length of the non-Nav1.6 + region component (the length of the Nav1.6 component subtracted from the length of the Ankyrin<sup>G</sup> staining). The ratio of Nav1.6 length to total AIS length was calculated for each cell and ranged narrowly around a mean of 0.88 ± 0.04 (**Figure 3C**, range 0.81–0.96 with one outlier at 0.68). Plotting soma size vs. the Nav1.6/AIS ratio revealed a weak and slightly negative correlation that was not significant (**Figure 3D**, p = 0.0817). The ratio did not co-vary with any other morphological property of the cell (not shown).

The mean ratio found here (0.88) is higher than the twothirds value described previously for unclassified types of RGCs in the rat retina (Van Wart et al., 2007). Few quantification details are provided in the earlier study and thus it is difficult to reach any definitive conclusions regarding the discrepancy in AIS composition between the two studies. It is possible of course that differences in species and/or cell-type contribute to the variability, but further work will be required to elucidate the actual reason(s). Nevertheless, the high level of consistency in AIS composition across the large number of α S RGCs studied here suggests that the relative proportion of channel sub-types may be essential for optimizing one or more functions of the AIS. There was no significant difference between the ratios for ON- vs. OFFα S RGCs (**Figure 3E**, ON: 0.88 ± 0.04, range 0.81–0.96; OFF: 0.88 ± 0.04, range 0.81–0.95; p = 0.9366).

#### Light Responses Are Independent of Cell Size

The wide range of morphological variability across α S RGCs raises the question as to whether light responses would remain consistent across such a wide variation. Previous studies have shown that light responses from nearby cells of the same type (e.g., those found within the spatial spread of a single multielectrode array) are highly consistent but it is not known whether this consistency persists across the full extent of cell variability. We therefore measured light responses from a large number of ON-α S RGCs across the full extent of the nasaltemporal axis (**Figure 4**).

Light stimuli consisted of 1-s flashes that ranged in size from 100 to 1500 µm (see section Materials and Methods). Consistent with much previous work (Pang et al., 2003; Margolis and Detwiler, 2007; van Wyk et al., 2009), response strength varied considerably with stimulus size but was strongest when the size of the stimulus closely matched the size of the dendritic field (**Supplementary Figure S4**). Thus, for example, the strongest response from a small cell, located at the temporal edge of the retina, arose when the diameter of the flashed spot was 200 µm (**Figure 4A**, top) while the strongest response from a large cell, found at the nasal edge of the retina, was elicited by a much larger (500 µm) spot (**Figure 4A**, bottom). Despite the large size difference between the two cells, their responses were quite similar. Indeed, the strongest response of each ONα S RGC appeared similar across the entire population of cells tested (**Figure 4C**, n = 39). To quantitatively compare responses, we calculated the peak firing rate, the sustained firing rate, the sustained firing rate normalized by the peak firing rate, and, the time to peak and plotted each as a function of the size of the stimulus that produced the strongest response (**Figures 4D**1−4). The differences across cells were not statistically significant (p = 0.5557, p = 0.8660, p = 0.5438, and p = 0.4263, respectively) suggesting that the peak responses of individual ON-α S RGCs remain similar across the population, despite a wide range of cell sizes.

## AIS Size and Location Influence RGC Excitability

Because scaling was so prevalent in α S RGCs, we sought to understand whether it contributed to cell function. In particular,

because the AIS mediates spike initiation, we questioned whether this aspect of scaling influenced the sensitivity of spike generation and propagation. To explore this, we ran a series of computer simulations in which individual neuronal properties of model cells were systematically varied while exploring the effects on (1) spike threshold, (2) the frequency and consistency of spike trains, and (3) the effectiveness with which AIS-initiated spikes triggered somatic spikes.

Seven model cells were created, each from an actual ON-α S RGC for which the entire morphological structure of the cell had been captured (see section Materials and Methods). Dendritic field diameters of the 7 model cells ranged from 231 to 422 µm, approximating the extent of sizes found naturally. In addition to replicating the anatomy of individual cells, the density of voltagegated ion channels was customized for individual neuronal compartments using previously established values (Fohlmeister et al., 2010) (**Supplementary Table S1**, see section Materials and Methods). Prior to exploring the role of individual neuronal features, the functionality of model cells was first verified by comparing the kinetics of simulated action potentials to that from physiological measurements (**Supplementary Figure S5A**, middle column). The close match between simulated and actual spikes suggested the spike generation mechanism in model cells was accurately capturing key elements of normal physiology. In addition, action potentials in model cells were always initiated in the AIS, suggesting that the underlying mechanisms of activation in the model replicated that of normal physiology.

Threshold in model cells was defined as the minimum amplitude of a 1 ms somatic current injection required to elicit an action potential. Individual AIS features were varied systematically and a separate calculation of threshold made for each iteration of each parameter. Because the size of individual features typically varied across the seven model cells, all variations were made relative to the measured feature size in each cell, e.g., the length of the AIS was varied from 50–200% of the nominal (measured) value for that cell. The effect reported is the mean across all seven cells.

Reducing the length of the AIS resulted in higher activation thresholds (**Figure 5A**1); the largest increase occurred when AIS length was set to its minimum value (increase of 2.9 ± 1.1% for a length of 50%). Conversely, increasing the length of the AIS lowered activation threshold with the largest reduction occurred when the length of the AIS was set to its maximum value (8.9 ± 4.2% reduction for an AIS length of 200%). Because the observed variations in AIS length (**Figure 2B**) are slightly smaller than the 50–200% range tested here, the simulations suggest that the AIS variability arising naturally produces only a modest change in threshold but nevertheless, that AIS length modulates the sensitivity with which the cell responds to a given stimulus. Changes to the distance between the soma and the AIS (AIS D) also influenced threshold but the effect was smaller (**Figure 5A**2, 50%: +0.7 ± 0.6%; 200%: −2.0 ± 1.3%). When threshold was mapped across the full range of AIS lengths and distances (**Supplementary Figure S5B**), the iso-threshold lines were near vertical, further suggesting the stronger influence of AIS length over distance in modulating activation threshold.

Changes to soma size also influenced sensitivity with reductions in soma diameter leading to lower thresholds (**Figure 5A**3); the smallest diameter tested (75% of nominal) led to a threshold reduction of 4.0 ± 0.9% while the largest diameter (125% of nominal) led to a threshold increase of 5.1 ± 0.6%. Note that the sensitivity to size changes was opposite for soma size vs. that of AIS length (or AIS distance), i.e., larger AISs resulted in lower thresholds while larger somas resulted in higher thresholds. This is not surprising given that larger somas require larger amounts of current injection to depolarize to a given

level but nevertheless indicates that uniform increases of size in all cellular features may not result in uniform and predictable changes in threshold levels (see below). The final parameter tested, the diameter of the initial portion of the axon, had only a negligible effect on threshold (**Figure 5A**4, 75%: −0.2 ± 0.1%; 125%: +0.2 ± 0.1%).

To gain insight as to how scaling of all parameters simultaneously might influence thresholds across the population of α S RGCs, we constructed two new models in which all neuronal features (AIS L, AIS D, Soma Ø and Axon Ø) were varied together. The LARGE model had all values set to maximum while the SMALL model used all minimum values. Comparison of the sensitivity of these two cells allowed the effect of comprehensive scaling of all features to be evaluated. Threshold for the SMALL model cell increased by 1.9 ± 1.6% (over nominal) while threshold in the LARGE cell decreased by 3.7 ± 2.3% (**Figure 5A**5). As mentioned above, increases to some neuronal elements reduced threshold while increases to others lowered threshold, e.g., increased soma size raised threshold in the LARGE model while the increased AIS length caused a reduction and therefore, the range of thresholds across the SMALL to LARGE models was smaller than the range induced by some neuronal elements in isolation. This suggests the possibility that scaling may be to help stabilize response sensitivity across the population of a given cell type even across a wide range of feature sizes.

## AIS Properties Influence the Properties of Spike Trains

The second modeling experiments explored the influence of the AIS in shaping the properties of elicited spike trains, i.e., not just the threshold for single spikes. In previous studies, the loss of Nav1.6 channels resulted in an inability to produce highrate spike trains in mouse RGCs (Van Wart and Matthews, 2006). Similarly, in cultured hippocampal pyramidal neurons from newborn mice, the loss of the structural proteins needed to maintain a high density of sodium channels in the AIS reduced the precision of spike timing (Lazarov et al., 2018). To explore the relationship between individual properties of the AIS and properties of the cell's spike trains, we used the same models and general approach described above but increased the duration of the current injection from 1 to 400 ms, so that multiple spikes would be generated from each stimulus (100 pA).

Analogous to the threshold simulations above, variations in the AIS had small but significant effects on firing rate (**Figure 5B**). For example, when AIS length was set to 50% of nominal, the mean reduction in firing rate was 3.9 ± 1.4%; doubling the length of the AIS increase firing rate by an average of 6.0 ± 2.0% (**Figure 5B**1). The effects of varying AIS distance were also analogous to the single spike threshold findings with a 50% reduction in AIS D leading to a 1.2 ± 1.5% reduction of firing rate while a doubling of AIS D led to a 2.5 ± 2.2% increase (**Figure 5B**2). Soma diameter also influenced firing rate (**Figure 5B**3) however its effect was smaller than it was for singlespike threshold (75%: +1.6 ± 1.5%; 125%: −1.9 ± 1.4%). The effect was smaller in the single spike experiments because the size of the soma was linearly related to the amount of charge needed to depolarize the cell membrane and thus produce the spike while for the longer duration stimulus in the spike rate experiments, the cell membrane remained depolarized once it was charged and thus less charge was required to generate subsequent spikes. Also similar to the results from the threshold experiments, changes to the diameter of the initial axon had

only a minimal effect on firing rate (**Figure 5B**4). After testing the sensitivity of all parameters in isolation, we re-created the SMALL and LARGE models and tested the resultant firing rates (**Figure 5B**5). Interestingly, the increase in firing in the LARGE model (vs. nominal) was 8.2 ± 4.1%, larger than the effect due to any one parameter in isolation and also nearly twice that for single-spike threshold (3.7 ± 2.3%). This larger difference arose because AIS length and AIS distance both had a stronger effect on firing rate while soma size did not and is in contrast to the single-spike threshold results which were strongly affected by soma size (and AIS length). The results, taken together, therefore suggest that the influence of specific neuronal elements as well as the interplay between multiple elements is not constant for all modes of operation. Firing rate in the SMALL model was lowered by 2.0 ± 2.3%, comparable to the 1.9 ± 1.6% reduction for single spike thresholds. It is worth noting that the increase firing rates described in the large model cells were not matched by physiological responses – at least not for light responses (**Figure 4**). This suggests that other factors, not incorporated into the model, are likely contributing to spike rate (see section Discussion).

#### Scaling Influences the Infiltration of AIS Spikes Into the Soma

In the simulations above, variations in the diameter of the initial portion of the axon were found to have little effect on either threshold or pulse rate. What then was the functional role of variability in this part of the neuron? Results from a previous modeling study in neocortical pyramidal neurons suggested that the taper of the proximal axon influences the effectiveness with which AIS-initiated spikes trigger somatic spikes (Mainen et al., 1995). The results of **Figure 5A** suggest that taper does not directly influence the sensitivity of spike threshold but the shape of the action potential was altered by some of the changes in the previous simulations (**Supplementary Figure S5A**), including taper, leading us to question the specifics of this effect and, whether the effectiveness of back-propagation was also influenced.

Plots of membrane voltage (V) vs. the time derivative of membrane potential (1V/1t) are referred to as phase plots and allow the fine details of action potential kinetics to be examined. They are especially useful for comparing specific time segments of the action potential during periods where either V or 1V/1t are changing rapidly. **Figure 6A** shows phase plot overlays of 10 spikes from an actual cell (left) and 10 spikes from a model cell (right). As expected, individual spikes were highly consistent from trial to trial and many aspects of the spike kinetics were matched by the model cell. Overlay of individual spikes from 10 different α S RGCs (**Figure 6B**, left) revealed high consistency across the population and many of the subtle variations in spike kinetics could be largely replicated in the different model cells (right). Although phase plots report somatic potentials, the AISinduced spike can be observed in the waveform as the portion of the curve prior to the inflection point (arrows in panels A and B); the inflection point, referred to as the initial segmentsomatodendritic (IS-SD) break, occurs at the transition between the initial depolarization arising from the AIS-initiated spike and the onset of the (somatic) action potential (Coombs et al., 1957; Yu et al., 2008) suggesting that the axial current arising from the AIS-initiated spike helps to trigger the somatic spike. The presence of an IS-SD break in all recorded cells is a marker that indicates that spikes are always initiated in the AIS suggesting the process is very reliable in α S RGCs.

As in previous simulations, we varied individual neuronal elements in all 7 model cells and examined the effect on membrane dynamics via phase plots (**Figure 6C**). The largest differences occurred in response to variations in AIS length and were most noticeable around the IS-SD break with a longer AIS (blue) leading to a sharper rise during the initial phase of the action potential. This leads to a more pronounced IS-SD break for longer AISs while the IS-SD break is almost eliminated for shortened AISs (red). To quantitatively compare changes in phase plots, we calculated onset rapidness (Lazarov et al., 2018), defined as the slope in 1V/1t when a rate of 25 V/s was reached; the red lines in **Figure 6C** (right) depict the onset rapidness calculations for two of the sample traces from the main panel with the one on the left corresponding to an increased AIS length (200%) and the one on the right to a reduced AIS length of (50%). Reduction of AIS length to 50% of nominal led to a decrease of onset rapidness (−33.6 ± 19.0%) whereas doubling led to an increase (479 ± 117%) (**Figure 6D**1). This occurs because the increased length of the AISs results in a stronger inward current during the AIS spike and thus stronger axial currents are delivered to the soma. Changes to AIS distance (**Figure 6D**2) had a similar but less pronounced effect as onset rapidness was reduced by 21.7 ± 13.0% for distance reduction to 50% and increased by 190 ± 41% for a distance of 200%. Soma diameter had only a small influence on action potential shape as onset rapidness changed by less than 3% (**Figure 6D**3, 75%: −0.5 ± 7.8%; 125%: +2.7 ± 8.4%). Thus, in contrast to their relatively small effect on single-spike threshold and firing rate, changes to the initial axon diameter (**Figure 6D**4) had a more substantial effect on spike kinetics with an onset rapidness increase of 30.0 ± 18.3% for a diameter reduction to 75% of nominal and an onset rapidness decrease of 11.7 ± 3.7% when diameter was increased to 125%. Because reducing the size of most elements (relative to that of nominal) resulted in a reduction in onset rapidness while reducing the size of the initial axon diameter resulted in an increase in onset rapidness, these model results suggest that adjustments to the initial axon diameter might be essential to optimize the consistency of the somatic spike both within spikes from the same cell as well as across cells of the same cell type. Use of the LARGE and SMALL models revealed that, similar to the effects with threshold, the simultaneous increase in size of all neuronal elements mitigates the effect of changes to any one parameter change and thus provides further support for the notion that scaling may help to maintain consistency of many response features across a wide range of morphological variations (**Figure 6D**5).

The plots of **Figures 6C,D** suggest that the shape of the somatic action potential is sensitive to the properties of at least several neuronal elements. The most noticeable change in spike shape was the IS-SD break, suggesting that changes to

the neuronal elements in question alter not only the timing of individual spikes but also the strength and effectiveness with which the AIS-initiated spike triggers the somatic spike (Yu et al., 2008). As with the previous modeling experiments, we found here that multiple elements could have an effect and that the polarity could vary for individual elements. Therefore, similar to the experiments with threshold sensitivity, the effect on somatic spike initiation was smaller when multiple parameters were changed simultaneously vs. when the effect of individual parameters. Whereas the diameter of the initial axon (and the corresponding taper of the initial axon segment) had only small effects on threshold and spike rate, it had a more substantial effect on the triggering of the somatic spike, and had the strongest counter-balancing effect to changes in AIS properties. It is of course possible that factors not considered in the model, e.g., the density and/or expression patterns of specific types of voltagegated potassium channels, could also play a role in normalizing spike thresholds and/or the effectiveness with which the AISinitiated spike triggers the somatic spike and it will be interesting to explore such effects in future studies.

The change in kinetics of the action potential as a function of AIS length (**Figure 6C**), suggest that part of the reason for customizing AIS length is to optimize the initiation of the somatic spike. Note that in **Figure 6C**, the longer AIS (blue) resulted in a faster initial change in voltage (1V/1t) but a lower level in overall depolarization (lower maximum level of V). While our results do not explain why this occurs, it is likely that a 'toofast' delivery of current to the soma is simply not effective for charging the large capacitance of the somatic membrane; it leads to inactivation of some portion of somatic voltage-gated sodium channels with the net result that the somatic action potential has a weaker rise and reaches a lower peak voltage. At the other end of the spectrum, a 'too-small' delivery of current (from an AIS that is too short) offers no boost to the somatic spike (no IS-SD break), i.e., the AIS-spike does little to help trigger the somatic spike.

## DISCUSSION

#### Summary

Detailed anatomical measurements revealed systematic correlations in size between a wide range of morphological features in α S RGCs of the mouse. For example, cells with large dendritic fields tended to also have large somas. In addition, the AISs of large cells were longer and further from the soma than those of smaller cells. Because the AIS is the portion of the cell that mediates spike initiation, our results suggest that this function is not mediated by a uniform structure across all cells of a given type but instead is sized relative to the rest of the cell. To explore the functional role of this scaling, we developed morphologically- and biophysically realistic computational models that allowed individual aspects of the AIS to be systematically varied. The models suggest that scaling helps to reduce sensitivity variations for the initiation of spikes across the cells of an individual RGC type. This helps to further stabilize the temporal properties of elicited spike trains across the population, and ensure consistency in the conversion of the AIS-initiated spike to a somatic spike. Thus, in addition to a myriad of previously identified pre-synaptic processes that shape the responses of RGCs, here we identify a novel post-synaptic mechanism that completes these other processes. Further, scaling is also likely to contribute to the strong similarities in both the kinetics of individual spikes as well as the spike trains arising in response to light during physiological experiments.

#### Somatodendritic and AIS Scaling

fncel-13-00436 September 26, 2019 Time: 18:4 # 13

Our finding that both soma size and dendritic field diameter increase systematically along the nasal temporal axis in α S RGCs (**Figure 1B**) differs from an earlier study of these same cells which found that only dendritic field extent (not soma size) increases along this axis (Bleckert et al., 2014). To verify our findings, we performed additional measurements of somatic volume using a detailed 3-dimensional approach in a subset of cells; these measurements confirmed that soma size does indeed vary across cells and that it is strongly correlated to dendritic field size (**Figure 1D**). The 3-d measurements also revealed that the shape of the soma in α S RGCs was slightly 'flattened' along the z-axis (perpendicular to the plane of the retina, **Figures 1C,E**) and thus the 2-d measurements systematically overestimated the actual soma size (**Figure 1E**). Nevertheless, there was a linear correlation between the two estimation techniques, and thus, taken together, our results show that soma size is indeed variable across the α S RGC population and that it scales with dendritic field size. We found similar levels of scaling in both ON and OFF sub-types of α S RGCs (**Figure 1B** and **Supplementary Figure S2**). Scaling in these cells is consistent with previous reports in brisk transient (BT) RGCs of the rabbit retina (Peichl et al., 1987) as well as in midget and parasol RGCs of the primate retina (Watanabe and Rodieck, 1989). While this indicates that scaling is not unique to α S RGCs at least one well studied cell type of the mouse retina does not exhibit scaling (Warwick et al., 2018). At any given location in the mouse retina, ON-α S RGCs were slightly larger than neighboring OFF-α S RGCs (**Supplementary Figure S2**), analogous to previous reports in ON and OFF midget and parasol RGCs in both human and non-human primate retinas (Dacey and Petersen, 1992; Chichilnisky and Kalmar, 2002).

Previous studies have shown that the properties of the AIS can be variable, both within (Hamada et al., 2016) and across individual cell types (Kuba et al., 2006); such variability is thought to help optimize one or more aspects of neuronal function. These previous findings outside the retina led us to analyze the variability in the AIS properties of α S RGCs and we found that both the length of the AIS as well as its distance from the soma increased as a function of cell size (**Figure 3B**), i.e., AIS properties were scaled to the overall size of the cell. AIS scaling in α s RGCs is intriguing because it suggests that nature tailors the spike initiating region of each cell based on the size of other cellular features. Interestingly, the relative proportion of the Na<sup>v</sup> components of the AIS both remained remarkably constant across the entire population (**Figure 3**). The relative proportion of Nav1.6 channels within the AIS (88 ± 4%) was nearly identical in both ON- and OFF-α S cells suggesting that whatever role served by this particular ratio, it is similar in both cell populations. Interestingly, the ratio measured here, from a single cell type in mouse retina, was different from that of a previous study in which the Nav1.6 portion comprised only ∼67% of the total length across unspecified RGC types in rat retina (Van Wart et al., 2007). It will be interesting in future studies to learn the functional reason for the ratio difference, and to determine whether the ratio varies for different types of RGCs and/or across different species. Finally, our anatomical measurements revealed that the cross-sectional diameter of the axon at the point from which it emerges from the soma, also increased linearly with cell size. Thus, there was a wider taper that persisted over a longer extent of the proximal-most portion of the axon in larger cells. Because this portion of the axon serves as the direct link between AIS and soma, the fact that it too was scaled provides additional support for the notion that AIS properties are functionally linked to the size of the soma and perhaps the overall size of the cell.

#### Scaling and AIS Function

To gain insight into the functional role of the anatomical scaling observed here, we developed a series of morphologicallyand biophysically realistic computational models. Each model matched the precise morphology of a single α S RGC that had been dye-filled, stained and captured via confocal imaging. The models allowed individual features of the cell to be systematically varied and thus could provide insight as to the functional role of each. Simulations were run to test all cellular features that been anatomically characterized in the first part of the study (soma size, dendritic field, AIS length, AIS distance and the angular taper of the proximal axon). Not surprisingly, alterations to each of the individual features led to changes in neuronal function, particularly in the initiation and/or propagation of action potentials (**Figures 5**, **6**).

Prior to exploring the role of AIS scaling, we sought to first gain insight into the functional role of the scaling observed between the soma and dendritic field diameter (**Figure 1B**). In preliminary simulations (not shown), we compared the synaptic input arriving at the soma between two cells that were identical except for the size of their dendritic fields. Because the density of synaptic inputs along the dendrites was the same in both cells, a larger amount of synaptic current could be delivered to the soma of the cell with the larger dendritic field. Further, because soma size was identical in the two cells, the larger amount of synaptic input in the cell with the larger dendritic field produced a stronger depolarization in its soma. Increasing the soma size of the cell with the larger dendritic field (as occurs with scaling) reduces the level of somatic depolarization and thus helps to normalize the peak level of depolarization between the different size cells. This therefore suggests that the scaling between soma size and dendritic field diameter observed here (**Figure 1B**) may help to normalize responses across the full population of cells and is consistent with the highly similar physiological responses found in neighboring cells of the same type as well as across cells of the same type that are located much further apart (**Figure 4**).

Simulations that explored the functional role of the AIS revealed that its scaling may also help to normalize responses across the population of α S RGCs. Changes to both the length and the location of the AIS did not alter the absolute level of somatic depolarization but instead modulated the level of somatic depolarization required to elicit an action potential, i.e., spike threshold. Interestingly, the longer and more distal AISs found in larger α S RGCs acted to reduce the threshold for spike initiation, suggesting an opposite relationship for some features, i.e., while increased soma size reduced the level of

somatic depolarization (and thus increases threshold), increased length of the AIS as well as the increased distance from the soma (as found in large cells) both acted to reduce threshold. Thus, scaling of multiple features may act to fine tune sensitivity in each cell and ultimately, to normalize sensitivity across the entire population. The ability to fine tune sensitivity via scaling of multiple features might also be particularly attractive during development as it would allow the properties of one feature to be adjusted after other features were already sized, e.g., AIS properties could be fine-tuned after the soma and dendritic field sizes had already been established. The demonstration of plasticity of both the length and location of the AIS (Grubb and Burrone, 2010; Kuba et al., 2010) lends support to this possibility. Our results do not preclude the possibility that other features of the cell, e.g., those not explored in this study, also shape sensitivity as well.

Scaling had an analogous influence on the generation of spike trains with synergistic interactions between different neuronal elements again working to stabilize spike rates. The effects of soma size were again opposed by those of AIS length and distance although soma size had a smaller effect on spike rate (than it did on single spike thresholds). Thus, individual neuronal features do not exert the same influence on all aspects of cell function and the resulting interplay between different elements varies as well. The simulations also revealed that changes to the angular taper of the proximal-most portion of the axon had little effect on either spike threshold or the rate of spiking but instead altered the efficacy with which the AIS-initiated spike triggered the somatic spike. The wider tapers associated with larger cells (**Figure 2C**), resulted in a slower rise in somatic depolarization (slower onset rapidness, **Figure 6D**4), and thus a smaller IS-SD break. This was in contrast to the effects of longer AISs in large cells, which increased onset rapidness (**Figures 6C,D**1). Thus, for all aspects of neuronal function tested here, increasing the size of some neuronal elements drove the response in one direction while increasing the size of others drove the response in the opposite direction. Taken together, this suggests that slight changes to the size of individual elements can be used to fine tune the performance of a wide range of spiking-related functions. We did not probe the role of onset rapidness or the IS-SD break in detail, but changes to the waveforms (**Figure 6C**) suggest that if onset rapidness is too steep, the AIS-initiated depolarization of the soma occurs faster than the soma can respond (e.g., faster than the large somatic capacitance can be charged), and thus the somatic spike is delayed; further delays eventually led to failure of the somatic spike. This suggests the rate of increase may influence the efficacy with which the AIS-initiated spike helps to trigger the somatic spike and thus, analogous to the simulations above, the simultaneous scaling of multiple components helps to optimize this aspect of cell function. It is worth nothing that spike kinetics were highly similar across all measured α S RGCs (**Figure 6B**), even when, for example, axo-somatic and axo-dendritic axons were compared, suggesting that nature tries to keep activation thresholds constant and maintain response consistency across the population of α S RGCs.

#### Analysis of Model Sensitivity

Our simulation results were dependent upon the underlying anatomy of the cell as well as the distribution and kinetics of the channels used in the model. As such, we evaluated the sensitivity of the results to many different model parameters to ensure that the results were not being artificially driven (biased) by any one (or few) feature of the model. Anatomy of individual cells closely matched those of actual cells and we chose cells that spanned the full range of sizes found in nature. The consistency of results across this population suggests that the model was not inappropriately sensitive to any one specific cell size or morphological feature. Channel kinetics largely matched those developed by Fohlmeister et al. (2010) and are similar to those used previously by our group. The close match between physiological action potentials and those from the model (**Figure 6A** and **Supplementary Figure S5A**) suggests key elements of normal physiology were captured by the model, including the fact that action potentials were always initiated in the AIS in both actual and model cells. Further, similar to physiological measurements across the population of α S RGCs, the action potential kinetics of all model cells were also highly similar, suggesting physiological responses of model cells were not inappropriately sensitive to any specific aspect of the model. Nevertheless, estimates for channel densities in RGCs have varied considerably across previous studies (Fohlmeister et al., 2010; Jeng et al., 2011; Werginz et al., 2014; Guo et al., 2016) and the timing of individual spikes could vary if channel conductances were altered significantly. For example, the incorporation of both low- and high-voltage activated calcium channels into the dendrites of model cells (Margolis et al., 2010) could alter spike timing and thus their effect, especially in relationship to the effect of varying AIS properties, will need to be further investigated, including the possibility that the effects are different for ON vs. OFF sub-types.

#### α S RGC Properties Influence the Sensitivity to Artificial Stimulation

Our findings may help to improve strategies for selective targeting of specific RGC types with electric stimulation, e.g., for use in basic research studies or as part of a retinal prosthesis. Previous studies have shown that the AIS is the portion of the RGC that is most sensitive to electric stimulation (Sekirnjak et al., 2008; Fried et al., 2009) and further, that differences in AIS properties can influence sensitivity (Jeng et al., 2011). Thus, our findings that show that at any given retinal eccentricity ON-α S RGCs are slightly larger than OFF-α S RGCs (**Supplementary Figure S2**), including the fact that the AIS is longer and more distant from the soma in ON cells (**Figure 2B**), coupled with previous work that found that increases to both AIS length and distance reduce activation threshold in response to electrical stimulation (Jeng et al., 2011), suggests that at any given location ON cells have a slightly lower threshold than do OFF cells. This is important as the ability to selectively target ON vs. OFF pathways would allow natural signaling patterns to be

more accurately reproduced with electric stimulation and thus might lead to better quality percepts (Freeman et al., 2011; Werginz et al., 2015; Weiland et al., 2016). Interestingly, previous studies have reported that ON and OFF cells have similar thresholds to electric stimulation (Fried et al., 2009; Tsai et al., 2012), but such studies did not carefully account for comparisons at similar eccentricities.

Note that the ability to capitalize on these small differences in sensitivity will require knowledge of the precise location of each AIS as well as the ability to selectively target each from a nearby electrode; this could be accomplished, for example, with high-density arrays of electrodes along with detailed measurements of the responses from the array (Jepson et al., 2014). Developing strategies that are clinically relevant will also require confirmation that the AIS size differences found here in mouse α S RGCs persist in human RGCs. This may be the case however as it has already been established that ON midget and parasol cells in the human retina have larger somas and dendritic fields, raising the possibility that the AIS scaling found here will persist there as well.

The AIS size difference for ON vs. OFF RGCs could also explain earlier findings in which more complex patterns of electric stimulation were able to differentially activate the two populations (Cai et al., 2013; Twyford et al., 2014). While the mechanism underlying differential sensitivity of the two types has yet to be unequivocally identified (but see Kameneva et al., 2016; Guo et al., 2019), the sensitivity differences between ON and OFF cells persist in the presence of synaptic blockers, suggesting that the differences arise from features intrinsic to the two cell types, most likely within the AIS themselves. The improved understanding of the AIS anatomy found here may lead to a better understanding of the mechanism underlying preferential selectivity and may also help to identify stimulation paradigms that provide even higher levels of selectivity.

#### DATA AVAILABILITY STATEMENT

The raw datasets generated for this study are available on request to the corresponding author.

#### REFERENCES


#### ETHICS STATEMENT

The animal study was reviewed and approved by Institutional Animal Care and Use Committee (IACUC) of the Massachusetts General Hospital.

#### AUTHOR CONTRIBUTIONS

VR, PW, and SF conceived the study, analyzed the results, wrote the manuscript, and prepared the figures. VR performed the immunochemistry and confocal imaging experiments. PW performed the electrophysiology experiments and computational modeling.

## FUNDING

Research was supported by the Veterans Administration - Rehabilitation Research and Development Service (1I01RX001663), by the National Institute of Neurological Disorders and Stroke (U01-NS099700 and R01-NS110575), and by the Austrian Science Fund (FWF J3947).

## ACKNOWLEDGMENTS

We would like to thank Steve Massey (UT Houston) for help with immunohistochemistry, Molly McGoldrick (Boston College) for assistance with immunohistochemistry experiments, and Aditya Datye (MGH) and Hannah Potter (UMass Amherst) for assistance with image processing and analysis. We would also like to thank Russell Huber (Boston University, VA Boston), Tim McKenna (Harvard University, VA Boston) for their assistance with confocal imaging, and Brian Timko (Tufts University) for helpful discussions during the preparation of the manuscript.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00436/full#supplementary-material




**Conflict of Interest:** 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 © 2019 Raghuram, Werginz and Fried. 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(s) 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.

# Impact of Auditory Experience on the Structural Plasticity of the AIS in the Mouse Brainstem Throughout the Lifespan

#### Eun Jung Kim<sup>1</sup> , Chenling Feng<sup>2</sup> , Fidel Santamaria<sup>2</sup> and Jun Hee Kim<sup>1</sup> \*

<sup>1</sup> The Department of Cellular and Integrative Physiology, UT Health San Antonio, San Antonio, TX, United States, <sup>2</sup> The Department of Biology, University of Texas, San Antonio, TX, United States

Sound input critically influences the development and maintenance of neuronal circuits in the mammalian brain throughout life. We investigate the structural and functional plasticity of auditory neurons in response to various auditory experiences during development, adulthood, and aging. Using electrophysiology, computer simulation, and immunohistochemistry, we study the structural plasticity of the axon initial segment (AIS) in the medial nucleus of the trapezoid body (MNTB) from the auditory brainstem of the mice (either sex), in different ages and auditory environments. The structure and spatial location of the AIS of MNTB neurons depend on their functional topographic location along the tonotopic axis, aligning high- to low-frequency sound-responding neurons (HF or LF neurons). HF neurons dramatically undergo structural remodeling of the AIS throughout life. The AIS progressively shortens during development, is stabilized in adulthood, and becomes longer in aging. Sound inputs are critically associated with setting and maintaining AIS plasticity and tonotopy at various ages. Sound stimulation increases the excitability of auditory neurons. Computer simulation shows that modification of the AIS length, location, and diameter can affect firing properties of MNTB neurons in the developing brainstem. The adaptive capability of axonal structure in response to various auditory experiences at different ages suggests that sound input is important for the development and maintenance of the structural and functional properties of the auditory brain throughout life.

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des canaux Ioniques et de la Synapse, France

#### Reviewed by:

Maren Engelhardt, University of Heidelberg, Germany Claire Cheetham, University of Pittsburgh, United States Matthews Grubb, King's College London, United Kingdom

> \*Correspondence: Jun Hee Kim kimjh@uthscsa.edu

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 24 May 2019 Accepted: 25 September 2019 Published: 15 October 2019

#### Citation:

Kim EJ, Feng C, Santamaria F and Kim JH (2019) Impact of Auditory Experience on the Structural Plasticity of the AIS in the Mouse Brainstem Throughout the Lifespan. Front. Cell. Neurosci. 13:456. doi: 10.3389/fncel.2019.00456 Keywords: axon initial segment, auditory brainstem, MNTB, auditory experience, mouse

## INTRODUCTION

Continuous auditory input is necessary for the proper development and maintenance of the auditory system. Peripheral hearing deficits can occur during development (congenital deafness) and through aging (presbycusis), lead to reduced auditory input, and generate a reorganization of central auditory circuits (Butler and Lomber, 2013; Lin et al., 2014). Alterations in the structure and function of the central auditory system impair auditory processing even after peripheral sound sensitivity is restored, such as with hearing aids (Sweetow, 2005; Atcherson et al., 2015). To restore proper circuit processing, it is essential to understand how sound-evoked activity refines and modulates the structural plasticity, and thereby the functional connectivity of the central auditory system. In animal models,

sound deprivation in congenital deafness or by surgical ablation of the cochlea resulted in anatomical and functional changes in subcortical nuclei (Russell and Moore, 1995; Grande et al., 2014). In the auditory brainstem, congenital deafness is associated with a reduction in the number and size of neurons in the cochlear nucleus (Hashisaki and Rubel, 1989; Saada et al., 1996), decreased inhibitory inputs on medial superior olivary neurons (Kapfer et al., 2002; Tirko and Ryugo, 2012), and disruption of the tonotopic organization in the MNTB (von Hehn et al., 2004; Leao et al., 2006). Although the structural consequences of congenital and early-onset deafness have been studied in several animal models, the physiological consequences or homeostatic adaptation processes in the central auditory system in response to sound experiences throughout life are not yet determined.

As the key axonal domain for generating action potentials (APs), the AIS determines neuronal excitability, modulates neuronal output, and controls auditory processing along the ascending auditory pathway (Kuba et al., 2006; Gründemann and Häusser, 2010). In the chick brainstem, structural properties of the AIS depend on its tonotopic location - the spatial arrangement of where sounds of different frequencies are processed in the brain (Kuba et al., 2006, 2014). The AIS of chick neurons elongates to increase excitability when synaptic inputs are removed by cochlear ablation, suggesting a contribution of the AIS to the homeostatic control of neural activity (Kuba, 2012). In cultured hippocampal neurons, the AIS is located farther from the soma when neuronal activity is increased (Grubb and Burrone, 2010). When the AIS is located proximal to the soma, APs are easier to initiate, thus increasing neuronal excitability, whereas a more distal location reduces neuronal excitability (Grubb and Burrone, 2010; Kole and Stuart, 2012). Thus, adaptive changes in AIS structure and position have been thought to alter intrinsic excitability in a homeostatic direction (Kole and Stuart, 2012; Wefelmeyer et al., 2016). However, depending on somatodendritic morphology in various neurons, the distal shift of the AIS location theoretically reduces the threshold and rheobase of AP and promotes AP generation (Gulledge and Bravo, 2016; Kole and Brette, 2018). Importantly, the structural properties and plasticity of the AIS vary among individual neurons across brain regions (Chand et al., 2015; Höfflin et al., 2017). Although the structural plasticity of the AIS has been studied in the chick brainstem, concerning the heterogeneity of AIS structure across species, it is important to explore AIS plasticity in response to auditory input within a mammalian system. Understanding how in vivo auditory experience alters the AIS of auditory neurons throughout the lifespan of the mammalian brain from development to aging is critically important for developing targeted strategies to remedy potential long-term deficits of the auditory brain at specific ages.

Here, we investigated the spatial distribution and location of the AIS in the mouse auditory brainstem at different ages, focusing on AIS length, position, and tonotopic differentiation. Sound modifications alter the structural properties of AIS and affect tonotopy in the auditory brainstem. Electrophysiological and computer modeling studies indicate that there is a relationship between AIS structural plasticity and neuronal excitability in the MNTB. The results demonstrate that structural plasticity of the AIS in auditory neurons is influenced by soundevoked activity.

#### MATERIALS AND METHODS

#### Animals

Either sex of C57BL/6 mice and whirler mice with a C57BL/6 background were used in accordance with the guidelines approved by the University of Texas Health Science Center, San Antonio (UTHSCSA) Institutional Animal Care and Use Committee protocols. All mice were housed in the institutional animal facilities on a 12-h light/dark cycle.

## Sound Modification in Mice

Mice in the sound stimulation group were given acoustic stimulation with 80dB single tones of 16 kHz for 7 days, 3 h per day from P13 to P19 (in postnatal development) or from P38 to P44 (in early adulthood) in a sound attenuation chamber (Med Associates, Albans, VT). Acoustic stimuli were generated by an auditory evoked potentials workstation [Tucker-Davis Technologies (TDT), Alachua, FL]. The signals consisted of a series of amplitude-modulated square waves (duration 0.1 ms, repeat rate 16/s) through TDT multifield magnetic speakers. Whirler mice, a model of congenital deafness (Xu et al., 2017), were used for the sound deprivation model and were provided by Dr. M. A. Bhat's laboratory (UTHSCSA). As a model of hearing loss during adulthood, mice (at P70) were exposed to highpressure air (13 psi shock wave, ∼183 dB) generated by a large (17-inch diameter) compressed-air shock tube (Cho et al., 2013; Choi et al., 2015). ABR test and immunostaining were performed in 1 week after the blast exposure (at P80).

#### Slice Preparation

After rapid decapitation, the brains were quickly removed from the skull and immediately immersed in ice-cold low-calcium artificial cerebrospinal fluid (aCSF) containing (in mM): 125 NaCl, 2.5 KCl, 3 MgCl2, 0.1 CaCl2, 25 glucose, 25 NaHCO3, 1.25 NaH2PO4, pH 7.3–7.4 bubbled with carbogen (95% O2, 5% CO2; osmolarity of 310–320 mOsm). For c-fos staining, animal was sacrificed within 1 h after sound stimulation. Then, transverse 200-µm-thick brainstem slices containing the MNTB were collected using a Vibratome (VT1200S, Leica, Germany). Collected slices were prepared for electrophysiology or immunohistochemistry experiments.

#### Electrophysiology

After vibratome sectioning, slices were further incubated in a chamber containing normal aCSF bubbled with carbogen at 35◦C for 30 min and then were kept at room temperature. The normal aCSF was the same as the low-calcium aCSF, except that 3 mM MgCl2 and 0.1 mM CaCl2 were replaced with 1 mM MgCl2 and 2 mM CaCl2. Whole-cell patch-clamp recording was carried out on postsynaptic principal neurons in the MNTB nuclei at room temperature (∼24◦C). Action potentials (APs) were recorded in normal aCSF using the voltage or current-clamp mode of the EPC-10 (HEKA Electronik, Lambrecht/Pfalz, Germany). The

pipettes were filled with an internal solution containing (in mM) 125 K-gluconate, 20 KCl, 5 Na2-phosphocreatine, 10 HEPES, 4 Mg-ATP, 0.2 EGTA, and 0.3 GTP, pH adjusted to 7.3 with KOH. The holding potential was −70 mV in the voltage-clamp mode. Current-clamp protocols were 200 ms in duration with current steps from −50 to 250 pA (50 pA increments). Patch electrodes had resistances of 4–5 M . Series resistance was < 20 M , with 80% compensation. In our solution composition (extracellular K <sup>+</sup> concentration of 2.5 mM and intracellular K<sup>+</sup> concentration of 150 mM), the calculated equilibrium potential for potassium is around −106 mV, and liquid junction potential is ∼20 mV. Membrane potentials were not corrected for this constant liquid junction potential between the extracellular and pipette solution. In the current clamp recordings, the baseline potential was around −70 mV with ∼ −20 pA injection, and the amplitude of action potential was defined as the potential between the baseline potential to the peak. The threshold of action potential (AP) was determined by the point where dV/dt exceeds 10V/s and the amplitude of AP from this threshold to the AP peak in the plot of dV/dt and voltage. Data were analyzed and displayed with Igor Pro (Wavemetrics, Lake Oswego, OR, United States).

#### Immunohistochemistry

Brainstem slices were fixed with 4% (w/v) paraformaldehyde in phosphate-buffered saline (PBS) for 20 min and were washed with PBS three times. Free-floating slices were blocked in 4% goat serum and 0.3% (w/v) Triton X-100, 0.1% Tween 20 in PBS for a 1 h and then were incubated with primary antibody overnight at 4◦C. The following primary antibodies were used: rabbit anti β4 spectrin (1:250) as previously described (Saifetiarova et al., 2018), mouse monoclonal anti-MAP2 (1:200; Millipore Cat# MAB3418, RRID:AB94856), mouse monoclonal anti-ankyrinG (AnkG; 1:100; UC Davis/NIH NeuroMab Facility Cat# 75-146, RRID:AB\_10673030), mouse monoclonal anti-Kv1.2 (1:250; UC Davis/NIH NeuroMab Facility Cat# 75-008, RRID:AB\_10673030), mouse monoclonal anti-Na-pan (1:100; Sigma-Aldrich Cat# S8809, RRID:AB\_10673030), and rabbit polyclonal anti-c-Fos (1:100; Synaptic System Cat# 226003). After 3 washes with PBS containing 0.1% Tween 20, slices were incubated with different Alexa-488 goat anti-mouse IgG1 or 568 goat anti-mouse IgG2b or 568 goat anti-rabbit or 647 goat antiguinea pig secondary antibodies (1:1000; Invitrogen) accordingly for 2 h at room temperature. Slices were then rinsed with PBS containing 0.1% Tween 20 and were coverslipped using the mounting medium (Vectashield; Vector Laboratories). Stained slices were viewed on a confocal laser-scanning microscope (Carl Zeiss LSM-710) at 488, 568, and 633 nm using a pinhole of 1 AU and 20x (0.8 NA), 40x (oil-immersion, 1.30 NA) objectives. Z-stack images were acquired at a digital size of 1,024 × 1,024 pixels with optical section separation (z interval) of 0.5 um. The images were imported into Fiji (Image J, Schindelin et al., 2012), ZEN (Carl Zeiss) and Amira software (FEI, Netherlands) for the analysis. To analyze AIS structure, either the 2D compressed or the 3D reconstructed Z-stack confocal images of MNTB neurons were utilized. Most analyses were performed using the 2D compressed images because there was no significant difference between the results from the 2D- and 3D- analysis (the AIS from normal mice, 16.89 ± 0.245, n = 18 for 2D vs. 17.17 ± 0.36, n = 18 for 3D, p = 0.5245). The AIS was determined as the axonal domain where the fluorescence intensity of β4 spectrin was > 10% of the peak signal. We did not perform background subtraction of images, because the signal of β4 spectrin is very specific to axonal domains including the AIS. For the analysis of AIS structure, we utilized a line profile of AIS from the end of distal edge of the AIS, which was defined by a paranodal protein, caspr, to the end of the proximal edge of the AIS, where the signal of β4 spectrin was < 10% of the peak signal. 3D image (Amira) confirmed the AIS structure including length, volume, and diameter obtained from 2D images by Fiji or ZEN software. For analyzing the AIS with a strong curvature, we utilized the segmental line profile in the ImageJ. For c-fos analysis, the double staining against MAP2 and c-Fos were performed from normal hearing group (P20) and sound stimulation group (P20) simultaneously to exclude the difference of fluorescence intensity. MAP2- and c-fos-positive cells were counted using cell counter plugin of Fiji software. Only the cells with c-fos-positive nucleus were counted and the constant threshold level of fluorescence intensity was used in each slices. The percentage of c-fos-positive cells were calculated by dividing the number of MAP2 -positive MNTB neurons in each slices.

#### In vivo Auditory Brain Stem Response (ABR) Test

ABR recordings were conducted as described previously (Kim et al., 2013). Briefly, mice were anesthetized with 4% isoflurane and maintained with 2% isoflurane during recording (1 l/min O2 flow rate). During ABR recordings, the body temperature was maintained between 35 and 37◦C using a non-electric heating pad and equally controlled in different experimental groups. ABR recordings were performed in a sound attenuation chamber (Med Associates, Albans, VT). Subdermal needle electrodes (Rochester Electro-Medical, Lutz, FL, United States) were placed on the top of the head, ipsilateral mastoid, and contralateral mastoid as the active, reference, and ground electrodes, respectively. The signal differences in the ABRs between the vertex and the mastoid electrodes were amplified and filtered (100–5,000 Hz). Acoustic stimuli were generated by an auditory evoked potentials workstation [Tucker-Davis Technologies (TDT), Alachua, FL, United States]. Closed-field click stimuli were presented to the left ear. The signals consisted of a series of amplitudemodulated square waves (duration 0.1 ms, repeat rate 16/s) through TDT multifield magnetic speakers. The sound stimuli were delivered through a 10-cm plastic tube (Tygon; 3.2-mm outer diameter) at a repeat rate of 16/s. Sound intensities ranged from 90 to 20 dB, with 5-dB decrements, and responses to 512 sweeps were averaged.

#### Computer Simulation

A compartmental model of an MNTB cell was implemented based on previous publications (Leão et al., 2008; Wang et al., 1998). The structure of the cell consisted of one primary dendrite with a length of 40 µm and a uniform diameter of 3 µm. The dendrite was connected to a spherical soma with a diameter of 30 µm. The axonal segment was divided between the hillock and the initial segment (AIS), both with a diameter of 2 µm. The length of the hillock was 16 µm and the length of the AIS was 13 µm (**Figure 3**). The model had active conductance. The density and kinetics are described in the following **Tables 1**, **2**.

Simulations consisted of injecting constant current to the soma and quantifying the shape and number of spikes generated over a period of 700 ms. The model was implemented in Python-NEURON (ver 7.3) and analyzed with custom routines in Matlab (Mathworks, Natick, MA, United States).

#### Statistical Analysis

fncel-13-00456 October 14, 2019 Time: 15:14 # 4

All statistical analyses were performed in Prism (GraphPad Software). Normality of datasets was analyzed using the D'Agostino and Pearson's omnibus test. Parametric or nonparametric tests were carried out accordingly. α values were set to 0.05, and all comparisons were two-tailed. To compare two groups, unpaired t-test or Mann–Whitney U test was carried out, respectively. For three or more groups, the Kruskal–Wallis test with Dunn's post hoc test or one-way ANOVA with Turkey's multiple comparison test was used. For the comparison of the AIS of HF and LF MNTB neurons from three groups, we analyzed the mean value from individual animal as the experimental unit, and utilized 2-way ANOVA with Sidak's multiple comparison test. The significance was determined at P-values < 0.05. To analyze the tonotopy of AIS structure, we analyzed the mean value from individual animal as the experimental unit using 2 way ANOVA with Sidak's multiple comparison test. Data were shown as the mean ± standard error of the mean (s.e.m.) with n values representing the number of animals per experimental group or the number of neurons per group where indicated.


TABLE 2 | Kinetics of active conductance.


In box and whisker plot, boxes indicate 25–75% interquartile range and horizontal lines in boxes indicate the median. Whiskers show 5% ∼ 95% range and dots show outliers that reside outside the whisker range.

## RESULTS

#### The AIS of Auditory Neurons Are Differentiated by Structure and Function Along the Tonotopic Axis in the Mouse MNTB

We characterized structural properties of the AIS in the mouse MNTB (P20) using β4 spectrin immunostaining, which was present along the AIS and co-localized with ankyrin G, represented the AIS of MNTB neurons (**Figure 1A**). β4 spectrin was also co-localized with voltage-activated Na<sup>+</sup> and K <sup>+</sup> channels at the AIS of MNTB neurons (**Figure 1B**). To analyze AIS structure, either the 2D compressed or the 3D reconstructed Z-stack confocal images of MNTB neurons were utilized (**Figure 1C**). We selected the AIS with the distinct distal end, which was defined by a paradonal protein, Caspr (Xu et al., 2017), and with the proximal end, where β4 spectrin intensity was < 10% of the peak intensity, for the analysis of AIS structure (**Figure 1D**). To quantify AIS length and position, we measured the length of the region, where the intensity of β4 spectrin was > 10% of the peak signal, and the distance from soma to the proximal end of the AIS (**Figures 1E,F**).

To quantify AIS length and location along the medial-lateral axis in the MNTB from individual mouse brainstems (n = 6 mice at P20), the MNTB was proportionally defined by the percent of the total distance from medial to lateral edges of the MNTB, where 0% represents the medial edge and 100% represents the lateral edge (**Figure 2A**). High-frequency sound responding neurons (HF neurons) were defined as neurons located within 0–30% of the total distance from medial to lateral edges, and low-frequency responding neurons (LF neurons) were defined as neurons located within 70–100% of the distance from the medial to the lateral edge (**Figures 2A,B**). AIS length was gradually increased from medial to lateral MNTB neurons. Plotting AIS length against the proportional distance showed the distribution of AIS length as estimated by linear regression analysis (R <sup>2</sup> = 0.293, n = 24 cells, p = 0.0063; **Figure 2C**). AIS length was significantly shorter in HF neurons than LF neurons. AIS length in HF and LF neurons was 15.1 ± 0.23 µm (n = 79 cells) and 19.9 ± 0.37 µm (n = 64 cells), respectively (p < 0.0001, Mann–Whitney U test; **Figure 2D**). The spatial location of the AIS was quantified by the distance between the proximal end of the AIS and the soma, which was gradually decreased along the medial-lateral axis with a linear correlation (R <sup>2</sup> = 0.342, n = 22 cells, p = 0.0042; **Figure 2E**). The AIS of HF neurons were located more distally from the soma than the AIS of LF neurons, which were located proximal to the soma. Thus, AIS distance was significantly longer in HF than LF neurons (10.4 ± 0.34 µm, n = 63 cells in HF neurons vs. 6.2 ± 0.24 µm, n = 74 cells in LF neurons, p < 0.0001, Mann–Whitney U-test; **Figure 2F**).

images (left) and 3D reconstructed Z-stack images using Zen (middle) and Amir (right) of the same MNTB neuron immunostained with MAP2, β4 spectrin. Yellow arrows indicate AIS length. (D) Immunostaining of the MNTB with β4 spectrin and caspr. White arrows indicate the AIS proximal and distal ends. Capsr (magenta, yellow arrows) was located at the next of the AIS distal end. (E) (Top) Diagram of the MNTB neuron with soma (green), AIS (cyan), and paranode (magenta) shows the AIS length and distance from the soma. (Bottom) MNTB neurons immunotained with MAP2 (green), β4 spectrin (magenta) and caspr (cyan). A dotted line indicates the length (L, white) and distance (D, yellow) of AIS structure. (F) The intensity profiles of β4 spectrin (magenta) and caspr (cyan) immunostaining along the AIS of MNTB neuron indicated by length and distance in E.

To examine how structural differentiation of the AIS along the tonotopic map influences intrinsic properties of MNTB neurons, we recorded action potentials from HF (n = 11 cells from 5 mice) and LF neurons (n = 7 cells from 3 mice), which were evoked by step-current injections in whole-cell recording (**Figure 2G**). There was no difference in the threshold and half-width of APs, and the rheobase current (threshold: -45.3 ± 2.53 mV in HF neurons vs. -48.3 ± 0.74 mV in LF neurons, p = 0.3189; halfwidth: 0.5 ± 0.04 ms in HF neurons vs. 0.5 ± 0.03 ms in LF neurons, p = 0.8917, the rheobase current: 106.5 ± 11.47 pA in HF neurons vs. 107.1 ± 27.66 pA in LF neurons, p = 0.8573, Mann–Whitney U test; **Figures 2H–J**). However, HF neurons displayed smaller APs with amplitudes of 94.1 ± 2.66 mV (n = 10 cells), while APs from LF neurons had larger amplitudes of 102.8 ± 1.12 mV (n = 7 cells, p = 0.0250, Mann–Whitney U-test; **Figure 2K**). Taken together, HF neurons with a shorter AIS distally located from the soma displayed a smaller AP, whereas LF neurons with a longer AIS proximally located from the soma exhibited a larger AP in the MNTB. This indicates that MNTB neurons have structural and functional differentiation of the AIS along the tonotopic axis, which is associated with differentiation of their firing properties.

### AIS Tonotopy Is Initiated After Hearing Onset, Progressively Developed, and Stabilized in Adulthood

In hearing mammals, a rough tonotopy is established before hearing onset, then later refined by sound-evoked activity, generating the sophisticated tonotopy of the mature

system (Kandler et al., 2009). To determine when tonotopic differentiation of AIS structure initiates in the mouse auditory brainstem, we examined AIS length and location throughout postnatal development into early adulthood (P9: n = 4 mice, P16: n = 3 mice, P40: 4 mice, P60: 3 mice and P80: 4 mice). At P9 (before hearing onset at P12), the AIS was distinctly detectable and its length was similar in HF and LF neurons (20.2 ± 0.40 mm, n = 61 cells in HF neurons vs. 20.1 ± 0.39 mm, n = 47 cells in LF neurons, p = 0.8867, Mann–Whitney U test; **Figures 3A,B**). The AIS from both groups was closely located to the soma, and the distance between the proximal end and the soma was 3.8 ± 0.24 mm (n = 61 cells) in HF neurons and 4.7 ± 0.37 mm (n = 45 cells) in LF neurons (p = 0.0505, Mann–Whitney U test; **Figures 3A,C**). There was no significant difference in AIS length and location between HF and LF neurons at P9. At P16 after hearing onset, a significant difference in AIS length and location between HF and LF neurons was observed. The AIS of HF neurons was significantly shorter than the AIS of LF neurons (16.3 ± 0.30 mm, n = 84 cells in HF neurons vs. 20.2 ± 0.58 mm, n = 59 cells in LF neurons, p < 0.0001, unpaired t-test; **Figures 3A,B**). In parallel with changes in length, the AIS of HF neurons moved further away from the soma during postnatal development, resulting in a significant difference between HF and LF neurons in the distance

Kim et al. Structural Plasticity of the AIS

of the AIS from the soma at P16 (10.69 ± 0.64 mm, n = 44 cells in HF neurons vs. 6.9 ± 0.31 mm, n = 33 cells in LF neurons, p < 0.0001, unpaired t-test; **Figures 3A,C**). The refinement of AIS length and location was progressively enhanced through P40 and stabilized in adulthood at P80. Notably, the progressive shortening of the AIS occurred specifically in HF neurons during postnatal development. The AIS of HF neurons was shortened by ∼29.30% by P40 (from P9 to P40, p < 0.001, Kruskal–Wallis test with Dunn's post hoc test; **Figure 3D**). However, there was no significant change in the AIS length of LF neurons, which maintained AIS length throughout adulthood from when the AIS began to be detected at an early postnatal age (from p9 to P80, p = 0.2264, Kruskal–Wallis test with Dunn's post hoc test; **Figure 3D**). The AIS of both HF and LF neurons were relocated more distally from the soma during postnatal development and maintained their spatial distance from the soma in adulthood (HF neurons from P9 to P40, p < 0.0001 and LF neurons from P9 to P40, p < 0.001, Kruskal–Wallis test with Dunn's post hoc test; **Figure 3E**). However, the distance of the AIS from the soma was much longer in HF neurons than LF neurons, thus resulting in the tonotopic difference of AIS location in the MNTB. The AIS of HF neurons was located distally, whereas the LF neuron AIS was located closer to the soma. The refinement of AIS length and location progressively developed in postnatal ages. Around P40, AIS length and distance reached a plateau and then stabilized in adulthood, maintaining tonotopic differentiation. The AIS of HF neurons preferentially and dynamically underwent developmental refinement, resulting in the tonotopy of the AIS in the auditory brainstem.

## Sound Modification During Early Postnatal Development Influences AIS Length, Location, and Tonotopic Differentiation

The structural refinement of the AIS was initiated and progressively developed after hearing onset. To determine whether in vivo auditory experience contributes to the initiation and development of structural plasticity and tonotopy of the AIS in the auditory nervous system, we tested the effects of sound deprivation or stimulation on AIS plasticity in the MNTB neurons compared to the age-matched normal hearing mice during postnatal development. As a model of sound deprivation, we utilized a mouse with congenital deafness (hereafter, Deaf) caused by a stereocilia defect due to a mutation of whirlin (DFNB3, Lane, 1963; Xu et al., 2017). For mild sound stimulation, we established a mouse model (hereafter, Sound) exposed to additional sound inputs (80 dB, 16kHz, 3 h./day for 7 days) immediately after hearing onset from P13 to P19, which were chosen to determine whether early sound exposure sped developmental changes in MNTB neurons. We utilized 16 kHz tone sound to target HF neurons and determine if the AIS length during development would be altered by sound experience, because HF neurons displayed a change in AIS length during development. In vivo ABRs (n = 11 mice in Normal, n = 12 mice in Sound) and c-fos staining of the MNTB (n = 3 mice for each group) indicated that neuronal activity was significantly increased in the MNTB of the auditory brainstem in the Sound. The amplitude of ABRs was significantly increased in the Sound (wave I: 0.8 ± 0.13 mV in normal mice vs. 1.8 ± 0.13 mV in Sound, p = 0.0003; wave II: 1.3 ± 0.15 mV in Normal vs. 2.6 ± 0.35 mV in Sound, p = 0.0047; wave III: 0.7 ± 0.24 mV in Normal vs. 2.4 ± 0.42 mV in Sound, p = 0.0052, unpaired t-test; **Figures 4A–C**). In the Sound, the number of c-fos + cells was significantly increased (31.7 ± 3.55% in Normal vs. 90.1 ± 3.83% in Sound, p = 0.0286, unpaired t-test; **Figure 4C**). Sound deprivation and stimulation significantly altered AIS length and location in HF neurons (**Figures 4D,E**). Compared to mice in a normal auditory environment (n = 6 mice), AIS length was significantly longer as a result of sound deprivation in the Deaf (n = 5 mice), whereas AIS length was significantly shorter in the Sound (n = 8 mice) compared to the Normal (21.5 ± 0.52 mm, n = 67 cells in Deaf vs. 15.1 ± 0.23 mm, n = 79 cells in Normal vs. 13.4 ± 0.20 mm, n = 94 cells in Sound, p < 0.0001, oneway ANOVA with Turkey's multiple comparison test; **Figure 4F**). In the developmental time course of AIS length (as shown in **Figure 3D**), sound deprivation seemed to inhibit the shortening of AIS, while sound stimulation enhanced the shortening of AIS specifically in HF neurons (**Figure 4G**). However, LF neurons did not exhibit any changes in AIS length in response to either sound deprivation or stimulation (20.9 ± 0.57 mm, n = 50 cells in Deaf vs. 19.9 ± 0.37 mm, n = 64 cells in Normal vs. 19.7 ± 0.34 mm, n = 54 cells in Sound, p = 0.3188, Kruskal–Wallis with Dunn's post hoc test; **Figure 4H**). The AIS structural plasticity of the HF neurons to sound inputs consequently influenced the tonotopic differentiation of AIS length. The analysis of AIS length of HF and LF neurons using animal as the experimental unit indicated the MNTB did not display the tonotopic differentiation of AIS length in Deaf (n = 5 mice), whereas in Sound, the tonotopy of AIS length was enhanced (n = 8 mice, 2-way ANOVA with Sidak's multiple comparison test).

In terms of AIS location, the AIS of HF neurons in the Deaf and the Sound were significantly different from the Normal (13.7 ± 0.71 mm, n = 54 cells in Deaf vs. 10.4 ± 0.34 mm, n = 63 cells in Normal vs. 5.9 ± 0.23 mm, n = 57 cells in Sound, p < 0.001, Kruskal–Wallis test with Dunn's post hoc test; **Figure 4I**). The AIS in Deaf mice is more distally located from the soma compared to those in the Normal. However, in the Sound, the location of the AIS was more proximal to the soma. This proximal shift of the AIS position resulted in an increase in the spatial distance between the proximal edge of AIS and the soma in the Deaf, whereas there was a significant decrease in this distance in the Sound compared to the normal age-matched mice (as shown in **Figure 3E**) in the natural auditory environment (**Figure 4J**). AIS distance was increased in LF neurons of the Deaf, but no significant change was observed in the Sound (6.2 ± 0.24 mm, n = 74 in Normal vs. either 10.1 ± 0.51 mm, n = 43 cells in Deaf, p < 0.001, or 6.6 ± 0.38 mm, n = 67 cells in Sound, p > 0.05, Kruskal–Wallis test with Dunn's post hoc test; **Figure 4K**). In the analysis of AIS location of HF and LF neurons using animal as the experimental unit, there was no tonotopic differentiation of AIS location in the Sound whereas in Deaf the tonotopy of AIS location

FIGURE 4 | Sound deprivation and stimulation impact developmental refinement of AIS structure, position, and tonotopy in the MNTB. (A) Examples of the ABRs of normal (black) and sound stimulated mice (blue) are recorded in response to a click stimulus of sound (80 and 85 dB). Roman numerals indicate peak waves I to IV (B) Summary of the amplitude of waves I to III in response to click stimulus (85 dB) in normal and sound stimulated mice at P20. ∗∗p < 0.01, unpaired t-test. (C) Immunostaining of the MNTB with c-fos and MAP2 from normal and sound stimulated mouse with the tonotopic axis (M: medial MNTB, L: lateral MNTB). Note, the number of c-fos positive cells is increased in the MNTB of the sound stimulation group. (D) HF neurons, immunostained with MAP2 and β4 spectrin from deaf mice (Deaf), age-matched normal hearing mice (Normal), and sound stimulation group (Sound). The dotted line and white arrow indicate AIS length and distance, respectively. (E) Diagram of AIS length and location in HF neurons from Deaf (red), Normal (black), and Sound (blue). (F) Summary of AIS length in HF neurons from Deaf, Normal, and Sound at P20. ∗∗∗p < 0.0001, one-way ANOVA with Turkey's multiple comparison test. (G) The plot of AIS length of HF neurons from normal mice from P9 to P80 (black, as shown in Figure 3D), and those from Deaf and Sound at P20. (H) Tonotopic differentiation of AIS length between HF and LF neurons in Deaf, Normal, and Sound. ∗∗∗p < 0.0001, Mann–Whitney U test for HF and LF neurons; ns, non-significant, Kruskal–Wallis with Dunn's post hoc test for AIS length of LF neurons from Deaf, Normal, and Sound. (I) Summary of AIS location, as defined by the distance from the soma, of HF neurons in Deaf, Normal, and Sound at P20. ∗∗∗p < 0.001, Kruskal–Wallis with Dunn's post hoc test. (J) The plot of AIS location changes during postnatal development in normal mice from P9 to P80 (black, as shown in Figure 3E), and those in Deaf and Sound at P20. (K) Tonotopic differentiation of AIS location between HF and LF neurons in Deaf, Normal, and Sound at P20. ∗∗∗p < 0.0001, either Mann–Whitney U test or unpaired t-test for HF and LF neurons, Kruskal–Wallis test with Dunn's post hoc test for AIS distance of LF neurons from Deaf, Normal, and Sound.

existed (n = 8 mice vs. n = 6 mice for Normal, and n = 5 mice for Deaf groups, 2-way ANOVA with Sidak's multiple comparison test). These results indicate that excessively altered sound inputs in different auditory environments critically impact AIS structure, location, and tonotopy in the mouse auditory brainstem during development.

## After the Stabilization of AIS Structure in Adulthood, Alteration of Sound Input Disrupts the Structural and Spatial Stability of the AIS Tonotopy

We next questioned whether auditory neurons maintained structural plasticity of the AIS following changes in the auditory environment in adulthood, even after AIS length, location, and tonotopy are stabilized. We tested adult mice (4 mice per each group) that experienced sudden hearing loss after blast exposure (Choi et al., 2015, see in method section) and those that experienced additional mild sound stimulation for a week (16kHz, 3 h/day, for 7 days). The AIS of HF neurons was significantly elongated in adult mice that experienced hearing loss (at P80), comparing to age-matched normal mice. Interestingly, there was no alteration in AIS length in the Sound (14.2 ± 0.30 mm, n = 66 cells in the Normal vs. either 19.0 ± 3.53 mm, n = 64 cells in hearing loss, p < 0.001 or 14.1 ± 0.34 mm, n = 57 cells in Sound, p > 0.05, Kruskal– Wallis test with Dunn's post hoc test; **Figures 5A,B**). In the developmental plot of AIS length (as shown in **Figure 3D**), the length at around P40 reached a steady state of ∼15 mm, which could be the maximum shortening of AIS during development (**Figure 5C**). Thus, further mild sound stimulation cannot enhance the shortening of the AIS beyond this plateau of AIS length after development. Consistent with the results seen in postnatal development, AIS length in LF neurons was not affected by either hearing loss or the Sound in adulthood (20.8 ± 0.41 mm, n = 55 cells in hearing loss vs. 19.7 ± 0.43 mm, n = 57 cells in Normal vs. 20.4 ± 0.42 mm, n = 56 cells in Sound; p = 0.2092, Kruskal–Wallis test with Dunn's post hoc test; **Figure 5D**). Thus, elongated AIS specifically in HF neurons in the hearing loss model resulted in the loss of tonotopic segregation of AIS length in the MNTB (n = 4 mice for each group, 2-way ANOVA with Sidak's multiple comparison test; **Figure 5D**).

AIS location of HF neurons in the hearing loss model was not changed, whereas the AIS was relocated close to the soma in the Sound, compared to the Normal (12.3 ± 0.62 mm, n = 40 cells in the Normal vs. either 10.6 ± 0.57 mm, n = 53 cells in hearing loss, p > 0.05 or 6.1 ± 0.32 mm, n = 37 cells in the Sound, p < 0.0001, one-way ANOVA with Turkey's multiple comparison test; **Figure 5E**). It is also interpreted that adult HF neurons have reached a maximum distance between the AIS and the soma (∼13 mm; **Figure 5F**). This plateau of the developmental plot of the spatial distance between the AIS and soma might be the limit for the physical distance to generate APs by the integration of somatic and dendritic signals (Hamada et al., 2016). AIS location of LH neurons was dynamically altered in the Sound and affected the tonotopy of AIS location (2-way ANOVA with Sidak's multiple comparison test; **Figure 5G**). The results demonstrated that, after developmental refinement, AIS plasticity in adulthood following auditory experience occurred only within the structural and spatial boundaries of the AIS.

## AIS Structural Alterations Are Distinctively Observed in Age-Related Hearing Loss

Age-related hearing loss critically changes auditory brain structure in humans (Lin et al., 2014; Peelle et al., 2011). In the elderly, a decline in hearing sensitivity is one prominent phenomenon of aging. Thus, we examined how age-related hearing loss impacts AIS structure in the auditory nervous system using aged mice (14-month-old; 14M, C57BL/6 mice), which showed an elevated threshold and reduced amplitude of ABRs (Hunter and Willott, 1987). In aged mice (n = 4 mice), AIS length in HF neurons was significantly increased, compared to those in normal adult mice (14.5 ± 0.29 mm, n = 96 cells in adult mice at P80, as shown **Figure 3** vs. 19.9 ± 0.59 mm, n = 60 cells in aged mice (14M), p < 0.0001, Mann–Whitney U-test; **Figures 6A,B**). However, LF neurons in aged mice did not show any difference in AIS length compared to normal adult mice (19.7 ± 0.36 mm, n = 84 cells in adult mice vs. 20.9 ± 0.53 mm, n = 57 cells in aged mice, p = 0.0745, Mann– Whitney U-test; **Figure 6B**). Although there was a significant difference in AIS length between HF and LF neurons, this elongated AIS of HF neurons lessened the tonotopic segregation of AIS length in aged mice (HF vs. LF neurons of either adult mice, p < 0.0001 or aged mice, p = 0.0669, Mann–Whitney U-test; **Figure 6C**).

As for AIS location, the AIS of both HF and LF neurons in aged mice were located more proximally to the soma, decreasing the spatial distance between the AIS and soma (HF: 12.2 ± 0.42 mm, n = 78 cells in adult mice vs. 4.5 ± 0.25 mm, n = 50 cells in aged mice, p < 0.0001, Mann–Whitney U test and LF: 7.9 ± 0.33 mm, n = 66 cells in adult mice vs. 4.2 ± 0.23 mm, n = 59 cells in aged mice, p < 0.0001, unpaired t-test; **Figure 6D**). However, the change in AIS distance from the soma was greater in HF neurons than LF neurons, and thus the tonotopy of AIS location decreased in aged mice (HF vs. LF neurons of either adult mice, p < 0.0001, Mann–Whitney U test or aged mice, p = 0.3440, unpaired t-test; **Figure 6E**). Taken together, these data demonstrate that AIS structure was elongated and relocated close to the soma, and the tonotopy of AIS structure and location was significantly impaired in aged mice with hearing loss.

### Sound Modification Influences Firing Pattern and Excitability of MNTB Neurons

AIS structure in HF neurons underwent dynamic refinement during development and aging, as well as in response to various auditory experiences. Next, we explored how sound modification influence physiological properties of HF neurons of MNTB as well as the structural alterations of the AIS. Using whole-cell patch clamp recordings, we recorded APs in

FIGURE 5 | Auditory experience regulates AIS structural and spatial plasticity in adulthood. (A) HF MNTB neurons, immunostained with MAP2 and β4 spectrin from hearing loss (HL), Normal, and Sound. The dotted line and white arrow indicate AIS length and distance, respectively. (B) Summary of AIS lengths in HF neurons from HL, Normal, and Sound. ∗∗∗p < 0.001, Kruskal–Wallis test with Dunn's post hoc test. (C) The plot of AIS length in HF neurons from normal mice from P9 to P80 (black, shown in Figure 3D), and those from HL (at P80, red), and Sound (at P45, blue). (D) Tonotopy of AIS length between HF and LF neurons from HL, Normal, and Sound groups. ∗∗p < 0.01, ∗∗∗p < 0.0001, Mann–Whitney U test for HF and LF neurons; ns, non-significant, Kruskal–Wallis with Dunn's post hoc test for AIS length of LF neurons from HL, Normal, Sound. (E) Summary of AIS distance in HF neurons from HL (red), Normal (black), and Sound (blue). ∗∗∗p < 0.0001, one-way ANOVA with Turkey's multiple comparison test. (F) The plot of AIS distance in HF neurons from Normal from P9 to P80 (black, shown in Figure 3E), and those from HL (red) and Sound (blue). (G) Tonotopy of AIS location between HF and LF neurons from HL, Normal, and Sound. ∗∗∗p < 0.0001, unpaired t-test for HF and LF neurons; ∗∗p < 0.01, one-way ANOVA with Turkey's multiple comparison test for AIS distance of LF neurons from hearing loss, normal, sound group.

MNTB neurons from mice that experienced different sound inputs (P17-P20, Deaf, Normal, or Sound, **Figure 7A**). In the current clamp recordings, there was no difference in the baseline potential, which was around −70 mV with ∼ −20 pA injection (−72.1 ± 0.83 mV for Normal, n = 17 cells, −72.1 ± 0.77 mV for Sound, n = 18 cells, −70.7 ± 0.71 for Deaf, n = 15 cells). We examined the waveform of single APs and found that the AP amplitude was increased in both Sound and Deaf compared to the Normal (n = 12 cells in Normal vs. either n = 11 cells in Deaf, p = 0.174 or n = 23 cells in the Sound, p = 0.0215, one-way ANOVA with Dunnett's multiple comparison test; **Figures 7B,C** and **Supplementary** **Data-Table 1**). Other parameters of AP waveforms, including half-width, AP threshold, rheobase current, input resistance, membrane constant were not significantly different between the three groups (**Figure 7D** and **Supplementary Data-Table 1**). In addition, we analyzed the number of APs in response to a 100 ms current injection of 200 pA in HF neurons in the Deaf, the Normal, and the Sound. The number of APs was significantly increased in the Sound (1.5 ± 0.29, n = 14 cells in Normal vs. 10.5 ± 2.91, n = 25 cells in Sound, p < 0.01, Kruskal–Wallis test with Dunn's post hoc test; **Figures 7E,F**). Incremental current injection did not increase AP number in the HF neurons of the Deaf, which was similar to the response in those of the Normal

length in HF (black) and LF (gray) neurons through lifetime from P9 to 14M and AIS length of HF (red) and LF (pink) in aged mice. (C) Tonotopy of AIS length in MNTB neurons from adult (at P80, black) and aged (14M, magenta) mice. ∗∗∗p < 0.0001, Mann–Whitney U test. (D) The plot of AIS location in HF (black) and LF (gray) neurons through lifetime from P9 to 14M and AIS location of HF (red) and LF (pink) in aged mice. (E) Tonotopy of AIS location from adult (at P80, black) and aged (14M, red) mice. ∗∗∗p < 0.0001, unpaired t-test.

(2.1 ± 0.68, n = 15 cells in Normal vs. 1.5 ± 0.23, n = 12 cells in Deaf, p > 0.05, Kruskal–Wallis test with Dunn's post hoc test; **Figures 7E,F**). Although AP amplitude was increased in both Sound and Deaf mice, only sound stimulation increased neuronal excitability of HF neurons in the MNTB.

## Computer Simulation Indicates That Structural Changes of AIS Directly Influence the Firing Properties of MNTB Neurons

To test the effects of AIS structural changes on the excitability of MNTB neurons of Deaf, Normal, and Sound, we used a computer model. We established a model of an MNTB neuron to replicate the spiking response to somatic current injection in Normal (**Figure 8A** and **Supplementary Data-Table 2**). In order to replicate the changes in excitability, we had to make two assumptions. The first is that the density of the channels in the AIS is inversely proportional to its length, which is altered in the different auditory experience conditions compared to control.

$$\mathbf{g}\_{\mathbf{f}} = \frac{L\_N}{L\_f} \mathbf{g}\_N \tag{1}$$

Where L<sup>N</sup> is the length of the AIS of Normal; L<sup>f</sup> is the final length of the AIS of Deaf or Sound; g<sup>N</sup> is the channel density (S/cm2) of Normal; and g<sup>f</sup> is the channel density of Deaf or Sound. Secondly, we assume that the total surface of the AIS from Sound or Deaf is identical to the surface area of the Normal:

$$d\_f = \frac{L\_N}{L\_f} d\_N \tag{2}$$

Where d<sup>N</sup> is the diameter of the AIS from Normal; and d<sup>f</sup> the AIS diameter of Sound or Deaf. Finally, we obtained the equation (3) by combining the equations 1 and 2:

$$\mathbf{g}\_{\text{total}\_f} = \pi \frac{L\_N}{L\_f} d\_N L\_f \frac{L\_N}{L\_f} \mathbf{g}\_N = \left(\frac{L\_N}{L\_f}\right)^2 \mathbf{g}\_{\text{total}\_N} \tag{3}$$

Where gtotalN and gtotalf are the total conductance (in Siemens) of the Normal and Sound, respectively. We used equation (3) to calculate the total conductance for each channel of the AIS from the Deaf and Sound. For each case, we calculated the excitability response to somatic current injections. The models replicate our findings that HF neurons from the Sound had shorter AIS length and distance and increased excitability (**Figure 8B**). Assuming only morphological changes, a fixed morphology with changes in the density of ion channels, or one of the above processes at a time failed to reproduce the data (**Supplementary Data-Table 2**). Thus, changes in AIS morphology can affect as well as be influenced by a change in the excitability of MNTB neurons including AP amplitude in different auditory environments.

Furthermore, the simulation reveals axon diameter as an additional key condition for structural changes to reproduce firing patterns from different models (Deaf, Normal, and Sound). The model predicted a 23% increase in the diameter of the axon in the Sound compared to the Normal mice (**Figures 8B,C**). To verify this finding, we assessed the diameter of AIS in MNTB neurons (P20 mice) that are immunostained with β4 spectrin and MAP2 using 2D Z-stack compression and 3D reconstruction of confocal images (**Figure 8D**). The AIS diameter from Sound was significantly increased by 31% compared to the Normal (0.60 ± 0.018 mm, n = 69 cells from 3 Normal mice vs. either 0.55 ± 0.020 mm, n = 66 cells from 3 Deaf mice, p > 0.05 or 0.79 ± 0.018 mm, n = 90 cells from 3 Sound, p < 0.0001, oneway ANOVA with Turkey's multiple comparison test; **Figure 8D**). Sound stimulation alters AIS length, location, and diameter, resulting in an increase in excitability.

#### DISCUSSION

#### Heterogeneity of AIS Structure Across Various Brain Regions in Different Species

Recent studies have demonstrated AIS plasticity during development (Gutzmann et al., 2014; Kuba et al., 2014), neuronal activity alterations (Grubb and Burrone, 2010; Wefelmeyer et al., 2015), sensory deprivation (Kuba et al., 2010; Gutzmann et al., 2014), and brain disorders (Hsu et al., 2014). Furthermore, heterogeneity of the AIS has been considered in various cell types, brain regions, and across different species (Wefelmeyer et al., 2015; Höfflin et al., 2017). In the auditory system, development and plasticity of AIS structure have been studied in the nucleus laminaris (NL) and nucleus magnocellularis (NM) of the chick brainstem (Kuba et al., 2006, 2010, 2014). Consistent with what has been shown in chick NL neurons, mouse MNTB neurons display a similar tonotopic differentiation of AIS structure and AP waveform (**Figure 2**). HF neurons, which had a shorter AIS length and longer distance from the AIS to the soma, had smaller amplitude APs than those in LF neurons. However, the chick AIS from both LF and HF neurons was shortened during development (Kuba et al., 2014), whereas, in the mouse, MNTB specifically HF neurons significantly underwent AIS refinements until early adulthood. The developmental refinement of the AIS in HF neurons affects spike waveform in mouse MNTB neurons as well as in the chick (Kuba et al., 2014). Discrepancies in AIS plasticity data between the chick and mouse might be related to differences in audiograms from chick (from 2 Hz to 9 kHz, Hill et al., 2014) and mouse (from 4 kHz to 64 kHz, Greich and Strutz, 2012). The MNTB is a well-developed nucleus in rats and mice, which hear higher frequency sounds than chicks. The chick

NL is more comparable to the medial superior olivary (MSO) in rodents that preferably hear lower frequency sound, such as gerbils (Greich and Strutz, 2012).

Sound-evoked activity is important for the developmental refinement of the AIS. In congenital deafness, HF neurons of the mouse MNTB had a longer AIS compared to those in agematched normal mice. Sound input is critical for developmental shortening of the AIS, and thus sound deprivation in deafness inhibited this shortening and left longer immature AIS. AIS plasticity was more dynamic in HF neurons. In the mouse MNTB, AIS length of LF neurons was very consistent throughout life, regardless of sound modifications either during development or in adulthood, but AIS location of LH neurons was dynamically moved in response to sound modifications in the mouse MNTB. The AIS of LH neurons moved proximal to the soma in sound stimulation but moved distally in sound deprivation. In cultured hippocampal neurons and pyramidal cells, the AIS was moved away from the soma and relocated distally during prolonged depolarization (Grubb and Burrone, 2010; Wefelmeyer et al., 2015). In these cells, the dynamic shift of the AIS position contributes to the modulation of neuronal excitability (Grubb and Burrone, 2010). A possible explanation for the proximal movement of the AIS of MNTB neurons in sound stimulation could be cell-type specificity of GABAergic neurons. Contradictory to non-GABAergic neurons, GABAergic olfactory bulb interneurons show proximal lengthening of the AIS, which relocated closer to the soma after chronic 24h depolarization (Chand et al., 2015). Therefore, cell-type or brainregion specific structural plasticity of the AIS could explain these different responses from different brain areas.

## The Structural Plasticity of AIS Throughout Life From Development to Aging

Structural and functional properties of the mammalian brain change across the lifespan (Freitas et al., 2013; Yeatman et al., 2014). Understanding the profile of AIS structure in the perspective of an entire lifetime can provide essential information to identify the intrinsic molecules or signaling pathways underlying the regulation of AIS structure at different ages. The AIS undergoes shortening during development in the chick auditory brainstem and in monkey prefrontal cortex (Cruz et al., 2009; Kuba et al., 2014). In the visual cortex of mice in vivo, AIS length steadily increases until P15, and then shortens dramatically after eye-opening until the beginning of the critical period of cortical ocular dominance plasticity at P21 (Gutzmann et al., 2014). Developmental plasticity of AIS length and position may be associated with the individual functional state of a given neuron in specific brain regions (Gutzmann et al., 2014; Schlüter et al., 2017). In the mouse auditory brainstem, we found that the plot of AIS location (or length) formed a parabola (or inverse parabola) when plotted against age from neonatal development to aging (**Figure 9A**). In postnatal development, AIS dynamically underwent shortening and then stabilization of AIS structure and location, resulting in a steady plateau of the developmental plot of AIS length and location in adulthood (**Figure 9A**). The structural plasticity of the AIS occurs within a specific range, with a minimum and maximum in terms of AIS length and location, indicating that the AIS is structurally resilient (**Figures 9B–D**). In aging, if the structural resilience of the AIS is lost, similar to the loss in elasticity of a spring over time, the AIS might be altered, as we observed in the auditory brainstem (**Figure 6**). The mechanism of this elongation in aging is different from AIS elongation due to homeostatic processes to compensate for decreased neuronal activity (Gründemann and Häusser, 2010; Wefelmeyer et al., 2016). The levels of ankyrinG, spectrin, and actin in the AIS are reduced in aged mice (Bahr et al., 1994). Primary visual cortical neurons in aged rats displayed shortening of the AIS and reduction of NaV1.6 channel expression along the AIS, which accompanies enhanced neuronal activity (Ding et al., 2018). A decline in sensory inputs seems to impair the structural stability of the AIS in the sensory system. However, the implication of age-related alterations in the AIS or the link between morphological changes in the AIS and neuronal excitability remains unclear in the aged brain. Further investigation of molecular mechanisms targeting AIS reorganization during aging will provide a new strategy for central auditory disorders following age-related hearing loss.

## AIS Changes in Auditory Environmental Modification

In modern society, there is increased exposure to sensory inputs in technologically advanced environments. Increase in chronic exposure to various sounds (from mild to severe) might affect the development and maturation of the auditory nervous system. Sound stimulation facilitated AIS shortening during development, but did not further change AIS length in adulthood. The structural plasticity of AIS driven by sound inputs might stay within a particular range, preventing the AIS from becoming overly shortened (**Figures 9B–D**). Regarding the AIS position, either during development or in adulthood, sound stimulation proximally moved the AIS of MNTB neurons. This spatial relocation was contrary to previous studies in cultured hippocampal neurons or organotypic brain slices, showing a distal shift of the AIS along the axon in response to elevated neuronal activity (Grubb and Burrone, 2010; Wefelmeyer et al., 2015), indicating a cell-specific effect of sound stimulation in the auditory system. These results demonstrate significant alterations in cellular structures of the auditory brain as a result of sound stimulation.

In the mammalian auditory system, the superior olivary complex is the first major convergence point for binaural information, where the MNTB-the lateral superior olive (LSO) circuit contributes to binaural intensity processing and lateralization (Heffner and Masterton, 1990). Computationally, changes in excitability could affect the non-monotonic responses to regular spiking input in MNTB cells (Arnoldt et al., 2015). Increased ABRs and c-fos signal in the MNTB shown in sound stimulation mice suggest that an increase in spontaneous activity and/or changes in the peripheral plasticity upstream of the auditory brainstem can occur in sound enhanced condition. In deaf mice, it is unclear how sound deprivation affect spontaneous

activity in the auditory brainstem. Our model might be of interest to interaural sound processing where models of MNTB neurons are needed (Ashida et al., 2017). Thus, severe alterations in AIS structure in the MNTB might impact sound localization.

## The Physiological Role of AIS Structural Refinement in Intrinsic Excitability of Auditory Neurons

A key question is how AIS plasticity drives the adaptation of neuronal excitability. The AP amplitude of MNTB neurons is critical for their fast spiking properties (Kim and von Gersdorff, 2012). It is hypothesized that the AP amplitude is mediated by ion channel properties and location. This is consistent with findings from Leão et al. (2005) showing that the location of sodium channels in the nerve terminal impacts the AP waveform. The computer model predicts that the location of Na channels closer to the terminal may result in a larger AP with higher amplitude (Leão et al., 2005). Here our model suggests that AIS length and location can affect AP amplitude, which is associated with fast spiking properties of MNTB neurons in the auditory brainstem. Unlike our expectation in the model, our wholecell recordings showed a larger AP with higher amplitude in MNTB neurons from both deaf and sound stimulation mice. One possible explanation is that several factors including non-AISrelated features such as soma size (Weatherstone et al., 2017) or somatic Na<sup>+</sup> or K<sup>+</sup> channel density (Leao et al., 2006; Leão et al., 2008) are associated with these alterations in MNTB excitability in deaf and sound stimulation mice. Another possibility is that congenitally the cochlea dysfunction in deaf mice can influence central ion channel expression during development (Leao et al., 2006). The physiological role of non-AIS related features and how they act synergistically with AIS plasticity to mediate intrinsic excitability of auditory neurons needs to be addressed in future studies. In the sound stimulation group, MNTB neurons had a shorter AIS relocated closer to the soma and displayed an increase in spike number in response to current injection compared to the normal and deaf mice. The greatest level of excitability possible in a neuron occurs when the AIS is at a certain distance from the soma, but there is a maximum distance necessary to overcome the charge dissipation and generate APs (Hu and Jonas, 2014; Hamada et al., 2016). In the sound stimulation group, the proximal location of the AIS with a shorter length may maximize the excitability of MNTB neurons, isolating the AIS from somatodendritic compartments and reducing the shunting conductance (Gulledge and Bravo, 2016; Yamada and Kuba, 2016). Differential responses of the AIS to neuronal activity may be affected by stimulation conditions (e.g., in vitro stimulation or in vivo environmental stimulation) and by the duration of the stimuli (e.g., short-term or long-term). This could explain the

REFERENCES

Arnoldt, H., Chang, S., Jahnke, S., Urmersbach, B., Taschenberger, H., and Timme, M. (2015). When less is more: non-monotonic spike sequence processing in neurons. PLoS Comput. Biol. 11:e1004002. doi: 10.1371/journal.pcbi.100 4002

discrepancies between our study and previous studies showing a distal shift along the axon in elevated neuronal activity (Grubb and Burrone, 2010; Wefelmeyer et al., 2015). Understanding the physiological consequences or homeostatic adaptation processes in response to sound deprivation or stimulation in the central auditory system throughout life is critically important for developing targeted strategies to remedy potential long-term deficits of the auditory brain at specific ages.

## DATA AVAILABILITY STATEMENT

All datasets generated for this study are included in the manuscript/**Supplementary Files**.

## ETHICS STATEMENT

The animal study was reviewed and approved by the University of Texas Health Science Center, San Antonio (UTHSCSA) Institutional Animal Care and Use Committee protocols.

## AUTHOR CONTRIBUTIONS

EK performed the experiments, analyzed the data, and wrote the manuscript. CF performed the computer modeling. FS performed the computer modeling, discussed the data, and wrote the manuscript. JK conceived and performed the experiments, analyzed the data, wrote the manuscript, provided the financial support, and supervised the study.

## FUNDING

This work was supported by a grant from the National Institute on Deafness and Other Communication Disorders (NIDCD; R01 DC03157) to JK and NIH R01 EB026939-01A1 to FS.

## ACKNOWLEDGMENTS

We would like to thank Michael Patton and Jake Chung for providing technical assistance.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel. 2019.00456/full#supplementary-material


during visual cortex development. Cereb. Cortex 27, 4662–4675. doi: 10.1093/ cercor/bhx208

Sweetow, R. W. (2005). Training the auditory brain to hear. Hear. J. 58, 10–16.


**Conflict of Interest:** 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 © 2019 Kim, Feng, Santamaria and Kim. 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(s) 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.

# Mutual Suppression of Proximal and Distal Axonal Spike Initiation Determines the Output Patterns of a Motor Neuron

#### Nelly Daur<sup>1</sup> , Yang Zhang<sup>2</sup> , Farzan Nadim1,2 and Dirk Bucher<sup>1</sup> \*

<sup>1</sup> Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers University-Newark, Newark, NJ, United States, <sup>2</sup> Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, United States

Axonal spike initiation at sites far from somatodendritic integration occurs in a range of systems, but its contribution to neuronal output activity is not well understood. We studied the interactions of distal and proximal spike initiation in an unmyelinated motor axon of the stomatogastric nervous system in the lobster, Homarus americanus. The peripheral axons of the pyloric dilator (PD) neurons generate tonic spiking in response to dopamine application. Centrally generated bursting activity and peripheral spike initiation had mutually suppressive effects. The two PD neurons and the electrically coupled oscillatory anterior burster (AB) neuron form the pacemaker ensemble of the pyloric central pattern generator, and antidromic invasion of central compartments by peripherally generated spikes caused spikelets in AB. Antidromic spikes suppressed burst generation in an activity-dependent manner: slower rhythms were diminished or completely disrupted, while fast rhythmic activity remained robust. Suppression of bursting was based on interference with the underlying slow wave oscillations in AB and PD, rather than a direct effect on spike initiation. A simplified multi-compartment circuit model of the pacemaker ensemble replicated this behavior. Antidromic activity disrupted slow wave oscillations by resetting the inward and outward current trajectories in each spike interval. Centrally generated bursting activity in turn suppressed peripheral spike initiation in an activity-dependent manner. Fast bursting eliminated peripheral spike initiation, while slower bursting allowed peripheral spike initiation to continue during the intervals between bursts. The suppression of peripheral spike initiation was associated with a small after-hyperpolarization in the sub-millivolt range. A realistic model of the PD axon replicated this behavior and showed that a sub-millivolt cumulative after-hyperpolarization across bursts was sufficient to eliminate peripheral spike initiation. This effect was based on the dynamic interaction between slow activitydependent hyperpolarization caused by the Na+/K+-pump and inward rectification through the hyperpolarization-activated inward current, Ih. These results demonstrate that interactions between different spike initiation sites based on spike propagation can shift the relative contributions of different types of activity in an activity-dependent manner. Therefore, distal axonal spike initiation can play an important role in shaping neural output, conditional on the relative level of centrally generated activity.

Keywords: ectopic spikes, dopamine, axon, neuromodulation, neural oscillations, central pattern generation, after-hyperpolarization

#### Edited by:

Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

#### Reviewed by:

Oscar Herreras, Spanish National Research Council (CSIC), Spain Jürg Streit, University of Bern, Switzerland Lidia Szczupak, University of Buenos Aires, Argentina

> \*Correspondence: Dirk Bucher bucher@njit.edu

#### Specialty section:

This article was submitted to Cellular Neurophysiology, a section of the journal Frontiers in Cellular Neuroscience

Received: 07 June 2019 Accepted: 10 October 2019 Published: 23 October 2019

#### Citation:

Daur N, Zhang Y, Nadim F and Bucher D (2019) Mutual Suppression of Proximal and Distal Axonal Spike Initiation Determines the Output Patterns of a Motor Neuron. Front. Cell. Neurosci. 13:477. doi: 10.3389/fncel.2019.00477

## INTRODUCTION

fncel-13-00477 October 21, 2019 Time: 15:32 # 2

Canonically, action potentials (spikes) are initiated at a single site, usually the soma or proximal axon, as the result of integration of somatodendritic synaptic inputs or endogenous membrane oscillations. Spikes then propagate along the axon with high fidelity to distal presynaptic sites. However, it has long been known that some neurons have more than one initiation site and can generate activity from spatially separated signal integration (Calabrese and Kennedy, 1974; O'Shea, 1975; Vedel and Moulins, 1977; Moulins et al., 1979), or use dendritic spike initiation to amplify synaptic information transfer to the axon (Reyes, 2001; Canals et al., 2005). In addition, some neurons exhibit distal axonal spike initiation, not directly resulting from somatodendritic integration (Bucher and Goaillard, 2011; Debanne et al., 2011; Sasaki, 2013; Bucher, 2015; Rama et al., 2018). Such spike initiation is unequivocally "ectopic" when it occurs in abnormal places, which is a common phenomenon in a range of neuropathies associated with injury, demyelination, inflammation, or seizure activity (Stasheff et al., 1993; Pinault, 1995; Poliak and Peles, 2003; Ma and LaMotte, 2007; Krishnan et al., 2009; Connors and Ahmed, 2011; Hamada and Kole, 2015; Meacham et al., 2017). However, spike initiation in more distal axonal compartments can also occur under normal physiological conditions. For example, hippocampal interneurons and pyramidal cells generate such spikes in a range of different network states, which has been proposed to contribute to network oscillations and memory formation (Pinault, 1995; Avoli et al., 1998; Epsztein et al., 2010; Bahner et al., 2011; Connors and Ahmed, 2011; Sheffield et al., 2011; Dugladze et al., 2012; Bukalo et al., 2013; Sheffield et al., 2013; Buzsaki, 2015).

Distal axonal spike initiation can be independent of direct synaptic inputs, but instead be due to local integration of environmental signals and activity-dependent changes in membrane excitability (Pinault, 1995; Bucher and Goaillard, 2011; Bucher, 2015). This is often associated with modulatory effects mediated by high-affinity non-synaptic receptors, either G protein-coupled or ionotropic. For example, in hippocampal and cortical neurons, distal spike initiation is thought to arise from spillover-activation of high-affinity GABA<sup>A</sup> receptors, sometimes in conjunction with axonal gap junction coupling and persistent Na<sup>+</sup> currents (Avoli et al., 1998; Keros and Hablitz, 2005; Bahner et al., 2011; Bukalo et al., 2013; Muller et al., 2018). In the crustacean stomatogastric nervous system (STNS), distal spike initiation in descending, sensory, and motor axons occurs in response to aminergic or peptidergic modulation, and affects sensorimotor integration (Daur et al., 2009; Stadele and Stein, 2016; Stadele et al., 2018), circuit activity (Bucher et al., 2003; Goaillard et al., 2004; Daur et al., 2009), and motor output to muscles (Meyrand et al., 1992; Bucher et al., 2003; Ballo and Bucher, 2009).

Different spike initiation sites in the same neuron can be functionally separated and operate independently (Calabrese and Kennedy, 1974; Dugladze et al., 2012), but in many cases, they influence each other. In some neurons, distal spiking is elicited in response to repetitive activity propagated from proximal sites (Meyrand et al., 1992; Le et al., 2006; Sheffield et al., 2011, 2013; Suzuki et al., 2014; Elgueta et al., 2015). In others, spikes propagated from one site suppress initiation at the other (Calabrese, 1980; Nagy et al., 1981; Maranto and Calabrese, 1983; Pinault, 1995; Cattaert and Bevengut, 2002; Weidner et al., 2003; Blitz and Nusbaum, 2008). Neither the degree to which such interactions shape neuronal output activity nor the underlying cellular mechanisms are well understood. We address these aspects in the pyloric dilator (PD) neuron in the STNS. We show that output activity of the pyloric dilator (PD) motor neuron in the STNS is shaped by suppressive interactions between centrally generated bursting activity and dopamine (DA)-elicited spike initiation in the peripheral axon. As the two initiation sites are electrotonically well separated, the bidirectional interactions depend on propagating spikes, and are mediated by different mechanisms. Some of these results were previously published in abstract form (Daur et al., 2015).

## MATERIALS AND METHODS

## Experimental Preparation

All experiments were performed on the STNS of adult (∼500 g) lobsters, Homarus americanus, of either sex. Animals were obtained from Yankee Lobster Co. in Boston, MA, United States, or from local seafood stores in Newark, NJ, United States, and kept unfed in tanks at 10–13◦C. Prior to dissection, animals were cold-anesthetized in ice for ∼15 min. The STNS was dissected from the stomach and pinned in a transparent Sylgardlined (Dow Corning) 100 mm experimental dish in physiological saline. Saline composition was as follows (in mM): 479.12 NaCl, 12.74 KCl, 13.67 CaCl2, 10 MgSO4, 3.91 Na2SO4, and 10 HEPES. The pH was adjusted to 7.4 –7.5.

A schematic of the STNS with the main nerves is shown in **Figure 1A**, with the established nomenclature (Maynard and Dando, 1974). The esophageal ganglion (OG), the paired commissural ganglia (CoG), and the proximal inferior ventricular nerve (ivn) contain neuromodulatory neurons with axons that project to the STG. All experiments involved the PD neurons, which have their cell bodies in the STG. The PD neurons have a dual role as part of the pacemaker kernel of the pyloric central pattern generator and as motor neurons innervating pyloric dilator muscles (Marder and Bucher, 2007). In some experiments, we also recorded from the anterior burster (AB) neuron. There are two copies of PD, and they are not bilateral homologs but each projects to muscles on both sides of the stomach. Therefore, all nerves in the path to PD innervated muscles contain both axons. We discarded all muscles but kept the axon path to the pyloric dilator nerve (pdn) intact. In animals of the size used, the path length from the STG to the pdn is ∼4–5 cm, with a spike conduction delay of ∼30–50 ms (Bucher et al., 2003, 2005; Ballo and Bucher, 2009; Ballo et al., 2012).

#### Electrophysiological Recordings

In most experiments, a PD neuron was recorded intracellularly from the soma in the STG (sometimes simultaneously with the AB neuron), and extracellularly from the pdn. The STG

was desheathed with the tip of a fine tungsten wire. PD neurons were identified by their characteristic waveform and correspondence of spiking activity with the extracellular nerve recordings. AB neurons were identified by their characteristic waveforms, soma size, and burst phasing in relation to PD. Only those recordings of PD and AB were analyzed in which the membrane potential troughs during bursting activity were more negative than −50 mV, and the slow wave depolarizations at least 10 mV in amplitude.

In some experiments, we obtained intracellular recordings from the PD axon in the dvn, at 0.5–2 cm distance to the STG. To facilitate access to the axons, the nerve was mechanically desheathed and slit with a tungsten wire as described before (Ballo and Bucher, 2009). As in soma recordings, PD neurons were identified by their characteristic spike pattern and correspondence of spiking with the extracellular nerve recordings. Only those recordings were analyzed in which the membrane potential troughs during bursting activity were more negative than −55 mV, and the spikes were overshooting, indicating no impalement damage.

During all recordings, preparations were superfused with saline cooled to 12◦C by a custom-made Peltier cooling device. For intracellular soma recordings, sharp glass electrodes were pulled with a Flaming-Brown P-97 puller (Sutter Instruments) and filled with 0.6 M K2SO<sup>4</sup> and 20 mM KCl to minimize alteration of chloride conductances present in the STG. These electrodes yielded tip resistances of 20–30 M. For intracellular recordings of the PD axon, electrodes with sharper tips were used, filled with 3 M KCl. These electrode yielded tip resistances of 20–30 M. Signals were amplified using Axoclamp 2B and 900A amplifiers (Molecular Devices).

Extracellular recordings from the pdn were obtained by placing stainless steel wires inside and outside of a petroleum jelly well around the distal part of the nerve, and amplifying the signals with a differential AC amplifier (A-M Systems, model 1700). Electrical nerve stimulation of the pdn or dvn was achieved through the same type of electrodes, using an isolated pulse stimulator (A-M Systems, model 2100). Pulse durations were between 200 and 500 µs and the amplitude was adjusted to be just enough above threshold to sustain repetitive stimulation.

All electrophysiological signals were acquired using a micro 1401 digitizing board (Cambridge Electronic Design) and the accompanying Spike2 software (versions 6-8). Stimulation protocols were generated using either the time settings on the stimulator, or the sequencer interface of the digital-to-analog converter of the micro 1401, connected to the trigger input of the stimulator.

## Drug Applications

In some experiments, descending modulatory input to the STG or activity in the STG itself was blocked with 1 µM tetrodotoxin citrate (TTX; Biotium) and 750 mM sucrose (Sigma) in a petroleum jelly well around the stomatogastric nerve (stn) or the STG. For bath application of 1 µM DA (dopamine; 3-hydroxytyramine hydrochloride; Sigma), freshly made stock solutions were diluted in saline right before use. Application was done through the superfusion system with the use of switching manifolds.

## Data Analysis

Primary data analysis to extract spike times, spike and burst frequencies, and voltage trajectory measures was performed using Spike2 and programs written in its script language. Secondary analyses, statistical tests, and plots were generated in SigmaPlot (version 12.0, Systat Software). Statistical tests used were One Way (1W) or Two Way (2W) Repeated Measures Analysis of Variance (RM-ANOVA), with subsequent Holm–Sidak post hoc comparisons, or Friedman Repeated Measures ANOVA on Ranks (RM-Rank-ANOVA), with subsequent Tukey post hoc comparisons. Significance was assumed at p < 0.05, and is indicated as <sup>∗</sup> (p < 0.05), ∗∗ (p < 0.01), and ∗∗∗ (p < 0.001). Error bars indicate Standard Error of Means. Figures were produced in CorelDRAW (versions X7 and X8, Corel) and Canvas (version 11, ACD Systems).

## Multicompartment Modeling of the PD Axon and Pyloric Pacemaker

This study includes two sets of computational models. The first is a circuit model of the pyloric pacemaker group AB and two PD neurons, in which we examined the effect of ectopic spiking in the PD axon on centrally generated bursting activity in the pacemaker group. The second is a model of a single PD axon, in which we examined the effect of burstpattern stimulations of the axon on the ectopic tonic spiking activity produced by DA neuromodulation. All simulations were done in NEURON<sup>1</sup> + Python (version 7.6.7; Python Software Foundation, version 3.71) (Hines et al., 2009).

#### The Pyloric Pacemaker Model

fncel-13-00477 October 21, 2019 Time: 15:32 # 4

The circuit model of the pyloric pacemaker group included three electrically coupled neurons and was modified from the AB and PD model neurons in Soto-Treviño et al. (2005), but with a simpler, more generic set of ionic conductances (**Table 1**). The AB neuron was modeled as a single compartment, representing the soma and neurite (S/N), and included a leak current (ILeak), a slow and inactivating Ca2<sup>+</sup> current (ICaS), a slow non-inactivating K<sup>+</sup> current (IKS), and the modulator-activated inward current (IMI). The PD neurons each had 4 compartments: one S/N compartment, connected to a 3-compartment axon. The proximal axon compartment was modeled with twice the membrane surface area each of the two distal compartments. This provided enough electrotonic separation for S/N subthreshold voltage fluctuation not to interfere with distal spike initiation, and stimulus artifacts from the distal compartment not to be transmitted to the S/N compartment. The S/N compartment included the same currents as AB, plus the hyperpolarizationactivated inward current (Ih), and the axial current from the

<sup>1</sup>http://neuron.yale.edu


proximal axon compartment (Iaxial). To introduce a small amount of heterogeneity, the S/N compartments of the two PD neurons differed in their ILeak reversal potential by 1 mV. The axon compartments included ILeak, an instantaneous Na<sup>+</sup> current (INa), a delayed rectifier K<sup>+</sup> current (IKd), and Iaxial from adjacent compartments. The three neurons were symmetrically electrically coupled through their S/N compartments (Ielec). In isolation, AB produced slow wave oscillations, whereas PD only produced tonic spiking. To study the effect of antidromic activity, 1 ms current pulses of 1.5 nA amplitude were injected either simultaneously into the distal axon compartments of both PDs to elicit spikes, or directly into AB to mimic the effect of antidromic spikes on its membrane potential. All ionic currents were based on the standard Hodgkin–Huxley formalism, with activation (and inactivation) state variables (x) obeying the standard equation

$$\frac{d\mathbf{x}}{dt} = \frac{\mathbf{x}\_{\infty}(V) - \mathbf{x}}{\mathbf{t}\_{\mathbf{x}}(V)}.$$

Maximal conductances and reversal potentials for all currents are listed in **Table 1**. The equations for activation and inactivation state variables (x<sup>8</sup> and τx) are provided in **Table 2**.

#### The PD Axon Model

We previously published a model of the PD axon that reproduced DA effects on spike conduction (Zhang et al., 2017). This model contained ILeak, INa, IKd, Ih, a fast transient K<sup>+</sup> current (IA), and the Na+/K<sup>+</sup> pump current. Here, we used the same model, with two modifications. First, the effect of DA on the axon was simulated by increasing the maximal conductance of I<sup>h</sup> to 0.25 mS/cm<sup>2</sup> [rather than the 0.1 mS/cm2 used in Zhang et al. (2017)]. This increased level reproduced the rate of tonic spiking activity produced by 1 µM DA in the biological PD axon (Bucher et al., 2003). Second, the length of the axon was limited to 1 mm, divided into 11 compartments (rather than 1 cm divided into 101 compartments, as in Zhang et al., 2017). This second modification was simply to reduce computation time, since the length of the axon was irrelevant for the results obtained. Burst stimulation patterns were produced at one end of the axon with 2 ms current


pulses of 5 nA amplitude, and recordings were made from the midpoint of the axon.

## RESULTS

## Centrally and Peripherally Generated Spikes Are Readily Identified by Differences in Conduction Delay

In H. americanus, DA elicits peripheral spike initiation in the PD motor axons (Bucher et al., 2003; Ballo and Bucher, 2009; Ballo et al., 2010). In the presence of centrally generated rhythmic bursting activity, these spikes occur exclusively during the interval between bursts. While focal DA application can elicit spikes along almost the entire length of the PD axons, spikes are consistently generated close to the dvn/lvn junction (0.5–2 cm from the STG, **Figure 1A**) during bath applications (Bucher et al., 2003).

Simultaneous intracellular PD soma and extracellular pdn recordings during mixed activity allowed a clear distinction between centrally generated bursting and "extraburst" peripheral spiking (**Figure 1B**). Note that STG neurons are typical unipolar invertebrate neurons with unexcitable somata, and therefore only show substantially attenuated spikes, usually on top of slow wave depolarizations which, in contrast, are only minimally attenuated (Golowasch and Marder, 1992). The different sites of spike initiation can be confirmed by determining the conduction delay between soma and nerve recording (Bucher et al., 2003; **Figure 1C**). Spikes generated during bursts on top of slow wave depolarizations show a longer delay, indicating that they are generated in the STG and propagate the entire length of the nerves to the pdn. Extraburst spikes show a shorter delay, indicating that they are generated in the axon at some distance to the STG, and then propagate both antidromically to the soma, and orthodromically to the pdn (arrows in **Figure 1A**). The positive delay indicates that the peripheral spike initiation site is closer to the soma than to the pdn, as no delay would indicate equidistance, and negative delay would indicate a more distal initiation site.

#### Antidromic Spikes Interfere With Slow Central Burst Generation

In H. americanus, the isolated STNS produces continuous pyloric rhythms with cycle frequencies of ∼0.4–1 Hz (Bucher et al., 2005, 2006). This activity is characterized by bursts in the pacemaker neurons (AB and PD), followed by bursts in follower neurons which rebound from inhibition by the pacemaker, and is dependent on descending neuromodulatory input to the STG (Marder and Bucher, 2007). When descending input is blocked, follower neurons fall silent, but AB and PD continue to cycle at a lower frequency (∼0.1–0.4 Hz) (Thirumalai and Marder, 2002; Bucher et al., 2003). These two states of the pyloric circuit in vitro are somewhat representative of fast and slow activity in the intact animal, but with some caveats. Pyloric activity in the intact animal is also dependent on hormonal modulation via the hemolymph (Marder and Bucher, 2007), which is absent in vitro. Inhibitory neuromodulators can substantially slow or disrupt rhythmic pyloric activity (Claiborne and Selverston, 1984; Cazalets et al., 1987; Skiebe and Schneider, 1994; Pulver et al., 2003; Kwiatkowski et al., 2013), but that is likely not associated with a complete absence of excitatory neuromodulation, as is the case in vitro, when all inputs to the STG are blocked. Nevertheless, we used these states as approximations of different modulatory conditions in which the pyloric rhythm is either fast or slow.

When modulatory inputs are blocked and DA is bath applied onto the entire STNS, pacemaker burst frequency initially increases. However, with some delay, peripheral spike initiation increases and burst generation decreases and eventually ceases completely (Bucher et al., 2003). Therefore, we asked if antidromic propagation of peripherally generated spikes directly causes inhibition of central burst generation, even when DA is not present in the STG. We blocked descending inputs to the STG and electrically stimulated the distal pdn to elicit antidromic spikes, while recording intracellularly from a PD soma (**Figure 2A**). Under these conditions, even relatively low frequency antidromic spiking had an inhibitory effect on centrally generated bursting in PD. **Figure 2B** shows four different ways bursting was disrupted. Stimulus artifacts were minimal in all intracellular recordings, and antidromic spikes occurred with a consistent delay from stimulation (30–50 ms, dependent on preparation). We excluded those spikes from the calculation of burst frequency, number of spikes per burst, and the mean rate of centrally generated spikes. Slow wave oscillations were obtained by low-pass filtering. In all experiments and at all frequencies, antidromic spikes had stable amplitudes throughout the 40 s stimulation interval, suggesting that membrane refractoriness and the ability to generate spikes were not affected. In some cases, there was little effect on burst frequency, but the number of spikes per burst decreased during antidromic stimulation, associated with a decrease in slow wave amplitude (**Figure 2B**, upper left). In others, the predominant effect was a decrease in burst frequency (**Figure 2B**, upper right). However, in some of these cases, smaller slow wave oscillation that did not give rise to spikes were still present in the prolonged intervals between bursts (arrow in **Figure 2B**, upper right). Cases in which central spike initiation was completely suppressed either still showed diminished slow wave oscillations (**Figure 2B**, lower left, arrow), or not (**Figure 2B**, lower right). There was variability, both across experiments and across stimulation frequencies within experiments, of whether the effect on burst frequency or the effect on spikes per burst was dominant. Therefore, we used the mean rate of centrally generated spikes (that is independent of the precise temporal structure) as a measure of activity (top plots in **Figure 2B**). **Figure 2C** shows that this rate declined linearly with increasing stimulation frequency. The linear relationship suggests that, on average, stimulation above 10 Hz should reliably completely disrupt central burst and spike initiation.

The single interneuron AB is the dominant oscillator in the pacemaker group, and both PD neurons are strongly electrically coupled to AB and to each other (Marder and Bucher, 2007; Daur et al., 2016). The reduced amplitude slow wave oscillations in PD, shown in **Figure 2B**, could either be due to reduced oscillations in AB, or to a decreased responsiveness of PD to stable

FIGURE 2 | Suppression of slow rhythmic activity of the pyloric pacemaker group by antidromic PD axon stimulation. (A) Schematic of the STNS. Descending modulatory input through the stn was blocked and antidromic spikes were elicited by stimulating the pdn (kinked arrow). (B) Four examples of intracellular recordings of PD during antidromic stimulation. Low-pass filtered PD voltage traces were generated to visualize slow-wave oscillations by plotting the moving average of voltage (time constant: 100 ms), and are not shown at the same scale as the original recordings. Arrows point to small slow wave oscillations that did not give rise to bursts of spikes. Burst frequency, number of spikes per burst, and central mean rate were calculated after removing stimulated antidromic spikes from the original spike detection. Burst frequency plots are instantaneous frequencies obtained as the inverse of intervals between the first spike of a burst and the first spike in the preceding burst. Central mean rates were obtained from 40 s windows before, during, and after stimulation, and are shown as skyline plots. (C) Central mean rate (mean rate of centrally generated spikes) decreased with increasing antidromic stimulation frequency (n = 8; 1W-RM-ANOVA, p < 0.001). Asterisks show significance obtained from post hoc pairwise comparisons. (D) Example simultaneous AB and PD recording during antidromic stimulation, showing complete disruption of centrally generated bursts. The dashed box indicates the time range shown in (E). (E) Expanded section of the recording shown in (D). Antidromic PD spikes caused spikelets in the electrically coupled AB neuron (gray arrows), that could elicit spikes in AB (black arrow), which in turn caused spikelets in PD (white arrow).

AB oscillations. In three experiments, we therefore recorded simultaneously from AB and PD. In all three experiments, antidromic PD stimulation reduced or disrupted AB slow wave oscillations (**Figure 2D**), and we consistently observed AB responses corresponding to individual antidromic PD spikes (**Figure 2E**). These responses were spikelets (gray arrows in **Figure 2E**), and were sometimes sufficient to cause the AB neuron to fire after a small delay (black arrow in **Figure 2E**). Spikes generated in AB in turn then caused spikelets in the PD recordings (white arrow in **Figure 2E**). These interactions are an indication that fast signals are efficiently transmitted between PD and AB, and that antidromic PD spikes can have a fairly global influence on AB.

## Fast Rhythmic Pyloric Activity Is Robust to Antidromic Spiking

Next, we tested the influence of antidromic spiking on fast pyloric activity with intact descending inputs (**Figure 3A**). Intracellular soma recordings of PD alone, or simultaneous recordings of PD and AB, showed effects of antidromic spikes on slow wave oscillation amplitudes and burst frequency when stimulated at relatively high frequency (**Figure 3B**). In contrast to the effects seen when descending modulatory inputs were blocked, bursting activity never ceased when inputs were intact. In fact, with intact inputs, burst frequency was slightly but significantly increased from the unstimulated pattern when antidromic spikes were delivered at 10 or 20 Hz (**Figure 3C**). We also analyzed the effect on mean spike rates (**Figure 3D**). Particularly at higher stimulation frequencies, antidromic spikes replaced some spikes generated centrally at the peak of the slow wave oscillations. At 10 and 20 Hz stimulation, the mean centrally generated spike rate was significantly lower than the unstimulated pattern, despite the increase in burst frequency.

#### A Pyloric Pacemaker Model Replicates the Effects of Antidromic Spiking on Rhythm Generation

To address whether the circuit structure of the pyloric pacemaker kernel and common ionic mechanisms are sufficient to give rise to the influence of ectopic spikes on centrally generated activity, we used a simplified circuit model of the AB and two PD neurons (**Figure 4A**). The AB neuron was represented with a single soma-neurite compartment as a non-spiking oscillator, whereas each PD neuron in addition was connected to a 3-compartment axon that produced spikes. As in the biological circuit, the three neurons were electrically coupled. The model produced activity with similar temporal features as the pyloric pacemaker, and we modeled different modulatory states that produced fast or slow activity by varying the modulator-activated inward current, IMI. IMI is the primary activator of neuropeptide-induced rhythmic activity in the STG (Sharp et al., 1993a,b; Swensen and Marder, 2000; Marder and Bucher, 2007; Daur et al., 2016), and increases pacemaker frequency (Sharp et al., 1993b).

We started with a level of g¯MI that gave rise to regular rhythmic activity with a cycle frequency of 0.71 Hz in the unperturbed state, similar to fast pyloric activity in the biological circuit. Ectopic spikes were then produced by stimulating the distal PD axon compartments. As in the biological neurons, antidromic spikes were attenuated in the soma and evoked spikelets of a few millivolt amplitude in the AB neuron (**Figure 4B**, upper traces). In order to test directly if brief depolarizations of AB were sufficient to influence pacemaker oscillations and bursting in PD, we also generated brief current injections directly into the AB neuron. These injections evoked depolarizing potentials of a few millivolts amplitude and a similar time course as electrically transmitted spikelets, and in turn evoked small potentials in the PD neurons, but no active responses (**Figure 4B**, lower traces). We stimulated either the PD axon (**Figure 4C**) or the AB neuron (**Figure 4D**) at different frequencies and measured the effect on burst frequency and mean rate of centrally generated spikes (**Figures 4E,F**). As in the experimental data (**Figure 3**), burst generation was fairly robust to stimulation. Burst frequency increased linearly, but maximally by a few percent. However, the rate of centrally generated PD spiking decreased linearly. Both effects were larger with PD axon stimulation than with AB stimulation, potentially because of asymmetric coupling between AB and PD due to impedance mismatch (see g¯Leak values in **Table 1**).

Next, we tested the effect of antidromic spikes on different burst frequencies. To mimic modulatory states that produce slower or faster pyloric frequencies, we reduced or increased the conductance level of IMI proportionally in both AB and PD. At lower g¯MI values and burst frequencies, antidromic spiking at a fixed frequency of 5 Hz disrupted or greatly reduced central bursting (**Figure 5A**). Like in the experimental data, both the burst frequency and the number of spikes per burst varied across conditions. Therefore, we also determined the mean rate of centrally generated spikes as a measure of circuit activity. **Figure 5B** shows the mean rates and burst frequencies as a function of g¯MI values for both unperturbed activity and during axon stimulation. The mean rate was always lower during axon stimulation, even at increased g¯MI values at which burst frequency was greater during stimulation than in the unperturbed state. This was due to a reduction in the number of spikes per burst, and it replicated the experimental findings for fast pyloric activity (**Figures 3C,D**). When g¯MI was reduced by more than 25% compared to the original value, centrally generated activity ceased completely during axon stimulation (arrows in **Figure 5B**).

In general, changes in membrane potential occur when the total inward and outward currents are not at balance. In the case of slow oscillations in the pyloric pacemaker model, small but continuous changes in inward and outward currents following a burst slowly moved the total current to more negative values until the next burst occurred (**Figure 5C**). Therefore, the effects of antidromic spikes on bursting mean that very brief but repetitive voltage events interfered with much slower current trajectories. **Figure 5D** shows AB voltage and current trajectories during antidromic PD stimulation for the same g¯MI values as in **Figure 5A**. Overlaid traces are from each interspike interval during the latter two thirds of a burst cycle. During fast bursting (large g¯MI), consecutive sweeps showed large offsets because antidromic spike-evoked deflections simply rode on top of largely

stimulation frequency (n = 8; RM-Rank-ANOVA, p < 0.001). Asterisks show significance obtained from post hoc pairwise comparisons.

unperturbed slower changes. At intermediate burst frequency, when antidromic stimulation reduced but did not eliminate centrally generated activity, offset was reduced but still present. With g¯MI values at which antidromic stimulation eliminated bursting, slow dynamics was completely eliminated, resulting in virtually identical voltage and current trajectories in each interspike interval.

## Centrally Generated Bursts Inhibit Peripheral Spike Initiation

In the absence of centrally generated activity, lower than nanomolar concentrations of DA can elicit peripheral spikes. However, during robust and fast rhythmic pyloric activity, peripheral spiking is much less prevalent, even at micromolar concentrations of DA (Bucher et al., 2003). We therefore quantified the dependence of peripheral spike initiation on centrally generated bursting. To this end, we disconnected the STG from the peripheral nerves by cutting the dvn, bath applied DA, and stimulated the dvn (**Figure 6A**). We selected a burst stimulation pattern based on PD activity during unperturbed pyloric rhythms in vitro (Ballo and Bucher, 2009; Ballo et al., 2012). Bursts consisted of 19 stimuli with a parabolic interval structure, with a burst duty cycle of 0.35. We then varied the cycle period between 0.5 and 6 s. During normal pyloric activity, duty cycle and number of spikes in PD neurons do not change with cycle period across preparations (Bucher et al., 2005). Therefore, we changed burst duration proportionally to the cycle period and kept the number of stimuli per burst constant.

Recordings of the pdn during dvn burst stimulation at different periods showed that DA elicited prominent axonal spiking at longer cycle periods, but faster burst stimulation eliminated it (**Figure 6B**). Analysis of the dependence of mean peripheral spike rate on the period of PD burst stimulation showed that peripheral spike initiation was mostly eliminated at periods of 1 s or less, and still partially suppressed at cycle periods of several seconds (**Figure 6C**). In addition, the temporal structure of inhibition of peripheral spiking was dependent on the stimulus pattern. We analyzed the temporal distribution of peripheral spikes for stimulation periods of 2, 3, and 5 s by determining the percentage of spikes that occurred during the first second following a burst, in 100 ms bins (**Figure 6D**). At 2 s stimulation period, peripheral spiking was suppressed long enough that it increased throughout the whole 1s analysis window. This is consistent with an earlier observation that peripheral spikes during mixed activity predominantly occur in the second half of the interval

FIGURE 4 | The effects of antidromic spikes on fast pyloric activity in the model pacemaker circuit. (A) Schematic of the multi-compartment circuit model and the rhythmic activity it produced. Resistor symbols indicate electrical coupling between the soma-neurite (S/N) compartments. Recording sites are indicated with electrode symbols, stimulation sites with kinked arrows. (B) Voltage responses to PD axon or AB stimulations during the interval between bursts. Depolarizing current injection of 1 ms amplitude into the distal axon elicited antidromic spikes that were attenuated to non-overshooting but substantial depolarizations in the PDS/<sup>N</sup> compartment, and transmitted to AB as much smaller depolarizations through electrical coupling (upper traces). Direct injection into AB caused small depolarizations that were transmitted to PD through electrical coupling with little attenuation (lower traces). (C) AB voltage traces and instantaneous burst frequencies during antidromic PD axon stimulation at different frequencies. (D) AB voltage traces and instantaneous burst frequencies during direct AB stimulation at different frequencies. (E) Mean burst frequencies at different frequencies of PD axon and AB stimulation. (F) Mean rate of centrally generated spikes at different frequencies of PD axon and AB stimulation. Stimulated antidromic spikes were excluded.

between bursts (Bucher et al., 2003). However, at stimulation periods of 3 and 5 s, peripheral spiking was only suppressed in the first 100 ms bin after the end of a burst, and constant thereafter.

#### Inhibition of Peripheral Spike Initiation by Centrally Generated Bursts Coincides With a Cumulative Slow After-Hyperpolarization

We wanted to test if the inhibition of peripheral spiking can be explained by subthreshold membrane potential changes in the axon. Peripheral spiking is due to an enhancement of the hyperpolarization-activated inward current (Ih) by DA (Ballo et al., 2010). As the activation threshold of I<sup>h</sup> is substantially more positive than the resting membrane potential, DA-mediated increase in I<sup>h</sup> causes a depolarization of several millivolt in the quiescent axon, which is sufficient to reach spike threshold. Importantly, it also causes an increase in inward rectification, i.e., it counteracts activity-dependent hyperpolarization. In normal saline, bursting activity hyperpolarizes the axonal resting membrane potential, an effect that slowly accumulates over consecutive bursts and is likely caused by the Na+/K<sup>+</sup> pump (Ballo and Bucher, 2009; Ballo et al., 2012; Zhang et al., 2017). In the presence of DA, when I<sup>h</sup> is enhanced, this hyperpolarization is comparatively small. It is therefore reasonable to ask whether realistic bursting activity in the presence of DA can hyperpolarize the axon membrane potential enough to explain the inhibition of DA elicited peripheral spiking shown in **Figure 6**.

We performed intracellular axon recordings from PD close to the dominant peripheral spike initiation site in the dvn

(**Figure 7A**). We then blocked centrally generated activity, applied DA, and stimulated the pdn with our realistic pattern at a burst frequency of 1 Hz. Intracellular PD axon recordings show overshooting spikes with little to no fast after-hyperpolarization, and slow enough repolarization to cause summation during bursts (Ballo and Bucher, 2009; Ballo et al., 2012; **Figure 7B**). Burst stimulation of the pdn confirmed that slow afterhyperpolarization in DA is modest even at steady state after 5 min (300 bursts; only first and last bursts shown). However, inhibition of peripheral spiking often happened immediately or after just a few cycles of bursting activity. Therefore, we specifically focused on hyperpolarization and peripheral spike initiation within the first five cycles of burst stimulation (**Figure 7C**). We only included recordings in which peripheral spiking was not completely abolished after the first burst, which was the case in 6 of 14 experiments. Across those experiments, the rate of extraburst spiking decreased to <10% within 5 cycles (red line plot in **Figure 7C**). This decrease in spiking was associated with a small cumulative hyperpolarization (<−0.8 mV) that followed a similar time course (purple line plot in **Figure 7C**). We also tested whether the time course of hyperpolarization matched the time course of peripheral spiking within the interval between bursts, as described in **Figure 6D**. Across experiments, peripheral spiking occurred predominantly in the later part of each interval (red bar plots in **Figure 7C**). This increase in spiking was associated with a partial recovery from hyperpolarization (purple bar plots in **Figure 7C**).

## The Balance Between Ih-Mediated Depolarization and Na+/K<sup>+</sup> Pump-Mediated After-Hyperpolarization in a Model Axon Determines the Activity-Dependence of Axonal Spike Initiation

We used a modified version of our previously published model of the PD axon (Zhang et al., 2017; **Figure 8A**) to test whether its known ionic mechanisms are sufficient to give rise to the observed experimental results. In the model, we set g¯<sup>h</sup> to a value that produced tonic axonal spiking at 12 Hz, which is within the range of peripheral spike initiation in the PD axon when central activity is blocked and 1 µM DA is applied (Bucher et al., 2003). We then stimulated one end of the axon with the same burst patterns at different frequencies as shown in **Figure 6**. As in the biological axon, slow burst stimulation allowed for continuous axonal spike initiation during the interval between bursts, while spiking diminished with increasing burst frequency (**Figure 8B**).

p < 0.001). Post hoc testing revealed significant differences for all pairwise comparisons of any of the periods between 0.5, and 2 s with any of the periods between 3 and 6 s (p < 0.001, asterisks), and for pairwise comparisons between 3 s period with any of the periods between 4 and 6 s (p < 0.05, asterisk). (D) Mean normalized spike counts during the first second after a burst, divided into ten 100 ms bins, for 2, 3, and 5 s burst stimulation periods. Analysis included only experiments in which peripheral spiking occurred at all three periods (n = 7). In each experiment, the number of spikes per bin was normalized to the total number of spikes in the 1 s window. Dashed lines at 10% indicate the expected level if peripheral spiking had been equal throughout the analysis window. 2W-RM-ANOVA revealed differences across bins and a significant interaction between bins and stimulation periods (p < 0.001 for both). At 2 s stimulation period, post hoc testing showed significant differences in 21 of the 45 pairwise comparisons across bins, indicating that peripheral spiking increased over the course of the whole 1 s analysis window. At 3 and 5 s stimulation periods, pairwise comparisons only showed differences between the first bin and a subset of the other bins, indicating that a time-variant effect on peripheral spiking did not exceed 100 ms. Post hoc testing also showed that none of the bins differed between 3 s and 5 s periods. However, some bins (darker shading) were different between 2 s and both 3 s and 5 s periods, indicating that the temporal structure of peripheral spiking was different at 2 s, compared to 3 s and 5 s.

The model also replicated the experimental observation that at intermediate burst frequencies, spiking occurred predominantly in the later part of each interval (middle two traces in **Figure 8B**).

We then asked to which degree suppression of axonal spiking was associated with cumulative hyperpolarization, and whether the dynamic interactions between pump-mediated hyperpolarization and inward rectification through I<sup>h</sup> were sufficient to explain the effect. As in the biological axon, cumulative hyperpolarization was present but in the submillivolt range (**Figure 9A**, top two panels). Underlying this hyperpolarization was the fact that inward rectification through I<sup>h</sup> did not completely balance Ipump, as the sum of both still yielded an outward current that built up across consecutive bursts (**Figure 9A**, lower panel). As in the biological axon, peripheral spike initiation occurred predominantly in the later part of the interval, associated with the partial recovery of outward current and hyperpolarization between bursts. To further test whether the dynamics of Ipump and I<sup>h</sup> were necessary for the suppression of axonal spiking, we fixed g<sup>h</sup> and Ipump at their mean values before stimulation. Under these conditions, burst stimulation did not suppress axonal spiking (**Figure 9B**). We then injected a negative ramp current into the axon with fixed g<sup>h</sup>

and Ipump values (**Figure 9C**). Again, baseline hyperpolarization in the sub-millivolt range was sufficient to suppress spiking. As the ramp current and resulting hyperpolarization increased continuously, without partial recovery between bursts, peripheral spike initiation decreased continuously.

## DISCUSSION

## Interdependence of Different Spike Initiation Sites in the Same Neuron

We show here that in the PD neurons, central burst generation and distal axonal spike initiation in response to DA have mutually inhibitory effects. Different spike initiation sites in the same neuron can be functionally separated by external inputs, for example in CA3 pyramidal cells during gamma oscillations (Dugladze et al., 2012), but interactions across integration and initiation sites are more prevalent. One site can influence the other through subthreshold potentials only if both sites are electrotonically close to each other. In CA1 pyramidal cells, somatodendritic synaptic potentials do not decay completely over the first few hundred µm of axon length, and can therefore promote or suppress distal axonal spike initiation (Bahner et al., 2011; Thome et al., 2018). In the PD neurons, the electrotonic distance between central and peripheral spike initiation sites exceeds three length constants (Ballo and Bucher, 2009), and interactions must therefore be mediated by propagating spikes.

Spikes propagating from one site and invading the other can either suppress or promote spike initiation. Distal axonal spike initiation is promoted by highly repetitive spiking propagated from the proximal initiation site in hippocampal and cortical interneurons (Sheffield et al., 2011, 2013; Suzuki et al., 2014; Elgueta et al., 2015), as well as some stomatogastric motor neurons (Meyrand et al., 1992; Le et al., 2006). Suppression of spike initiation by invading spikes can exert functional dominance across different initiation sites in leech neurons (Calabrese, 1980; Maranto and Calabrese, 1983), an STG interneuron (Blitz and Nusbaum, 2008), and peripheral branches

of C-fibers (Weidner et al., 2003). In some sensory neurons, peripheral spike initiation resulting from sensory integration can be partially suppressed by spikes backpropagating from central initiation sites (Pinault, 1995; Cattaert and Bevengut, 2002; Stadele et al., 2018).

While the examples above are well described at a phenomenological level, the cellular mechanisms underlying suppression of spike initiation by propagating spikes are not well understood. One possibility would be classical membrane refractoriness. In this case, spikes propagating from one initiation site to another would cause the membrane at the second site to become unexcitable or even extinguish spikes generated at the other site by collision (Gossard et al., 1999; Rossignol et al., 2006). However, the classic description of membrane refractoriness based on inactivation of Na<sup>+</sup> channels and delayed deactivation of K<sup>+</sup> channels only includes processes that occur at the time scale of a few milliseconds (Hodgkin and Huxley, 1952). Beyond the classical refractory period, excitability is usually enhanced (Krishnan et al., 2009; Bucher and Goaillard, 2011; Bucher, 2015). Consequently, suppression of activity at the other site would only be substantial at high spike frequencies, and spike collisions would only occur with high likelihood if the total propagation time from the first to the second initiation site exceeded the intervals of spikes generated at the first (Bucher et al., 2003; Daur et al., 2009). In the PD neuron, spike collisions during bursts have a very low likelihood, as the delay between STG and main peripheral spike initiation site in the dvn is only about 12 ms (Bucher et al., 2003), and extinction of peripherally generated spikes could only outlast each burst by these 12 ms. Therefore, suppression of activity by propagating spikes in the PD axon and elsewhere is more likely based on ionic mechanisms involving slower processes.

#### Suppression of Central Bursting

Invading spikes could suppress activity by affecting the ability to generate spikes, or by interfering with the mechanisms underlying depolarization to threshold. For example, in CA1 pyramidal cells, backpropagating spikes can cause long-term depression of proximal synaptic potentials (Bukalo et al., 2013). The inhibitory effect of backpropagating PD spikes on slow pyloric pacemaker activity was due to a decrease in burst frequency and/or number of spikes per burst (**Figure 2B**). This was associated with a decrease in frequency and/or amplitude of slow wave depolarizations, which suggests that suppression of centrally generated spiking was mostly due to changes in subthreshold oscillatory behavior. Still, the decrease in the number of spikes per burst could have been either due to weaker oscillations or to a change in spike threshold or decrease in the ability to sustain repetitive spiking. However, antidromic spikes during sustained stimulation had stable amplitudes in soma recordings (**Figures 2B,D,E**), suggesting that at least there was no increase in refractoriness and the ability to generate spikes was robust at these stimulation frequencies.

AB is the only true oscillator in the pyloric circuit and crucial to rhythm generation (Miller and Selverston, 1982; Marder and Eisen, 1984; Marder and Bucher, 2007; Daur et al., 2016). Therefore, antidromic PD spikes likely do not just exert their effect through changes in PD excitability, but also have a substantial effect on AB's oscillatory properties. Antidromic

trace: Expansion of the lower voltage region. Lower trace: Negative current

spikes invading the STG can fail to reach the sites of chemical synapses (Mulloney and Selverston, 1972), and electrical synapses are thought to be located at distal neurite branches (Cabirol-Pol et al., 2000; Rabbah et al., 2005). However, the prominent spikelets and even spiking responses in AB (**Figure 2C**) indicate that antidromic PD spikes are well transmitted through gap junctions. Pyloric cycle frequency can easily be manipulated by sustained current injections into AB, without much effect on burst duty cycle or activity phases of follower neurons (Sharp et al., 1993b; Hooper, 1997). As antidromic PD spikes are well transmitted to AB, the resultant net depolarization could explain the small to moderate increase in cycle frequency when modulatory input were intact and bursting otherwise robust (**Figure 3**).

We used a model of the pyloric pacemaker circuit to test whether the circuit structure and a fairly generic set of ionic conductances can replicate the effect of antidromic spiking on centrally generated activity. The model contained a simpler set of conductances than experimentally described and included in a prior model (Soto-Treviño et al., 2005) (see Materials and Methods), but produced activity with similar temporal features as the pyloric pacemaker, and allowed us to model different modulatory states that produced fast or slow activity. The latter was achieved by varying the modulator-activated inward current IMI, a low-threshold, non-inactivating, voltagegated current elicited by a range of different neuromodulators, mostly neuropeptides. It is a potent activator of rhythmic activity and an important determinant of frequency in the pacemaker neurons (Sharp et al., 1993a,b; Swensen and Marder, 2000; Marder and Bucher, 2007; Zhao et al., 2010; Daur et al., 2016; Golowasch et al., 2017).

The model replicated both the robustness of fast burst generation (**Figure 4**) and the sensitivity of slow burst generation (**Figure 5**) to antidromic spiking. At a descriptive level, the suppression of slow bursting at lower values of g¯MI was associated with a disruption of the slow trajectory of out-ofbalance inward and outward currents. Complete cessation of bursting occurred when the consecutive intervals of antidromic spikes produced a fixed pattern of virtually identical current trajectories (**Figure 5D**). Thus, at low values of g¯MI, each antidromic spike delayed the onset of subsequent burst, which, with sufficiently high stimulus frequency, resulted in an indefinite delay and the disruption of bursting.

A more mechanistic analysis of the underlying ionic mechanisms exceeded the scope of this study. Our model had reduced complexity, but neuronal slow wave oscillations are simple to generate and generally due to low-threshold regenerative inward currents that destabilize the resting state enough to slowly depolarize the cell, which in turn allows the activation of outward currents which return the voltage to more hyperpolarized values and restart the cycle (Bose et al., 2014; Golowasch et al., 2017). As such, oscillations only require a minimal set of inward and outward currents with the right kinetics and in the right quantitative balance, as little as a single inward and a single outward current in the generic Morris– Lecar model (Ermentrout and Terman, 2010). While the exact complement and the kinetics of currents determine the details

ramp.

of voltage trajectories, conductances interact in a highly nonlinear fashion and can therefore only be tentatively mapped to specific membrane behavior (Taylor et al., 2009; Ermentrout and Terman, 2010). However, in general, for the transition from silent or tonic spiking to oscillatory behavior, the identity of currents matters less than the total balance of inward and outward currents (Amarillo et al., 2014; Golowasch et al., 2017). For example, pyloric pacemaker and follower neurons express the same type of currents, but follower neurons do not produce oscillations on their own due to higher levels of high-threshold K <sup>+</sup> currents (Golowasch et al., 2017). For these reasons, it is more useful to functionally characterize oscillators according to their behavior, including responsiveness to perturbations (Izhikevich, 2000; Ermentrout and Terman, 2010). The fact that antidromic spiking could only disrupt slow bursting indicates that fast bursting activity in the same neurons obeyed a distinct phase resetting rule, and was therefore a qualitatively distinct type of bursting oscillator (Izhikevich, 2000). A mechanistic explanation of the behavior would therefore require a full mathematical analysis of burst disruption. However, minimally we can conclude that this behavior arises from common oscillator properties and does not depend on undescribed ionic mechanisms.

#### Suppression of Peripheral Spike Initiation

The inhibitory effect of fast bursting on peripheral spike initiation outlasted each burst end by several hundred milliseconds (**Figure 6**), and could be due to a range of different phenomena. The PD axon exhibits a slow after-hyperpolarization that accumulates across consecutive bursts (Ballo and Bucher, 2009; Ballo et al., 2012). This is a common phenomenon in axons, often due to Na+/K<sup>+</sup> ATPase activation (Baker, 2000; Kiernan et al., 2004; Moldovan and Krarup, 2006; Scuri et al., 2007; Bucher and Goaillard, 2011), and often counterbalanced by inward rectification through I<sup>h</sup> (Grafe et al., 1997; Soleng et al., 2003; Baginskas et al., 2009; Bucher and Goaillard, 2011; Bucher, 2015). In the PD axon, DA increases I<sup>h</sup> and consequently substantially reduces activity-dependent hyperpolarization, while blocking I<sup>h</sup> increases it (Ballo et al., 2010, 2012). DA modulation of I<sup>h</sup> is also the mechanism underlying peripheral spike initiation (Ballo and Bucher, 2009; Ballo et al., 2010). During quiescence, the threshold for spike initiation in the dvn is very close to the resting membrane potential, and DA/Ih-mediated depolarization of less than 1 mV can elicit spikes (Ballo and Bucher, 2009). We show that fast burst stimulation eliminated peripheral spike initiation within a few cycles (**Figure 7**). Peripheral spiking appeared well correlated with baseline membrane potential, both within and across cycles. However, the total cumulative hyperpolarization over those few cycles was in the sub-millivolt range. The intracellular recording sites were close to the dominant site of peripheral spike initiation (Bucher et al., 2003), so measurements of membrane potential changes were unlikely to be subject to electrotonic decay.

We asked whether sub-millivolt hyperpolarization alone would be sufficient to suppress peripheral spike initiation. Small changes in membrane potential may have large effects on spike initiation due to an intricate balance between DA/Ih-mediated depolarization, spike threshold, and slow after-hyperpolarization. Alternatively, there could be a decrease in excitability only indirectly or not at all related to changes in baseline membrane potential. One possibility is axonal shunting, that is, an activityor modulator-dependent decrease in input resistance (Jackson and Zhang, 1995; Zhang and Jackson, 1995; Cattaert et al., 1999). Co-activation of opposing currents like Ipump and I<sup>h</sup> is not accompanied by substantial changes in membrane potential, but can increase the total conductance level (Bucher and Goaillard, 2011). However, the increase in g<sup>h</sup> with cumulative Ipump activation had a negligible effect on total membrane resistance of our axon model (not shown). Another possibility is a change in spike threshold caused by the ambiguous effects of slow changes in membrane potential. The immediate effect of hyperpolarization is that it moves the membrane potential away from the spike threshold, but more sustained hyperpolarization can dynamically change spike threshold and excitability by removing inactivation from both Na<sup>+</sup> and A-type K<sup>+</sup> channels (Debanne et al., 1999; De Col et al., 2008; Bucher and Goaillard, 2011; Bucher, 2015; Jiang et al., 2017). The PD axon expresses an A-type current and, as a result, spike amplitude and width are exquisitely sensitive to changes in membrane potential during repetitive activity (Ballo and Bucher, 2009; Ballo et al., 2012). We cannot exclude a contribution of shunting and spike threshold changes, but the results from our axon model suggest that the small hyperpolarization is important. The net cumulative outward current during sub-millivolt hyperpolarization was required for spike suppression (**Figures 9A,B**), and sub-millivolt hyperpolarization in the absence of changes in Ipump and I<sup>h</sup> was sufficient to suppress axonal spike initiation without disrupting burst propagation (**Figure 9C**).

## Dynamic Regulation of the Relative Contributions of Two Spike Initiation Sites to Output Activity

An interesting aspect of our findings in the PD axons is that the suppressive effects of propagating spikes are bi-directional. Therefore, the contributions of each site to PD output activity can shift in an interdependent manner. During fast rhythmic pyloric activity, occurrence of peripheral spike initiation is unlikely. Resting hemolymph levels of biogenic amines are below 10 nM (Livingstone et al., 1980), and while in the absence of bursting activity the threshold for peripheral spike initiation is below 1 nM DA(Bucher et al., 2003), peripheral spiking is mostly extinguished even at 1 µM when cycle periods are ∼1 s or faster (**Figure 6**, Bucher et al., 2003). In vitro control pyloric periods are mostly between 1 and 2 s in H. americanus (Bucher et al., 2005, 2006). However, in vivo recordings in the closely related H. gammarus have shown that pyloric periods are longer than in vitro, and can increase to several seconds in the context of feeding and molting, and under hypoxic conditions (Clemens et al., 1998a,b, 1999, 2001). Experimentally, rhythmic activity can be slowed or interrupted by inhibitory neuromodulators (Cazalets et al., 1987, 1990; Pulver et al., 2003; Kwiatkowski et al., 2013). Under such conditions, peripheral spiking is likely to occur and can either

produce tonic spiking output of PD, or give rise to mixed patterns in which bursts and lower frequency spiking alternate (**Figures 1**, **6**). The relative contributions of each would then depend on the balance of the mutually inhibitory effects.

A similar interdependence has been described in a stomatogastric proprioceptor which has a peripheral spike initiation site that is activated by normal sensory transduction of in response to muscle stretch, and an additional central initiation site that is activated by neuromodulators and synaptic feedback from its target motor circuit (Daur et al., 2009; Stadele and Stein, 2016; Stadele et al., 2018). Activity generated at either site has specific distinguishable effects on central circuit operation, and their competitive interactions arising from mutual inhibition suggest that signal integration at either site can be dynamically adjusted. Therefore, interactions between proximal and distal spike initiation can shape both motor neuron output to stomach muscles and sensory feedback from muscle contractions. It would be interesting to assess the postsynaptic consequences of mixed PD activity at the target neuromuscular junctions, particularly because, in contrast to the sensory neuron, responses can be measured without the confound of recurrent connectivity. Crustacean stomach muscles are multi-terminally innervated and do not show fast Na<sup>+</sup> spikes. However, synaptic responses can show substantial dynamics, due to combinations of different forms of short-term synaptic plasticity and non-linear muscle membrane properties (Lingle, 1981; Sen et al., 1996; Jorge-Rivera et al., 1998; Stein et al., 2006). In addition, stomach muscles have slow contraction properties that transform rhythmic input into mixtures of tonic baseline tension and phasic movements, integrating rhythmic input over multiple cycles (Morris and Hooper, 1998; Morris et al., 2000; Morris and Hooper, 2001). Therefore,

#### REFERENCES


the dynamic interactions between centrally and peripherally generated PD activity could play an important role in the production of movement.

#### DATA AVAILABILITY STATEMENT

The datasets generated for this study are available on request to the corresponding author.

#### AUTHOR CONTRIBUTIONS

ND, FN, and DB conceived and designed all experiments, and ND carried them out. YZ and FN conceived, designed, and carried out all modeling approaches. ND and DB analyzed the experimental data and generated the corresponding figures. FN analyzed the theoretical results and generated the corresponding figures. DB wrote the original draft of the manuscript. FN and ND critically reviewed and edited the text.

#### FUNDING

This work was supported by NIH Grants NS083319 and MH060605 to DB and FN.

#### ACKNOWLEDGMENTS

The authors thank Aleksander W. Ballo for providing additional recordings.



nucleotide-gated channel activation. J. Neurosci. 35, 4131–4139. doi: 10.1523/ JNEUROSCI.3671-14.2015



**Conflict of Interest:** 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 © 2019 Daur, Zhang, Nadim and Bucher. 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(s) 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.

# Diversity of Axonal and Dendritic Contributions to Neuronal Output

Jean-Marc Goaillard\* † , Estelle Moubarak † , Mónica Tapia and Fabien Tell

UMR\_S 1072, Aix Marseille Université, INSERM, Faculté de Médecine Secteur Nord, Marseille, France

Our general understanding of neuronal function is that dendrites receive information that is transmitted to the axon, where action potentials (APs) are initiated and propagated to eventually trigger neurotransmitter release at synaptic terminals. Even though this canonical division of labor is true for a number of neuronal types in the mammalian brain (including neocortical and hippocampal pyramidal neurons or cerebellar Purkinje neurons), many neuronal types do not comply with this classical polarity scheme. In fact, dendrites can be the site of AP initiation and propagation, and even neurotransmitter release. In several interneuron types, all functions are carried out by dendrites as these neurons are devoid of a canonical axon. In this article, we present a few examples of "misbehaving" neurons (with a non-canonical polarity scheme) to highlight the diversity of solutions that are used by mammalian neurons to transmit information. Moreover, we discuss how the contribution of dendrites and axons to neuronal excitability may impose constraints on the morphology of these compartments in specific functional contexts.

#### Edited by:

Haruyuki Kamiya, Hokkaido University, Japan

#### Reviewed by:

Izumi Sugihara, Tokyo Medical and Dental University, Japan Hiroyuki Hioki, Juntendo University, Japan

#### \*Correspondence:

Jean-Marc Goaillard jean-marc.goaillard@univ-amu.fr

†These authors have contributed equally to this work

Received: 30 August 2019 Accepted: 09 December 2019 Published: 22 January 2020

#### Citation:

Goaillard J-M, Moubarak E, Tapia M and Tell F (2020) Diversity of Axonal and Dendritic Contributions to Neuronal Output. Front. Cell. Neurosci. 13:570. doi: 10.3389/fncel.2019.00570 Keywords: dendrite, axon, morphology, ion channels, neurotransmitter

#### INTRODUCTION

More than a century ago, Santiago Ramon y Cajal provided us with a tremendously extensive description of the various morphologies of the neuronal types constituting the mammalian brain and other species' nervous systems (Cajal, 1952). From this meticulous observational work, Cajal hypothesized the role of the different neuronal compartments in information processing. One of his most famous contributions in that sense was the law of ''dynamic polarization'' that originally stated that, within a neuron, information is transmitted from the dendrites towards the soma (cellulipetal) and then in the axon away from the soma (cellulifugal). However, noticing the morphological peculiarities of several neuronal types, Cajal soon revisited this law, because it could only fit neuronal types where the axon directly arose from the cell body onto which all dendrites converged. In particular, Cajal made the observation that in many invertebrate neurons and even in some vertebrate neuronal types (such as the crook-shaped cell in the optic lobe of birds), the axon arose from a dendrite, hence compromising the theory of cellulipetal and cellulifugal propagation of information. Cajal noticed that these dendrite-emanating axons were also present in many neuronal types in mammals (e.g., the substantia nigra pars compacta dopaminergic neurons), and that other neuronal types, such as the dorsal root ganglion (DRG) neurons, presented a unipolar morphology incompatible with the first version of the dynamic polarization law. In light of these findings, Cajal had no choice but to reconsider the propagation of information in neurons and reformulate his law of dynamic polarization. The second version then stated that information flows towards the axis-cylinder (axipetal) away from the soma and dendrites (somafugal and dendrofugal). In doing so, Cajal admitted that the soma of neurons should be merely considered as ''...the place of the protoplasmic apparatus or the chunk of dendrite where the nucleus of the neuron sits and where chromatic inclusions are concentrated''. Therefore, Cajal acknowledged that the soma is not a central compartment in terms of information transfer, but merely in terms of cellular metabolism, due to the presence of the nucleus.

In spite of Cajal's caution about the division of labor in neurons, our view of neuronal function is still largely dominated by the classical ''mostly passive'' dendrites receiving information, and an active axon propagating and transmitting it to target neurons. However, since Cajal's first observations, many more examples of ''misbehaving'' neurons (with a non-canonical polarity scheme) have been identified. For instance, some neurons faithfully propagate and sometimes initiate action potentials (APs) in their dendrites (oriens-alveus interneurons, midbrain dopaminergic neurons, olfactory bulb mitral cells, Gonadotropin-Releasing Hormone, GnRH neurons, DRG neurons; Hausser et al., 1995; Bischofberger and Jonas, 1997; Chen et al., 1997; Martina et al., 2000; Roberts et al., 2008; Iremonger and Herbison, 2012), some neurons release neurotransmitter from their dendrites (midbrain dopaminergic neurons, mitral cells from the olfactory bulb; Schoppa and Urban, 2003; Vandecasteele et al., 2008; Yee et al., 2019), other types of neurons have no canonical axon but produce APs and release neurotransmitter from their dendrites (retinal amacrine cells; olfactory bulb granule cells, parvalbumin and tyrosinehydroxylase interneurons; Kosaka and Kosaka, 2008a; Wilson and Vaney, 2008; Bloomfield, 2009; Chand et al., 2015; Ona-Jodar et al., 2017; Nunes and Kuner, 2018), and some neurons possess neurites that seem to have a mixed dendrite/axon identity, such that they are called dendrons (GnRH neurons; Iremonger and Herbison, 2015). Much like Cajal was urged to correct the dynamic polarization law, these examples oblige us to reconsider the respective functional contributions of dendrites and axons to neuronal excitability in a case by case manner. Here, we propose to review a few cases exemplifying the diversity of dendroaxonal ''solutions'' used by different neuronal types. Rather than providing an exhaustive view of these variations, we will attempt to highlight the differences in functional and morphological constraints that may explain the variety of dendritic and axonal properties observed.

## STRUCTURAL AND FUNCTIONAL DEFINITION OF THE AXON

Before describing the variations in the functional contribution of axons and dendrites in different neuronal types, it is important to remind what is meant when we define a given compartment as an axon or a dendrite. Dendrites and axons exhibit important differences in their anatomical, functional and structural properties.

Anatomically, axons are usually longer than dendrites and their diameter is more or less constant, even after collateral branching. In contrast, the dendritic diameter is known to taper off with distance from the soma (Craig and Banker, 1994). Moreover, the dendrites of many, but not all, mammalian neurons are covered with specialized protrusions called dendritic spines, whereas axons are considered to be devoid of spines. In addition some axons are ensheathed by myelin (produced by Schwann cells or oligodendrocytes) while dendrites are considered to be non-myelinated. Functionally, axons contain clusters of synaptic vesicles at release sites that confer them the role of the pre-synaptic compartment while dendrites, as post-synaptic compartments, generally contain essentially neurotransmitter receptors. Moreover, APs are usually initiated in the proximal part of the axon, the axon initial segment (AIS). The molecular composition of axons and dendrites also differ substantially. Dendrites essentially contain all the somatic organelles (ribosomes, endoplasmic reticulum, Golgi apparatus) while axons contain little, if any, of these components. The ion channels expressed by both compartments can also differ substantially (reviewed in Craig and Banker, 1994; Harris, 1999; Jan and Jan, 2001). One of the most important structural differences concerns the cytoskeleton composition observed in axons and dendrites: in particular, microtubules display different polarities in dendrites and axons, the latter containing only plus-end-out oriented microtubules (Baas et al., 1988; Craig and Banker, 1994). This structural peculiarity is associated with differences in microtubule dynamics, protein trafficking and Microtubule-Associated Proteins (MAP2 in dendrites, MAP1B and tau in axons) and plays a major role in neuronal polarization (reviewed in Conde and Caceres, 2009; Neukirchen and Bradke, 2011). The maintenance of neuronal polarity then depends on the establishment of the AIS in the proximal portion of the axon. The AIS constitutes an axonal subdomain that serves as: (i) a barrier that controls the mobility and diffusion of dendritic proteins along the axolemma; and (ii) a cytoplasmic selectivity filter ensuring the differential trafficking between the somatodendritic (SD) and axonal compartments (Winckler et al., 1999; Burack et al., 2000; Song et al., 2009). The AIS is characterized by an ankyrin-G and βIV-spectrin sub-membranous cytoskeletal scaffold enabling the anchoring of ion channels (sodium channels in particular) and cell-adhesion molecules (CAMs), such as Neurofascin, through its interactions with microtubules and actin filaments (Rasband, 2010). As a consequence, immunostainings of ankyrin-G, βIV-spectrin or voltage-gated sodium channels are routinely used to define the geometry of the AIS (start, end, proximal and distal parts) while the selective dendritic expression of MAP2 is often used to identify dendrites.

Therefore, important anatomical, functional and structural differences exist between dendrites and axons, which should allow us to easily distinguish these two compartments. From the perspective of the current review, we will rely mainly on structural arguments to define a given neurite as a dendrite or an axon. In this respect, it is noteworthy that most of the studies providing us with distinctive characteristics of axons and dendrites have been performed on bi- or multipolar neurons, which we will call a ''classical polarity'' in the next section. We will see that, depending on the neuronal type, ''axonal'' structural and/or functional properties can be also found in dendrites.

## DENDRITIC AND AXONAL PROPERTIES IN NEURONS WITH A "CLASSICAL POLARITY"

The canonical division of labor assumed for dendrites and axons is presented in **Figure 1A** and corresponds for instance to the behavior of cortical output neurons, such as neocortical and hippocampal pyramidal neurons or cerebellar Purkinje neurons. Although some important differences exist between these neuronal types, synaptic inputs are received by the dendrites, travel more or less passively towards the soma, and are integrated at the level of a soma-juxtaposed AIS where a high density of voltage-gated sodium channels supports the triggering of an AP (**Figure 1A**). In pyramidal neurons, the AP has been shown to be initiated specifically in the distal part of the AIS, at 35–45 µm from the soma (Palmer and Stuart, 2006; Kole et al., 2008; Hu et al., 2009). This privileged AP initiation site seems to be explained by: (i) its relative electrical isolation from the ''current sink'' effect of the soma (Brette, 2013; Thome et al., 2014; Telenczuk et al., 2017); and (ii) a high density of Nav1.6 sodium channels (Hu et al., 2009; Lorincz and Nusser, 2010) with (iii) hyperpolarized voltage sensitivities (Rush et al., 2005; Hu et al., 2009). Patch-clamp recordings, sodium imaging and immunogold labeling on neocortical and hippocampal pyramidal neurons have demonstrated that the sodium conductance density is as high as 2,500–3,000 pS/µm<sup>2</sup> at the initiation site (Kole et al., 2008; Lorincz and Nusser, 2010). Both studies also concluded that sodium channel density is at least 30–40 times lower in the pyramidal cell soma and apical dendrites, consistent with the ∼40 pS/µm<sup>2</sup> dendritic conductance density measured by Stuart and Sakmann (1994). While in most experimental conditions this density is too low to allow the triggering of dendritic APs by incoming excitatory post-synaptic potentials (EPSPs), it underlies a partial back-propagation of AIS-initiated APs (**Figure 1B**; Stuart and Sakmann, 1994; Stuart et al., 1997; Vetter et al., 2001; Waters et al., 2003). In fact, a number of studies suggested that back-propagating APs might be involved in short-term and long-term synaptic plasticity mechanisms (for review, see Waters et al., 2005).

The same general behavior is observed in cerebellar Purkinje neurons, albeit with significant differences in the distribution of sodium channels (Stuart and Hausser, 1994). In fact, sodium channels are virtually absent from dendrites (≤20 pS/µm<sup>2</sup> ), leading to very weak back-propagation of APs (**Figure 1B**) and to passive forward propagation of synaptic inputs (Stuart and Hausser, 1994; Roth and Häusser, 2001). In Purkinje neurons, although the AP initiation site has long been debated (Clark et al., 2005), it is now admitted that it is located in the distal AIS at a distance of 20–25 µm from the soma (Khaliq and Raman, 2006; Foust et al., 2010). Interestingly, the very short distance between the AIS and the soma in this cell type (Clark et al., 2005) is also associated with a significant density of sodium channels in the soma (Stuart and Hausser, 1994): these two conditions explain why somatic sodium channels may play an important role in modulating the frequency of AIS-initiated APs in Purkinje neurons (Khaliq et al., 2003; Khaliq and Raman, 2006).

To recapitulate, in pyramidal and Purkinje neurons, the AP is initiated in the distal AIS due to a high density of sodium channels and fails to back-propagate efficiently (although to different extents in the two cell types) due to a low density of dendritic sodium channels. Interestingly, an elegant theoretical study (Vetter et al., 2001) demonstrated that the morphological constraints imposed by the dendritic arborization in these two cell types also have a major influence on the efficiency of AP back-propagation. The densely ramified Purkinje dendrites are highly unfavorable to AP back-propagation, while the back-propagating AP linearly attenuates in the apical trunk but vanishes when entering the apical tuft of pyramidal cells (Vetter et al., 2001; Grewe et al., 2010). In some way, the density of sodium channels and the dendritic morphology have synergistic effects explaining why AP back-propagation is not faithful in these cell types.

Based on the strong differences in sodium channel density between the AIS and the dendrites in these cell types, AIS geometry (distance from the soma and length) has been postulated to have a major influence on excitability, as it may modify AP threshold or the threshold current needed to trigger an AP (Grubb and Burrone, 2010b; Bender and Trussell, 2012; Kole and Brette, 2018). Indeed, several studies have shown that chronic changes in pyramidal neuron activity (induced by KCl application, optogenetic stimulation or M-type current inhibition) were associated with a displacement of the AIS away from the soma (Grubb and Burrone, 2010a; Muir and Kittler, 2014; Wefelmeyer et al., 2015; Lezmy et al., 2017). Although the shifts in the distance were rather small (<20 µm), all studies reported parallel decreases in neuronal excitability. Along the same line, a series of beautiful studies performed on the nucleus laminaris of birds showed that the variations in AIS position and length are associated with the variation in the preferred frequency of these auditory neurons (Kuba et al., 2006, 2014; Kuba, 2012). Specifically, these authors demonstrated that high-frequency neurons displayed a significantly shorter and more distal AIS than low-frequency neurons, the middle-frequency neurons presenting an intermediate phenotype (**Figure 1C**; Kuba et al., 2006). The resulting differences in AP initiation site location appear to be optimized to provide the lowest AP threshold for the preferred frequency, improving the discrimination of characteristic frequencies and the detection of interaural time differences, a critical property for determining sound location. This cell-type-specific spatial tuning of the AIS is achieved in two phases during embryonic development (Kuba et al., 2014), and is partly shaped by sensory inputs, as demonstrated by the effect of sensory deprivation (Kuba et al., 2014). Interestingly, similar results have been obtained in pyramidal neurons of the mouse

visual cortex, showing a developmental activity-dependent control of AIS geometry during the first post-natal weeks (Gutzmann et al., 2014).

In summary, in cell types with low SD excitability, AIS geometry (and the resulting sodium channel distribution) seems to play a predominant role in defining neuronal activity. Consistently, changes in AIS geometry in these cell types are associated with variations in neuronal excitability.

#### MISBEHAVING NEURONS

#### When Dendrites Propagate and Initiate Action Potentials

In contrast to the examples described above, some neuronal types display a highly excitable SD compartment, such that APs can be faithfully propagated or even initiated in dendrites in physiological conditions (Hausser et al., 1995; Bischofberger and Jonas, 1997; Chen et al., 1997; Martina et al., 2000). The contribution of the SD compartment to AP waveform was already observed in the early intracellular recordings obtained from different vertebrate neurons in the 1950s (Coombs et al., 1957a,b; Fatt, 1957). However, the first evidence for faithful dendritic back-propagation of APs was only obtained in 1995 from rat substantia nigra pars compacta dopaminergic neurons (Hausser et al., 1995). This cell type has the particularity of spontaneously generating at a regular frequency (pacemaking activity) broad biphasic APs, suggesting a strong involvement of SD sodium channels (Grace and Bunney, 1983). Two interesting observations were made in this cell type: (i) the axon mainly arises from a dendrite (axon-bearing dendrite or ABD), at distances from the soma reaching 200 µm (**Figure 2A**; Hausser et al., 1995; Gentet and Williams, 2007; Meza et al., 2018; Moubarak et al., 2019); and (ii) the AP recorded in different compartments of the neuron (ABD, soma or non-ABD) shows virtually no attenuation in its amplitude (**Figure 2B**) although it is always initiated at the AIS (Hausser et al., 1995; Gentet and Williams, 2007; Moubarak et al., 2019). This faithful back-propagation, which appears highly reliable during spontaneous pacemaking (Gentet and Williams, 2007; Blythe et al., 2009; Moubarak et al., 2019) may be abolished under specific conditions, for instance when barrages of EPSPs onto the ABD are used to trigger firing or when dopamine is used to dampen somatic excitability (Gentet and Williams, 2007). Since the seminal observation of Hausser et al. (1995), faithful back-propagation has been described in at least two other mammalian cell types, the olfactory bulb mitral cells (**Figure 2A**; Bischofberger and Jonas, 1997; Chen et al., 1997; Xiong and Chen, 2002) and the oriens-alveus interneurons of the hippocampus (**Figure 2B**; Martina et al., 2000). Interestingly, these three cell types share a common property, in that they express a rather high density of sodium channels at the dendritic level: the measured conductance density is ∼75, ∼80 and ∼110 pS/µm<sup>2</sup> in dopaminergic neurons (Moubarak et al., 2019), mitral cells (Bischofberger and Jonas, 1997) and oriens-alveus interneurons (Martina et al., 2000), respectively. Moreover, these three cell types present morphological peculiarities favoring AP back-propagation. In mitral cells, the primary dendrite is mainly unbranched and of constant diameter (Shepherd, 1966), thus limiting low-safety points for current spread. The secondary dendrites have also few branching points and are therefore favorable to AP propagation (Price and Powell, 1970a; Xiong and Chen, 2002). Along the same line, Vetter et al. (2001) demonstrated that the rather simple dendritic arborization of dopaminergic neurons (with much less branching points than pyramidal or Purkinje neuron dendrites) favors faithful back-propagation of APs, even for low densities of dendritic sodium conductances. Interestingly, oriens-alveus interneurons exhibit a dendritic morphology very similar to dopaminergic neurons, with a large soma, short and seldom branched dendrites and a dendrite-emanating axon (McBain et al., 1994; Hausser et al., 1995; Hajos and Mody, 1997; Martina et al., 2000; Moubarak et al., 2019). Therefore in these three cell types, dendritic morphology and SD sodium channel density may have synergistic effects favoring faithful back-propagation of the AP in the entire dendritic arborization.

In addition to faithfully back-propagating APs, mitral cells and oriens-alveus interneurons are also able to initiate full APs from the dendrites in specific experimental conditions (Chen et al., 1997, 2002; Martina et al., 2000). In mitral cells, AP initiation occurs in the distal apical dendrite when: (i) the soma is transiently inhibited by local interneurons (Chen et al., 1997) or (ii) when a strong glutamatergic input onto the distal dendrite is recruited (Chen et al., 2002). This second mode of triggering of dendritic initiation is reminiscent of the oriensalveus interneurons, where brief high-intensity stimulation has to be used to displace the initiation site from the AIS to the non-axon-bearing dendrite (Martina et al., 2000). What may be the role of dendritic initiation in these two cell types? In mitral cells, synaptic inputs are strongly compartmentalized, with excitatory olfactory nerve inputs impinging specifically on the distal tuft of the primary dendrite and local inhibitory inputs projecting onto secondary dendrites near the soma (for review, see Schoppa and Urban, 2003). While AIS geometry has not been closely examined in this cell type, the axon seems to always arise from the soma, with a rather proximal AIS (Lorincz and Nusser, 2008). The existence of a dendritic initiation site remote from the soma may ensure that responses to sensory inputs persist in the presence of strong inhibition of the soma and AIS by local interneurons (Chen et al., 1997). Such a clear segregation of inputs does not seem to be present in oriens-alveus interneurons, where the axon can arise either from a subiculum- or a CA3-oriented dendrite (Martina et al., 2000). The sensitivity of dendritic initiation to strong excitatory inputs suggests that it may ensure fast and reliable activation of these neurons. Alternatively, it could be important for the induction of long-term changes in synaptic efficacy (Martina et al., 2000). In contrast to these two cell types, dendritic initiation of APs has so far not been observed in dopaminergic neurons. As suggested by several publications, the presence of a high density of sodium channels in the SD compartment may not only serve AP back-propagation in this cell type but also play a central role in the generation of regular spontaneous firing (Wilson and Callaway, 2000; Tucker et al., 2012; Jang et al., 2014; Moubarak et al., 2019). Pharmacological blockade, dynamic-clamp experiments and computational modeling indeed suggest that SD sodium channels control pacemaking frequency (Tucker et al., 2012; Jang et al., 2014; Moubarak et al., 2019), even though the AP is always initiated at the AIS. Interestingly, oriens-alveus interneurons have also been shown to generate a spontaneous pacemaking pattern of activity in vitro (McBain et al., 1994), involving, in particular, the H-type current (carried by HCN channels) as a source of depolarization (Maccaferri and McBain, 1996). In substantia nigra dopaminergic neurons, pacemaking in juvenile neurons has been postulated to be HCN and sodium channel-dependent (Chan et al., 2007). The expression of a high density of both types of channels in the dendrites of oriensalveus interneurons (Maccaferri and McBain, 1996; Martina et al., 2000) suggests that pacemaking activity might be generated in a similar way in this neuronal type. Knowing that these interneurons project a densely branched axon onto the apical dendrites of CA1 pyramidal cells (McBain et al., 1994; Martina et al., 2000), these data suggest that oriens-alveus interneurons may be able to provide a tonic inhibition of CA1 pyramidal dendrites in the absence of synaptic drive (Maccaferri and McBain, 1996).

In summary, we provided examples demonstrating that, in cell types with a high density of SD sodium channels, APs can be faithfully propagated in the entire dendritic arborization and sometimes be initiated at the dendritic level. While the functional constraints explaining the need for a highly excitable SD compartment may vary between cell types, the next section suggests that it may be necessary when dendrites fulfill another ''axonal'' function: releasing neurotransmitters.

FIGURE 2 | Neurons faithfully back-propagating APs and releasing neurotransmitters from their dendrites. (A) Schematics corresponding to a dopaminergic neuron of the substantia nigra pars compacta (left) and a mitral cell of the olfactory bulb (right). (B) AP back-propagation in substantia nigra dopaminergic neurons (top) and oriens-alveus interneurons (bottom). (C) Dendritic release of dopamine from substantia nigra dopaminergic neurons measured in paired recordings of dopaminergic neurons. The post-synaptic neuron shows a substantial hyperpolarization (red trace) in response to APs in the pre-synaptic neuron. (D) Dendritic release of glutamate from mitral cells of the olfactory bulb measured by calcium fluorescence in the post-synaptic cells. Mitral cells were filled with Alexa 594 (A1 panel), and regions of interest (ROI) on post-synaptic periglomerular cells (A3) were used to measure post-synaptic responses around the apical tuft of the mitral cell (12). Calcium transients were measured in all ROIs after spiking of the mitral cell (top right) and were blocked by antagonists of glutamate receptors (bottom right). (B) Top, adapted from Gentet and Williams (2007) © 2007 Society for Neuroscience; bottom, adapted from Martina et al. (2000), with permission. (C) Reproduced from Vandecasteele et al. (2008) © 2008 National Academy of Sciences. (D) Reproduced from Castro and Urban (2009) © 2009 Society for Neuroscience.

## When Dendrites Release Neurotransmitters

The SD release of dopamine (DA) by midbrain dopaminergic neurons was first demonstrated in the late 70s in both acute midbrain slices and in vivo (Geffen et al., 1976; Nieoullon et al., 1977). In parallel, dendro-dendritic synapses containing DA-filled vesicles were observed between neighboring DA neurons (Wilson et al., 1977). More recently electrophysiological measurements demonstrated that the SD release of DA was associated with hyperpolarization of the post-synaptic neuron (**Figure 2C**; Beckstead et al., 2004; Vandecasteele et al., 2008). Although many proofs of the SD release of DA between neighboring dopaminergic neurons have been gathered, the details about the release mechanisms are still debated (for review, see Ludwig et al., 2017; Gantz et al., 2018). What is clearly admitted is that DA released at dendro-dendritic synapses binds to D2 receptors on the post-synaptic neuron, which triggers a hyperpolarization mainly due to GIRK channel activation (Beckstead et al., 2004). This release appears to depend at least partly on back-propagating APs (Vandecasteele et al., 2008) and on extracellular Ca2<sup>+</sup> (Yee et al., 2019) and would involve vesicular and/or tubulo-vesicular release of DA (Groves and Linder, 1983; Nirenberg et al., 1996a,b; Bergquist et al., 2002; for review, see Ludwig et al., 2017). Interestingly, a recent study suggested that bursts of APs may fail to faithfully back-propagate to the entire dendritic arborization (Gentet and Williams, 2007), suggesting that dendro-dendritic release of DA would not follow high-frequency discharge of APs, in contrast with the documented potentiation of axonal DA release in the striatum during bursting patterns of activity of midbrain dopaminergic neurons (Gonon, 1988; Heien and Wightman, 2006; Zweifel et al., 2009). This suggests that, at least in some conditions, axonal and SD release of DA might be dissociated. It is noteworthy that the axonal and dendritic release sites are separated by several millimeters in the rodent brain. In addition, the dendro-dendritic release of DA onto neighboring GABAergic neurons has also been functionally described and would involve D1 receptors coupled to TRPC3 ion channels, resulting in an increase of activity of the post-synaptic target (Zhou et al., 2009).

The olfactory bulb is a region where multiple cell types seem to use the dendritic release of neurotransmitters (for review, see Schoppa and Urban, 2003, see also next ''When Dendrites do all the Job: Neurons Lacking a Canonical Axon'' section). Among these, the dendro-dendritic synapses formed by mitral cells onto other types of neurons are the best documented (Schoppa and Urban, 2003). The synapses between mitral cells and granule cells were the first dendro-dendritic synapses described (Hirata, 1964), and their functional role in the processing of olfactory information was identified early on by the electrophysiological and computational studies of Rall et al. (1966). These synapses are formed by the secondary dendrites of the glutamatergic mitral cells contacting specific dendritic structures (gemmules) of the GABAergic granule cells. Interestingly, these dendrodendritic synapses are reciprocal in 90% of the cases, providing very fast feedback inhibition in response to mitral cell activation (Shepherd, 1966; for review, see Schoppa and Urban, 2003; Shepherd et al., 2007). Moreover, as APs are back-propagating faithfully along mitral cell secondary dendrites (Xiong and Chen, 2002) and each granule cell contacts several mitral cells (for review, see Shepherd et al., 2007), these synapses allow long-range lateral inhibition via the activation of granule cells. Interestingly, mitral cells also make dendro-dendritic synapses with another type of interneurons, the periglomerular cells, via their primary dendrite (**Figure 2D**; for review, see Schoppa and Urban, 2003; Nagayama et al., 2014). These dendrodendritic synapses made by mitral cells play an essential role in olfactory processing as they mediate interglomerular (mitralgranule) and intraglomerular inhibition (mitral-periglomerular), respectively (Schoppa and Urban, 2003; Nagayama et al., 2014). The synchronous activation of mitral cells belonging to the same glomerulus is also important for olfactory processing, and evidence has been found that overlapping mitral cells can be coupled by reciprocal excitation (Schoppa and Westbrook, 2002; Urban and Sakmann, 2002). Interestingly, this excitation would be mediated by glutamate released at the apical tuft of the primary dendrite and activating neighboring synapses by spillover (Schoppa and Westbrook, 2002). It must be noted that tufted cells, another group of excitatory projection neurons located in a different layer than mitral cells, present very similar patterns of dendro-dendritic interactions with olfactory interneurons (Schoppa and Urban, 2003; Nagayama et al., 2014).

Dopamine, glutamate, and GABA are not the only neurotransmitters to be released from dendrites. Dendritic release of the neuropeptides oxytocin and vasopressin by the magnocellular neurons of the supraoptic and paraventricular nuclei has been shown to play a critical role in the regulation of activity of this neuronal population (Ludwig et al., 2002; for review, see Ludwig and Leng, 2006; Ludwig and Stern, 2015; Ludwig et al., 2017). Somata and dendrites of these neurons have been shown to contain large amounts of neurosecretory granules (Pow and Morris, 1989) and SD release is induced by Ca2<sup>+</sup> increase (Ludwig et al., 2002). SD release is not strictly dependent on APs, suggesting that axonal release in the neurohypophysis and SD release might be sensitive to different stimuli and regulated separately, at least to some extent (Ludwig, 1998; Wotjak et al., 1998; Ludwig et al., 2002). Moreover, this release does not seem to occur at well-defined synapses (Pow and Morris, 1989). The SD released neuropeptides would exert their effects mainly by autocrine and paracrine actions, which are allowed by the long-lasting half-lives of these peptides in the cerebrospinal fluid (Mens et al., 1983). Oxytocin and vasopressin released from the dendrites of magnocellular neurons are thought to exert powerful self-regulatory actions, inhibiting or promoting the activity of the neurons releasing them on a long-term range (Wotjak et al., 1998; for review, see Ludwig and Leng, 2006; Ludwig and Stern, 2015; Ludwig et al., 2017).

In summary, we provided examples showing that several types of neurons are releasing neurotransmitters from their dendritic compartment. In the cases discussed here, it seems that long-range projecting neurons rely on dendritic release to exert a local control on activity: dendritic dopamine release inhibits neighboring dopamine neurons (and may also have an inhibitory autocrine effect on the releasing neuron), dendritic glutamate release by mitral cells produces short-range lateral inhibition via the activation of interneurons and dendritically released oxytocin and vasopressin exert a self-regulatory action on magnocellular neuron activity. Interestingly, the differences in release mechanisms between the axon and the dendrites (magnocellular neurons) or the possibility to gate back-propagating APs (dopamine neurons, mitral cells) seem to provide these cell types with the possibility to control independently axonal and dendritic release of neurotransmitter, hence considerably expanding the computational repertoire of these cell types. In contrast, we will see now that the functional impact of some interneurons can be restricted to very local actions by the total absence of an axon.

#### When Dendrites do all the Job: Neurons Lacking a Canonical Axon

The first observation of axonless cells was made by Camillo Golgi in the mid-1870s on the mammalian olfactory bulb: Golgi identified small cells in the mitral cell body layer exhibiting long branching dendrites but apparently lacking an axon (for review, see Shepherd et al., 2007). Golgi was one of the main supporters of the reticular theory stating that nerve cells are all connected via a continuous network of axon collaterals. As a consequence, Golgi questioned the ''nervous'' identity of these newly identified cells. The neuronal identity of axonless granule cells of the olfactory bulb was later inferred by Cajal who suggested that granule cells could spread excitatory signals between mitral cells through ''avalanche conduction'' (for review, see Shepherd et al., 2007). Despite the early observation that neurons without an axon do exist in the mammalian brain, little work was done on these peculiar cells and their physiology until the late 1960s. Since then, several other axonless neurons have been identified in vertebrate (Price and Powell, 1970b,c; Toida et al., 1994; Shepherd et al., 2007; Wilson and Vaney, 2008; Bloomfield, 2009) and invertebrate nervous systems (Laurent et al., 1993; Laurent, 1993; Wilson and Laurent, 2005), and seem to be mainly present in sensory systems such as the visual or the olfactory systems. Although axonless neurons in invertebrates appear to be mainly non-spiking neurons (Laurent et al., 1993; Laurent, 1993; Wilson and Laurent, 2005), it is not the case for vertebrate axonless neurons, which seem to fire APs and participate in network activity via the dendro-dendritic release of neurotransmitters.

In the olfactory bulb, three axonless neuronal types have been identified: the granule cells (**Figure 3A**), the parvalbumine interneurons of the external plexiform layer (EPL) and the juxtaglomerular tyrosine hydroxylase interneurons (Rall et al., 1966; Toida et al., 1994; Chand et al., 2015). Unlike what Cajal initially suggested, granule cells of the olfactory bulb are in fact inhibitory interneurons, releasing GABA on mitral cell secondary dendrites through reciprocal dendro-dendritic synapses (Rall et al., 1966; Rall and Shepherd, 1968; Price and Powell, 1970b,c). Granule cell dendrites express Nav1.2 clusters throughout the cell surface, allowing the generation and propagation of full dendritic APs in response to current injection or stimulation by odorants (**Figure 3B**, Egger et al., 2003; Margrie and Schaefer, 2003; Zelles et al., 2006; Egger, 2008; Nunes and Kuner, 2015, 2018; Ona-Jodar et al., 2017). Nav1.2 channel deletion leads to the abolition of AP generation and dendritic GABA release, consequently removing mitral cell inhibition and delaying odor discrimination (Nunes and Kuner, 2018). Parvalbumine interneurons also seem to release GABA onto mitral and tufted cells in the EPL via reciprocal synapses (Toida et al., 1994, 1996), and electrophysiological recordings of unidentified ''axonless'' interneurons in the EPL suggested that these cells were able to fire APs under current injection (Hamilton et al., 2005). Interestingly, in the case of the juxtaglomerular tyrosine hydroxylase interneurons, only a fraction of the cells seems to be deprived of an axon, even though stainings against specific axonal markers were not performed to ascertain the total absence of an axon (Kosaka and Kosaka, 2008b; Chand et al., 2015; for review, see Kosaka and Kosaka, 2016). The axonic and axonless subpopulations can be distinguished: (i) morphologically, as the axonless neurons exhibit a smaller soma and a shorter dendritic arborization than their axonic counterpart but also (ii) functionally, as axonic interneurons appear to be more excitable and generate biphasic APs while axonless interneurons are less excitable and fire monophasic APs (**Figure 3C**, Chand et al., 2015; Galliano et al., 2018). Both axonic and axonless tyrosine hydroxylase interneurons are able to release GABA and DA from their dendrites (Borisovska et al., 2013; Vaaga et al., 2017; for review, see Kosaka and Kosaka, 2016).

In the retina, the main type of axonless neurons seems to be the AII amacrine cells, a class of interneurons mediating day and night vision by transferring information from the rod bipolar cells to the ON and OFF cone pathways via electrical synapses and dendritic release of glycine, respectively (Strettoi et al., 1992; Tsukamoto et al., 2001; for review, see Bloomfield and Dacheux, 2001). These unipolar neurons exhibit two levels of dendritic branching reaching proximally the ON-sublamina and more distally the OFF-sublamina. Rod information is transmitted to AII amacrine cells via electrical synapses (Tsukamoto et al., 2001), AII amacrine cells then amplify and accelerate the post-synaptic response through SD Nav1.1 channels (Tian et al., 2010; Wu et al., 2011) and the initiation of small and broad sodium spikelets (<10 mV and >5 ms) in the primary dendritic level (Boos et al., 1993; Tamalu and Watanabe, 2007; Cembrowski et al., 2012). These sodium spikelets could act as a threshold mechanism to selectively amplify rod signals (Smith and Vardi, 1995; Tian et al., 2010) and potentially affect AII amacrine cells' output to the ON and OFF cone pathways, although it is important to note that this output persists under TTX application (Tian et al., 2010). This last finding suggests that, in specific cases, compact axonless vertebrate neurons may be able to transmit information in the absence of APs, similar to what is known for invertebrate axonless neurons (Laurent et al., 1993; Laurent, 1993; Wilson and Laurent, 2005).

One question that arises from the observation of axonless neurons is whether the AP is still generated from a preferred site in the dendritic tree? Although the mechanisms of AP initiation in most of these cell types are poorly understood, some evidence suggests the presence of one or more AIS-like compartments in the dendrites of parvalbumine interneurons and potentially granule cells of the olfactory bulb (Kosaka and Kosaka, 2008a; Kosaka et al., 2008), and AII amacrine cells of the retina (Wu et al., 2011). Indeed, immunohistochemical studies by Kosaka et al. (2008) revealed that each parvalbumine interneuron could exhibit 2–7 clusters of βIV-spectrin, sodium channels and ankyrin-G along their dendrites (**Figure 3D**). These clusters measured between 3 and 28 µm and could be located up to 50 µm away from the soma, on a 1st to 9th order dendrite (Kosaka and Kosaka, 2008a; Kosaka et al., 2008). Although they did not study olfactory bulb granule cells directly, the authors also mentioned that multiple AIS-like hotspots could also be observed on their dendrites (Kosaka et al., 2008). The idea of multiple sites for AP initiation in granule cells is also supported by the variability in amplitude of somatically recorded APs, which could be a consequence of the morphological characteristics of the specific branch it

was generated from, as suggested by Zelles et al. (2006), Egger (2008) and Nunes and Kuner (2018). Unlike olfactory bulb axonless neurons, AII amacrine cells exhibit a single hotspot containing Nav1.1, Neurofascin and ankyrin-G (**Figure 3E**, Wu et al., 2011). Moreover, disrupting the AIS-targeting motif of Nav1.1 channels results in the abolition of firing, confirming the implication of this AIS-like compartment in AP generation (Wu et al., 2011).

Interestingly, in several brain regions (olfactory bulb, neocortex, striatum), neurons produced during adulthood (adult neurogenesis) are devoid of an axon (Kosaka and Kosaka, 2009; Le Magueresse et al., 2011; Inta et al., 2015; Galliano et al., 2018). For instance, calretinin-positive interneurons with a granule cell-like morphology and a single primary dendrite are produced in the striatum by post-natal neurogenesis (Inta et al., 2015). The post-natally born neocortical axonless neurons (GABA CR+/5HT3A interneurons) also display a granule cell-like morphology and make dendro-dendritic synapses (Le Magueresse et al., 2011). In the olfactory bulb, while both axonic and axonless tyrosine hydroxylase interneurons are produced by embryonic and perinatal neurogenesis, adult neurogenesis only produces axonless neurons (Kosaka and Kosaka, 2009; Galliano et al., 2018).

In summary, some neurons involved in local treatment of information in sensory systems seem to have evolved to carry out their function without the need of a specific output compartment, the axon. While in invertebrates the axonless neurons do not rely on APs and use graded synaptic transmission, many of the vertebrate axonless neurons display dendritic features usually considered to be ''axon-specific'' such as ankyrin-G expression and high-density clusters of sodium channels allowing the dendritic initiation of APs and subsequent dendritic transmitter release.

#### When Dendrite and Axon Are the Same Neurite

The hypothalamic GnRH neurons do not really fall into any of the categories that we described so far, as they seem to not have well-distinguished dendrites and axon, but instead, display a neurite with mixed properties hence named the ''dendron'' (**Figure 4A**, for review, see Iremonger and Herbison, 2015). GnRH neurons lie in the medial septum, rostral pre-optic area and anterior hypothalamic area and project to the median eminence where the release of GnRH regulates luteinizing and follicle-stimulating hormone release from the anterior pituitary. These neurons most often have a very simple fusiform/bipolar morphology with unbranched neurites arising from opposite sides of the soma (for review, see Silverman et al., 1994). Interestingly, the lack of immunostaining against classical axonal proteins (Herde et al., 2013) and the presence of spines (Campbell et al., 2005) indicate that both of these processes are dendrites, even though they are not labeled by anti-MAP2 stainings (Herde et al., 2013). In most GnRH neurons, at least one of these primary dendrites projects to the median eminence over considerable lengths (>1,000 µm, Campbell et al., 2005, 2009; Herde et al., 2013; Herde and Herbison, 2015), displaying spines over its whole length, although spine density within the first 50 µm from the soma is much higher than at more remote locations (Campbell et al., 2005). Since no axon could be found in these neurons, several groups wondered whether these dendrites were capable of initiating and propagating APs (Roberts et al., 2008; Campbell and Suter, 2010; Iremonger and Herbison, 2012; Herde et al., 2013). Indeed, using double soma-dendrite recordings, Roberts et al. (2008) demonstrated that APs could back-propagate from the soma to the dendrites and that spontaneous dendritic AP initiation occurred in GnRH neurons. The use of Na+ sensitive dyes and dendritic recordings confirmed the faithful propagation of APs and suggested that the spike initiation site is located within the first 200 µm of one of the two dendrites (**Figure 4B**, Iremonger and Herbison, 2012). Consistently, ankyrin-G stainings labeled a short segment located on average 90 µm away from the soma on the dendrite projecting towards the median eminence (**Figure 4C**, Herde et al., 2013), leading these authors to name this process ''dendron'' (Herde et al., 2013; Herde and Herbison, 2015; Iremonger and Herbison, 2015). Interestingly, a more recent study suggested that 40% of GnRH neurons indeed possess an axon, although they also display a dendron projecting towards the medial eminence (Herde and Herbison, 2015). Surprisingly, despite the presence of an axon, ankyrin-G staining was overall predominantly located on a dendrite (75% of the time). Since the targets of the GnRH axon are currently unknown, while dendrons projecting onto the median eminence have been clearly identified (Herde et al., 2013), it is still currently assumed that the dendron is the main output of GnRH neurons involved in the control of luteinizing and follicle-stimulating hormone release in the anterior pituitary.

In summary, although recent evidence suggested that GnRH neurons can possess an axon, the functional output of these neurons seems to substantially rely on a long-range projecting spiny dendrite that can initiate and faithfully propagate APs, due to the presence of ankyrin-G and clustering of sodium channels, and has therefore been considered to be neither an axon nor a dendrite, but a dendron.

#### The Specific Case of Unipolar Neurons

Unipolar neurons are defined as having a single neurite arising from the soma. At least one type of neurons in mammals is unipolar: the DRG neurons (Cajal, 1952). The DRG neurons constitute the first step of sensory pathways, conveying information about pain, temperature, proprioception, and mechanoreception. From an anatomical point of view, these neurons are unipolar, with a stem axon leaving the soma and two axonal branches projecting to the periphery and to the spinal cord, respectively (**Figure 5A**, for review, see Nascimento et al., 2018). Both branches are myelinated (for myelinated DRG neurons), the AP being initiated in the peripheral branch and conducted towards the spinal cord. However, several elements suggest that the peripheral branch might be more of a dendrite and that the ''pseudo-unipolarity'' of DRG neurons is in fact acquired during development (Nascimento et al., 2018). Cajal was the first one to describe in detail this process when he observed that bird DRG neurons are indeed bipolar during embryonic development and only become secondarily unipolar (Cajal, 1952), acquiring this peculiar morphology where the peripheral dendritic and central axonal branches are directly connected to each other. While the subject of the subcellular nature of the stem axon is still debated, one hypothesis is that it corresponds to a shrinking and elongation of the somatic membrane that would bring the dendritic and axonal branches in close apposition (Nascimento et al., 2018). Concerning the AIS, while several studies have observed a distinctive AIS in cultured embryonic DRG neurons (Zhang and Bennett, 1998; Dzhashiashvili et al., 2007; Hedstrom et al., 2007), there is no evidence of a well-defined AIS in adult DRG neurons in vivo (Nascimento et al., 2018). From a functional point of view, APs are initiated in the peripheral branch close to the peripheral endings where sensory transduction occurs (Carr et al., 2009), although the AP initiation site can slightly move depending on the level of hyperpolarization of the terminal. Consistent with this finding, in non-myelinated peripheral branches, Nav1.8 and Nav1.9 sodium channels were found to be distributed homogeneously in the peripheral endings (Black and Waxman, 2002).

While unipolar neurons represent an exception in the mammalian nervous system, it is interesting to note that most arthropod neurons are unipolar (Sánchez-Soriano et al., 2005; Rolls et al., 2007; Rivera-Alba et al., 2014; Triarhou,

2014; Hesse and Schreiber, 2015; Niven, 2015). In insects and crustaceans, most neurons have an ''externalized'' cell body from which emerges a single ''stem'' neurite giving rise to both dendrites and axons (Hesse and Schreiber, 2015; Niven, 2015). This organization seems to bear several advantages because: (i) it allows a clear segregation of a cell body area and a pure neuropil area where contacts are made between presynaptic and post-synaptic neurons (Rivera-Alba et al., 2014); and (ii) it removes an electrotonically unfavorable compartment (the soma) from the signal propagation path (dendrite to axon), thus preventing unnecessary signal attenuation (Hesse and Schreiber, 2015). In fact, two studies suggested that soma size may be one of the main constraints determining whether the soma is externalized (leading to a unipolar morphology), independent of the species studied (Rivera-Alba et al., 2014; Hesse and Schreiber, 2015). More precisely, using computational modeling of passive and active propagation of signals, Hesse and Schreiber (2015) demonstrated that soma externalization is beneficial only if the stem neurite is sufficiently resistive (in terms of axial resistance) compared to soma size. Indeed, data collected from various species (including insects, crustaceans and mammals) seem to confirm this conclusion, as the ratio stem neurite/soma size is significantly smaller in neurons displaying externalized somata (**Figure 5B**). Interestingly, the soma of DRG neurons is very large (20–100 µm in rats)

and the ratio stem axon/soma size follows the rule suggested by Hesse and Schreiber (2015; see **Figure 5B**). So far, it is still unclear why unipolar neurons are predominant in arthropods while multipolar neurons represent the vast majority of vertebrates and lower invertebrates (Bullock and Horridge, 1965; Triarhou, 2014). Interestingly, insect unipolar neurons have been shown to ''regress'' to a bipolar or multipolar morphology after a few days in culture (Sánchez-Soriano et al., 2005), similar to what has been observed for DRG neurons. One hypothesis for cell body externalization in higher invertebrates is that the cell body is displaced out of the neuropil area, and neurons become unipolar only during this process (Sánchez-Soriano et al., 2005). Therefore, while invertebrate neurons appear rather dissimilar to vertebrate neurons, this dissimilarity appears to be secondarily acquired during development due to cell body exclusion from the connecting path. Moreover, recent studies suggest that their dendrites and axons behave very much like their vertebrate counterparts (Sánchez-Soriano et al., 2005; Rolls et al., 2007). Consistent with this, although the presence of a distinctive AIS in invertebrates has long been questioned, recent evidence demonstrated that cultured drosophila neurons express a specific isoform of ankyrin in the proximal axonal region (Rolls et al., 2007; Jegla et al., 2016), much like ankyrin-G in vertebrate neurons.

In summary, many neurons in the animal kingdom are unipolar, departing from the classical neuronal morphology depicted in most textbooks. In spite of this particularity, recent evidence suggests that invertebrate unipolar neurons possess dendrites and axons with clearly segregated functions and specific molecular signatures (Sánchez-Soriano et al., 2005; Rolls et al., 2007; Rolls and Jegla, 2015; Jegla et al., 2016). On the other side, vertebrate DRG neurons display two neurites behaving like axons, even though their developmental origin suggests that the peripheral and central branches are a dendrite and an axon, respectively (Cajal, 1952; Nascimento et al., 2018).

## ARE DENDRITIC AND AXONAL PROPERTIES CO-TUNED?

So far, we reviewed examples demonstrating the diversity of morphological and functional properties of dendrites and axons in various neuronal types. Some neurons display a highly excitable axon together with fairly passive dendrites. In other neuronal types, dendrites are highly excitable and can initiate, propagate APs and release neurotransmitters. In the olfactory bulb and the retina, some interneurons are devoid of an axon, and all pre- and post-synaptic functions are carried out by the dendrites. Finally, some neurons, such as the DRG neurons, possess neurites that all behave more or less like axons.

From these observations, one may wonder whether general rules bind variations in dendritic excitability and morphology to variations in axon or AIS excitability and morphology. In other words, are dendritic and axonal properties balancing each other to ensure optimal neuronal output, such that axonal properties might differ between neurons with passive or active dendrites? We will see that in some neuronal types, dendritic and axonal properties seem to be co-tuned to optimize neuronal output, while in others axonal and dendritic properties appear fairly independent from each other. Since many morphological and biophysical parameters can influence both dendritic and axonal properties, these relationships are particularly difficult to demonstrate experimentally. Therefore, computational approaches have proved particularly useful in determining why co-tuning rules might exist or be absent from a specific neuronal type.

#### Evidence of Co-tuning of Axonal and Dendritic Properties

We already mentioned that, in the bird auditory nucleus laminaris, AIS geometry was correlated with the neuron preferred frequency in a manner consistent with the theoretical predictions (Kuba et al., 2006). Since the nucleus laminaris is tonotopically organized, such that neuronal position correlates with the preferred frequency encoded (with high-frequency and low-frequency neurons located in the rostromedial and caudolateral regions, respectively; Rubel and Parks, 1975), it means that AIS geometry depends on the neuron position within the nucleus (Kuba, 2012; Kuba et al., 2014). Interestingly, the tonotopic organization of the nucleus is also associated with a gradient in dendritic morphology (Smith and Rubel, 1979; Kuba et al., 2005; Kuba, 2012). Specifically, dendritic arborization length seems to be negatively correlated with preferred frequency such that high-, middle- and low-frequency neurons exhibit a small, medium and large dendritic arbor, respectively (Smith and Rubel, 1979; Kuba et al., 2005; Kuba, 2012). While the influence of soma size has been less studied, some observations suggest that the soma surface is also negatively correlated with preferred frequency (Kuba et al., 2005). This SD scaling seems to favor the integration of fast inputs and improve interaural time-detection sensitivity in high- and middle-frequency neurons as they are more electrotonically compact than low-frequency neurons (Kuba et al., 2005). Consistently, this tonotopic gradient of dendritic complexity across the nucleus laminaris is also associated with a gradient of EPSC filtering: more filtering occurs in low-frequency neurons due to a more complex and less compact dendritic tree leading to smaller and slower somatic EPSCs. On the other hand, EPSCs are larger and faster in the compact middle and high-frequency neurons (Kuba et al., 2005; Slee et al., 2010). In this scheme, the optimal output response of the neuron seems to depend mainly on the passive properties of the SD compartment. Indeed, other studies have suggested that higher interaural time-detection sensitivity and noise tolerance was achieved with a passive somatic compartment (Ashida et al., 2007) and that restricting the invasion of the AP in the dendrites could be necessary to avoid distortion in synaptic integration of high-frequency inputs (Scott et al., 2007). Thus, in auditory neurons, AIS geometry and SD morphology seem to co-vary (**Figure 6A**), such that the optimal detection of specific frequencies is achieved through the synergistic influence of SD compactness and AIS length and distance from the soma.

Another case of axonal and SD co-tuning has been recently reported in neocortical L5 pyramidal neurons, where the axon can arise directly from the soma or from a basal dendrite (Hamada et al., 2016). In this cell type, the distance between the AIS and the soma can vary from 1 to 20 µm and is negatively correlated with the diameter of the apical dendrite. While this may seem unfavorable for spike initiation, this co-scaling seems to stabilize the amplitude of the back-propagating AP recorded at the soma and may represent a homeostatic mechanism stabilizing neuronal output in the face of cell-to-cell variations in morphology (Hamada et al., 2016).

In an elegant computational study, Gulledge and Bravo (2016) specifically investigated the respective influence of the morphological and biophysical properties of the AIS and the SD compartment on neuronal excitability, their results suggesting that optimal neuronal output can only be achieved by coordinated regulation of both compartments. Using simplified and real-morphology models of several neuronal types (Purkinje neuron, dentate granule cells, neocortical and hippocampal pyramidal neurons), the authors demonstrated that the optimal length and location of the AIS is strongly dependent on SD size. In fact, smaller neurons tend to be more excitable when the AIS is medium in length and relatively close to the soma while in bigger neurons excitability is enhanced by a longer and more distal AIS (**Figure 6B**, Gulledge and Bravo, 2016). In addition to this general insight, this computational study also suggests that modifications in AIS length (and the associated sodium channel content) should have more impact than AIS-soma distance on excitability, while changes in SD morphology (and the associated capacitive behavior) are more critical than changes in SD ion channel density (Gulledge and Bravo, 2016). Interestingly, using models of 28 fully reconstructed L5 pyramidal neurons, Hay et al. (2013) reached similar conclusions. To ensure stereotypical activity (matching the experimentally recorded range of firing), their model predicts that the density of ion channels in the axon and soma have to scale linearly with the conductance load of dendritic and somatic surface area (Hay et al., 2013). Although formulated in a different way, the modeling work performed by Brette and colleagues also came to the conclusion that the ''current sink'' effect of the SD compartment needs to be counterbalanced by AIS location or ion channel content (Platkiewicz and Brette, 2010; Brette, 2013; Telenczuk et al., 2017). As mentioned by Gulledge and Bravo (2016), these results suggest that future studies should look

FIGURE 6 | Co-tuning of somatodendritic (SD) and AIS morphologies influences neuronal output in "classical polarity" neurons. (A) Schematics summarizing the results obtained by Kuba et al., 2005, 2006, 2014; Kuba, 2012 on bird auditory neurons (see main text for references). Auditory neurons responding preferentially to high-frequency sounds (top) display a compact SD compartment together with a short and distant AIS while low-frequency neurons (bottom) display a larger soma, longer dendrites and a longer AIS located close to the soma. Middle-frequency neurons display an intermediate morphology, both at the SD and AIS levels. (B) Schematics summarizing the results obtained by Gulledge and Bravo (2016) using computational modeling. While neurons with a small SD compartment display a higher excitability when the AIS is of intermediate length and/or close to the soma, larger neurons are more excitable when the AIS is longer and/or further away from the soma.

for potential co-variations of AIS architecture, SD morphology and neuronal output. To our knowledge, very few studies have been performed in that direction (Hamada et al., 2016; Moubarak et al., 2019).

It is noteworthy that all the studies cited in this section have been performed on neuronal types exhibiting what we previously named a ''classical polarity,'' i.e., with fairly passive dendrites. Depending on their morphology, passive dendrites can constitute a major impediment to neuronal excitability that may be overcome by modifications of AIS geometry or ion channel content. Unsurprisingly, we will see that other neuronal types with a higher SD excitability may not follow the same rules.

## Absence of Co-tuning: When Excitable Dendrites Make Neurons Robust to AIS Variations

Indeed, significant cell-to-cell variations in AIS geometry have been reported in neuronal types that faithfully back-propagate APs (Hausser et al., 1995; Martina et al., 2000; González-Cabrera et al., 2017; Meza et al., 2018; Moubarak et al., 2019). In the oriens-alveus interneurons, the soma-AIS distance was found to vary between 0 and ∼120 µm, the axon arising either from a subiculum- or CA3-oriented dendrite (Martina et al., 2000). This is a considerable range when we consider that variations under 20 µm in pyramidal neurons are correlated with (and compensated by) changes in apical dendrite diameter (Hamada et al., 2016). In spite of this range of variation, no obvious difference in output or in AP back-propagation was noticed between the neurons with a close or a remote AIS (Martina et al., 2000). In the substantia nigra dopaminergic neurons, it was noted early on that the axon could be located at distances from the soma exceeding 200 µm in the adult rat (Hausser et al., 1995). More recent studies performed on juvenile rats and mice have specifically measured the cell-to-cell variations in AIS geometry and their potential influence on neuronal output (González-Cabrera et al., 2017; Meza et al., 2018; Moubarak et al., 2019). Similar to what was observed in oriens-alveus interneurons, the AIS-soma distance was found to vary between 20 and 125 µm in the rat (Moubarak et al., 2019) and 10–70 µm (Meza et al., 2018) or 15–100 µm in the mouse (Goaillard, Moubarak, Tapia and Tell, unpublished observations). Interestingly, in rat dopaminergic neurons, neither variations in AIS distance nor in AIS length seemed to be associated with changes in neuronal output (AP back-propagation, AP shape, firing frequency; **Figure 7**; Moubarak et al., 2019). Measurements of sodium currents in the SD compartment and real-morphology modeling based on 37 fully reconstructed neurons suggested that SD excitability plays a predominant role in neuronal output, such that variations in AIS geometry are tolerated. On the other hand, this study also predicted that cell-to-cell variations in SD morphology may strongly influence firing frequency, although no simple relationship between these two parameters could be detected (Moubarak et al., 2019). The results concerning a potential relationship between AIS geometry and firing frequency are more contrasted in mouse dopaminergic neurons: while in vitro measurements of AIS geometry and firing frequency confirmed the lack of relationship between these variables (Goaillard, Moubarak, Tapia and Tell, unpublished observations), results obtained in vivo showed that AIS length was correlated with firing frequency (Meza et al., 2018). The presence of synaptic activity in vivo and the sensitivity of both ligand-gated and voltage-gated ion channels to anesthetics may explain the differences observed between these studies.

## OPEN QUESTIONS

in vitro. Reproduced from Moubarak et al. (2019).

In this review, we presented examples demonstrating that mammalian neurons use a wide variety of dendro-axonal solutions to generate APs and release neurotransmitters onto their post-synaptic targets. However, from these observations, it is difficult to extract a general rule that would relate dendritic and axonal morphologies and excitabilities. At one end, auditory neurons in birds seem to rely on an ''optimal'' co-tuning of SD morphology and AIS geometry that allow them to encode specific sound frequencies and interaural time differences (**Figure 6A**). In pyramidal neurons, the co-scaling of apical dendrite diameter and AIS distance from the soma seems to stabilize neuronal output (Hamada et al., 2016). However, in most other cases, it is difficult to see the variations in dendritic

length (bottom) and pacemaking frequency in 32 rat neurons recorded

and axonal morphologies as ''optimal'' solutions for neuronal activity. For instance, the SD morphology of dopaminergic neurons is extremely variable and independent of AIS geometry and is not really predictive of neuronal output (Moubarak et al., 2019). This lack of link between neuronal output and morphology could be due to several reasons. On one hand, neuronal morphology might not be sufficient to predict output because many other variables, including the heterogeneous densities of a variety of ion channels located in the soma, dendrites and AIS, need to be included in the equation (Weaver and Wearne, 2008; Moubarak et al., 2019; Otopalik et al., 2019). Another possibility is that neuronal morphology does not need to be ''optimal'' but just good enough for a given neuronal type. Indeed, in two recent studies, Otopalik et al. (2017a,b) demonstrated that crustacean motoneurons seem to be rather insensitive to variations in their dendritic morphology, such that synaptic integration is relatively stable in the face of cell-to-cell variations in morphology. This led the authors to postulate that the relationship between morphology and neuronal output might be many-to-one (Otopalik et al., 2017a,b), meaning that the same output can be produced by neurons with vastly different morphologies. As the specific biophysical properties of dendrites were not assessed in these studies, this many-to-one relationship could also hide some co-variations of dendritic morphology and biophysical properties, such that ion channel expression partly compensates for morphological variations. In fact, other studies performed on the development of crustacean motorneurons have elegantly demonstrated that neuronal output remains stable despite massive SD growth, suggesting that biophysical properties must change along with morphological growth to maintain neuronal output (Bucher et al., 2005). Even though computational simulations have suggested that neuronal activity might be more sensitive to morphological parameters than to biophysical ones (Weaver and Wearne, 2008; Moubarak et al., 2019), an interesting hypothesis is that the specific influence of dendrites and axon on neuronal output can only be understood if the biophysical properties and morphologies of each compartment are measured in each neuron together with its specific pattern of activity. In summary, the current state of knowledge suggests that, even within a same neuronal type, there might be many dendroaxonal morphological solutions allowing to produce the same output (Samsonovich and Ascoli, 2006), just as many biophysical solutions have been demonstrated to produce the same output (Prinz et al., 2004; Marder and Goaillard, 2006; Schulz et al., 2006; Taylor et al., 2009).

Across neuronal types, we showed that the division of labor between axons and dendrites can also take multiple

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#### CONCLUSION

In conclusion, many neuronal types in the mammalian nervous system do not comply with the classical polarity scheme that drove much of our understanding of information processing at the single-neuron level. Evidence suggests that classical ''axonal'' functions can be carried out by dendrites with peculiar biophysical properties and that the rule balancing dendritic and axonal morphologies and excitabilities might vary from one neuronal type to another. Even though it is unlikely that the properties of these compartments are independently regulated within one given neuronal type, the diversity of schemes and the wealth of parameters involved currently prevent us from easily understanding the logic that relates variations in axonal morphology/excitability to variations in dendritic morphology/excitability. Nonetheless, it is clear that mammalian neurons are using a tremendous diversity of solutions to carry out a similar function, initiating and propagating APs, and releasing neurotransmitters.

#### AUTHOR CONTRIBUTIONS

J-MG, EM, MT and FT wrote the manuscript.

#### FUNDING

This work was funded by the European Research Council (ERC CoG grant 616827 CanaloHmics to J-MG; supporting MT).

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**Conflict of Interest**: 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 © 2020 Goaillard, Moubarak, Tapia and Tell. 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(s) 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.

# Myelination Increases the Spatial Extent of Analog-Digital Modulation of Synaptic Transmission: A Modeling Study

Mickaël Zbili 1,2\* and Dominique Debanne<sup>2</sup> \*

<sup>1</sup>Lyon Neuroscience Research Center, INSERM U1028-CNRS UMR5292-Université Claude Bernard Lyon1, Lyon, France, <sup>2</sup>UNIS UMR 1072 INSERM, AMU, Marseille, France

Analog-digital facilitations (ADFs) have been described in local excitatory brain circuits and correspond to a class of phenomena describing how subthreshold variations of the presynaptic membrane potential influence spike-evoked synaptic transmission. In many brain circuits, ADFs rely on the propagation of somatic membrane potential fluctuations to the presynaptic bouton where they modulate ion channels availability, inducing modifications of the presynaptic spike waveform, the spike-evoked Ca2+ entry, and the transmitter release. Therefore, one major requirement for ADFs to occur is the propagation of subthreshold membrane potential variations from the soma to the presynaptic bouton. To date, reported ADFs space constants are relatively short (250–500 µm) which limits their action to proximal synapses. However, ADFs have been studied either in unmyelinated axons or in juvenile animals in which myelination is incomplete. We examined here the potential gain of ADFs spatial extent caused by myelination using a realistic model of L5 pyramidal cell. Myelination of the axon was found to induce a 3-fold increase in the axonal length constant. As a result, the different forms of ADF were found to display a much longer spatial extent (up to 3,000 µm). In addition, while the internodal length displayed a mild effect, the number of myelin wraps ensheathing the internodes was found to play a critical role in the ADFs spatial extents. We conclude that axonal myelination induces an increase in ADFs spatial extent in our model, thus making ADFs plausible in long-distance connections.

Keywords: myelin, axon, axonal space constant, analog digital facilitation, spike shape, ion channels, axonal length constant

## INTRODUCTION

Analog-digital facilitation (ADF) is a context-dependent modulation of synaptic transmission reported in local excitatory circuits (Alle and Geiger, 2006; Shu et al., 2006; Kole et al., 2007; Sasaki et al., 2012; Debanne et al., 2013; Bialowas et al., 2015; Rama et al., 2015; Zbili and Debanne, 2019). To date, two major types of ADF have been described: depolarizationinduced analog-digital facilitation (d-ADF) and hyperpolarization-induced analog-digital facilitation (h-ADF). In cortical circuits, d-ADF is an enhancement of the spike-evoked synaptic transmission following a long (3–10 s) subthreshold depolarization of the presynaptic cell.

#### Edited by:

Josef Bischofberger, University of Basel, Switzerland

#### Reviewed by:

Maarten H. P. Kole, Netherlands Institute for Neuroscience (KNAW), Netherlands Takuya Sasaki, The University of Tokyo, Japan

#### \*Correspondence:

Mickaël Zbili zbili.mickael@gmail.com Dominique Debanne dominique.debanne@inserm.fr

Received: 26 August 2019 Accepted: 10 February 2020 Published: 03 March 2020

#### Citation:

Zbili M and Debanne D (2020) Myelination Increases the Spatial Extent of Analog-Digital Modulation of Synaptic Transmission: A Modeling Study. Front. Cell. Neurosci. 14:40. doi: 10.3389/fncel.2020.00040 The mechanism underlying d-ADF in cortical networks relies on Kv1 channel inactivation. The subthreshold depolarization leads to inactivation of axonal Kv1 channels which provokes an increase in the presynaptic spike duration (spike broadening), an increase in the spike-evoked Ca2+ entry in the presynaptic bouton and an enhancement of the transmitter release (reviewed in Debanne et al., 2013; Zbili and Debanne, 2019). h-ADF is a much faster process relying on the recovery of axonal Nav channels from inactivation (or deactivation). A short hyperpolarization of the presynaptic cell (15–200 ms) leads to the deactivation of axonal Nav channels, which provokes an increase in the presynaptic spike amplitude, an increase in the spike-evoked Ca2+ entry and an enhancement of synaptic transmission. Importantly, for d-ADF and h-ADF to occur at a specific synapse, membrane potential variations of the soma (depolarization or hyperpolarization) have to propagate to the presynaptic bouton to impact the local spike shape (duration or amplitude). Therefore, the spatial extent of d-ADF and h-ADF and the number of synapses impacted by these phenomena are mainly determined by the axonal length constant. By increasing the axonal membrane resistance, myelination could increase the axonal length constant (Castelfranco and Hartline, 2015; Alcami and El Hady, 2019) and therefore expand the number of postsynaptic cells impacted by ADFs. The space constant of analog-digital modulation in unmyelinated axons has been shown to vary between 145 and 430 µm depending of the nature of the subthreshold signal used to induce ADF, the number of branch points, and the cell type (Alle and Geiger, 2006; Shu et al., 2006; Sasaki et al., 2012; Bialowas et al., 2015; Rama et al., 2015). In L5 pyramidal neurons which display a myelinated main axon and unmyelinated collaterals, the length constant of the main axon has been evaluated from 417 µm to 1,180 µm (Shu et al., 2006; Kole et al., 2007; Christie and Jahr, 2009; Cohen et al., 2020). We hypothesized that the development of myelin sheaths in L5 pyramidal neurons, which occurs mainly between P10 and P25 in rats (Battefeld et al., 2019), should increase the axonal length constant and therefore increase the spatial extent of ADFs.

Using a computational approach, we show here that myelination increases the axon length constant by a factor 3 leading to ADFs expression more than 2 mm away from the soma. In addition, the number of myelin layers wrapping the internodes were found to have a critical impact on ADF spatial extent.

### MATERIALS AND METHODS

#### Model Morphology

A multi-compartment model of a 36 days-old rat L5 pyramidal neuron was simulated with NEURON 7.6 (see **Supplementary Figure S1** for model morphology). The neuronal morphology was taken from a reconstructed neuron by Hay et al. (2011) available on Neuromorpho.org (Ascoli et al., 2007; Neuromorpho ID: NMO\_07763; Neuron Name: C080418A-1- SR). The dendritic tree of this neuron was fully reconstructed while the axonal tree was partially reconstructed (up to 1 mm from the soma). The neuron is composed of a dendritic tree, a soma, an axon hillock, an axon initial segment (AIS) and an axonal tree. The axonal tree is composed of the main axon presenting a diameter of 1.14 µm and six axonal collaterals with a diameter of 0.23 µm. The collaterals connect to the main axon at 128.5 µm, 129.6 µm, 300.9 µm, 301.5 µm, 810.1 µm, and 993.9 µm from the soma. We kept unchanged the morphology except for the axon. In fact, in order to observe the spatial extent of ADF on distal synapses, we extended the main axon (total length in our model: 20 mm) and added four distant collaterals branching the main axon 1,907.4, 2,922.4, 3,937.4 and 4,952.4 µm from the soma. Presynaptic sites containing presynaptic Ca2+ channels were placed every 8 µm into the axon collaterals (Romand et al., 2011) leading to a total number of 1,982 presynaptic sites into the model. The axial intracellular resistivity was fixed to 150 cm in all the model compartments. The membrane capacitance was fixed to 1 µF/cm<sup>2</sup> in all the model compartments except for myelin sheaths (see below). All simulations were run with 6.25 µs time steps and the nominal temperature of the simulation was 37◦C. The measurement locations for subthreshold voltage fluctuations and AP waveform were the nodes of Ranvier of the main axon (or the equivalent places in the case of unmyelinated and hybrid models). The measurement locations for spike evoked Ca2+ entry and synaptic transmission were the presynaptic sites located in the axon collaterals, leading to an evaluation of d-ADF and h-ADF at these presynaptic sites.

## Ionic Conductance

The model contains six types of conductance: leak channels, potassium delay rectifier channels (Kdr), Kv1 channels, Nav1.2 channels, Nav1.6 channels, and P/Q-type calcium channels. The biophysics of Kdr, Nav1.2, and Nav1.6 were taken from Hu et al. (2009), the biophysics for Kv1 channels were taken from Shu et al. (2007b) and the biophysics for P/Q type calcium channels were taken from Bischofberger et al. (2002). The equilibrium potentials for Na<sup>+</sup> , K<sup>+</sup> , Ca2+ were set respectively to +60 mV, −90 mV and +140 mV.

In all the simulations, the densities of the different channels in the dendrites, the soma, the axonal hillock, and the AIS were taken from a previously published model of L5 pyramidal neurons (Hu et al., 2009; see **Table 1**). These densities were unchanged in the different simulations. In contrast, the channel densities in the axon were modified according to the presence of myelin, the length of the internodes and the number of myelin wraps. These modifications of channel density were made in order to preserve the axonal spike waveform at resting membrane potential measured in the middle of the axon (10 mm away from the soma; **Supplementary Figure S2**). The preservation of the basal axonal spike waveform in the different simulations was mandatory in order to compare the various conditions we studied. In fact, ADFs depend on spike shape modifications and are highly sensitive to the basal spike waveform. The densities of axonal channels in the different simulations are specified in **Table 2**.

#### Myelin Modeling

To model the myelin sheath, one must consider that one passive plasma membrane can be considered as a parallel RC circuit.



To simulate the myelin sheath, we used the ''extracellular'' mechanism of the Neuron 7.6 software into the internodes of the model. This mechanism adds a layer of RC circuit to the internodes (**Supplementary Figure S3**). The passive conductance Gmy and the capacitance Cmy of this added layer depend on the number of myelin wraps. We assumed that the passive membrane conductance and the membrane capacitance of the myelin plasma membrane are equal to those of the axon, i.e., Gax, and Cax. As one myelin wrap is composed of two myelin membranes, a myelin sheath composed of one myelin wrap presents a conductance Gmy = Gax/2 and a capacitance Cmy = Cax/2. This reasoning extended to a myelin sheath composed of n myelin wraps gives Gmy = Gax/(2∗n) and Cmy = Cax/(2∗n). To evaluate the number of myelin wraps we used a g-ratio of 0.698 which has been evaluated in L5 pyramidal neurons of adult rats (Cohen et al., 2020), the diameter of the main axon (1.14 µm), the thickness of the periaxonal space (12.3 nm; Cohen et al., 2020) and the thickness of one plasma membrane (7.5 nm). The g-ratio is the ratio of the inner axonal diameter to the total outer diameter. Therefore, g = rax rax+tp+tmy , where g is the g-ratio, rax is the axonal radius, tp is the periaxonal space thickness and tmy is the myelin sheath thickness. From this equation, we can see that: tmy = rax ∗ 1 <sup>g</sup> − 1 − tp. With a g of 0.698, rax of 0.57 µm and t<sup>p</sup> of 0.0123 µm, we obtained tmy = 0.234 µm. Assuming a thickness of 7.5 nm for one plasma membrane, we obtained that the myelin sheath is constituted of 31.2 plasma membranes. As one myelin wrap is constituted of two plasma membranes, we concluded that the myelin sheath is composed of 15.6 myelin wraps. We chose to apply a value of 15 myelin wraps in our main model of myelinated axon which is in the range of the values observed with electron microscopy (Cohen et al., 2020). Consequently, Gmy = Gax/30 and Cmy = Cax/30 in our main model of a myelinated axon. The values of myelin conductance and myelin capacitance in the different simulations are listed in **Table 2**.

#### Postsynaptic Responses

To obtain the postsynaptic responses, we used Alpha Synapse Point Processes from Neuron 7.6 inserted into postsynaptic cells. The weights of the synapses were calculated using the charge of the spike-evoked Ca2+ entry in the presynaptic sites with the following power law:

$$W = A \ast (Q\_{Ca}{}^{2+})^{2.5}$$

where W is the synaptic weight, A is a scaling factor and QCa is the charge of the spike-evoked Ca2+ current (Scott et al., 2008). Therefore, an increase in the Ca2+ entry produced by an increase in presynaptic spike amplitude or duration led to an increase in the postsynaptic response amplitude.

#### Current Injection

AP was produced by a 3 nA current during 3 ms. The 15 mV subthreshold depolarization was produced by a 322 pA current during 10 s. The 15 mV hyperpolarization was produced by a −344 pA current for 200 ms. All these currents were injected into the soma.

#### Space Constants Calculation

The different phenomena we observed (subthreshold depolarization, subthreshold hyperpolarization, depolarizationinduced AP area increase, hyperpolarization-induced AP overshoot increase) propagated decrementally into the main axon. Due to the presence of axon collaterals and myelinated internodes, the propagations did not follow exactly a monoexponential decay, as it would be expected if the axon was a simple cable. However, in previously published experimental studies, the space constants were evaluated using fit with monoexponential decaying functions. Therefore, in order to compare the values obtained into our model and the values found in previous experimental studies, we chose to define the space constant as the distance at which a given phenomenon reaches 37% of its original value. For example, when we depolarized the soma by 15 mV, we defined the space constant of subthreshold depolarization propagation as the axonal point where the depolarization has decreased to the value of 5.55 mV (15<sup>∗</sup> 0.37 = 5.55). Importantly, in some conditions, the phenomena did not display a monotonic decay into the axon but evolved in a biphasic manner. We chose to not provide any space constant measurement for these cases.

#### RESULTS

In order to evaluate the impact of axonal myelination on ADFs spatial extent, we used a computational approach. We used a reconstructed morphology of an L5 pyramidal neuron from a young adult rat (Hay et al., 2011, see ''Materials and Methods'' section for details). The main axon is partially reconstructed (up to 1 mm from the soma) and present six collaterals located respectively at 128.5 µm, 129.6 µm, 300.9 µm, 301.5 µm, 810.1 µm, and 993.9 µm from the soma. In order to observe the propagation of ADFs to long-range connections, we extended the main axon (up to 20 mm from the soma) and we added four distant collaterals located 1,907.4, 2,922.4, 3,937.4 and 4,952.4 micrometers from the soma (the distant collaterals were 1 mm length). Supplemental parts diameters had the same values


as the original axon described in Hay et al. (2011): 1.14 µm for the main axon and 0.23 µm for the collaterals. In our model, dendrites, soma and axonal hillock contained Nav1.2 channels, potassium delay-rectifier channels (Kv) and leak channels. AIS contained Nav1.2 channels, Nav1.6 channels, potassium delayrectifier channels (Kv) and leak channels. The axon contained Nav1.6 channels, Kv1 channels and leak channels. To evaluate the effect of spike waveform on synaptic transmission, the axon collaterals also displayed presynaptic sites every 8 µm (Romand et al., 2011) which, contained a weak density of P/Q type calcium channels (1 pS/µm<sup>2</sup> ). Given the axonal tree extension, the model presented 1,982 presynaptic sites distributed all along the axon collaterals. Spike-evoked Ca2+ entry and corresponding postsynaptic responses were computed at these presynaptic sites (see ''Materials and Methods'' section). In all our simulations, the densities of channels in the dendrites, the soma, the axon hillock and the AIS were kept unchanged and were taken from a previous model of L5 pyramidal neurons (Hu et al., 2009; **Table 1**). We only modified the reversal potential of leak channels (Eleak = −69.5 mV) to obtain a resting membrane potential of −70 mV.

In a first step, we simulated a non-myelinated axon. In this model, the densities of Nav1.6 and Kv1 channels are homogenous all along the axonal tree (gNa1.6 = 370 pS/µm<sup>2</sup> and gKv1 = 26.8 pS/µm<sup>2</sup> ; **Table 2**: Non-Myelinated axon). The density of leak channels was homogeneous all along the axonal tree and equal to its value in other compartments (0.333 pS/µm<sup>2</sup> ). However, in order to maintain the resting potential at −70 mV, we had to fix Eleak at −38.3 mV in the axon.

#### Both d-ADF and h-ADF Are Expressed in the Model

The d-ADF occurs when the presynaptic neuron is depolarized before spike generation leading to an increase in transmitter release (**Figure 1A**). In pyramidal neurons, d-ADF is a slow process needing several seconds of depolarization to produce an increase in synaptic transmission (Shu et al., 2006; Kole et al., 2007; Sasaki et al., 2012; Bialowas et al., 2015). This slow time-constant is explained by the slow inactivation time-constant of Kv1 channels (1,500 ms; Shu et al., 2007b). In fact, d-ADF is a Kv1-dependent mechanism in pyramidal neurons: the subthreshold depolarization entails the inactivation of axonal Kv1 channels, leading to the broadening of the axonal spike, an increase in spike-evoked Ca2+ entry at the presynaptic bouton and an increased transmitter release (**Figure 1A**). Importantly, the subthreshold depolarization entails also the inactivation of axonal Nav channels leading to a decrease in the axonal spike amplitude (Shu et al., 2006). However, the interplay between the spike broadening and the decrease in spike amplitude leads to an overall increase in spike area leading to an enhancement of presynaptic Ca2+ entry and transmitter release (Shu et al., 2006; Kole et al., 2007; Bialowas et al., 2015). To verify the presence of d-ADF in the model, we injected current into the soma in order to produce a spike either generated from the resting membrane potential (V<sup>m</sup> = −70 mV) or after a 10 s subthreshold depolarization of the soma at −55 mV. Then, we measured the subthreshold

FIGURE 1 | Depolarization-induced analog digital facilitation (d-ADF) and hyperpolarization-induced analog digital facilitation (h-ADF) are expressed in the model. (A) Schematic description of the d-ADF mechanism. A long somatic depolarization provokes the inactivation of axonal Kv1 channels leading to a broadening of the presynaptic spike and an increase in the transmitter release. (B) Schematic description of the h-ADF mechanism. A brief somatic hyperpolarization provokes the deinactivation of axonal Nav channels leading to an increase in both the presynaptic spike amplitude and the transmitter release. (C) d-ADF is present in the model. A spike generated from the depolarized Vm (red trace) is broader than the spike generated from the resting membrane potential (black trace). Therefore, the spike generated from a depolarized Vm leads to a larger presynaptic Ca2+ entry and a bigger EPSP in the postsynaptic cell. Note that the depolarization is induced by somatic current injection and that the traces were recorded in a presynaptic site, 134 µm from the soma. (D) h-ADF is present in the model. A spike generated from the hyperpolarized Vm (purple trace) presents a larger amplitude than the spike generated from the resting membrane potential (black trace). Therefore, the spike generated from a hyperpolarized Vm leads to a larger presynaptic Ca2+ entry and a bigger EPSP in the postsynaptic cell. Note that the hyperpolarization is induced by somatic current injection and that the traces were recorded in a presynaptic site, 134 µm from the soma.

depolarization value, the spike waveform, the spike-evokedcalcium entry and the postsynaptic response amplitude at the first presynaptic site (located 134 µm from the soma). We found that a 15 mV subthreshold depolarization of the soma propagated decrementally into the axon leading to a value of 9.43 mV at the presynaptic site (**Figure 1C**). This depolarization provoked the inactivation of axonal Kv1 channels leading to a broadening of the presynaptic spike, and the inactivation of Nav1.6 channels, producing a decrease in the presynaptic spike amplitude. Overall, the spike area was increased by 15.8%, leading to a 13.4% increase in spike-evoked calcium entry and a 36.8% increase in synaptic transmission (**Figure 1C**). Therefore, d-ADF amounted to 136.8% of the control amplitude at 134 µm from the soma in our model, which is similar to previously published d-ADF in pyramidal neurons (Shu et al., 2006; Kole et al., 2007; Bialowas et al., 2015).

The h-ADF is a much faster process that has been described in CA3 and L5 pyramidal neurons (Rama et al., 2015). A 200 ms hyperpolarization of the presynaptic neuron is enough to entail a recovery from inactivation of axonal Nav channels (Nav1.6 in pyramidal neurons), leading to an increase in axonal spike amplitude which produces an increase of spike-evoked Ca2+ entry and transmitter release (**Figure 1B**). Due to the slow recovery from inactivation of Kv1 channels, a 200 ms hyperpolarization has no effect on their availability. Therefore, h-ADF is a purely spikeamplitude dependent phenomenon (Rama et al., 2015). To verify the presence of h-ADF in the model, we injected current into the soma in order to produce a spike either generated from resting membrane potential (V<sup>m</sup> = −70 mV) or after a 200 ms subthreshold hyperpolarization of the soma at −85 mV. Then, we measured the hyperpolarization value, the spike waveform, the spike-evoked-calcium entry and the postsynaptic response amplitude at the first presynaptic site (located 134 µm from the soma). We found that a 15 mV hyperpolarization of the soma propagated detrimentally into the axon leading to a value of 9.13 mV at the presynaptic site (**Figure 1D**). This hyperpolarization provoked the recovery from inactivation of axonal Nav1.6 channels, leading to a 17.8% increase in the presynaptic spike overshoot (without modification of its duration), an 11.9% increase in the spike-evoked Ca2+ entry and a 32.7% increase in synaptic transmission (**Figure 1D**). Therefore, h-ADF is similar to what has been obtained experimentally in pyramidal neurons (Rama et al., 2015).

We concluded that both d-ADF and h-ADF are reproduced by the model.

## d-ADF Spatial Extent Is Increased by Myelination

To quantify the spatial extent of d-ADF, we measured the subthreshold depolarization and the AP area all along the main axon. We found that the depolarization propagated with a space constant of 303.4 µm into the main axon, close to previously published values in L5 pyramidal neurons (Shu et al., 2006; Kole et al., 2007; **Figure 2A**, black trace). This led to a space constant for depolarization-induced AP area increase of 338.4 µm into the main axon (**Figure 2B**, black trace). Then, in order to observe d-ADF, we computed synaptic transmission in the 1982 presynaptic sites located in axon collaterals (**Figure 2C**, black trace). In this configuration, we found that 31.4% of the presynaptic sites presented a d-ADF of at least 5% (**Figure 2C**, black dots). These presynaptic sites were all located in the proximal collaterals and were on average 307 ± 94.5 µm away from the soma. In order to determine the spatial extent of d-ADF

FIGURE 2 | Axonal myelination increases d-ADF spatial extent. (A) Somatic subthreshold depolarization propagates farther in the myelinated axon than in the unmyelinated axon. Left, voltage traces showing the propagation of the somatic depolarization all along the axon (unmyelinated model: black to gray traces, myelinated model: red to yellow traces). Right, plot of the depolarization in the function of the distance from the soma in the unmyelinated (black) and the myelinated (red) model. (B) Plot of the depolarization-induced AP area increase in function of the distance from the soma in the unmyelinated (black) and the myelinated (red) model. (C) Plot of the depolarization-induced synaptic facilitation (d-ADF) in the function of the distance from the soma in the 1,982 presynaptic sites located in axon collaterals (black dots: unmyelinated model, red dots: myelinated model). Note that d-ADF is present in presynaptic sites located into distant collaterals only in the myelinated model (red arrows). (D) Plot of d-ADF measured in the first presynaptic site of each collateral in the function of the distance from the soma (black: unmyelinated model, red: myelinated model).

in the model, we plotted the value of d-ADF measured at the first presynaptic site of each collateral as a function of the distance from the soma (**Figure 2D**, black trace). We defined the spatial extent of d-ADF as the point where this curve crossed the value of 105% for d-ADF. We found that the spatial extent of d-ADF was 836 µm (**Figure 2D**, black trace). Therefore, d-ADF in an unmyelinated axon is a local phenomenon restricted to proximal synapses (i.e., corresponding to an axonal path smaller than 1 mm; Sasaki et al., 2012).

To evaluate the impact of myelination on the d-ADF spatial extent, we simulated myelinated internodes in the main axon while we left the collaterals unmyelinated. In this model, the main axon was myelinated except at the branching points of the collaterals where 1.5 µm-long nodes of Ranvier were simulated. However, if the distance between two branching points was longer than 200 µm, this part of the main axon has been divided into 100 µm-long internodes with nodes of Ranvier in between. Therefore, the myelinated internodes present a length that varies from 99 to 180 µm (mean value of 101.1 µm), which corresponds to previously published values in L5 pyramidal neurons (Arancibia-Cárcamo et al., 2017). To simulate myelinated internodes, we removed the voltage-gated conductance (Nav1.6 and Kv1) from these compartments, and we added a layer of myelin sheath which conductance and capacitance correspond to 15 myelin wraps (see ''Materials and Methods'' section and **Supplementary Figure S3** for myelin modeling). In that case, the myelin sheath conductance was equal to the axonal leak channels conductance divided by a factor 30 and the myelin sheath capacitance was equal to the axonal capacitance divided by 30 (see ''Materials and Methods'' section and **Table 2**: Myelinated axon 1). These values of myelin membrane conductance and capacitance corresponds to what could be expected for a myelin sheath constituted of 15 myelin wraps, a value that we deduced from a g-ratio of 0.698 found in L5 pyramidal neurons (Cohen et al., 2020), the diameter of the main axon in the reconstructed neuron (1.14 µm) and a periaxonal space of 12.3 nm between the internode's plasma membrane and the myelin sheath (Cohen et al., 2020; see ''Materials and Methods'' section for myelin wraps modeling). Finally, the periaxonal space resistivity was set to 53.7 Ωcm (Cohen et al., 2020). The myelinated internodes are separated by nodes of Ranvier. We simulated nodes of Ranvier by increasing voltage-gated sodium and potassium conductance in order to ensure the spike propagation all along the axon (**Table 2**: Myelinated axon 1). Importantly, the exact densities of Nav1.6 and Kv into the nodes of Ranvier were determined in order to preserve the spike waveform at resting membrane potential in the middle of the main axon (10 mm from the soma; **Supplementary Figure S2**). Finally, the density of the leak channels in the nodes of Ranvier was the same as in the non-myelinated axon.

As expected, we found that myelination increased the velocity of the AP conduction (**Supplementary Figure S4**). More importantly, we found that the subthreshold depolarization of the soma propagated into the myelinated main axon with a space constant of 906.6 µm (**Figure 2A**, red trace). Therefore, the myelination entailed a 2.99-fold increase in axonal length constant in our model. In consequence, the myelination increased the spatial extent of the depolarization-induced AP area enhancement (**Figure 2B**, red trace). Importantly, it was not possible to extract a space constant for the depolarizationinduced AP area enhancement because it did not present a monotonic decay in the myelinated axon (see ''Materials and Methods'' section for space constant calculation). In fact, this parameter evolved in a biphasic manner along the axon: it was stable during the first 650 micrometers then it decreased with the distance from the soma (**Figure 2B**, red trace). This is easily understandable if one takes into account the two opposite effects of the subthreshold depolarization on the AP shape: it increases its duration and reduces its amplitude. The interplay between these two effects creates the biphasic behavior of the Zbil and Debanne Myelination Extends ADF Space Constant

AP area increase in our myelinated model. However, despite the impossibility to calculate a space constantly, our model showed that myelination led to a major increase in the axonal portion affected by the depolarization-induced increase in the AP area. Consequently, we found an increase in the presynaptic sites proportion that presents at least 5% d-ADF (36% instead of 31.4%; **Figure 2C**, red dots). These presynaptic sites were located both on proximal and distal collaterals and were on average 382.7 ± 318.2 µm away from the soma. Importantly, we found that some presynaptic sites presented d-ADF while they were located more than 2,000 µm away from the soma (**Figure 2C**, red dots). In fact, the spatial extent of d-ADF was found to be 3,124 µm in this configuration (**Figure 2D**, red trace). Therefore, the myelination of the main axon allowed the propagation of the somatic subthreshold depolarization to distant collaterals and entailed a major increase in the d-ADF spatial extent.

## h-ADF Spatial Extent Is Increased by Myelination

To evaluate the spatial extent of h-ADF, we measured the hyperpolarization and AP overshoot all along the main axon. We also measured the synaptic transmission at presynaptic sites located in axon collaterals. In the unmyelinated model, we found that the hyperpolarization propagated with a space constant of 294.2 µm (**Figure 3A**, black trace). This leads to a space constant for an AP overshoot increase of 360.3 µm (**Figure 3B**, black trace). 29.6% of the presynaptic sites displayed an h-ADF of at least 5% (**Figure 3C**, black dots). These presynaptic sites were all located in the proximal collaterals and were on average 300.3 ± 91.8 µm away from the soma (**Figure 3C**, black dots). The h-ADF spatial extent was found to be 815 µm (**Figure 3D**, black trace).

In the myelinated model, the hyperpolarization propagated into the main axon with a space constant of 858.5 µm (**Figure 3A**, purple trace). Therefore, the space constant of the propagation of subthreshold hyperpolarization is increased by a factor 2.92 compared to an unmyelinated main axon. This leads to an augmentation of the space constant of hyperpolarizationinduced AP overshoot increase (**Figure 3B**, purple trace). Consequently, we found an increase in the proportion of presynaptic sites that displayed at least 5% h-ADF (from 29.6 to 34%; **Figure 3C**, purple dots). These presynaptic sites were located both on proximal and distal collaterals and were on average 365.5 µm ± 281.24 µm away from the soma. Importantly, as for d-ADF, we found that some presynaptic sites still present h-ADF while they were located more than 2,000 µm away from the soma (**Figure 3C**, purple dots). In fact, we found that the h-ADF spatial extent was 2,894 µm in the myelinated model (**Figure 3D**, purple trace). Therefore, similar to its effect on d-ADF, the myelination induced a major increase in the h-ADF spatial extent.

## The Enhanced Spatial Extent of ADFs Is Not Due to Hot Spots of Ion Channels at Nodes of Ranvier

One major difficulty of our approach is the fact that Nav1.6 and Kv1 axonal densities were different in the myelinated and the

FIGURE 3 | Axonal myelination increases h-ADF spatial extent. (A) Somatic subthreshold hyperpolarization propagates farther in the myelinated axon than in the unmyelinated axon. Left, voltage traces showing the propagation of the somatic hyperpolarization all along the axon (unmyelinated model: black to gray traces, myelinated model: purple to blue traces). Right, plot of the hyperpolarization in the function of the distance from the soma in the unmyelinated (black) and the myelinated (purple) model. (B) Plot of the hyperpolarization-induced AP overshoot increase in function of the distance from the soma in the unmyelinated (black) and the myelinated (purple) model. (C) Plot of the hyperpolarization-induced synaptic facilitation (h-ADF) in the function of the distance from the soma in the 1,982 presynaptic sites located in axon collaterals (black dots: unmyelinated model, red dots: myelinated model). Note that h-ADF is present in presynaptic sites located into distant collaterals only in the myelinated model (purple arrows). (D) Plot of h-ADF measured in the first presynaptic site of each collateral in the function of the distance from the soma (black: unmyelinated model, purple: myelinated model).

unmyelinated model (**Table 2**). Therefore, the increase in ADFs spatial extent in the myelinated axon could arise either from the presence of myelin sheaths at the internodes or from the increase in ion channels densities into nodes of Ranvier. To determine the key parameter controlling the increase in ADF spatial extent, we performed a simulation with a hybrid main axon presenting the same parameters values than the unmyelinated main axon except at specific hot spots located at the same location than nodes of Ranvier of the myelinated model (**Table 2**: Hybrid axon). At these hot spots, the parameters values are identical to those of the nodes of Ranvier of the myelinated model. Therefore, this main axon is a hybrid model that presents nodes of Ranvier-like hot spots separated by portions of non-myelinated axon.

In this hybrid model, we found that the subthreshold depolarization propagated into the main axon with a space constant of 301.6 µm, close to the value found in the unmyelinated main axon (303.4). The depolarization-induced enhancement of the AP area propagated into the main axon with a space constant of 327 µm, close to the value found in the unmyelinated main axon (338.4 µm). We found that 31.2% of the presynaptic sites presented a d-ADF of at least 5% and that they were located on average 306.1 ± 93.9 µm from the soma. These values are close to the values we found for the unmyelinated model (31.4% and 307 ± 94.5 µm). Moreover, d-ADF has a spatial extent of 816 µm in the hybrid axon, close to the value of 836 µm found in the unmyelinated axon. Concerning h-ADF, we found that the hyperpolarization propagated into the main axon with a space constant of 293.4 µm which is close to the value found in the unmyelinated main axon (294.2). The hyperpolarization-induced increase in AP overshoot propagated into the main axon with a space constant of 349 µm, close to the value found in the unmyelinated main axon (360.3 µm). We found that 29.6% of the presynaptic sites presented an h-ADF of at least 5% and that they were located on average 299.5 ± 89.3 µm from the soma. These values are close to the values we found for the unmyelinated model (29.6% and 300.3 ± 91.8 µm). Additionally, h-ADF presented a spatial extent of 808 µm in the hybrid axon, close to the value found in the unmyelinated model (814 µm). Therefore, the spatial extents of d-ADF and h-ADF were similar in the non-myelinated model and in the hybrid model. We conclude that the increase in the ADFs spatial extents in the myelinated model was due to the presence of myelinated internodes and was not an artifact due to high Nav1.6 and Kv1 densities in the nodes of Ranvier.

## Effect of Myelination Parameters on ADFs Spatial Extent

Several studies showed that the length of the internodes is variable during development and among neuronal types, which may impact the axonal length constant. In L5 pyramidal neurons, they have been shown to vary between 30 and 150 µm from cell to cell (Arancibia-Cárcamo et al., 2017). In order to observe the effects of internodal length modifications on ADFs spatial extents, we divided all the internodes lengths by 2 (average internodal length: 50.59 µm) or 4 (average internodal length: 25.35 µm) while keeping the distance of collaterals from the soma constant (**Figure 4A**). For each condition (internodal length divided by 2 or 4), the axonal densities of Nav1.6 and Kv1 channels were modified in order to keep the axonal spike waveform at the resting membrane potential similar to the one in the non-myelinated axon (**Table 2**: Myelinated axon 1, 2, 3; **Supplementary Figure S2**). Moreover, Eleak was slightly modified to maintain the resting membrane potential at −70 mV in the axon (**Table 2**: Myelinated axon 1, 2, 3). We found a mild decrease in the propagation of subthreshold depolarization with the internodal length reduction (**Figure 4A**, red trace). Consequently, the internodal length

depolarization (red) or a 200 ms somatic hyperpolarization (purple) in the function of the internodal length. (B) Plot of the depolarization-induced AP area increase in function of the distance from the soma for the different average internodal lengths. (C) Plot of the hyperpolarization-induced AP overshoot increase in function of the distance from the soma for the different average internodal lengths. (D) Plot of d-ADF measured in the first presynaptic site of each collateral for the different internodal lengths. (E) Plot of h-ADF measured in the first presynaptic site of each collateral for the different internodal lengths.

reduction provoked a small decrease in the space constant for depolarization-induced enhancement of the AP area (**Figure 4B**). This led to a limited diminution of the d-ADF spatial extent with internodes shortening (**Figure 4D**). In fact, d-ADF spatial extent was found to be 2,501 µm, 2,830 µm and 3,124 µm for average internodal lengths of respectively 25.35 µm, 50.59 µm and 101.1 µm (**Figure 4D**). Similarly, we found a decrease in the axonal length constant for hyperpolarization when the internodal length was reduced (**Figure 4A**, purple trace). As a result, hyperpolarization-induced AP overshoot enhancement displayed a shorter space constant (**Figure 4C**) leading to a decrease in h-ADF spatial extent (**Figure 4E**). We concluded that internodal length mildly influences ADFs spatial extents in our model.

The number of myelin wraps increases during development (Looney and Elberger, 1986; Battefeld et al., 2019). Moreover, the number of myelin wraps has been found to vary between 5 and 20 in mature L5 pyramidal neurons (Cohen et al., 2020). We, therefore, explored the effect of myelin wraps number on d- and h-ADF spatial extents. For this, we compared the spatial extents of ADFs into axons which internodes are ensheathed by 0, 2, 5, 10, 15 or 20 myelin wraps (**Figure 5A**; see ''Materials and Methods'' section for the modeling of myelin wraps number). We had to modify the densities of Nav1.6 and Kv1 channels in the axon in order to keep the axonal spike waveform and the Eleak to maintain the resting membrane potential for each myelin wraps number (**Table 2** and **Supplementary Figure S2**: Non-myelinated axon and Myelinated axon 1, 4, 5, 6, 7). We found that the subthreshold depolarization space constant for an axon which internodes are ensheathed in 0 myelin wraps was 303.4 µm while it was 531.2 µm, 702.2 µm, 834.3 µm, 906.6 µm and 949.8 µm for axons which internodes are ensheathed respectively into 2, 5, 10, 15 and 20 myelin wraps (**Figure 5A**, red trace). The depolarization space constant followed the exponential relationship sp = 313.24 + 636.2 <sup>∗</sup> (1 − e <sup>−</sup>0.189∗N) where sp is the depolarization space constant and N the number of myelin wraps. Consequently, the spatial extent of both depolarization-induced AP area enhancement and d-ADF greatly increased with the number of myelin wraps ensheathing internodes (**Figures 5B,D**). In fact, the spatial extent of d-ADF was found to be 836 µm, 1,827 µm, 2,453 µm, 2,840 µm, 3,124 µm and 3,351 µm when the internodes were ensheathed into respectively 0, 2, 5, 10, 15 or 20 myelin wraps. Similarly, we found that the subthreshold hyperpolarization space constant greatly increased with the number of myelin wraps following the relationship sp = 303.02 + 604.3<sup>∗</sup> (1 − e <sup>−</sup>0.175∗N) (**Figure 5A**). Therefore, increasing the number of myelin wraps led to an increase in the spatial extent of both hyperpolarization-induced AP overshoot enhancement and h-ADF (**Figures 5C,E**). We conclude that the number of myelin wraps ensheathing the internodes is a major determinant of both d-ADF and h-ADF spatial extents, suggesting that in the young adult rat ADFs may extend to more than 2 mm away from the soma.

#### DISCUSSION

In this study, we show using a computational approach that the axonal myelination may expand both the axonal length constant as well as d- and h-ADF spatial extents by around a factor 3. Furthermore, we show that ADFs spatial extents are critically determined by the number of myelin wraps ensheathing the axon and more modestly by the internodal length. Our work, therefore, suggests that myelinated projection paths such as cortico-striatal or cortico-collicular pathways with an axonal distance ranging between 2 and 3 mm may well express dand h-ADF.

#### Axonal Length Constant

Axonal length constant depends on several geometrical and electrical parameters as the axonal diameter, the presence of myelin, the number of branch-points or the duration of the voltage shift imposed in the soma. A length constant of ∼2 mm has been estimated in myelinated axons of motoneurons (Gogan

et al., 1983). In hippocampal axons, the length constant is inversely proportional to the number of branch-points (Sasaki et al., 2012). In L5 pyramidal neurons, length constant is 120 µm for a 10 ms depolarization whereas it can reach 1,000 µm for a 200 ms depolarization (Christie and Jahr, 2009), showing that the propagation of voltage along the axon depends on the frequency of the signal imposed in the somatic compartment.

In L5 pyramidal neurons, the value of the main axon length constant has been estimated between 417 and 1,180 µm for a long subthreshold depolarization (0.2–10 s; Kole et al., 2007; Shu et al., 2007a; Christie and Jahr, 2009; Cohen et al., 2020). Based on our modeling, we propose that this large range of reported values is due to the variability of the axonal myelination in the different studies. In fact, the myelination increases the axonal length constant in our model (**Figures 2A,B**). Importantly, the study from Shu and colleagues was performed on ferrets, a species in which L5 pyramidal neurons myelination starts distally (<350 µm from the soma; Shu et al., 2007a). This could explain the smaller axonal length constant found in this study (417 µm) compared to other studies performed on rats (553–1,180 µm; Kole et al., 2007; Christie and Jahr, 2009; Cohen et al., 2020) in which the axonal myelination starts just after the axonal initial segment (Battefeld et al., 2019). Moreover, we propose that the large range of axonal length constants found in rat L5 pyramidal neurons is due to the variability of myelination between neurons. In fact, the number of myelin wraps can vary between 5 and 20 in mature L5 pyramidal neurons (Cohen et al., 2020). In our model, the axonal length constant increases with the number of myelin wrap leading to a value of 531 µm for 5 myelin wraps and a value of 949.8 µm for 20 myelin wraps (**Figure 5A**). However, while we found a 3-fold effect of myelination on axonal length constant in our simulations, this still needs to be experimentally explored by performing recordings of L5 pyramidal neurons treated by demyelinating drugs such as cuprizone (Hamada et al., 2017).

Importantly, axonal length constant also depends on the axonal membrane resistance. One must consider that somatodendritic membrane resistance decreases during the development (Atkinson and Williams, 2009) which leads to a decrease in the dendritic length constant. If this phenomenon also occurs in axons, we may have overestimated the axonal length constant of mature L5 pyramidal neurons. Nevertheless, the value of 0.333 pS.µm−<sup>2</sup> for leak channel density used in our model corresponds to a membrane resistance of 30.03 k.cm<sup>2</sup> which is close to the value of 24.6 k.cm<sup>2</sup> recently estimated by Cohen and colleagues in mature L5 pyramidal neurons (Cohen et al., 2020). Moreover, some studies suggest that the axonal membrane resistance may be much lower than dendritic membrane resistance leading to a large axonal length constant (Dover et al., 2016).

#### ADF Spatial Extent

The axonal length constant and ADFs spatial extents are biophysically related as ADFs tightly depend on the propagation of somatic subthreshold voltage shifts into the axon leading to the modulation of AP parameters in the presynaptic bouton. The space constant of the depolarization-induced AP broadening underlying d-ADF has been estimated to be near 675 µm in L5 pyramidal cell axons (Kole et al., 2007). In our study, we found that the space constant of the depolarization-induced AP broadening is approximately 338.4 µm for the unmyelinated model but was greatly enhanced in the myelinated model (**Figure 2B**). In fact, we showed that increasing the length of internodes or the number of myelin wraps, which occurs during the development of L5 pyramidal neurons (Battefeld et al., 2019), leads to an increase in axonal length constant and ADFs spatial extent (**Figures 4**, **5**).

#### Myelination Parameters

What is the number of myelin wraps in axons? Myelin wraps in peripheral axons linearly depend on the axon diameter and may vary between 10 and 160 (Arbuthnott et al., 1980; Berthold and Carlstedt, 1982). In the CNS, the number of myelin wraps has been estimated to vary between 5 and 20 wraps (Looney and Elberger, 1986; Bakiri et al., 2011; Harris and Attwell, 2012; Snaidero et al., 2014; Arancibia-Cárcamo et al., 2017; Cohen et al., 2020). Our results suggest that the number of myelin wraps has a critical impact on both the axonal length constant and the ADFs spatial extents (**Figure 5**). In fact, the space constant for subthreshold depolarization and hyperpolarization went from ∼500 µm with 2 myelin wraps to ∼900 µm for 20 myelin wraps in our model (**Figure 5A**). As a consequence, the spatial extent for d- and h-ADF was found to increase in proportion (**Figures 5D,E**). Therefore, we suggest that the variability of the myelin wraps number found in mature L5 pyramidal neurons could entail a variability of ADFs spatial extent in this cell type. During development, the number of myelin lamellae increases from 0 before birth to maximal levels before sexual maturity (Berthold and Carlstedt, 1982). The myelin thickness also depends on electrical activity (Kaller et al., 2017; Suminaite et al., 2019). Therefore, our model suggests that ADFs spatial extent may increase during the development and vary as a function of neuronal electrical activity.

Regarding the internodal length, we found that this parameter, known to critically determine the conduction velocity (Rushton, 1951; Wu et al., 2012), mildly influenced the axonal length constant and ADFs spatial extents in our model (**Figure 4**).

## Extended ADF in Myelinated Axonal Paths in situ?

Due to a large amount of missing data about axonal physiology, our model presents several unconstrained parameters such as the exact axonal channels density and nature at nodes of Ranvier and internodes or the precise axonal membrane resistance. While it seems likely that the electrical isolation provided by the myelination increases the axonal length constant and ADFs spatial extents, experiments are needed to assess if ADFs can occur at distal synaptic connections (>2 mm). In fact, d-ADF and h-ADF have been mostly studied either in unmyelinated axons or in immature brain circuits in which the myelin is weakly present during early development. As a consequence, the presence of ADFs has never been evaluated in fully myelinated axonal paths. Our data suggest that short projection paths as thalamocortical projection may well express d- and h-ADF. Indeed, in this structure myelination starts rapidly during postnatal development, the length of thalamic axons (∼2 mm) is compatible with ADF and pairedrecording from thalamocortical neurons can be obtained in vitro (Hu and Agmon, 2016) and in vivo (Bruno and Sakmann, 2006). Further experimental work will probably help answer this question.

## DATA AVAILABILITY STATEMENT

The datasets generated for this study are available on request to the corresponding author.

#### AUTHORS CONTRIBUTIONS

MZ and DD designed the article and wrote the manuscript. MZ performed the simulations and built the figures.

#### FUNDING

This study was supported by ANR (Axode 14-CE13-0003-02 to DD), LABEX Cortex of Université de Lyon (NR-11-LABX-0042), INSERM and CNRS.

#### ACKNOWLEDGMENTS

We thank Drs. M. Russier and S. Rama for reading the manuscript.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel.2020.000 40/full#supplementary-material.

#### REFERENCES


FIGURE S1 | Model morphology. Representation of the model morphology based on the reconstructed neuron NMO\_07763. Note the axonal portion that has been added to the reconstructed neuron to extend the axonal tree.

FIGURE S2 | Axonal spike waveform at the resting membrane potential is similar in the different simulations. (A) Schematic representation of the different models of the study. (B) Spike waveform at the resting membrane potential (−70 mV) recorded in the middle of the axon (10 mm from the soma) in the different models. Note the similarity of basal axonal spike waveform in the different models.

FIGURE S3 | Myelin sheath modeling. Up, schematic representation of two internodes and one node of Ranvier. Down, equivalent electric circuit used in the model. Gmy, myelin sheath conductance; Cmy, myelin sheath capacitance; Rp, periaxonal space axial resistance; Gax, axonal passive conductance; Cax, axonal capacitance; Ra, intra-axonal axial resistance; Kv1, Kv1 channels conductance; Nav, axonal Nav channels conductance (Nav1.6 channels conductance).

FIGURE S4 | Myelination increase velocity of spike propagation into the main axon. Left, voltage traces showing AP propagation along the main axon in the unmyelinated and the myelinated model (Table 2: Myelinated axon 1). Right, plot of the AP latency in the function of the distance from the soma in the myelinated and the unmyelinated model.


**Conflict of Interest**: 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 © 2020 Zbili and Debanne. 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(s) 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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