From the early studies on spike-evoked release modulation via presynaptic membrane potential, we can conclude that spikes contain more information than usually thought. In fact, the synaptic strength depends on the subthreshold membrane potential of the presynaptic cell, indicating that the presynaptic spike transmits this analog information to the postsynaptic cell. However, the direction of this modulation of synaptic transmission seems to depend on the type of synapse. In fact, in some studies, the rule is: the more depolarized is the presynaptic cell, the bigger is the PSP (also called depolarization-induced Analog-Digital Facilitation or d-ADF), while in others the rule is the opposite (hyperpolarizationinduced Analog-Digital Facilitation or h-ADF). We will see that the recent developments on the subject have extended the observations made on invertebrate preparations to mammalian synapses and have resolved this apparent paradox via the description of the ion channels responsible for the two types of ADF.

# Depolarization-Induced Analog-Digital Facilitation (d-ADF) in Mammalian Brain

The first descriptions of d-ADF in mammalian CNS have been made in Calyx of Held (Turecek and Trussell, 2001; Awatramani et al., 2005), CA3 area (Saviane et al., 2003), hippocampal mossy fibers (Alle and Geiger, 2006) and L5 pyramidal neurons (Shu et al., 2006; **Figures 3Ai,Bi**; **Table 1**). In all these cases, a depolarization of the presynaptic cell preceding the AP leads to an increase in synaptic transmission from 30% to 100% depending on the studies. However, a precise examination shows that different mechanisms are responsible for these d-ADFs.

## d-ADF via Basal Ca2+ Accumulation at the Terminal

The first mechanism described for d-ADF is not due to spike shape modulation. A weak opening of synaptic Cavs during the subthreshold depolarization leads to an increase in the basal Ca2+ concentration at the terminal, and consequently, an enhancement of synaptic release when the spike invades the presynaptic terminal (Debanne et al., 2013; Rama et al., 2015b; Zbili et al., 2016). This mechanism has been described at the Calyx of Held (Turecek and Trussell, 2001; Awatramani et al., 2005; Hori and Takahashi, 2009), cerebellar molecular layer interneurons (Bouhours et al., 2011; Christie et al., 2011) and at the dendro-dendritic synapses between mitral cells of the olfactory bulb (Fekete et al., 2014). Due to the slow dynamics of Ca2+ accumulation, several seconds of depolarization are needed to fully facilitate synaptic transmission. Interestingly, basal Ca2+ accumulation induces synaptic release facilitation in two different ways. First, the increase in basal Ca2+ concentration directly enhances the release probability, probably via the promotion of the vesicles priming and of the coupling between vesicles and Cav channels (Neher and Sakaba, 2008). Second, it can provoke a Ca2+-dependent hyperpolarizing shift of Cav channel activation (Borst and Sakmann, 1998; Cuttle et al., 1998), leading to an increase of the spike-evoked Ca2+ transient (Hori and Takahashi, 2009; Christie et al., 2011). Importantly, these two effects can occur at the same synapse (Hori and Takahashi, 2009).

## d-ADF via Modulation of Presynaptic Spike Width

The second mechanism underlying d-ADF in mammals is the inactivation of Kv channels during the subthreshold depolarization. This phenomenon provokes broadening of the presynaptic spike (**Figures 3Aii,Bii**), leading to an increase in the spike-evoked Ca2+ transient and an enhancement of synaptic release (Debanne et al., 2013; Rama et al., 2015b; Zbili et al., 2016; **Figures 3Ai,Bi**). Importantly, the time constant of this type of d-ADF depends on the inactivation time-constant of the Kv involved in the phenomenon. In L5 pyramidal neurons, CA3 pyramidal neurons and CA1 pyramidal neurons, slowly inactivating Kv1 channels are responsible for the d-ADF, and therefore the phenomenon presents a slow time constant (several seconds; Saviane et al., 2003; Shu et al., 2006, 2007; Kole et al., 2007; Sasaki et al., 2011, 2012; Zhu et al., 2011; Kim, 2014; Bialowas et al., 2015). In contrast, in inhibitory interneurons of the cerebellum (stellate cells), d-ADF depends on fast Kv3.4 inactivation and is, therefore, quicker to take place (100 ms of depolarization to have an effect and 1 s for a full increase in synaptic transmission; Rowan and Christie, 2017). Importantly, at invertebrates' synapses, the d-ADF via basal Ca2+ accumulation and the d-ADF via Kv inactivation are not mutually exclusive and may occur at the same synapses (Bialowas et al., 2015; Rama et al., 2015b).

### A Peculiar Case: d-ADF at Mossy Fiber Boutons

In granule cells of the Dentate Gyrus, an EPSP can propagate from the dendrites to the presynaptic bouton and increase spike-evoked synaptic transmission at mossy fiber bouton/CA3 synapses (Alle and Geiger, 2006). Surprisingly, this d-ADF seems to be Ca2+-independent. In fact, it does not go along with an increase in basal Ca2+ concentration or spike-evoked Ca2+ transient (Scott et al., 2008), and it is not

blocked by application of 10 mM EGTA (Alle and Geiger, 2006) or 1 mM BAPTA (Scott et al., 2008). However, it should be noted that the increase in Ca2+ entry can be too subtle to be seen with Ca2+ fluorescent indicators. Moreover, at the Calyx of Held, it is necessary to apply 10 mM EGTA + 1 mM BAPTA to efficiently block d-ADF (Hori and Takahashi, 2009). Therefore, the mechanism of d-ADF at this synapse could be Ca2+-dependent and needs further studies to be unraveled (Debanne et al., 2013).

# Hyperpolarization-Induced Analog-Digital Facilitation (h-ADF) in Mammalian Brain

Recent studies showed that a presynaptic hyperpolarization before the spike leads to an increase in spike-evoked

#### TABLE 1 | Analog-digital facilitation.

neurotransmitter release in hippocampal cultures (Thio and Yamada, 2004), L4 pyramidal neurons (Cowan and Stricker, 2004), CA3 pyramidal neurons and L5 pyramidal neurons (Rama et al., 2015a; **Figure 3Ci**; **Table 1**). This facilitation ranges between 10% and 100% depending on the studies and the cell type. At CA3/CA3 and L5/L5 synapses, the mechanism underlying h-ADF has been fully described: a presynaptic hyperpolarization results in the recovery from inactivation of presynaptic Nav channels, which provokes an increase in presynaptic spike amplitude (**Figure 3Cii**), leading to an enhancement of spike-evoked Ca2+ entry and synaptic release (Rama et al., 2015a; **Figure 3Ci**). This phenomenon Zbili and Debanne Analog-Digital Transmission

is likely to occur at hippocampal mossy fiber, in which a somatic hyperpolarization results in an increase of spike-evoked Ca2+ transient at small axonal varicosities (Ruiz et al., 2003). Interestingly, due to the fast biophysics of Nav channels, h-ADF is extremely fast and occurs within 15–50 ms of hyperpolarization. Therefore, it can be induced by a unique IPSP preceding the spike. Hence, rebound spiking should have a bigger impact on the postsynaptic cell if h-ADF is present at the synapse. One can think that h-ADF is a widespread phenomenon because it depends on Nav channels which are present in all spiking neuron types. However, it should be noted that a strong Nav channel density should attenuate the impact of their de-inactivation on the spike amplitude, and therefore decrease the h-ADF (Rama et al., 2015a). Moreover, Nav1.6 channels, which are the main subtype in pyramidal cells axons, are strongly inactivated at resting potential (Hu et al., 2009), and therefore are suited to underlie h-ADF. Parvalbumin positive (PV+) fast-spiking interneurons contain axonal Nav1.1 channels, a subtype that display less inactivation at resting membrane potential than Nav1.6 (Patel et al., 2015), and a much higher density of axonal Nav channels than pyramidal cells (Hu and Jonas, 2014; Hu et al., 2014). Therefore, one can expect that this type of interneuron lacks spike amplitude modulation and h-ADF.

# Coexistence of d-ADF and h-ADF at the Same Synapses

d-ADF and h-ADF are due to different mechanisms and present different time constants (100 ms to several seconds for d-ADF, 15–50 ms for h-ADF). It has been shown that d-ADF and h-ADF coexist and can be summed at CA3/CA3 synapses (Rama et al., 2015a). In fact, a long depolarization (10 s) followed by a brief hyperpolarization (200 ms) entails a bigger increase in spikeevoked synaptic transmission than a long depolarization or a brief hyperpolarization alone. Why has this coexistence not been shown in early studies in invertebrates? For synapses that display h-ADF but not d-ADF, we can assume a lack of inactivating potassium channels at the synapses studied, which prevents spike broadening by depolarization (giant synapse of the squid and frog neuromuscular junction). In the case of studies that report only d-ADF, it should be noted that the protocol used is not relevant to observe h-ADF. In fact, a brief hyperpolarization (15–200 ms) is needed to unravel h-ADF at synapses that also present d-ADF. A long hyperpolarization (several seconds) can induce de-inactivation of Kv1 channels and spike sharpening, which can thwart h-ADF (Bialowas et al., 2015; Rama et al., 2015a). In the studies made on invertebrates that report d-ADF but no h-ADF, the resting membrane potential was modified for several seconds before spike emission, which may explain why the h-ADF has not been reported. Therefore, additional studies are needed to unravel the degree of coexistence of d-ADF and h-ADF at invertebrates and mammals synapses.

# Physiological Consequences of ADFs Spatial Extent of ADFs

One of the main issues concerning Analog-Digital Facilitations is the spatial extent of these phenomena along the axon. In fact, ADFs are produced by subthreshold modifications of the somatic potential that spreads to the presynaptic terminal and modifies presynaptic spike shape or basal Ca2+ (Debanne et al., 2013; Rama et al., 2015b). Therefore, the axonal space constant is a major determinant of the spatial extent of ADF. The axonal space constant varies among neuronal types, depending on the axonal diameter, the density of axonal branching and the axonal membrane resistance (Sasaki et al., 2012).

In CA3 hippocampal neurons, the axonal space constant has been evaluated around 200–500 µm (Sasaki et al., 2012; Bialowas et al., 2015; Rama et al., 2015a). In L5 pyramidal neurons, the value estimated ranges between 500 µm (Shu et al., 2006; Kole et al., 2007) and 1,000 µm (Christie and Jahr, 2009). In CA1 pyramidal neurons, the axonal space constant was found to be around 700 µm (Kim, 2014). Therefore, ADFs seem to be restricted to local brain circuits. For example, d-ADF has been found between CA3 neurons but not at the synapses between CA3 and CA1 neurons (Sasaki et al., 2012). However, several lines of evidence suggest that ADFs could also occur between more distant neurons. First, most of the recordings have been made in young animals (14–30 days after birth), in which the myelin sheet is still in development, and may have underestimated the axonal space constant in myelinated axons, such as CA1 and L5 pyramidal neurons. In fact, cortical myelin has been shown to develop up to 22 months after birth (Hill et al., 2018). Moreover, in myelinated axons of cat motoneurons, the axonal space constant was found to be 1,700 µm (Gogan et al., 1983). Second, neuromodulation can induce direct subthreshold potential modifications of presynaptic terminals by presynaptic receptor activation. Presynaptic glycinergic receptor activation depolarizes the Calyx of Held, leading to an increase in spike-evoked synaptic release (Turecek and Trussell, 2001). Similarly, presynaptic GABAA receptor activation depolarizes the presynaptic terminal, leading to an enhancement of spikeevoked synaptic transmission at mossy fiber giant bouton and Purkinje cells (Ruiz et al., 2010; Zorrilla de San Martin et al., 2017). In contrast, in L5 pyramidal neurons, axonal GABAA receptor activation leads to a hyperpolarization, a decrease of axonal spike width and a decrease of spike-evoked Ca2+ entry (Xia et al., 2014). Finally, glutamate released by astrocytes depolarizes terminals in CA3 pyramidal neurons, leading to an increase in spike width and synaptic release (Sasaki et al., 2011). In these latter cases, ADFs are not dependent on subthreshold membrane potential spreading from the soma and could occur even at long range connections.

# Time Constant of ADFs

ADFs present various time constants which determine their potential roles in network physiology. In fact, in most of the studies, d-ADF needs 100 ms to several seconds of presynaptic depolarization to occur. On the contrary, h-ADF can be produced by fast presynaptic hyperpolarization (15–50 ms; Rama et al., 2015a). This difference is well explained by the underlying mechanism of d-ADF and h-ADF: slow accumulation of basal Ca2+ (Bouhours et al., 2011; Christie et al., 2011) or slow Kv inactivation for d-ADF (Shu et al., 2006, 2007; Kole et al., 2007; Bialowas et al., 2015), fast recovery from inactivation of Nav for h-ADF (Rama et al., 2015a; Zbili et al., 2016). Therefore, d-ADF and h-ADF should have different consequences on information transfer in neuronal networks.

## d-ADF May Maintain Excitatory Synaptic Strength During Cortical Up-States

It has been proposed that d-ADF, due to its slow timeconstant, occurs during global network state modifications such as slow-wave sleep associated cortical up and down states (Shu et al., 2006). During an up state, all the neurons of a network will depolarize leading to a global increase in synaptic release through d-ADF. At the same time, the global depolarization should decrease the driving force associated with synaptic excitatory current. In fact, while d-ADF increases synaptic strength by a factor around 1% per mV of presynaptic depolarization (Kole et al., 2007; Bialowas et al., 2015), calculations of driving force for AMPA-driven synaptic current predict a synaptic strength decrease of around 1.5% per mV of postsynaptic depolarization. Therefore, in the case of a globally depolarized neuronal network, d-ADF can be considered as a homeostatic process that maintains an excitatory synaptic strength constant despite the decrease of the driving force.

## d-ADF May Maintain Excitatory-Inhibitory Balance During Up-States

Interestingly, at connections between L5 pyramidal neurons, a depolarization of the presynaptic pyramidal neuron entails both an increase of the monosynaptic EPSP (i.e., classical d-ADF) and an increase in disynaptic inhibition (Zhu et al., 2011). This depolarization-induced facilitation of disynaptic inhibition results from d-ADF occurring at a synapse between L5 pyramidal neurons and neighboring interneurons, leading to an increase in interneuron firing. This phenomenon has been proposed to be important for the persistence of excitatory-inhibitory balance during up-states where d-ADF may increase excitatory and inhibitory activity at the same time (Zhu et al., 2011).

## h-ADF May Participate to Network Synchronization

Because of the fast de-inactivation time constant of Nav channels, h-ADF can be induced by a single IPSP preceding the presynaptic spike (Rama et al., 2015a). Therefore, h-ADF modulates synaptic strength on a short time scale and may participate in fast network processing. First, it is well known that hyperpolarization produced by interneurons is able to synchronize the spiking of neighboring pyramidal neurons. Usually, one explains this phenomenon by a transient silencing of the pyramidal cells as a whole, causing the post-hyperpolarization spiking to occur in synchrony. It can also be enhanced by the so-called ''rebound spiking,'' which is often due to the recovery from inactivation of T-type Ca2+ channels and Nav channels during the hyperpolarization. Interestingly, the h-ADF, which increases the inter-pyramidal synaptic strength after a transient hyperpolarization, has been shown to increase the interneurondriven network synchronization (Rama et al., 2015a). Second, it has been shown that sequences of co-activated pyramidal neurons are often preceded and can be produced by interneuronal firing (Sasaki et al., 2014). It would be interesting to examine whether the increase in inter-pyramidal synaptic strength through h-ADF participates in the production of neuronal ensembles by interneurons. Third, h-ADF could be a detection mechanism for unexpected spikes. In fact, when the neuron is hyperpolarized, the spiking probability decreases. However, due to h-ADF, if a spike occurs during a low spiking probability state, the synaptic release is increased, compared to a spike produced at the resting membrane potential. Therefore, h-ADF increases the informational content of unexpected spikes in cortical networks. Finally, it has been proposed that h-ADF participates in the increase of synaptic transmission during silent states of the slow wave sleep, in which cortical neurons can be hyperpolarized by 5–15 mV (Timofeev and Chauvette, 2017).

# CONCLUSION AND FUTURE DIRECTIONS

We have reviewed evidence showing that the informational content of the spike is dependent on the context of its emission. In fact, the presynaptic spike waveform varies as a function of the neuronal firing rate, the neuro-modulatory state or the subthreshold voltage fluctuations. Moreover, this information is transmitted to postsynaptic neurons by modulation of spike-evoked calcium entry and neurotransmitter release. In this view, the neurotransmission in mammalian CNS needs the occurrence of a digital signal (the spike), whose waveform is modulated by the sub-threshold signal. It has been proposed that synaptic transmission relies on a hybrid between analog and digital signaling, called Analog-Digital synaptic transmission (Clark and Häusser, 2006; Alle and Geiger, 2008). Consequently, the description of APs as purely digital events to study information processing of neuronal networks should be abandoned. In fact, it has been shown that an ''AP waveform code'' is highly reliable and more informative than a purely digital code (de Polavieja et al., 2005; Juusola et al., 2007). Several issues have to be solved to unravel the physiological implications of context-dependent spike waveform modulation. First, ADFs should be tested at various stages of neuronal development. One could expect that context-dependent modulation of spike waveform is larger in developing networks, which present a lower density of voltagegated channels and therefore a less stable spike shape. Second, d-ADF and h-ADF have to be studied in adult networks, in which the myelination process is completed, to confirm the spatial extent of these phenomena. In fact, two published studies report paired recordings of thalamo-cortical connections (Bruno and Sakmann, 2006; Hu and Agmon, 2016), making it possible to test if ADFs occur at long range connections when the axon is myelinated. Third, it would be interesting to observe the extent of ADFs in interneurons. In fact, due to their high voltage-gated channel density, it seems that fast-spiking cortical interneurons do not present spike waveform modulation in function of the membrane potential (Tateno and Robinson, 2006; Goldberg et al., 2008). In contrast, cerebellar stellate cells present depolarization-induced spike broadening and an increase in synaptic release (Rowan and Christie, 2017). Therefore, GABAergic transmission may undergo ADF, depending on the type of interneuron studied. Finally, the spike waveform effects may not be restricted to synaptic release and may affect dendritic computing. In fact, it has been proposed that a spike broadening causes a shunting of incoming PSPs and a decrease in their summation, promoting a low firing rate (Hausser et al., 2001; Juusola et al., 2007). Interestingly, in L5 pyramidal neurons, depolarization-induced spike broadening has been shown to have a shorter time-constant in the soma than in the axon (Shu et al., 2007), due to local differences in potassium current expression (fast inactivating IA current in the somato-dendritic compartment and slow inactivating ID current in the axon). Moreover, in contrast with the axonal spike broadening, it seems that the dendritic spike broadening reduces the Ca2+ entry through the decrease of the driving force promoting the Ca2+ tail current in granule cells of the dentate gyrus (Brunner and Szabadics, 2016). Therefore, it is

# REFERENCES

likely that subthreshold depolarization has different effects on somato-dendritic and axonal computing. The pursuit of the investigation on neuronal computation via spike waveform will certainly unravel the physiological importance of this phenomenon on networks dynamics.

# AUTHOR CONTRIBUTIONS

MZ and DD wrote the manuscript and built the figures.

# FUNDING

This work was supported by ANR (AXODE-14-CE-13-0003- 02 to DD), FRM (FDT20150-0532147 to MZ) and LABEX Cortex of Université de Lyon (NR-11-LABX-0042).

**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 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.

# Modeling Analysis of Axonal After Potential at Hippocampal Mossy Fibers

### Haruyuki Kamiya\*

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

Action potentials reliably propagate along the axons, and after potential often follows the axonal action potentials. After potential lasts for several tens of millisecond and plays a crucial role in regulating excitability during repetitive firings of the axon. Several mechanisms underlying the generation of after potential have been suggested, including activation of ionotropic autoreceptors, accumulation of K+ ions in the surrounding extracellular space, the opening of slow voltage-dependent currents, and capacitive discharge of upstream action potentials passively propagated through axon cable. Among them, capacitive discharge is difficult to examine experimentally, since the quantitative evaluation of a capacitive component requires simultaneous recordings from at least two different sites on the connecting axon. In this study, a series of numerical simulation of the axonal action potential was performed using a proposed model of the hippocampal mossy fiber where morphological as well as electrophysiological data are accumulated. To evaluate the relative contribution of the capacitive discharge in axonal after potential, voltage-dependent Na+ current as well as voltage-dependent K + current was omitted from a distal part of mossy fiber axons. Slow depolarization with a similar time course with the recorded after potential in the previous study was left after blockade of Na+ and K+ currents, suggesting that a capacitive component contributes substantially in axonal after potential following propagating action potentials. On the other hand, it has been shown that experimentally recorded after potential often showed clear voltage-dependency upon changes in the initial membrane potential, obviously deviating from voltage-independent nature of the capacitive component. The simulation revealed that activation of voltage-dependent K+ current also contributes to shape a characteristic waveform of axonal after potential and reconstitute similar voltage-dependency with that reported for the after potential recorded from mossy fiber terminals. These findings suggest that the capacitive component reflecting passive propagation of upstream action potential substantially contributes to the slow time course of axonal after potential, although voltage-dependent K+ current provided a characteristic voltage dependency of after potential waveform.

#### Edited by:

Shin-ya Kawaguchi, Kyoto University, Japan

#### Reviewed by:

Yousheng Shu, Beijing Normal University, China Mitsuharu Midorikawa, Tokyo Women's Medical University, Japan

> \*Correspondence: Haruyuki Kamiya<EMAIL_ADDRESS>
#### Specialty section:

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

> Received: 13 February 2019 Accepted: 25 April 2019 Published: 14 May 2019

#### Citation:

Kamiya H (2019) Modeling Analysis of Axonal After Potential at Hippocampal Mossy Fibers. Front. Cell. Neurosci. 13:210. doi: 10.3389/fncel.2019.00210

Keywords: axon, action potential, after potential, capacitive discharge, simulation

# INTRODUCTION

fncel-13-00210 May 11, 2019 Time: 14:9 # 2

The axon carries neuronal information reliably to the presynaptic terminal as a form of the action potential (Debanne et al., 2011). Propagation of action potential along axon has been considered as a highly reliable digital process (Bean, 2007), although the excitability of axons is slightly modulated for a short period after generation of action potential up to tens to hundreds of milliseconds (Gardner-Medwin, 1972; Zucker, 1974). This post-stimulus change in the excitability of axon was mediated, at least in part, by depolarizing after potential which often follows action potential in the axon (Barrett and Barrett, 1982). After potential in axon may be important for temporal integration of neuronal signaling in the brain by affecting short-term plasticity of presynaptic transmitter release (for review, Ohura and Kamiya, 2016). For the candidate cellular mechanisms of axonal after potential, several possibilities have been suggested so far. These include not only passive mechanism reflecting an intrinsic property of axonal membrane (i.e., capacitive discharge of upstream action potentials; Barrett and Barrett, 1982; Borst et al., 1995; David et al., 1995), but also active mechanism due to slow activation of voltagedependent channels (i.e., persistent-type or resurgent-type Na+ channels; Kim et al., 2010; Ohura and Kamiya, 2018b) or extrinsic mechanisms such as K+ accumulation (Malenka et al., 1981; Meeks and Mennerick, 2004) or autoreceptor activation (Kamiya et al., 2002; de San Martin et al., 2017). The relative contribution of active and passive mechanisms varies among different type of axons (Barrett and Barrett, 1982; Borst et al., 1995; Kim et al., 2010; Ohura and Kamiya, 2018b), although passive mechanisms due to capacitive discharge commonly underlie axonal depolarizing after potential. Despite functional significance in temporal integration (Ohura and Kamiya, 2018a), however, the property and the underlying mechanism of after potential was not thoroughly studied experimentally, especially in thin axons in the central nervous system, because of the extremely small size of axon diameter does not allow direct recordings from the axonal membrane in thin axons.

So far, several studies tried to characterize the axonal after potential by direct recording from axon terminals exceptionally large enough for patch-clamp recording, i.e., calyx of Held (Borst et al., 1995; Kim et al., 2010) and hippocampal mossy fiber terminal (Ohura and Kamiya, 2018b). Although previous studies have suggested that after potential at soma was mediated by several different mechanisms (Raman and Bean, 1997; Yue and Yaari, 2004; Gu et al., 2005; Metz et al., 2005; Yue et al., 2005; D'Ascenzo et al., 2009; Martinello et al., 2015). In this study, it was attempted to describe the quantitative contribution of the capacitive component in axonal after potential by a numerical simulation of membrane potential. For this purpose, we adopted a realistic model of hippocampal mossy fiber (Engel and Jonas, 2005) assuming typical en passant structure with large boutons implemented with voltage-dependent Na+- and K + conductance reflecting properties of those recorded from mossy fiber terminals. A series of simulation analysis revealed the relative contribution of the capacitive component due to the passive propagation of upstream action potential. The simulation also illustrated the characteristic voltage-dependency of after potential recorded from mossy fiber terminals (Ohura and Kamiya, 2018b). The early phase of after potential is mainly determined by voltage-dependent K+ conductance (Storm, 1987; Geiger and Jonas, 2000; Dodson et al., 2003), while the later phase is mediated by capacitive discharges of the axonal membrane. The sequential contribution of voltagedependent K+ conductance and capacitive component nicely reconstructed the time course and voltage-dependency of axonal after potential observed experimentally (Geiger and Jonas, 2000; Ohura and Kamiya, 2018b).

# MATERIALS AND METHODS

# Simulation

The simulated membrane potential (Vm) was calculated according to the model suggested by Engel and Jonas (2005) based on the data recorded from mossy fiber boutons. The model basically assumed a Hodgkin Huxley-type gating model adapted to channels those recorded in mossy fiber terminals, and K+ channel inactivation (Geiger and Jonas, 2000) was reconstructed by implementing multiplicatively with parameters of recombinant KV1.4 channels (Wissmann et al., 2003). Simulations were performed using NEURON 7.5 for Windows (Hines and Carnevale, 1997). The passive electrical properties of the axon were assumed to be uniform, with a specific membrane capacitance Cm of 1 µF cm−2 , a specific membrane resistance Rm of 10,000 cm2 , and an intracellular resistivity Ri of 110 cm. The structure of the mossy fiber (Acsády et al., 1998; Henze et al., 2000) was approximated by a soma (diameter, 10 µm), 10 axonal cylinders (diameter, 0.2 µm; length, 100 µm), and 10 en passant boutons (diameter, 4 µm). The number of segments was 1 µm−1 , and the time step (dt) was 5 µs in all simulations. The resting potential was assumed to be −80 mV, although it was changed to −90 or −100 mV in some series of simulation. The reversal potential of the leak conductance was set to −81 mV to maintain stability. Voltage-gated Na+ channels, K+ channels, and leakage channels were inserted into the soma, axon, and boutons, respectively. The Na+ conductance density was set to 50 mS cm−2 for the axon and boutons and 10 mS cm−2 for the soma. The K+ conductance density was set to 36 mS cm−2 throughout all parts of the neurons. Action potentials were evoked by injection of depolarizing current into the 9th bouton (0.2 ms, 0.1 or 0.2 nA) or the soma (2 ms, 0.2 nA). The equilibrium potentials for Na+ and K+ ions were assumed to be +50 and −85 mV, respectively. In the simulation in **Figure 5**, equilibrium potentials of K+ ions were varied from −65 to −105 mV,

# RESULTS

# Passive Propagation of Action Potential Along the Mossy Fiber Model

Capacitive discharge of axonal membrane due to upstream action potential might contribute to a downstream action

potential. To evaluate the relative contribution of components reflecting passive propagation, voltage-dependent Na+- and K+ conductance was removed from distal portions of mossy fibers, and spatial profile of depolarization was examined. In the control condition, reliable propagation of action potential was reconstructed by simulation (**Figure 1A**). A small increase in the peak amplitude at the 10th bouton is possibly due to the seal end effect at the last bouton in the model. When Na+ and K+ conductance was omitted from distal axons from the eighth axon and bouton, substantial depolarization propagated passively (**Figure 1B**), but the amplitude declined along with the distance and the time course was slowed (**Figure 1C**), possibly reflecting the electrical filtering property of axon cable. The amplitude was plotted against distance from the 7th bouton, end of the compartment which expresses normal Na+ and K+ conductance. Data points were fitted with single exponential, and the distance with a reduction to 1/e (37%) was evaluated as 53 µm (**Figure 1D**). These results suggest that passively propagated depolarization partly contributed to the after potential recorded from downstream boutons. Conversely, passive propagation from the downstream compartment may affect upstream action potential. Passive depolarization may spatially distribute both backward and forward directions at a certain time point, although ionic component travels only forward direction by propagation of action potential. In support of this notion, action potential recorded at the 7th bouton was slightly smaller than that recorded from the upstream bouton as illustrated in **Figure 1B**. The rising phase of action potentials at downstream bouton concurs with the peak of an action potential at the upstream bouton, and therefore affecting the peak of the upstream action potential.

The value of spatial decay constant of 53 µm for passive propagation was relatively short. This may partly due to the filtering of fast voltage transient of the action potential by axon cable. In line with this notion, the length constant of mossy fiber model, as measure by spatial decay of steady-state hyperpolarization in response to current injection of longer steppulse (4 pA for 500 ms, **Figure 1E**) was estimated as 171 µm (**Figure 1F**). This value is much close to that evaluated for EPreSP (subthreshold passive propagated somatic EPSP at mossy fiber axon (430 µm, Alle and Geiger, 2006).

# Voltage-Dependency of Axonal After Potential in Mossy Fiber Model

Previous studies in the calyx of Held (Sierksma and Borst, 2017), in the cerebellar basket cells (Begum et al., 2016), and in the hippocampal mossy fibers (Ohura and Kamiya, 2018b), have shown that the amplitude of after potential was negatively correlated with the initial membrane potentials. To test if a similar voltage dependency is reconstructed in simulation, resting membrane potential was changed by altering the equilibrium potential of leak conductance. At resting potential of −80 mV, after potentials are hyperpolarizing in polarity (**Figures 2A,B**). At −90 or −100 mV, depolarizing after potential with similar time course with those recorded experimentally were reconstructed (**Figures 2C–F**).

Superimposed traces of the reconstructed action potentials and after potentials (**Figures 2G,H**) clearly illustrated that the early phase, the initial 5 ms, converges around equilibrium potential of K+ ions (−85 mV) as shown by an asterisk. It should be noted that the action potential onset was delayed at −90 or −100 mV (**Figures 2G,H**), possibly reflecting the slightly slower conduction at these negative membrane potentials than at −80 mV.

Simulation at −80 to −100 mV in which voltage-dependent Na+- and K+ conductance was removed from distal portions of mossy fibers shown in red (**Figure 2I**) left capacitive component which basically shows no voltage-dependency as in **Figure 2G**, although the small difference in amplitude (**Figure 2J**) possibly reflect changes in the amplitude of upstream action potential at different membrane potentials (at −80 to −100 mV). In line with this notion, action potentials at the 9th bouton show similar changes in amplitude as in **Figures 2K,L**. The difference in onset of action potentials (**Figures 2K,L**) and the downstream capacitive components (**Figures 2K,L**) may also be caused by the slower conduction at −90 or −100 mV.

# Ionic and Capacitive Components Underlying Propagating Action Potential

To get insight into the relative contribution of ionic and capacitive mechanisms in shaping time course of axonal after potential, a series of simulation to replace voltage-dependent Na+ and K+ conductance in the axonal membrane were carried out. Propagating action potential recorded from the 10th bouton (**Figure 3A**, black) was broadened by removal of voltagedependent K+ conductance from the 10th axon and bouton as shown in red (**Figure 3A**, blue). Further removal of voltagedependent Na+ conductance reduced the amplitude substantially (**Figure 3A**, green), although substantial depolarization, which possibly reflects the capacitive component due to passive propagation of upstream action potential. Superimposed traces in **Figure 3B** shows crosspoint between black and green traces, suggesting that K+ conductance curtails passive components to shape the characteristic waveform of after potential. Using these data, components of membrane potential changes due to activation of Na+ channels (VmNa, orange) or K+ channels (VmK, purple) were calculated by subtraction. Sum of VmNa and VmK was calculated and shown in red (**Figure 3C**). Superimposed traces in **Figure 3D** clearly illustrate the temporal relationship of these components.

Similar simulation analysis was also performed at the resting potential of −100 mV, in which the waveform of after potential (**Figures 3E,F**) closely resembles with those of the recorded waveform of depolarizing after potential in the experiment (Geiger and Jonas, 2000; Ohura and Kamiya, 2018b). Na+- (orange) and K+-channel dependent (purple) components were calculated (**Figure 3G**), and the time course was compared with capacitive component (green) isolated by removing Na+- and K +- conductance. **Figure 3H** also illustrated that the relative contribution of each component, although a small effect of shunting of passive depolarization by large ionic components could not be excluded entirely. The amplitude of the early

passant axon with 10 boutons evenly spaced every 100 µm ("a pearl chain model"). Brief current injection into the soma elicited action potential which propagates faithfully to the 10th bouton without attenuation. (B) Distance-dependent decay of the amplitude of action potential without voltage-dependent ionic conductance. Voltage-gated Na+- and K+-channels were omitted from the distal portion of mossy fiber axon from 8th (green) to 10th (orange) boutons and axon, as shown in red. The amplitude of depolarization decreased successively, and the time course was slowed down along the distance, consistent with the notion that it reflects passive propagation due to capacitive discharge by an upstream action potential. (C) Traces in B were expanded in time for comparison. (D) Spatial profiles of passive propagation. The decay of the peak amplitude along the distance was fitted by a single exponential with 53 µm for the length with a reduction to 1/e (37%). The amplitude of propagating action potentials with Na+- and K+-channels (black) was shown for comparison. (E) Hyperpolarizing responses to long pulse current injection of 4 pA for 500 ms into the 10th bouton, which were used for estimation of the length constant of steady-state hyperpolarization. (F) The decay of the peak amplitude along the distance was fitted by a single exponential with 171 µm.

FIGURE 2 | Voltage-dependency of components of axonal after potential. (A) Propagating action potentials recorded from every bouton in which the resting potential was set at –80 mV. (B) Action potential at the 10th bouton was shown in green. An asterisk (∗ ) shows the hyperpolarizing after potential. (C–F) Similar traces in which the resting potential was set at –90 mV (C,D) or at –100 mV (E,F). After potential (∗ ) was reversed in polarity to depolarizing one. (G) Superimposed traces in panels (B,D,F). (H) Traces in panel (G) were aligned by subtracting baseline soon before the response to compare the time course of after potential at various membrane potentials. (I) Capacitive component due to passive propagation was calculated by removing Na+- as well as K+-channels from 10th axon and bouton (red). (J) Traces in panel (I) were adjusted for the baseline to compare the time course. (K) Action potential waveforms at the 9th bouton in the above simulation. (L) Traces in panel (K) were adjusted for the baseline to compare the time course.

phase of after potential is close to the equilibrium potential of K+ ions (EK, −85 mV), in line with the notion that the early phase is dominantly determined by the K+ channeldependent component.

# Capacitive Current Underlying Propagating Action Potential

To illustrate the exact time course and the sequence of activation of ionic and capacitive components, capacitive current (Icap) propagating from upstream axon was simulated. Outward Icap (red) preceded the onset of inward Na+-current (INa, blue) and outward K+-current (IK, green) during propagating action potential elicited by somatic stimulation (**Figure 4A**), as highlighted with an asterisk (∗ ). The delay in activation of ionic currents reflects passive propagation due to capacitive discharge from the upstream axonal membrane. In contrast, when action potentials were evoked by current injection to the recorded bouton, there was no delay between the onsets of Icap and INa (**Figure 4B**). Arrow indicates capacitive current due to current injection. The delay from capacitive to the ionic component is much obvious when the resting potential was set at −100 mV (**Figure 4C**). Direct stimulation at the recorded bouton also elicited Icap and INa without delay at −100 mV (**Figure 4D**).

# Potassium Conductance Determines the Initial Phase of After Potential

Then it was examined whether potassium channel-dependent fast repolarization dominate time course of the initial phase of after potential. For this purpose, the equilibrium potential for K+ ions around the 10th axon and bouton (EK10) was changed systematically to vary the driving force of K+ ions across the axonal membrane. Upon changes in EK10 from −65 to −105 mV, initial phase (or breakpoint) was changed (**Figure 5A**). When EK10 was set at more positive (−65 or −75 mV) than resting potential (−80 mV), after potential reversed polarity to depolarizing. A passive propagating component as measured by blocking voltage-dependent Na+- and K+ conductance was unchanged by an alteration in EK10 (**Figure 5B**). Similar results were obtained when resting potentials were set at −100 mV (**Figures 5C,D**). These results suggest that activation of K+ conductance determines fast repolarization and the breakpoint of the initial phase of after potential.

# The Contribution of Passive Capacitive Discharge in the Late Phase of After Potential

Time course of the slow phase of afterpotential seems to be slow enough to be explained by the passive properties of the axonal membrane. To test this notion, the simulation of propagating action potential with stepwise current injection was performed. Time course of slow relaxation of membrane potential upon current step injection (triangle) was quite similar to that of the late phase of afterpotential (asterisk) as shown in **Figure 6A**. The time constant of hyperpolarizing responses was 7.9 ms, while that of the late phase of afterpotential was 7.1 ms. The similarity in the time courses was also illustrated in the simulation data

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), was linearly changed with alteration of EK. (B) Capacitive except for the resting potential was set at –100 mV.

with the initial membrane potential at −100 mV (**Figure 6B**). The contribution of capacitive components was also supported by the simulation changing the value of specific membrane capacitance (Cm) systematically. As expected from cable filtering by capacitance, increase in Cm reduce and prolonged the passive propagating component as shown in **Figure 6C**. Taking together, it was suggested that the capacitive component of passive propagation contribute substantially to the generation of depolarizing after potential.

# DISCUSSION

In this study, a series of numerical simulation using a realistic model of hippocampal mossy fiber was performed to illustrate the possible mechanisms underlying after potential following an axonal action potential. The early phase of after potential converges on the equilibrium potential of K+ ions (EK) and thereby the dominant contribution of voltage-dependent K+ channels was suggested. On the other hand, the later phase was most likely explained by the passive capacitive discharge of the axonal membrane. A characteristic waveform of action potential-after potential sequence was nicely reconstructed by a combination of a breakpoint due to fast repolarization by the opening of K+ channels and slow relaxation of polarization by the capacitive discharge of the axonal membrane.

# Evaluation of Passive Propagation of Action Potential Along the Mossy Fiber Model

In an experimental approach, it is difficult to estimate the spatial and temporal distribution of a passive component in a propagating action potential along the axon. Recordings from at least two distinct sites of the connecting axon, as well as spatially restricted blocking of voltage-gated conductance to eliminate an active component, are necessary for the evaluation of passive properties of axonal membranes (de San Martin et al., 2017).

fncel-13-00210 May 11, 2019 Time: 14:9 # 8

various membrane potentials in response to stepwise current injection (from +1 to –6 pA, 1 pA steps) to the recorded 10th bouton whose resting membrane potential was set at –80 mV. Note that the slow relaxation of membrane potential in response to stepwise current injection (triangle) shows a similar time course with that of after potential (asterisk). Lower traces are showing step-pulse current injection. (B) Similar records at –100 mV initial membrane potential. Again, time courses of hyperpolarization to step current injection (triangle) are similar to that of after potential. (C) Effect of the changes in the specific membrane capacitance Cm on passive capacitive component measured by removal of gNa and gK from the 10th axon and bouton.

These requirements are difficult to be achieved in the experimental conditions, while simulation readily figures out passive components in a propagating action potential.

The amplitude of passive components reflecting action potential at the next en passant bouton is estimated as 19 mV. The simulation also showed that the amplitude of the passive component declined along with the distance. The decay of the amplitude of passive components was fit with single exponential with the length for a reduction to 1/e as 53 µm. This value was similar to that estimated for GABAA-receptor mediated response in axons of cerebellar molecular layer interneurons and in axons of cultured Purkinje cells (de San Martin et al., 2015, 2017). Passive component inevitably involves in a substantial fraction in propagating action potential-after potential sequence. This notion should be directly tested experimentally by subcellular recording approach from two distinct sites of a connecting mossy fiber axon.

The amplitudes of experimentally observed depolarizing after potentials at mossy fiber terminals are 6.9 ± 0.6 mV in the rat (Geiger and Jonas, 2000) and 15.3 ± 1.3 mV in the mouse (Ohura and Kamiya, 2018b). In our simulation, the action potential of 121 mV was decayed to 19 mV at 100 µm and 5 mV at 200 µm by passive propagation as shown in **Figure 1D**, suggesting that interbouton distances are ranged between 100 and 200 µm. Although the cable properties also depend on Cm value and the diameter of mossy fibers, the simple model suggested by Engel and Jonas (2005), which we adopted in this study, reasonably approximated the experimental values of after potential amplitude.

# Voltage-Dependent K+ Channels Provide a Breakpoint in the Early Phase of After Potential

Previous studies consistently suggested that axonal after potential was mediated by the capacitive discharge of the axonal membrane. Contrary to expected from passive nature of capacitive component, however, it was shown that the amplitude of after potential shows clear voltage-dependency, i.e., after potential was smaller at depolarizing membrane potential, while it got bigger at hyperpolarizing membrane potential (Begum et al., 2016; Sierksma and Borst, 2017; Ohura and Kamiya, 2018b). The results of simulation in this study revealed that the characteristic waveform of after potential was reconstructed by a combination of fast repolarization by voltage-gated K+-channels and by the passive capacitive discharge of the axonal membrane. Time course of the late phase of after potential was similar to those of slow relaxation of membrane potential in response to stepwise hyperpolarizing current injection, in consistent with the passive nature of the capacitive component.

Combination of voltage-dependent K+ conductance and capacitive discharge might be a too simplified interpretation of the characteristic time course of after potential. Since previous studies pointed out that other voltage-dependent conductance, such as resurgent (Kim et al., 2010; Ohura and Kamiya, 2018b) as well as persistent Na+ current (Yue et al., 2005), are involved in the late phase of after potential. These voltage-dependent currents might additionally involve in boosting up the after potential. Several previous studies reported that after potential waveform was altered upon changes in the recording membrane potentials, and sometimes reverse in polarity at depolarized membrane potentials. The reversal potentials estimated or extrapolated from the recorded after potential waveforms varies considerably (Begum et al., 2016; Sierksma and Borst, 2017; Ohura and Kamiya, 2018b), possibly reflecting the various contribution of active (voltage-dependent conductance) and passive (capacitive discharge) components. Overall voltage-dependency is consistent with the notion that early phase is predominantly governed by voltage-dependent K+ conductance since the initial phase seems to reverse around EK. The later phase is likely to reflect voltage-independent passive components of slow depolarization. These notions suggested that voltage-dependent K+ channels and capacitive discharge involve as common mechanisms to shape the framework of after potential, while active conductance such as resurgent Na+ current or T-type Ca2+ current may additively contribute to the late phase of after potential.

One may argue that the model of hippocampal mossy fiber which we adopted in this study (Engel and Jonas, 2005) is too simple. For instance, if voltage-dependent conductance with activation voltage near resting potential like Ih or the persistenttype Na+ channels is expressed in mossy fibers, depolarizing after potential might be affected by these voltage-dependent conductance. So far, there is no evidence for the presence of Ih on mossy fibers (Chevaleyre and Castillo, 2002; but see Mellor et al., 2002). Presence of persistent Na+ channels on mossy fibers is also less likely since Na+ current recorded from mossy fiber fully inactivate during prolonged depolarization step (Engel and Jonas, 2005).

Passive depolarization might be shunted by large ionic conductance increase during an action potential and thereby reduced passive depolarization to some extent. It should be mentioned, as demonstrated in **Figures 4A,C**, capacitive current (Icap) often precede INa during an action potential, while still some fraction overlapped in the time domain. This implies shunting of passive depolarization, if any, is limited to the falling phase of Icap.

# Possible Contribution of Slow Activating Voltage-Dependent Na+ Current in After Potential

Mossy fiber model adopted in this study assumes equilibrium potentials of K+ ions (EK) at −85 mV. In this model, action potentials were followed by hyperpolarizing after potential at resting potential of −80 mV. This is expected if the initial phase of after potentials is governed by the opening of voltage-gated K + channels and thereby approaching to EK more negative than resting membrane potential. However, experimentally recorded action potentials from mossy fiber terminals displays robust depolarizing after potential (Geiger and Jonas, 2000; Ohura and Kamiya, 2018b), and the waveforms are quite similar to those obtained in the simulation assuming more positive EK value than the resting potential of −80 mV. The reason for the difference in polarity between experiment (depolarizing) and the model (hyperpolarizing) needs to be clarified in future studies.

It seems to be reasonable to assume additional involvement of slow activating voltage-dependent Na+ current such as resurgent Na+ current (Ohura and Kamiya, 2018b) in boosting slow depolarization observed in the experiment.

In summary, systematic simulation analysis using a model of mossy fibers revealed that action potential propagates passively via axon cable substantially, and thereby consists of a part of after potential following an action potential. The characteristic waveform of axonal action potential-after potential sequence, as well as apparent voltage-dependency of after potential, are reconstructed with the simple combination voltage-dependent K + channel component and a passive capacitive component. An initial breakpoint after action potential may be controlled by fast repolarization by the opening of K+ channels, while the later phase is dominantly mediated by the capacitive discharge of the axonal membrane. These notions may shed light on the common underlying mechanism of axonal after potential, although specific mechanisms may involve in fine-tuning of the axonal excitability.

# REFERENCES

# DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

# AUTHOR CONTRIBUTIONS

HK performed the simulation, analyzed the data, and wrote 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).

**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.

# The Slow Depolarization Following Individual Spikes in Thin, Unmyelinated Axons in Mammalian Cortex

### Morten Raastad\*

*Department of Physiology, School of Medicine, Emory University, Atlanta, GA, United States*

An important goal in neuroscience is to understand how neuronal excitability is controlled. Therefore, Gardner-Medwin's 1972 discovery, that cerebellar parallel fibers were more excitable up to 100 ms after individual action potentials, could have had great impact. If this long-lasting effect were due to intrinsic membrane mechanisms causing a depolarizing after-potential (DAP) this was an important finding. However, that hypothesis met resistance because the use of K+ sensitive electrodes showed that synchronous activation, as commonly used in excitability tests, increased extracellular K+ concentration sufficiently to explain much of the hyperexcitability. It is still controversial because intra-axonal recordings, which could have settled the debate, have not been made from parallel fibers or other axons of similar calibers. If it had not been for the fact that such thin axons are, by far, the most common axon type in cortical areas and control almost all glutamate release, it would be tempting to ignore them until an appropriate intra-axonal recording technique is invented. I will go through the literature that, taken together, supports the hypothesis that a DAP is an intrinsic membrane mechanism in cerebellar parallel fibers and hippocampal Schaffer collaterals. It is most likely due to a well-controlled process that stops the fast repolarization at a membrane potential positive to resting membrane potential, leaving the membrane more excitable for ∼100 ms during a slow, passive discharge of the membrane capacitance. The DAP helps reduce failures but can also cause uncontrolled bursting if it is not properly controlled. The voltage at which the fast repolarization stops, and the DAP starts, is close the activation range of both Na+ and Ca2+ voltage activated channels and is therefore essential for neuronal function.

Keywords: action potential, axon, unmyelinated axons, after-potentials, depolarizing after-potential, conduction failures, presynaptic

# INTRODUCTION

The after-potentials of the action potentials ("spikes"), either hyper- or de-polarizing relative to resting membrane potential, are excitability-controlling mechanisms. Such after-potentials have been extensively studied in regions near the soma where some of their functions are obvious: they reduce or increase the amount of current needed to reach threshold for spike initiation at the axon initial segment (AIS). In the axon, after the spike is triggered at the AIS, the functions of

#### Edited by:

*Shin-ya Kawaguchi, Kyoto University, Japan*

#### Reviewed by:

*Haruyuki Kamiya, Hokkaido University, Japan Lia Forti, University of Insubria, Italy Kenneth Paradiso, Rutgers University, The State University of New Jersey, United States*

\*Correspondence: *Morten Raastad<EMAIL_ADDRESS>
#### Specialty section:

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

> Received: *08 January 2019* Accepted: *23 April 2019* Published: *16 May 2019*

#### Citation:

*Raastad M (2019) The Slow Depolarization Following Individual Spikes in Thin, Unmyelinated Axons in Mammalian Cortex. Front. Cell. Neurosci. 13:203. doi: 10.3389/fncel.2019.00203*

**57**

after-potentials are less obvious. That may be one of the reasons considerably less is known about after-potentials in axons, particularly in the very thin, typical cortical axons (TCAs).

Also, when spikes in TCAs have been studied the focus has been mostly on the fast rather than the slow part of the spike. This is because the shape of the fast spike has a well-established impact on transmitter release (Augustine, 1990; Sabatini and Regehr, 1997; Borst and Sakmann, 1999). In contrast, the study of effects of after-potentials on transmitter release is relatively new (Clarke et al., 2016; Sierksma and Borst, 2017), and their influences on conduction properties like speed, endurance, bursting, and failures, which are the main topics of this article, have received even less attention.

However, the most important reason for the lack of knowledge is that TCAs may be the worst preparations for investigating spike mechanisms because the tiny diameters of these axons (on average 0.17µm, Westrum and Blackstad, 1962; Palay and Chan-Palay, 1974; Shepherd and Harris, 1998) have prevented the use of direct intracellular voltage recordings from intact axons. The revolution in genetic and molecular techniques has not solved this problem.

Unfortunately, we cannot get around the TCAs because they are by far the most common axon type in mammalian cortices (including hippocampal, cerebellar, and neo-cortex). Most of the brain's release of the excitatory transmitter glutamate is controlled by presynaptic "boutons" found along most of the paths of TCAs. They comprise the largest fractions of cortical volume (∼50%) and cellular membranes (∼60%) (Mishchenko et al., 2010) and are usually by far the largest part of neurons' volume and membrane surface (Braitenberg and Schüz, 1998; Wu et al., 2014).

The first data suggesting an after-potential in TCAs came from Gardner-Medwin in 1972 when he showed that cerebellar parallel fibers were more excitable up to 100 ms after individual action potentials. Although a depolarization after the spike was considered likely, the mechanism for this depolarization was suggested to be extracellular K+ accumulation due to the synchronized activation of many parallel axons. Many years later, Wigström and Gustafsson (1981) used almost identical tests of TCAs in hippocampal slices and found the same excitability changes but concluded that the post-spike hyperexcitability was due to an intrinsic mechanism of the axons. One of the main aims of this article is to detangle the excitability-increasing effects of changes in extracellular K+, and on the other hand the axonintrinsic mechanism that creates a depolarizing after-potential (DAP) in TCAs.

Despite the limited opportunity to record intra-axonal potentials, it has over many years from a variety of technical approaches accumulated important data on the TCA spike, its propagation, and the DAP. Because of the slow accumulation of data some reports may have gone unnoticed, and this review will therefore summarize and synthesize knowledge about the TCA spike and their DAP. Almost all data are from cerebellar parallel fibers and hippocampal Schaffer collaterals, but I will refer to them as "TCAs," for convenience, but also as a reminder that they a similar to most axons in cortical regions with respect to calibers, boutons, and transmitter type. Also those pyramidal neurons that have myelin around their proximal axon usually end up as thin terminal axons that fit the description of a TCA, although their spike or after-potentials have not been investigated. We must therefore keep in mind that axons other than Schaffer collaterals and parallel fibers may be different.

I will focus on the DAP in the context of excitability control and spike propagation in TCAs, and mostly ignore the TCAs' transmitter releasing function which is covered elsewhere (for example (Debanne et al., 2011; Fioravante and Regehr, 2011)).

The sum of the available information strongly suggests that that hippocampal and cerebellar thin axons, examples of TCAs, have two distinct phases of repolarization; one fast that stops relatively abruptly at a well-controlled membrane potential more positive than the resting membrane potential, and thereafter the DAP which is a slow, passive decay back to resting membrane potential.

# TCA POST-SPIKE HYPEREXCITABILITY—AN AXONAL MEMBRANE MECHANISM OR THE RESULT OF UNSPECIFIC INCREASE IN EXTRACELLULAR K+ CONCENTRATION?

# Hyperexcitability

The hyperexcitability that follows individual spikes in TCAs, which was the first hint of a DAP in such axons, can be reliably demonstrated through its effects on population spike amplitude and propagation speed (explained in **Figure 1**). These effects of a single conditioning stimulus were first shown by Gardner-Medwin (1972) in the cerebellar parallel fibers of the anesthetized cat, and by Wigström and Gustafsson (1981) in the Schaffer collaterals in hippocampal slices. Gardner-Medwin (1972) concluded that "The apparent increase of the conduction velocity of the parallel fibres is so marked that it distinguishes them from all the other fibres in the mammalian nervous system in which the after-effects of stimulation have been studied."

Both these studies found the maximal hyperexcitable effect around 20–30 ms after an electrical activation of the spikes, and they quantified the increase in excitability to 20–40% by studying how much they could reduce the strength of a second stimulus without losing any amplitude of the population spike amplitude. The similarity of these results, despite the large difference in the preparations, suggests that the hyperexcitability is a robust phenomenon.

# Hyperexcitability in Peripheral Axons

Excitability of peripheral axons in mammals and many other species has been extensively studied by recording changes in conduction speed. Particularly the thin, unmyelinated C-fibers have pronounced activity-dependent changes in conduction speed and may therefore help us understand mechanisms in TCAs. Many of these investigations use trains of stimuli at high frequency which activate many mechanisms, for example hyperpolarization due to the Na-K-pump (Ritchie and Straub, 1957) and depolarization due to increasing extracellular K+ (Frankenhaeuser and Hodgkin, 1956). These factors can lead

FIGURE 1 | Hyperexcitability specific to the activated axons can be detected and quantified by using conditioning and test stimuli on populations of TCAs. (A) Stimulation and recording electrodes are positioned typically 2–3 mm apart among the cerebellar parallel fibers or other TCAs. (B) A test stimulus is given 20 ms after the conditioning stimulus. When conditioning and test stimuli have equal strength, the test stimulus will activate the same axons as the conditioning stimulus and therefore the two spike population responses have similar amplitudes. However, the response to the test stimulus occurs at a shorter latency (green arrow) because the conditioned axons (violet in B1) are more excitable and the spike travels faster. This hyperexcitability can be quantified by reducing the stimulus strength of the test stimulus (dotted part of the stimulus artifact). At moderate reductions, typically 15–40%, the test response keeps its original amplitude. The interpretation is that the recently conditioned axons (violet in B1) have lower activation threshold, and even the reduced test stimulus is sufficient to activate all the violet, conditioned axons. (C) When the conditioning stimulus is stronger than the test (more violet, activated axons in C1 than in B1), but the test strength is the same as in (B), the test response will get a larger amplitude than in (B) (compare with dotted blue which is response to conditioning and test stimulus of equal strength). The interpretation is that the stronger conditioning stimulus leaves more axons with reduced threshold in (C) than in (B) (violet in B1) allowing the test stimulus in (C) to activate more axons than in (B).

to periods of speeding, slowing and failures. Because of the difficulty in interpreting such mixtures of mechanisms, I will focus on the excitability changes that occur after single spikes ("post-spike hyperexcitability").

Many peripheral axon types show post-spike hyperexcitability, with duration similar to or sometimes longer than that observed in Schaffer collaterals and parallel fibers. Human sympathetic C-fibers have a hyperexcitable period of ∼1,000 ms (Bostock et al., 2003). Because of the long conduction distances that can be investigated in humans, the speeding-up due to this hyperexcitability can be considerable. For example, in human Cfibers of mechano- and heat-insensitive type, two spikes triggered 50 ms apart caught up >65% of that interval over ∼500 mm conduction distance (Weidner et al., 2003). Most increases after single spikes in humans are, however, small (often <5%), possibly due to masking of some of the effect by parts of the axon with different activity-dependent properties (discussed in Bostock et al., 2003). Myelinated axons have a DAP with an underlying mechanism that relies on a high-resistance pathway between the cell membrane and the myelin sheet (Barrett and Barrett, 1982) and is therefore not directly similar to the DAP in TCAs.

To summarize, increases in population propagation speed and amplitude are robustly demonstrated in whole animals (Gardner-Medwin, 1972), cerebellar and hippocampal slices (Wigström and Gustafsson, 1981), at temperatures between 22 and 35◦C (Soleng et al., 2004; Pekala et al., 2016), and in peripheral cold-sensitive C-fibers and sympathetic axon in humans (Bostock et al., 2003).

# Does Extracellular Potassium Contribute to, or Even Fully Explain the Hyperexcitability?

Although there has not been doubt about the existence of the hyperexcitability in TCAs, there has been considerable uncertainty about its cause. The most likely causes are that the spike is followed by a depolarization due to (a) increased extracellular potassium concentration ([K+]o), or (b) an intrinsic membrane mechanism. This distinction is important because electrical activation synchronizing many axons may give [K+]o increases (1[K+]o) never occurring during normal brain activity, while an intrinsic membrane mechanism is likely to be important for normal axonal function.

Around the time Gardner-Medwin published his excitabilityincreasing effects there was an emerging awareness of the excitability-modifying effects of neurons' K+ efflux and accumulation in extracellular space (Frankenhaeuser and Hodgkin, 1956). Even individual bursting Purkinje cells could produce 1[K+]o of ∼1 mM in their vicinity (in turtle, Hounsgaard and Nicholson, 1983). Much of the magnitude and time-course of the excitability increase seen with repetitive extracellular electrical stimulation could be explained by [K+]o recorded by K+-sensitive electrodes (Malenka et al., 1981, 1983; Kocsis et al., 1983), but the critical question of whether single spikes could raise [K+]o enough to explain the large (15–20%) increase in conduction speed was not addressed.

If we as a starting point assume that the excitability-increasing effect of a fast rise in 1[K+]o in response to electrical activation of axons is similar to the effect of a slower increase in 1[K+]o achieved by increasing the bath concentration of K+, the post-spike hyperexcitability cannot be explained by 1[K+]o. Estimated 1[K+]o per stimulus in bundles of simultaneously activated unmyelinated axons in the brain is 0.2–0.5 mM (Fritz and Gardner-Medwin, 1976; Kocsis et al., 1983; Aitken and Somjen, 1986). In contrast, raising bath [K+]o from 2.5 to 4 mM increased conduction speed by only 4.6% (Kocsis et al., 1983; Soleng et al., 2004). So, a [K+]o 3–6 times higher than the singlestimulus concentration gives only 1/3 to ¼ of the speed increase caused by individual spikes.

However, fast stimulus induced 1[K+]o may have larger effects on excitability that the slower bath-applied 1[K+]o because with slow increase membrane stabilizing mechanisms like the H-current and the Na-K-pump will have time to counteract the depolarizing effect of 1[K+]o. This idea may be possible to test because postsynaptic structures contribute significantly to the stimulus-induced 1[K+]o. Around 50% reduction of 1[K+]o was reported when synaptic signals were blocked by low Ca2+ and high Mg2+, or Mn2+ in hippocampal slices, cerebellum in vivo, and dorsal horn of rat spinal cord slices (Nicholson et al., 1978; Urbán et al., 1985; Aitken and Somjen, 1986). One publication reported that post-spike hyperexcitability (speed) was not changed after block of synaptic signals with adenosine (Kocsis et al., 1984). If also adenosine-block of synaptic signals reduces 1[K+]o, that finding would suggest that 1[K+]o is not responsible for all of the post-spike hyperexcitability.

A third argument against K+ as a major factor is obtained by reducing 1[K+]o around the tested axon by spatially separating the conditioning and testing stimulus. This was done by using different branches of the same neuron for conditioning and test stimulus (Soleng et al., 2004). The threshold reduction obtained by this approach were similar to that of cerebellar axons in whole animals (14% reduction at 34◦C and 30 ms interval).

# Single Axon

The critical experiment to test if the hyperexcitability is specific to the activated axon is of course to measure the excitability when only one axon is activated. This was done on cerebellar parallel fibers with a somatic tight-seal electrode triggering a somatic spike and a separate electrode testing the threshold for spike activation of the axon (Palani et al., 2012). In this configuration the threshold reduction and its time course (maximal threshold reduction 25% at 20 ms after a spike) was similar to the post-spike hyperexcitability described for parallel fibers in whole animals (Gardner-Medwin, 1972), supporting the idea that the post-spike hyperexcitability is an intrinsic property of the parallel fibers.

# How Much Does the Combined K+ Efflux From Many Adjacent Axons Influence the Excitability?

Although synchronous electrical activation of axons is unphysiological, its effect is relevant in experiments and clinical CNS stimulations using electrodes. One way to better understand the impact of such stimulation is to activate a bundle of axons and record the antidromic spike at the soma of only one of them. Then it is possible to find the axonal activation threshold of the recorded unit, obtaining both successful activations and failures with the same stimulation strength, while maintaining a relatively constant number of activated axons (Pekala et al., 2016). In such experiments, a failure at the first stimulus increased the failure rate at the second stimulus (changed from 50% to 75% failures at 30 ms interval), suggesting a slightly reduced excitability after a single stimulus. In contrast, a success on the first stimulus almost eliminated failures at the second stimulus (<0.1% failures, Pekala et al., 2016). This means that the excitability-increasing effect of a spike in the tested unit's axon was much stronger than the influence from adjacent synchronously activated axons. Similar results were reported from hippocampal CA3 cell's axons (Soleng et al., 2004).

# SHAPE OF THE DAP

The initial part of the DAP is important because, as I will explain below, evidence from grease-gap recordings and backpropagating spikes suggest that the DAP initial amplitude is close to the activation range for Na+ and Ca2+ channels. I will go through the background for those claims in the

section called "How does the DAP influence axonal functions." The start of the DAP is difficult to investigate by studying excitability (speed or threshold) because the refractory period of a spike stretches into the hyperexcitable period. A further complication is that the refractory period varies between axons (Raastad and Shepherd, 2003).

Recording the membrane potential would give information during the early period but direct intracellular voltage recordings of the traveling spike in TCAs have not been possible yet. Various methods have been used to overcome the difficulty in recording intracellularly from TCA, particularly the distal parts of the axonal arbor. These include intracellular recordings from soma with backpropagating spikes, "grease gap" methods, recordings from the bleb that forms when the axon is cut, and voltage sensitive dye (VSD) recordings. Most of these recordings have focused on the amplitude and width of the fast part of the spike, well-motivated by the importance of those parameters for control of transmitter release. Few have investigated spike after-potentials and their influence on conduction properties like speed, endurance, bursting, and failures.

To illustrate the findings, interpretations and qualifications, I will use a simple cable model implemented with the simulator NEURON (Hines and Carnevale, 1997). This is meant as a minimalistic model that approximately reproduce spike propagation properties discussed in this article. Details of the model are explained in **Figure 2** and in section Methods.

# Backpropagating Spikes

One opportunity to get information about the TCA spike, at least in neurons that have TCAs attached directly to soma without interposed myelination, like the cerebellar granule cells and rodent hippocampal Schaffer collaterals, is to use tightseal somatic voltage recordings with backpropagating, electrically triggered spikes. This is illustrated with the model neuron in **Figure 3A**. Contributions from near-soma regions can be reduced or avoided by hyperpolarizing the soma by current injection to prevent the fast part of the spike from invading the soma. If there is a DAP following the axonal spike it may still be recorded at the soma, as shown in **Figure 3A**, red curve.

That approach (Palani et al., 2012; Pekala et al., 2014) was used to show a DAP starting on average 12 mV positive to a −63 mV resting potential and a decay to 1/e in 52 ms (Palani et al., 2012). Those publications also utilized threshold activation of the axon, with ∼50% activation failures of the recorded neuron. The DAP never occurred without a spike (at somatic voltages that allowed the spikes to invade the soma), showing that the DAP is an integral part of the spike. Furthermore, at the stochastic stimulation failures there was no detectable depolarization even though many axons were activated by the constant stimulus. This means that the depolarizing effect from other axons or cells, for example by their K+ efflux, was not contributing much to the DAP recorded at the soma.

# Grease-Gap

"Electrical gap" methods (Stampfli, 1954), like air-, sucrose-, or grease-gap have been useful for recording membrane potential changes of axons that are hard to record from

FIGURE 2 | A model to illustrate essential features of the DAP and post-spike hyperexcitability. (A) A simple model is used to illustrate findings and interpretations from various publications. A soma with 10µm diameter connects to a 150µm ascending axon with 0.3µm diameter, and divides in two branches, each 1 mm long (∼3 space constants each) and 0.2µm diameter. Those dimensions resemble a granule cell in cerebellum and have axonal diameters compatible also with Schaffer collaterals (Palay and Chan-Palay, 1974; Shepherd and Harris, 1998). The neuron is given uniformly distributed conductances and other membrane properties (see section Methods). At 30◦C, commonly used in slice experiments, small currents (100 ms square pulses) give firing, measured at the site of current injection in the axon, but a DAP cannot be identified because the spikes occur from a depolarized potential relative to resting membrane potential. (B) When measuring the traveling spike, a DAP becomes apparent because the spike starts at a membrane potential more negative than the voltage at which the fast repolarization stops ("breakpoint," red arrow). In this model, the breakpoint depends on the midpoint voltage for Kv's steady state activation curve (see section Methods), shown here with three values. For the rest of the simulations I used 0 mV (black curve) as midpoint. (C) With recording from the distal axon, as in (B), the currents through Na+, K+, and passive channels (iNa, IK, ipas) are shown during the black spike in (B). At one time point (red arrow) the passive current (green) becomes larger than iK and from there the DAP starts (hatched area) and follows the membrane time constant if, as here, the voltage sensitive iK is negligible.

with intracellular electrodes (Stys et al., 1991). With the grease-gap method the fast decay and the much slower DAP (in parallel fibers and hippocampal Schaffer collaterals) can be distinguished (Palani et al., 2012). The time course of the DAP recorded with the grease-gap method is similar to the decay of the hyperexcitability and to the antidromic somatically recorded potential. This supports the hypothesis that the hyperexcitability is caused by a slowly decaying axonal potential. With both grease-gap and somatically recorded backpropagating spikes, the DAP starts immediately when the fast

compatible with a passive decay and similar to the results in Palani et al. (2012). (C) With three stimuli 20 ms apart the latency was shorter for the second than for the first spike, but similar for the second and third (green bars). One likely explanation is that the second and third spike traveled in an axon that was depolarized to the same voltage, by the DAP, in contrast to the first spike that had to overcome a more hyperpolarized axon.

repolarization stops (see **Figures 2B**, **3A**, blue), without any interposed hyperpolarization.

# Bleb Recordings

Although recordings from axonal blebs that form when axons are cut (Shu et al., 2007) have given very precise knowledge about spike initiation and membrane currents in the proximal 300– 400µm of axons, it has also become clear that this part of the axon is a specialized region different from more distal parts of the axons (Hu and Bean, 2018). Additionally, such recordings have been made mostly from layer 5 neocortical pyramidal cells which are myelinated (Shu et al., 2007) and relies less than the TCAs on voltage sensitive channels for fast spike repolarization (Chiu et al., 1979; Kaars and Faber, 1981). These differences in axonal mechanisms may explain that no DAP has been identified in bleb recordings.

# Voltage-Sensitive Dyes

Voltage sensitive dyes have the potential to report voltages from axons which are difficult to access with electrical recording electrodes. VSD recordings from relatively proximal parts of the TCAs, up to 200–400µm from the soma, have not shown DAPs (Zhou et al., 2007; Foust et al., 2011; review by Popovic et al., 2015). In contrast, recordings that include distal parts of TCAs have shown apparently large DAPs (Sabatini and Regehr, 1997; Matsukawa et al., 2003). Hyperpolarizing afterpotentials have not been reported with VSD recordings from TCAs, but there is one example of a small, fast repolarization that goes below the pre-spike level from cultured hippocampal neurons, using a light-activated proton pump as fluorophore (Hoppa et al., 2014).

One problem in interpreting these results is that proximal and distal VSD recordings have used different dyes and labeling methods. There is no example yet of recordings from both proximal and distal regions of TCAs that could have clarified if it is the axonal region, the recording method, or the neuron type that causes these different results. I will go through the few publications that have used VSDs to record from TCAs, and at the end suggest some factors that theoretically may influence the opportunity to record a DAP if one were present.

With bath-applied voltage sensitive fluorescent dyes (VSFD) and transmitted light voltage sensitive probes a large DAP, starting at ∼30% of the amplitude of the fast spike, was recorded in rat cerebellar parallel fibers (Sabatini and Regehr, 1997; Matsukawa et al., 2003). Synaptic transmission was eliminated but [K+]o, either directly influencing membrane potential of the axons or depolarizing glia cells, were discussed as possible mechanisms. This seems unlikely because there was no addition of the DAP amplitudes at 10 ms spike intervals (Sabatini and Regehr, 1997) even though K+-sensitive electrode recordings show that [K+]o ads at such intervals (Fritz and Gardner-Medwin, 1976; Malenka et al., 1981, 1983; Kocsis et al., 1983). Also, with axonally targeted genetically encoded hybrid voltage sensors there seems to be a small long-lasting DAP in mossy fibers and mossy cell axons, both unmyelinated, although this was not specifically commented or analyzed (Ma et al., 2017).

Although I focus on mammalian TCAs in this review, VSFD recordings from crayfish neuromuscular junction (Lin, 2008) are interesting because they show several features that resemble the VSFD recordings from Sabatini and Regehr (1997) and the grease-gap recordings from cerebellar parallel fibers (Palani et al., 2012). Common for these experiments is that they include the distal parts of thin, unmyelinated axons with en passant synapses, they have a hyperexcitable period after individual spikes (20–30% reduced activation threshold 15– 25 ms after the spike, for the crayfish synapse see Zucker, 1974), and they have a slowly decaying DAP following directly after the fast part of the repolarization that is the likely cause of the hyperexcitability.

Because the crayfish neuromuscular synapse gives the opportunity to record presynaptically with intracellular micro-electrodes it has been extensively used to study how presynaptic mechanisms influence transmitter release. In such intra-axonal recordings, the DAP occurs only when the axon and its terminals are relatively hyperpolarized (Dudel, 1971). Because the occurrence of a DAP often required injection of hyperpolarizing current it has been unclear whether the DAP was a natural part of the spike in the crayfish preparation. However, since intact terminals have a large reduction of activation threshold after a spike (Zucker, 1974), and since the VSFD recordings (Lin, 2008) show a DAP, it is likely that the intact terminals do have DAPs.

These observations showing that the DAP required relatively hyperpolarized membrane potentials, and my model showing that the DAP disappears at depolarized levels (black curve in **Figure 2A**), give the idea that one reason some VSD recordings from TCAs do not show a DAP (in addition to the obvious reason that neocortical pyramidal neurons may not have an axonal DAP) is that the recording site was depolarized. Factors that may contribute to depolarization is that spikes were elicited by depolarizing currents at the soma (which often influences the axon at the recording site as pointed out in Foust et al., 2011), and phototoxicity. Because TCAs have a much higher surfaceto-volume ratio than the soma, toxins produced by membraneassociated fluorophores will have a small cytoplasmic volume for dilution and may cause more phototoxicity in the TCA than at the soma.

# MECHANISMS CAUSING THE DAP IN TCAS

DAP mechanisms have been investigated at the soma, dendrites, large presynaptic terminals, and axons. Inward currents (Na+ and Ca2+) and passive components have been identified. For example, in hippocampal CA1 pyramidal neurons voltage sensitive R-type Ca2+ channels are important (Metz et al., 2005); in cerebellar granule cells a resurgent Na+ current contribute (Magistretti et al., 2006). In presynaptic structures large enough for intracellular recordings a DAP has been found in calyx of Held (Borst et al., 1995), and in mossy fiber boutons (Geiger and Jonas, 2000). In these terminals the DAP has both passive and active components (Kim et al., 2010; Lewis and Raman, 2014; Ohura and Kamiya, 2018). Myelinated axons usually have a passive DAP (Barrett and Barrett, 1982). The high resistance between the myelin sheet and the axonal membrane gives the DAP its slow decay and this mechanism is therefore unlikely to contribute in unmyelinated TCAs.

As I will explain in the following sections there is no evidence that inward currents contribute to the DAP in cerebellar parallel fibers or Schaffer collaterals. That does not mean that inward currents may not influence the DAP under conditions not yet tested, for example during longer spike trains. In the lack of data showing effects that need inward currents to be explained, I will exclude further discussions about the contribution of inward currents in other cells, presynaptic structures, or soma.

I will distinguish between mechanisms that determine the decay rate and those that determine the amplitude in TCAs. For all experiments referred in the three following sections, fast synaptic currents are blocked by CNQX, APV, and Picrotoxin. Under such block the shape of the DAP did not change with the addition of 200µM Cd2+, showing that neither release nor voltage sensitive Ca2+ currents contributed (Toda, 1976).

# DAP Decay in TCAs

Three observations suggest that the decay of the DAP is passive, meaning determined by the membrane capacitance and resistance. First, when the antidromic spike with its DAP is recorded at the granule cell's soma, and the recording is switched to voltage clamp, there is no detectable current that can explain the DAP, although a significant fast unclamped spike current persisted (Palani et al., 2012). This is expected from a capacitive current and can be illustrated with the model (somatic voltage clamp simulation in **Figures 3B,B1**).

Second, the decay rate of the post-spike hyperexcitability is not more than 20–30% different at 24 and 34◦C (Soleng et al., 2004). This is compatible with the temperature effect on the membrane time constants of several cell types (Kim and Connors, 2012) but does not rule out other mechanisms with low temperature sensitivity.

Third, spike activity that probably induce changes in membrane resistance change the decay rate of the hyperexcitability (Soleng et al., 2004). The background for that experiment is that the Na-K-pump is electrogenic and hyperpolarizes the membrane as it pumps out excess Na+ (Ritchie and Straub, 1957). In many axons this hyperpolarization is reduced by opening of HCN-channels, underlying the Hcurrent (Eng et al., 1990). This added conductance (reduced membrane resistance) will reduce the membrane time constant. So, when the post-spike hyperexcitability decays ∼3 times faster at 2 Hz spike frequency compared to 0.1 Hz and becomes ∼2 times slower at those frequencies when HCN channels are blocked, a likely explanation is that an HCN conductance reduces the membrane resistance and the membrane time constant and therefore gives a faster DAP decay (Soleng et al., 2004).

# Amplitude of the TCA's DAP

The mechanisms governing the DAP amplitude has been explored by studying how it is influenced by activity, changes in membrane potential, and drugs (next section).

Several lines of evidence suggest that the voltage at which the fast repolarization stops, and the DAP starts (the "breakpoint" in **Figure 2B**) is relatively constant and insensitive to pre-spike potential, and spike activity. Voltage sensitive channels that inactivate fast at relatively depolarized levels, like the channel mechanism I implemented in the model, could explain these properties of the breakpoint (**Figure 3C**). The evidence for the breakpoint's insensitivity to pre-spike potential and spike activity comes from experiments similar to those referred under "Shape of the DAP" above but includes trains of axonal spikes. The constant, depolarized voltage for the breakpoint during such trains (illustrated in **Figure 3C**) has been observed by using VSFD, transmitted-light voltage sensitive probes, greasegap recordings and somatic recordings with backpropagating spikes in cerebellar parallel fibers (Sabatini and Regehr, 1997; Matsukawa et al., 2003; Pekala et al., 2016). Those publications show that the second spike in such trains take off from the "back" of the DAP, a potential more depolarized than the resting membrane potential, but this difference in pre-spike voltage does not influence the breakpoint. The DAP also gives the spikes after the first one faster conduction speed, as seen in the green histogram in **Figure 3C**.

Those recordings from cerebellar parallel fibers are, with respect to constant breakpoint, very similar to recordings from the crayfish neuromuscular junction (Lin, 2008). A repolarization voltage relatively insensitive to pre-spike potential was also shown in vivo in the calyx of Held (Sierksma and Borst, 2017). Like spikes have a narrow voltage range for being triggered at the AIS, there may be a similarly narrow range for the end of their fast repolarization at the presynaptic structures in several neuron types and several species.

# Channels

The channels responsible for the fast repolarization which, according to data discussed above, also determine the DAP amplitude (measured from baseline to the breakpoint) have been explored by bath-applied drugs during grease-gap recordings (Pekala et al., 2014). The spike in cerebellar parallel fibers was not sensitive to 200µM Cd2+, ruling out Ca+ currents and Ca+ activated currents. Relative to baseline, the breakpoint moved 10% in depolarizing direction in response to 1 mM TEA, and 27% in response to 10 nM margatoxin (MgTX), when these drugs were applied alone. However, in combination these drugs took away most of the fast repolarization by moving the breakpoint 75% in depolarizing direction. The interpretation is that both MgTX-sensitive and TEA-sensitive channels contributed to the fast repolarization that stopped at the breakpoint and did a better job together than alone.

To interpret such grease-gap experiments it is important to be aware that by measuring the difference between baseline and the breakpoint we cannot, without further control experiments, know if it is the baseline (corresponding to resting membrane potential) or the breakpoint voltage that changes. Two additional observations help: First, conduction speed is sensitive to resting membrane potential, and no change was detected with either Cd2+, TEA, or MgTX (Pekala et al., 2014). Second, MgTX enhanced the post-spike hyperexcitability (Palani et al., 2010), supporting the interpretation that TEA and MgTX pushed the breakpoint and the decay of the DAP in depolarizing direction.

Low concentrations of TEA (≤1 mM) have preferential effect on Kv3-family of channels (Rudy and McBain, 2001) and because Kv3.1 and Kv3.3 double knockout mice (Matsukawa et al., 2003) lack most TEA effects on cerebellar parallel fibers, these channels are likely to mediate the TEA effects at least in those axons. MgTX blocks Kv1.3 channels with high affinity, although others in the Kv1 family may also be blocked.

# HOW DOES THE DAP INFLUENCE AXONAL FUNCTIONS?

The data referred above suggest that the DAP is a robust process, starting at a voltage controlled by more than one channel family, relatively insensitive to activity and temperature, with a decay determined mainly by the membrane time constant. How does a spike with those properties influence axonal function?

# The DAP Increases Reliability

The common view that TCAs never fail under physiological conditions may be biased by few rodent experiments using temperatures above 35–36◦C, while rodents, including their brains, often raise above 38◦C during moderate activity (Kiyatkin et al., 2002). Temperature dependent failures can be demonstrated by measuring populations of spikes at two sites along parallel fibers in cerebellum. When temperature increases just above 37◦C the fraction of spikes arriving at the distal electrode falls (Pekala et al., 2016). VSDF recordings have also shown reduced spread of signals in hippocampal slices at temperatures >37◦C (Takeya et al., 2002). Failures are provoked by higher temperature because Nav inactivation and Kv activation become faster (Hodgkin and Katz, 1949), both factors that reduce the spike amplitude and integral. Particularly fast activating Kv3 channels, present in Schaffer collaterals and cerebellar parallel fibers, would theoretically increase failure probability at high temperatures.

When spike propagation failures are provoked by temperature (illustrated with the model in **Figure 4A**), propagation reliability increases with the number of stimuli (**Figures 4B,C**). With somatic recordings and antidromic spikes some spikes occur only as a hump, but the next spike usually succeeds to propagate all the way to the soma (Pekala et al., 2016). This suggests that the post-spike hyperexcitability, due to the DAP, reduces the failures toward the end of the spike train. The proper test of that interpretation would be to move the "breakpoint" in hyperpolarizing direction to reduce its effect on failures. This has not been tested yet but may be possible using pharmacological tools (Kaczmarek and Zhang, 2017).

# Ca-Tail

Almost every bouton, which is one of the structures that defines a TCA, has machinery for transmitter release, including voltage sensitive Ca2+ channels. This makes the shape of the propagating spike important for transmitter release and a broad range of normal and pathological processes (Debanne et al., 2011; Fioravante and Regehr, 2011). Since subthreshold potentials between −60 mV and spike threshold have been shown to give asynchronous transmitter release (in crayfish neuromuscular junction: Wojtowicz and Atwood, 1984) and to open Ca2+ channels (mouse calyx of Held: (Awatramani et al., 2005); rat cerebellar interneurons: Christie et al., 2011) there is a theoretical possibility that the DAP may increase presynaptic Ca2+ or slow the deactivation of Cav channels. This may contribute to the early phase of the delayed transmitter release occurring at some synapses, for example between parallel fibers and Purkinje cells (Atluri and Regehr, 1998). Whether Cav channels activate or not may also depend on a finetuned control between membrane potentials immediately before the spike and the amplitude of the DAP (Clarke et al., 2016), suggesting that DAP amplitude may be decisive in such delayed transmitter release.

FIGURE 4 | The DAP reduces propagation failures. (A) At 30◦C the spikes triggered at the soma by current injection always arrived at the axon. However, at 37◦C they were still triggered at the soma (not shown) but failed to arrive at the distal axon where only a small voltage hump was seen. (B) Keeping the temperature at 37◦C it was possible to overcome the propagation block by repeating the somatically triggered spikes, in this case with 20 ms intervals. One likely explanation is that the slow DAP spread passively further than the fast part of the spike (as can be seen as a hump in response to the first stimulus) and facilitated the propagation of the second and third spike. (C) By recording from three sites in the model axonal arbor we see that the first spike failed to propagate between site 1 and 3, but a depolarizing hump, due to the DAP, propagates even 300µm past the branch point. That residual depolarization helped the second and third spike to propagate further than the first. (D) The resting membrane potential (RMP) was adjusted by changing the extracellular K+ concentration to obtain values between −60 and −75 mV (color coded). We see that the fast-deactivating K+ conductance implemented in the model gave very similar voltage levels for the breakpoint despite the large variation in RMP.

# Role in Bursting

It is not known if axonal (ectopic) bursts occurin vivo, but in slice experiments axonal bursts occurs in ∼30% of cerebellar granule cells. Such bursts come on the shoulder of the backpropagating spike's DAP, suggesting that the DAP is close to spike threshold (Pekala et al., 2014).

In the context of axonal bursting the temporal overlap between the refractory period (inhibiting bursting) and the DAP (promoting bursting) may be important. Since the postspike hyperexcitability is relatively insensitive to temperature (Soleng et al., 2004), but the refractory period is very temperature sensitive (Raastad and Shepherd, 2003), one hypothesis is that bursts occur with higher probability at high temperature because the Nav-channel inactivation becomes too shortlasting to protect against new spikes while the DAP is at its most depolarized levels. Theoretically, this could contribute to epileptic temperature-sensitive pathology, but that hypothesis has not been tested yet.

The stable voltage at which the fast repolarization stops has been shown to stabilize the shape of the spike during bursts, in crayfish neuromuscular junction (Lin, 2008) and in mouse calyx of Held (Sierksma and Borst, 2017). This may be important to minimize energy expenditure, and control transmitter release.

The constant breakpoint voltage will also, theoretically, stabilize the spike shape in situation where [K+]o increases, particularly relevant in pathology like epileptic seizures. **Figure 4D** illustrates how the model behaves at different RMPs, manipulated by changing [K+]o. We see that during a train of spikes the individual spikes take off from similar potential despite great differences in RMPs, protecting the spiking mechanism from variations in [K+]o.

# CONCLUSION

The main conclusion of this article is that there is good support for the hypothesis proposing that individual spikes in cerebellar parallel fibers and hippocampal Schaffer collaterals are followed by a DAP, and that the DAP is a well-controlled process that stops the fast repolarization at a membrane potential positive to resting membrane potential, leaving the membrane more excitable for ∼100 ms during a slow, passive discharge of the membrane capacitance.

It is important that the presented model is intentionally simple but still qualitatively compatible with the selected data. The data I have selected is related to excitability, like activation threshold, conduction speed, and propagation failures. There is much data for example on transmitter release properties that the model is not intended to explain. The excitability control of the TCAs is probably enormously more complex, with interactions between changes in intracellular ion concentrations, the Na-K-pump, structural inhomogeneities along the TCAs, and participation of a large number of ion channels.

# REFERENCES

## METHODS

# Neuronal Model

Two voltage sensitive channels, Nav and Kv, and a leak conductance (gL) were used for the cell model. Both were implemented with the NMODL and NEURON languages (Hines and Carnevale, 1997) and inserted uniformly in the membrane of a neuron with dimensions given in **Figure 1**. Membrane capacitance and cytoplasmic resistivity were set to 1 µF/cm2 and 150 Ωcm. The Nav had one variable for activation (m) and one for inactivation (h), and the Kv had one for activation (n), like the Hodgkin-Huxley (HH) model (Hodgkin and Huxley, 1952):

$$\mathbf{H} = \mathbf{C} \cdot \frac{dV}{dt} + \mathbf{g} \mathbf{K} \cdot \mathbf{n}^4 \cdot (V\_m - V\_K) + \mathbf{g} \mathbf{Na} \cdot \mathbf{m}^3 \cdot \mathbf{h} \cdot (V\_m - V\_{\mathbf{Na}}) + \mathbf{g} \mathbf{L} \ (V\_m - V\_L)$$

The gating variables were calculated as dx dt = 1 xTau · xInf − x0 , where x is n, m or h.

The values of xInf was calculated as  $x \text{Inf} f = \frac{1.0}{\left(1.0 + \exp\left(\frac{V}{-\text{stap}\,\text{mas}}\right)\right)}$ , and xTau as  $xTau = \frac{T\max}{qt} \cdot \left(0.05 + \left(\frac{1.9}{\exp\left(\frac{pL}{Tc}\right) + \exp\left(-\frac{pL}{Tc}\right)}\right)\right)$ , using  $qt = 2.3^{\frac{c\text{cl}\,\text{as}}{10}}$ ,  $\nu 1 = \nu - midpoint$ .

The "midpoint" for n, m, and h was 0, −25, −40. The "steepness" for n, m, and h was 18, 6, and 3. The "Tc" for n, m, and h was 25, 20, 10, and the "Tmax" for n, m, and h was 15, 0.51, and 7. Like HH, the conductance at each time step (0.01 ms) was calculated as gmax ∗ n 4 for Kv, and gmax ∗ m3∗h for Nav, with gmax (the maximal conductance) 0.05 and 0.08 S/cm2 for Nav and Kv, respectively. The parameters were chosen by manually selecting values that gave a fast Na+ and K+ current, and a fast

deactivation of the K+ current with the parameter "midpoint" set to a sufficiently depolarized value (0 mV) to give an almost complete deactivation at −45 mV.

The gL was set to 0.00002 S/cm2 (which gives a 50 ms membrane time constant, compatible with the decay of the DAP in grease-gap recordings in Palani et al., 2012). Equilibrium potentials were 50 mV for Nav, −85 mV for Kv, and −75 mV for gL, which are common values in the literature.

# AUTHOR CONTRIBUTIONS

The author confirms being the sole contributor of this work and has approved it for publication.

firing reliability at a CNS nerve terminal. J. Neurosci. 30, 15479–15490. doi: 10.1523/JNEUROSCI.3982-10.2010

individual regions of single axons, dendrites and spines. Adv. Exp. Med. Biol. 859, 57–101. doi: 10.1007/978-3-319-17641-3\_3

**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 Raastad. 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 Factors for Transmitter Release at Small Presynaptic Boutons Revealed by Direct Patch-Clamp Recordings

#### Shin-ya Kawaguchi1,2,3 \*

1 Society-Academia Collaboration for Innovation, Kyoto University, Kyoto, Japan, 2 Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto, Japan, 3 Institute for Advanced Study, Kyoto University, Kyoto, Japan

#### Edited by:

Josef Bischofberger, University of Basel, Switzerland

#### Reviewed by:

Stefan Hallermann, Leipzig University, Germany Dominique Debanne, INSERM U1072 Neurobiologie des Canaux Ioniques et de la Synapse, France

\*Correspondence:

Shin-ya Kawaguchi<EMAIL_ADDRESS>
#### Specialty section:

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

> Received: 26 April 2019 Accepted: 29 May 2019 Published: 12 June 2019

#### Citation:

Kawaguchi S-y (2019) Dynamic Factors for Transmitter Release at Small Presynaptic Boutons Revealed by Direct Patch-Clamp Recordings. Front. Cell. Neurosci. 13:269. doi: 10.3389/fncel.2019.00269 Small size of an axon and presynaptic structures have hindered direct functional analysis of axonal signaling and transmitter release at presynaptic boutons in the central nervous system. However, recent technical advances in subcellular patch-clamp recordings and in fluorescent imagings are shedding light on the dynamic nature of axonal and presynaptic mechanisms. Here I summarize the functional design of an axon and presynaptic boutons, such as diversity and activity-dependent changes of action potential (AP) waveforms, Ca2+ influx, and kinetics of transmitter release, revealed by the technical tour de force of direct patch-clamp recordings and the leading-edge fluorescent imagings. I highlight the critical factors for dynamic modulation of transmitter release and presynaptic short-term plasticity.

Keywords: axon, patch-clamp, transmitter release, presynaptic terminal, action potential, short-term plasticity

# INTRODUCTION

Direct patch-clamp recording from an axonal compartment tells a lot about the axon physiology and mechanisms of synaptic transmission. Unfortunately an axon and presynaptic terminals are usually too small to apply patch-clamp technique, except for unusually large structures, such as synapses of calyx of Held in the auditory brainstem and presynaptic boutons of hippocampal mossy fiber (Forsythe, 1994; Borst et al., 1995; Geiger and Jonas, 2000). Most conventional synapses in the central nervous system have much smaller presynaptic boutons (∼1 µm) containing only 1–2 active zones, from which direct recording has been almost impossible to perform. However, in this decade remarkable technical advances have been accomplished in recording even from conventional small presynaptic structures in primary culture system, such as boutons of hippocampal pyramidal cells (∼1 µm, Novak et al., 2013), cerebellar Purkinje cell (PC) axon terminals (∼2–3 µm, Kawaguchi and Sakaba, 2015), and cerebellar granule cell (GC) axon varicosities (∼1 µm, Kawaguchi and Sakaba, 2017). These advancements have provided detailed information about the mechanisms of presynaptic function, such as dynamics of presynaptic membrane excitability, Ca2+ influx and buffering, pool size of readily releasable synaptic vesicles, and functional coupling between Ca2+ and release machinery. In this article, I like to overview these recently clarified presynaptic mechanisms for transmitter release, particularly focusing on small synapses.

# FACTORS TO DETERMINE PRESYNAPTIC TRANSMITTER RELEASE

Fluorescent labeling of axons and presynaptic boutons makes it possible to precisely position a thin tip of glass pipette at a small structure for patch-clamp recordings. Voltage-clamp of an axon terminal allows to study quantitative relationship between the Ca2+ influx to a presynaptic bouton and the amount of exocytosis of synaptic vesicles (**Figure 1**). For example, a long-duration of depolarization pulse applied to a bouton triggers fusion of almost all release-ready synaptic vesicles to the cytoplasmic membrane, resulting in an increase of surface membrane area size which can be recorded as a sudden jump of membrane capacitance (Cm) (Lindau and Neher, 1988; **Figure 1**). The amount of Cm increase, that is, the number of synaptic vesicles in readily releasable pool (RRP) changes depending on the type of synapses. For example, calyx of Held synapse (diameter,

FIGURE 1 | Presynaptic transmitter releases studied by direct patch clamp recordings. (A,B) Patch-clamp recordings from a EGFP-labeled axon varicosity of a cerebellar PC (A) or of GC (B), adapted from Kawaguchi and Sakaba (2015, 2017), respectively, with permission from Elsevier. Top, images of EGFP-labeled axon terminals of each neuron. Middle, presynaptic Ca2+ currents (ICa) upon different durations of depolarization pulses to 0 mV. Bottom, presynaptic Cm increase triggered by Ca2+ currents indicated in the middle. Average Cm increases plotted against duration of depolarization pulses are also shown.

∼10 µm) shows about 400 fF of Cm increase upon a large Ca2+ influx as ∼2 nA upon a presynaptic depolarization pulse to 0 mV (Sun and Wu, 2001). On the other hand, ∼100 fF of Cm increase is caused by ∼200 pA of Ca2+ currents at mossy fiber boutons in hippocampus (∼5 µm) and those in the cerebellum (∼6 µm) (Hallermann et al., 2003; Delvendahl et al., 2013). Recently, an inhibitory neuronal presynaptic terminal, a PC bouton with a size of 2∼3 µm was patched, and a Cm increase of 80 fF was observed upon depolarization-induced Ca2+ influx of ∼300 pA (Kawaguchi and Sakaba, 2015; **Figure 1**). Thus, given that a single synaptic vesicle has a Cm of ∼ 0.1 fF, about 1,000 synaptic vesicles are exocytosed from a single presynaptic bouton of a mossy fiber or a PC within several hundred milliseconds. On the other hand, a much smaller conventional presynaptic structure (∼1 µm), an axon varicosity of a cerebellar GC, exhibited a ∼20 fF of Cm increase with ∼60 pA of Ca2+ currents upon the identical depolarization pulse (Kawaguchi and Sakaba, 2017; **Figure 1**). Thus, even at a small axon terminal about 200 synaptic vesicles rapidly undergo fusion, which surprisingly corresponds to one third of total synaptic vesicles in a single bouton, based on the estimation by an electron microscopic analysis (Xu-Friedman et al., 2001). It should be noted that the quality of patch-clamp recording (i.e., physical access to the cytosol reflected by the series resistance) is critical for precise activation and measurement (in the extent and time course) of Ca2+ currents and vesicular release. These measurements of presynaptic Cm increase upon strong Ca2+ influx suggests that substantial number of synaptic vesicles rapidly undergo exocytosis at most synapses irrespective of their being excitatory or inhibitory.

Interestingly, comparison of various neuronal terminals implies a relationship that the maximal Cm increase and presynaptic Ca2+ current amplitude likely depend on the first to second power of presynaptic diameter. Thus, we are tempted to assume that the RRP size estimated by Cm measurement simply reflects the surface area size of presynaptic structure, implying that the release machinery downstream of activation by Ca2+ may operate in a similar manner at various neuronal boutons. However, it should be noted that the vesicular release estimated by Cm increases upon depolarization for tens of ms sometimes reflects the fusion of multiple states of synaptic vesicles, including those already primed at and those loosely coupled to the release sites (Sakaba and Neher, 2001), and even newly recruited ones at an extremely rapid rate (∼ several ms) (Saviane and Silver, 2006; Kawaguchi and Sakaba, 2017). Recent elegant glutamate imaging coupled with super-resolution analysis of active zone proteins and electron microscopic analysis suggested that the exact number of release sites, which corresponds to synaptic vesicles maximally ready for immediate exocytosis upon Ca2+ influx, is defined by the number of protein complex clusters consisting of Ca2+ channels, and some active zone protein like Munc-13 (Miki et al., 2017; Sakamoto et al., 2018). Thus, the molecular organizations of presynaptic active zone and the vesicular recruitment mechanisms toward empty release sites determine the strength and sustainability of presynaptic transmitter release.

Different neuronal terminals show diversity in the process from Ca2+ channel activation to triggering of vesicular release. First, Ca2+ current is rapidly activated at a PC bouton (Kawaguchi and Sakaba, 2015) like a calyx of Held synapse (Borst et al., 1995), whereas a GC bouton exhibits slow activation of Ca2+ current upon the identical depolarization pulses (Kawaguchi and Sakaba, 2017; **Figure 1**). In addition, the Ca2+-release coupling estimated by the sensitivity to Ca2+ chelators like EGTA varies in different neuronal boutons: a PC bouton shows tight coupling with low sensitivity to EGTA (Díaz-Rojas et al., 2015; Kawaguchi and Sakaba, 2015), as in other inhibitory interneurons (Bucurenciu et al., 2008; Eggermann et al., 2012); a GC bouton shows loose coupling with high EGTA sensitivity (Kawaguchi and Sakaba, 2017), in a similar manner to hippocampal mossy fiber boutons (Vyleta and Jonas, 2014). Furthermore, even action potential (AP) waveforms are quite different in axon terminals of PCs and GCs (see **Figure 2**).

Simultaneous recordings both from a presynaptic bouton and a postsynaptic cell provide more quantitative information about synaptic transmission (Sakaba and Neher, 2001;

Presynaptic recordings from a bouton of PC axon and that of GC axon had similar recording conditions, precluding the possibility of the distinct kinetics being due to the quality of patch-clamp recordings. All traces are adapted from Kawaguchi and Sakaba (2015, 2017) with permission from Elsevier.

Sun and Wu, 2001). **Figure 2** illustrates time courses of presynaptic APs and Ca2+ influx recorded from a PC or GC bouton, together with the kinetics of vesicular release estimated from postsynaptic responses (Kawaguchi and Sakaba, 2015, 2017). The remarkably different AP waveforms, when applied to the voltage-clamped bouton as voltage commands, cause clearly distinct kinetics of Ca2+ influxes. This difference in Ca2+ influx might be partly due to the slower activation of Ca2+ channels in a GC than in a PC bouton (see **Figure 1**), in addition to the distinct AP kinetics (**Figure 2**). Furthermore, the initiation of transmitter release delays more in a GC axon varicosity after the Ca2+ influx (∼500 µs after the time of half-maximal ICa) than in a PC bouton (∼300 µs), in spite that once started the release kinetics are similar (**Figure 2**). This distinct delay of release onset may partially reflect the different Ca2+-release coupling: tight coupling at a PC bouton, whereas loose coupling in a GC bouton. On the other hand, similar time course of release rate by itself implies that release machinery may operate in a similar manner at these neurons. Thus, AP waveforms, the resultant activation of Ca2+ channels, and the Ca2+-driven activation of release machinery, seem to change depending on the neuronal type, and likely become as key factors to impact the transmitter release. Interestingly, recent imaging studies demonstrated that Ca2+ release coupling becomes tighter after the chemical induction of presynaptic long-term potentiation (LTP) in hippocampal mossy fiber boutons (Midorikawa and Sakaba, 2017).

# DIGITAL AND ANALOG SIGNALING IN AN AXON

Traditionally AP has been regarded as an all-or-none type of digital signal, reliably conveying information toward terminals in the central nervous system of vertebrates. However, direct recordings of APs by axonal patch-clamp methods and fluorescent imagings of membrane potential with a genetically encoded or chemical voltage indicator, have demonstrated activity-and/or location-dependent dynamic changes of AP waveforms in axon terminals (Kole et al., 2007; Hoppa et al., 2014; Kawaguchi and Sakaba, 2015; Rowan et al., 2016). In addition, sub-threshold electrical signals affect AP waveforms by modulating axonal K+ channels and/or by passively propagating into an axon over hundreds µm even around distal regions (Pouzat and Marty, 1999; Alle and Geiger, 2006; Shu et al., 2006; Kole et al., 2007; Paradiso and Wu, 2009; Trigo et al., 2010; Pugh and Jahr, 2013; Zbili et al., 2016), which results in the modulation of transmitter release from presynaptic terminals (Rama et al., 2015; Rowan and Christie, 2017; Zorrilla de San Martin et al., 2017). Thus, the axonal AP signaling is modified in a manner like a hybrid of analog and digital transmission (Clark and Häusser, 2006; Debanne et al., 2011).

Because all Ca2+ channels at a presynaptic structure are not necessarily activated by individual APs, change of an AP waveform potentially impacts the Ca2+ influx into presynaptic cytoplasm, leading to modulation of transmitter release. In a cerebellar PC, high frequency AP firing results in attenuation of AP amplitude at a bouton, decreasing peak Ca2+ influx,

and hence synaptic outputs (Kawaguchi and Sakaba, 2015). On the other hand, at hippocampal mossy fiber synapses, activitydependent attenuation of AP is accompanied with the slower decay and hence causes larger net influx of Ca2+, leading to augmented transmission (Geiger and Jonas, 2000). Distinct Ca2+-release coupling in PC boutons and mossy fiber boutons might be partially responsible for the apparently opposite effects of activity-dependent AP changes on transmitter release (Vyleta and Jonas, 2014; Kawaguchi and Sakaba, 2015). The synapses with tighter Ca2+-release coupling like PC boutons would show steeper dependence of transmitter release on the number of activated Ca2+ channels rather than the total amount of Ca2+ influx. Then, the AP amplitude controlling the maximal number of activated Ca2+ channels could be more influential for the release in such tightly coupled synapses than the decay time course affecting the duration of Ca2+ influx. In contrast, the total Ca2+ influx would more preferentially control transmitter release in loosely coupled synapses. Thus, the impact of AP waveform modulation is determined how the synapse is functionally designed at the molecular level.

The presence of receptors for neurotransmitters in an axon has been demonstrated at various brain region and influences axonal excitability and neurotransmitter release (Debanne et al., 2011). Because of the substantial passive traveling of electrical signals in an axon, even a limited number of receptors in individual boutons could cooperatively contribute to changing the local membrane potential in an axon. For example, the axonal GABAARs have been reported at various excitatory and inhibitory neurons, such as those in calyx of Held, posterior pituitary, cerebral cortex, hippocampus, and cerebellum (MacDermott et al., 1999; Trigo et al., 2008; Zorrilla de San Martin et al., 2017). Axonal GABAARs may monitor the level of GABAergic inhibition around the postsynaptic target, locally adjusting the amount GABA release. Perforated patch-clamp technique using gramicidin clarified the reversal potential of GABA-mediated current (EGABA) as ∼ −50 mV in a terminal of the calyx of Held synapse (Price and Trussell, 2006) and −45 mV in a PC bouton (Zorrilla de San Martin et al., 2017). Because of the depolarized EGABA, presynaptic GABAAR activation depolarizes presynaptic boutons, facilitating Ca2+ influx upon the subsequent AP arrival and hence synaptic transmission. In contrast, axonal GABAARs also exert inhibitory effects in different neurons (Xia et al., 2014).

# SHORT-TERM PLASTICITY

Activity-dependent short-term plasticity of synaptic transmission lasting for milliseconds to minutes is an important element in the neuronal computation (Abbott and Regehr, 2004; Regehr, 2012). A lot of central synapses exhibit increase or decrease of strength, termed short-term synaptic facilitation, or depression, respectively, upon repetitive activity at short time intervals (Zucker and Regehr, 2002; Fioravante and Regehr, 2011). Dynamic changes of presynaptic Ca2+ concentration and downstream processes of transmitter release mediate short-term plasticity. Residual Ca2+ hypothesis is the simplest candidate mechanism for facilitation (Katz and Miledi, 1968). Temporal summation of residual Ca2+ remaining in the cytoplasm after the first AP was suggested to facilitate the following AP-triggered transmitter release based on the ∼third power Ca2+-dependence of release (Neher and Sakaba, 2008). However, the residual Ca2+ increase is too small compared with the local Ca2+ to explain synaptic facilitation in most cases.

P/Q-type of Ca2+ channels, which predominantly mediates transmitter release at many synapses, exhibit remarkable facilitation of its current in a Ca2+-dependent manner, resulting in facilitation of transmitter release (Catterall and Few, 2008; Ben-Johny and Yue, 2014). The association of Ca2+ to C-lobe of calmodulin, which is basically bound with the P/Q-type channels, is thought to rapidly augment the Ca2+ current by increasing the probability of channel opening. Exogenous expression of mutant Ca2+ channels in superior cervical ganglion neurons in culture demonstrated a tight correlation between facilitation of Ca2+ current and that of synaptic transmission (Mochida et al., 2008). Paired recordings from pre- and postsynaptic structures of a PC-PC pair showed that facilitation is almost exclusively mediated by the Ca2+ current facilitation (Díaz-Rojas et al., 2015). Similar Ca2+-dependent facilitation of presynaptic Ca2+ influx takes place at glutamatergic boutons in the calyx of Held, which partly contributes to facilitation of synaptic transmission (Felmy et al., 2003; Müller et al., 2008; Hori and Takahashi, 2009). However, recently it was reported that a mutant mice lacking Ca2+-facilitation of P-type channels still exhibit short-term facilitation at many synapses in a physiological condition, suggesting just a minor contribution of Ca2+-current facilitation to short-term synaptic facilitation (Weyrer et al., 2019).

Another candidate mechanism for synaptic facilitation is the Ca2+ buffer saturation hypothesis. If Ca2+ buffer molecules remain occupied by Ca2+ that entered into a bouton upon the first AP, cytoplasmic free Ca2+ becomes more abundant upon the following APs, and leading to larger transmitter release. Indeed, calbindin contributes to the facilitation at hippocampal mossy fiber-CA3 excitatory synapses and inhibitory synapses in the cerebral cortex (Blatow et al., 2003). The buffer saturation model relies on the loose coupling between Ca2+ and release machinery (Neher, 1998; Rozov et al., 2001; Vyleta and Jonas, 2014). Recently, direct recordings from a cerebellar GC axon varicosity demonstrated that Ca2+-release coupling is indeed loose there, and facilitation depends on the presence of low concentration of fast Ca2+ buffer in the terminal (Kawaguchi and Sakaba, 2017), in line with the Ca2+ buffer saturation model.

The next hypothesis for short-term facilitation is the Ca2+-dependent facilitation of release sensors (Regehr, 2012). Recent accumulating results indicate the critical role of Syt7 as such a facilitation sensor at various synapses (Jackman et al., 2016; Turecek and Regehr, 2018). The mechanism how Syt7 contributes to facilitation of transmitter release remains to be clarified in the future. However, it should be noted that some facilitation remains even with the genetic ablation of Syt7, implying that different combination of several facilitation mechanisms described above would operate together at distinct synapses.

In addition to facilitation, short-term depression has also been studied, and the RRP depletion is thought to be the major mechanism (Zucker and Regehr, 2002; Fioravante and Regehr, 2011). Other mechanisms, such as Ca2+ current inactivation and AP conduction failure at axonal branches (Brody and Yue, 2000; Xu and Wu, 2005) and inactivation of release sites (Neher and Sakaba, 2008; Pan and Zucker, 2009), could also contribute. GABAergic synapses on deep cerebellar nuclei neurons innervated from PCs also exhibit short-term depression upon high frequency activation (Telgkamp and Raman, 2002; Pedroarena and Schwarz, 2003). Recently, direct axonal patchclamp recordings together with fluorescent imaging of synaptopHluorin demonstrated frequency-dependent attenuation of AP propagation from axonal tract toward the terminals in PCs (Kawaguchi and Sakaba, 2015). Smaller number of Ca2+ channels activated by a smaller AP is responsible for the depression of transmitter release at high-frequency activation in a PC bouton. Importantly, the AP conduction faithfulness seems to increase in PC axons along with the development, resulting in smaller frequency-dependent depression at this synapse in mature animals (Turecek et al., 2016).

# CONCLUSION AND FUTURE DIRECTION

As overviewed here, recent technical advances to study axon physiology are shedding light on rich computational ability of an axon affecting synaptic outputs, rather than the classical view of

# REFERENCES