PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

A model of the prespike at the calyx of Held synapse.
Martijn C. SIERKSMA1,2; J. Gerard G. BORST1
1

Erasmus MC, Rotterdam, The Netherlands
2Institut de la Vision, Paris, France

ABSTRACTThe calyx of Held synapse is a giant axosomatic synapse in the brainstem that functions as a fast and reliable
auditory relay. Because of its large size, the presynaptic action potential can be picked up in a recording of thepostsynaptic cell. This so-called prespike is caused by the ephaptic coupling of presynaptic membranecurrents via the synaptic cleft. We constructed an electric model of the prespike and estimated values for theleak conductance of the synaptic cleft, the capacitance of the release face and the presynaptic calcium current
density based on simultaneous pre- and postsynaptic voltage clamp recordings. These values allowed us toestimate an impact of presynaptic capacitive and ionic currents on the cleft potential, and suggested thatfenestration of the calyx of Held during development might be important to further reduce the cleft leakconductance of the cleft to minimize its impact on the presynaptic calcium channels.
Keywords: Ephaptic coupling, Synaptic transmission, Calyx of Held

1. INTRODUCTION

The calyx of Held synapse is a fast and reliable relay in the auditory brainstem. It forms between a
globular bushy cell and a principal neuron of the medial nucleus of the trapezoid body. Each principal
neuron is typically contacted by a single, giant, axosomatic terminal called the calyx of Held. The
accessibility of this giant terminal for patch-clamp slice recordings has allowed it to become a model
system for studying mammalian synaptic transmission (1). During whole-cell patch clamp recordingsof the principal neurons a prespike can be detected, which reflects the presynaptic action potential(AP) (2). This prespike is an example of ephaptic synaptic coupling (3), as it is generated bypresynaptic membrane currents involved in calyceal AP generation leading to a change in the cleft
potential, which is then detected in the postsynaptic cell. The shape of the prespike can thus beinformative about the shape of the intracellular calyceal action potential and the local presynaptic
membrane currents flowing at the release face. Indeed, analysis of the in vivo shape of the prespike has
been used to infer differences in calyceal spike depression in a mouse model for theneurodevelopmental disorder Angelman syndrome (4). However, despite the wealth of knowledge
about the calyceal AP and its underlying voltage-dependent ion currents, the relation between thepostsynaptically recorded prespike waveform and the presynaptic ion currents during the calyceal AP
has not yet been studied. Here, we therefore revisit simultaneous voltage clamp recordings from thecalyx of Held and its postsynaptic target (5) to evaluate the generation of the prespike. These
recordings helped to define a simple biophysical model of the prespike and to better delineate theelectrical properties of the synaptic cleft and the subcellular localization of presynaptic ion channels.

2. METHODS
2.1 Recordings
Simultaneous presynaptic current clamp and postsynaptic voltage clamp recordings from the rat
MNTB (Figure 1A) were originally described in refs. (6, 7). The simultaneous pre- and postsynaptic
voltage clamp recordings were originally described in ref. (11). Except for some details not provided
in the Methods sections of these papers, we therefore refer to them for experimental details.
Recordings were corrected for a 0.1 ms difference in delay due to differential filtering (10 kHz forpresynaptic current clamp recordings and 3 kHz for postsynaptic voltage clamp recordings). The
second derivative of the presynaptic action potential waveform (APW) command was filtered to 1.5

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kHz with a Gaussian filter to better match the recorded postsynaptic signal. To minimize interferenceby the EPSCs evoked by the presynaptic calcium currents, we used the last 30 stimulations of a 50
APW train. At the stimulation rate of 100 Hz, the EPSCs evoked by these stimuli were substantiallydepressed. The bi-exponential fit of the decay of the preceding EPSC was subtracted from thepostsynaptic currents. The remaining current, which we call the active prespike, was averaged. The
passive prespike was estimated by summing the presynaptic P/5 stimulations.
2.2 Model
Inspired by a published model (8), we designed an electrical circuit model to mimic the current flow
underlying the postsynaptically recorded prespike at the calyx of Held synapse (Figure 1B). We
assumed that the prespike is generated exclusively by currents that flow through the synaptic cleft.
According to Kirchhoff’s first law, the current that flows from the presynaptic release face into thecleft must be equal to the sum of the current that leaks out of the cleft and the current that flows into thepostsynaptic cell. The presynaptic current consists of a capacitive current across the capacitancecontacting the synaptic cleft (c pre ) and the currents via ion channels (Ich), which includes voltage-gatedsodium channels (VGSCs), voltage-gated high-threshold potassium channels (HTKs), voltage-gated
low-threshold potassium channels (LTKs) and voltage-gated calcium channels (VGCCs). The current
can escape the cleft via an ohmic leak conductance (g leak ) or enter into the postsynaptic cell via themembrane capacitance that is in contact with the synaptic cleft (ccp) or via a synaptic conductance(gsyn). The changes in the cleft potential (Vcl) will have an impact on the capacitive currents, on thedriving forces of the conductances and on the voltage-dependent channel kinetics. The ionic current
from the synaptic cleft into the postsynaptic cell is assumed to have a reversal potential of 0 mV. This
will give us two differential equations, one for the synaptic cleft:
�𝑐𝑐𝑝𝑝𝑝𝑝𝑝𝑝 + 𝑐𝑐𝑝𝑝𝑝𝑝 �𝑑𝑑𝑉𝑉𝑐𝑐𝑐𝑐
𝑑𝑑𝑑𝑑= 𝑐𝑐𝑝𝑝𝑝𝑝𝑝𝑝

𝑑𝑑𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝
𝑑𝑑𝑑𝑑+ 𝑐𝑐𝑝𝑝𝑝𝑝

𝑑𝑑𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑑𝑑𝑑𝑑− 𝑔𝑔𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑉𝑉𝑐𝑐𝑐𝑐 − 𝑔𝑔𝑠𝑠𝑠𝑠𝑠𝑠 �𝑉𝑉𝑐𝑐𝑐𝑐 − 𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 � − ∑ 𝐼𝐼𝑐𝑐ℎ(1),and one for the postsynaptic cell, which includes a resting conductance (g post ) that sets its resting
membrane potential (V rest ) :𝑐𝑐𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑑𝑑𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑑𝑑𝑑𝑑= 𝑐𝑐𝑝𝑝𝑝𝑝

𝑑𝑑𝑉𝑉𝑐𝑐𝑐𝑐
𝑑𝑑𝑑𝑑− 𝑔𝑔𝑠𝑠𝑠𝑠𝑠𝑠 �𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑉𝑉𝑐𝑐𝑐𝑐 � − 𝑔𝑔𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 �𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑉𝑉𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 �(2).

We assumed throughout that the presynaptic and postsynaptic capacitance facing the cleft were equal.
These capacitances were calculated from the surface area by multiplying their contact area with thespecific membrane capacitance (C m). Values of the parameters for each model are listed in Table 1.
Models for VGSCs, HTKs and LTKs were taken from ref. (9). Maximal conductance densities were 5.8
nS µm-2 and 0.7 nS µm-2 for g HTK and g LTK, respectively (9). The sodium channel density was adjusted
to generate a 10 nA peak current with our AP template (10), and this conductance was distributed over
20 pF, giving a density of 0.4 nS µm-2 . For the VGCCs we used the Hodgkin-Huxley model describedby ref. (11) for the calyx of Held. Maximal conductance was adjusted to generate a charge transfer of
1 or 0.75 pC and was 0.12 or 0.09 nS µm-2, respectively. The model values correspond to room
temperature kinetics. In all simulations, the postsynaptic resting potential was set to -70 mV, and theNernst potentials for Na+ , K+ and Ca 2+ were set to +50, -90 and +40 mV, respectively. Changes in Vcl
were taken into account when calculating the driving force. Total postsynaptic capacitance (c post ) was
25 pF, gpost was 4 nS and gsyn was 0 nS. Contact area to the cleft was set to 520 μm2 and cleft leakconductance was set to 0.83 μS unless they were varied to assess their contribution. These values givea cleft time constant of 6 μs and a transfer constant of 0.03 fA V-1 s2 , which was in the same range as
the experimental values.
Presynaptic APs were simulated using the same AP template that was used to elicit presynaptic
calcium currents, unless noted otherwise. To calculate the transfer constant from our simulations, wechanged the timing of the AP template to have a second derivative peak value of 1.67, 2.00, 2.32, 2.65
and 3.17 MV s -2 . The slope from the line fit between the AP’’ peak values and the maximal
postsynaptic response was used as the transfer constant (Figure 2B). Line fits were always near-perfect(r > 0.999). To estimate the time constant, the AP template for presynaptic calcium currents was used
to simulate the calcium current and the postsynaptic prespike with the only-VGCCs-model at a densityof 0.11 nS μm-2. The passive prespike was simulated using the capacitive-only model. The time
constant was estimated as shown in Figure 2E for an experimental example.

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Differential equations were numerically solved using the function IntegrateODE of Igor Pro 6.37
(Wavemetrics) at its default settings. Channel states were initialized at the values reached after 3 ms at
the first point of Vpre.
Data are presented as mean ± standard deviation.
Table 1. Default model parameters for simulations.
Homogen.

No

Only

Cap.-

VGSCs

VGCCs

only

Max. VGSC conductance

gNa

0.65

0

0

0

nS μm-2

Max. HTK conductance

gHTK

5.8

5.8

0

0

nS μm-2

Max. LTK conductance

gLTK

0.7

0.7

0

0

nS μm-2

Max. VGCC conductance

gCa

0.09

0.09

0.09

0

nS μm-2

3. RESULTS
3.1 An electrical circuit that generates prespikes
As the prespike is generated by currents that flow from the calyx to its target neuron, we simulated
an electrical circuit in silico consisting of the terminal’s release face, a synaptic cleft that is isolated
from the reference by a leak conductance, and a passive neuron that partly faces the synaptic cleft. We
did not include a resistive connection between calyx and target since capacitive currents are likely todominate the postsynaptic currents during the prespike: the admittance for 500 Hz across an area of1000 µm2 is 31 nS (2πfC mA), which is much larger than the postsynaptic resting conductance of 4 nS,
while no physiological evidence for gap junctions (12) has been found at the calyx of Held synapse.
The model is illustrated in Figure 1. If we disregard any currents through presynaptic ion channels
facing the release face, the cleft potential should be proportional to the presynaptic capacitive current,
which is proportional to the first derivative of the presynaptic AP waveform (AP’). In voltage clamp,
the currents during the prespike will be dominated by capacitive currents, which are proportional to thefirst derivative of the cleft potential. Under these conditions, the prespike should therefore match thescaled, inverted second derivative of the presynaptic AP.

Figure 1 – Model circuit to simulate the prespike. (A) Drawing of the calyx of Held synapse. The calyx ofHeld terminal (‘pre’) covers a large area of the soma of its target neuron (‘post’). In between is a small
space, called the synaptic cleft, where membrane currents will flow during a presynaptic AP. (B) An
electrical circuit for the capacitive and resistive currents that flow from the presynaptic membrane into thepostsynaptic cell to generate a prespike.

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Figure 2 – Relation between the calyceal AP and the prespike. (A) Left column, from top to bottom: APrecorded from the calyx of Held, inverted first and second derivatives, and postsynaptic voltage clamp
recording showing the accompanying prespike. Insets show on a longer time scale the same presynaptic AP(top) and the postsynaptic EPSC (bottom) elicited by the calyceal stimulation. Right: Only VGCCs-model
results. Vertical scale bars (from top to bottom panels): 80 mV, 0.8 kV/s, 8 MV/s2, 0.2 nA. Horizontal: 0.5
ms. (B) Relation between the delay between the first negative and positive peak of the prespike and the firsttwo peaks in the first (blue) and second (black) derivative of the presynaptic AP. Dashed line is the identity
line. (C) Relation between the prespike and the second derivative shown in A. Maximum correlation was
obtained when delaying the second derivative by 90 μs. Blue line shows the regression line with a slope(‘transfer constant’) of 0.019 fA V-1 s2. (D) Left column, from top to bottom: Presynaptic calcium current(after P/5 subtraction), its first derivative, postsynaptic currents (black) plus passive prespike (blue),difference between active and passive prespike. Right: corresponding model results. Vertical scale bars: 2
nA, 15 nA/ms, 0.15 nA, 0.1 nA. Horizontal: 1 ms. (E) Relation between the calcium component of theprespike and the first derivative of the presynaptic calcium current shown in D. Maximum correlation was
obtained when delaying the first derivative by 40 μs. Blue line shows regression line with a slope (‘time
constant’) of 5.6 μs. (F) Relation between the contact area and the cleft leak conductance for different
values of the transfer constant (magenta lines) and the time constant (black lines). Green dots show thevalues of the model for the five double VC recordings calculated from the measured transfer and time
constants. Calcium current density was 0.11 nS µm-2 in the simulations.

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3.1 A comparison of the prespike with model predictions
We first looked at simultaneous whole-cell presynaptic current clamp recordings with postsynaptic
voltage clamp recordings (6, 7). The afferent axon of the calyx of Held was stimulated with anelectrode to trigger an AP, its corresponding postsynaptic prespike and an EPSC (Figure 2A). The
prespike generally matched the scaled inverted second derivative of the AP (Figure 2A). Figure 2B
shows that the time course of the second derivative of the AP indeed provides a better match for theprespike than its first derivative in these recordings (n = 13). From the relation between the second
derivative of the AP and the prespike a transfer constant can be calculated (Figure 2C).
Next, we turned to simultaneous whole-cell pre- and postsynaptic voltage clamp recordings of thecalyx of Held synapse that were originally reported in ref. (5), which were re-analyzed to comparethem with model predictions. In these experiments the presynaptic compartment was voltage clampedwith an APW command while the presynaptic calcium currents were pharmacologically isolated. A
comparison of the second derivative of the APW and the prespike yielded a transfer constant of 0.04 ±0.02 fA V -1 s 2 (n = 5) in these recordings.
3.2 Contribution of presynaptic calcium currents to the prespikeBy subtracting the passive component from the postsynaptically recorded active prespike, a small
current emerged that had a similar time course as the first derivative of the presynaptic calcium current(Figure 2D, left column). Its time course closely matched the model predictions (Figure 2D, rightcolumn). The amplitude of its positive peak was on average 56 ± 44 pA (n = 5). A comparison between
the max rate of rise of the measured presynaptic calcium current and this peak provided a time constant(Figure 2E), which was on average 6.0 ± 2.0 µs. The combination of the transfer constant and the time
constant provided an estimate for the contact area of the calyx, which was on average 730 ± 230 μm2,
and for the leak conductance of the synaptic cleft, which was on average 0.9 ± 0.4 µS. With theseestimates we used the model to estimate the calcium conductances that would replicate theexperimental results, which was on average 0.10 ± 0.06 nS μm-2. To replicate the experimental changes
the simulated Vcl peaked on average to 3.5 ± 0.6 mV, then reached a minimum of -3.2 ± 1.4 mV after
which it returned to baseline. As expected, the calcium current did not affect the positive deflection of
Vcl (Cap.-only model: 3.5 ± 0.6 mV), but did affect the Vcl after the peak (Cap.-only model: -1.3 ± 0.2mV). This change in Vcl due to the calcium current is subsequently observed in the prespike.

Figure 3 – Impact of the cleft potential on presynaptic calcium currents. (A) Simulation of the impact of aslow and a fast AP (top; FWHM: left 1.0, right 0.2 ms) on the cleft potential (middle) and the presynaptic
calcium current (bottom) at three leak resistances, as indicated above the figure. Scale bar: 90 mV, 14 mV,
1nA. (B) Relation between peak calcium currents and leak resistance for the two APs. Driving force
increases slightly (not shown). (C) The change in delay between the calcium peak current and the AP for
the two APs (solid line). The dashed line shows the delay after correcting for the decrease in the calcium
current shown in B. Calcium conductance density was 0.1 and 0.2 nS μm-2 for the slow and fast AP,
respectively.

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3.1 Impact of cleft potential on the presynaptic calcium currents
During development the presynaptic AP narrows from a half width of 0.5 to 0.2 ms (13). The briefer
AP necessitates a much larger capacitive current, and may thus potentially result in a larger change inthe cleft potential. As the voltage-dependent calcium channels at the release face sense Vpre -Vcleft
instead of V pre, their kinetics depend on the cleft potential. We simulated the consequences of the cleft
potential on the calcium current by varying the cleft leak resistance (Figure 3). For a slow AP, the cleft
potential changes to +2.5 mV and then to -3.8 mV for a leak resistance of 1.5 MΩ and a surface area of
520 μm2 . This causes a delay of 50 μs in the onset of the calcium current (Figure 3C), but has little
effect on its size (Figure 3B). In contrast, with the faster AP we observe under the same conditions thatthe cleft potential changes to +11.4 mV and -5.9 mV. As a consequence, the peak calcium current isdelayed by 30 μs and reduced by 25% (-0.86 vs -0.65 nA). The observed delay corresponds to the delay
in reaching the V pre – Vcleft maximum compared to the Vpre maximum; the reduction is related to thesmaller effective AP, which determines the maximal opening probability of the calcium conductance.
We conclude that the developmental acceleration of the calyceal AP will increase the capacitive
current to a level that would impede the opening of calcium channels if the synaptic cleft leakconductance remained unchanged.
3.2 Predictions for the contribution of other presynaptic ion currents to the prespike
The estimates for the cleft leak conductance and of the coupling for the calcium current allowed us
to test the contribution of Na + and K+ currents to the postsynaptically recorded prespike. We estimatedtheir density based on literature values and assumed a homogeneous distribution within the terminal.
Figure 4 illustrates that the presence of these channels at the release face would have a large impact on
the shape and size of the prespike. Due to the gating differences, the timing of each current is different(Figure 4A), and thus their impact on the prespike as well (Figure 4B). A comparison with the recorded
prespike (Figure 2A) suggests that it does not resemble the prespike of the homogeneous model,suggesting that some voltage-gated ion channels are excluded from the release face. Also, the impact
of VGCCs on the prespike looks larger in our simulations than in the recorded prespikes. A morecomprehensive comparison may allow an inference to what extent these channels are present at therelease face.

Figure 4 – Impact on the prespike of voltage-gated ion channels located at the release face. (A) Timing ofdifferent voltage-gated currents at the release face during the AP. Note that the amplitudes of each of thecurrents depend on cleft potential, thus creating a mutual dependency. Vertical scale bars: 60 mV, 2.4 nA, 1
nA, 1 nA, 3 nA. Horizontal: 0.5 ms. (B) The cleft potential (top), the VC prespike (middle), and the CC
prespike (bottom) under different conductance density conditions. Homog.: homogeneous density; no
VGSCs: no sodium conductance at the release face; only VGCCs: calcium and capacitive currents at therelease face; no channels: the capacitive-only model. Scale bars: 4 mV, 0.2 nA, 1 mV.; 0.5 ms.

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4. CONCLUSIONS

We studied a form of synaptic ephaptic coupling in which a fraction of the currents flowing at thepresynaptic release face enter the postsynaptic cell to generate the prespike. By comparing model
predictions and experiments in which both the presynaptic and the postsynaptic membrane currents
could be measured, we could quantify the leak resistance of the synaptic cleft. The obtained value of~1 MΩ is higher than the value of 0.3 MΩ assumed for the cerebellar pinceau synapse (8), but much
lower than the value of at least 60 MΩ estimated for the synapse between cones and horizontal cells at
the retina based on an ultrastructural reconstruction (14), or up to 3 GΩ assumed for the mossy fiber
CA3 synapse (15). Our experiments were performed at room temperature in slices from pre-hearing
rats, and most of the calyces probably still had a cup shape (16). Our simulations showed that underthese conditions the impact of presynaptic currents on the cleft potential is modest. However, thespeedup of the AP at physiological temperature and after hearing onset would increase this impact
substantially. The large postsynaptic glutamate receptor current may also impact the cleft potential(17). We show that with the observed pre-hearing cleft leak resistance, the capacitive currents during
the adult presynaptic AP may affect the timing and size of the presynaptic calcium current. Apart fromthe often mentioned facilitation of glutamate clearance (18-20) or the resistance against Ca 2+ depletion(21), a lowering of the cleft leak resistance thus provides an additional argument for the desirability of
the fenestration of the mature calyx.
Our model also allowed us to simulate the contribution of other voltage-dependent ion channels tothe prespike. Interestingly, both sodium and potassium channels seem to largely avoid the release facein the mature calyx of Held (10, 22). A systematic comparison of modeled and measured prespikes may
further delineate their contribution to changes in the cleft potential and its subsequent impact on thepresynaptic action potential.

ACKNOWLEDGEMENTS

The research was supported by a grant from the Nederlandse Organisatie voor Wetenschappelijk
Onderzoek – Aard- en Levenswetenschappen (#823.02006, ‘Development of a giant synapse’).

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