Axons compensate for biophysical constraints of variable size to uniformize their action potentials

First, we explored the biophysical behavior of variable-caliber axons by simulating APs by sodium and potassium conductances that were homogeneously distributed in the morphology of a real mossy fiber axon originating from a hippocampal granule cell (Figs 1A and S1). As expected from simple morphology simulations [17–20], the passive biophysical properties and the waveforms of active conductance-evoked APs changed with the size of the axons. Both the rise and repolarization were generally slower in smaller structures. However, local AP shapes were also influenced by adjacent axonal regions, as sudden widening of the diameter can act as a capacitive sink. While the effects of size and capacitance mismatches on AP propagation (i.e., AP rise/sodium channel activation) have been previously investigated [18,21–26], how these biophysical constraints affect AP repolarization remains unknown. Modeling the subsequent functional steps, the differences in AP shapes were multiplied by the nonlinear correlations between AP shape and Ca²⁺ influx, and between Ca²⁺ influx and synaptic release, resulting in a 40% variability in release efficacy. The results showed that—consistent with previous predictions [17,19,20]—the biophysical consequences of variable axon diameter can lead to changes in AP repolarization in a range that can affect Ca²⁺ influx, which can add complexity to neuronal outputs. Although this simplified simulation did not capture all possible details, it provides a testable prediction: AP repolarization and shape are generally slower in smaller axons, and they are also variable due to mismatch effects at diameter changes.

Fig 1. Similar AP shapes in sMFs and LMFBs despite the different biophysical properties.

(A) Simulations in real MF morphology with uniform I_K and I_Na predict that AP kinetics, measured as AP area, is variable due to the size-dependent passive membrane properties. In general, smaller boutons have slower AP. A more detailed and extended versions of these simulations are shown in S1 Fig. (B) The recorded sMFs (upper image) were identified with subsequent in situ confocal imaging (lower image) or post hoc anatomy (see Methods). Inset shows an LMFB along the sMF-recorded axon that was used for its identification. LMFBs were recorded in the same conditions as sMFs. (C) Their diameters segregated the recorded structures into 2 populations. sMFs include small en passant boutons and main axons. Small dots show individual measurements, large black symbols are the mean, black vertical lines are the median, and diamonds and whiskers show 25%–75% and 10%–90% ranges, respectively. (D) The sMFs had smaller membrane capacitance, larger input resistance and slower membrane time constant compared to LMFBs (n = 50 sMF and 64 LMFBs). (E) APs were evoked by small current injections. (F) AP amplitudes and width at half-maximum (HW) were similar both in the raw recordings and after elimination of the instrumental filtering effect by post hoc simulation of the recording equipment and biological structures [38] (n = 15 sMF and 11 LMFBs). (G) The integral area of APs was similar in sMFs and LMFBs and did not correlate with the capacitance of individual boutons, which measures membrane surface and size of the recorded structures (n = 50 sMF and 64 LMFBs). Source data and codes available at https://repo.researchdata.hu/dataset.xhtml?persistentId=hdl:21.15109/ARP/BTK8A4. AP, action potential; LMFB, large mossy fiber bouton; sMF, small mossy fiber.

https://doi.org/10.1371/journal.pbio.3002929.g001

Next, we tested AP shapes in mossy fibers using direct patch clamp recordings from small axon terminals. These axons form small boutons and connecting segments, whose sizes match most cortical axons, and exceptionally large boutons [3,36]. Mossy fibers lack complex arborization and myelin sheaths, which would complicate their biophysical properties. Only unequivocally identified and intact mossy fibers were analyzed (Fig 1B), categorized either as small mossy fibers (sMFs, including both small boutons and main axons) or large mossy fiber boutons (LMFBs) (Fig 1C). Cut ends, called blebs [1], were not included. As expected from the smaller size, the membrane capacitance was smaller in sMFs, whereas their input resistance was larger. The measured membrane time constant was also slower in sMFs at resting conditions (Fig 1D and S1 Table) that would suggest that APs are also size dependent. However, the amplitude and kinetics of locally evoked APs were surprisingly similar in the raw recordings (Fig 1E and 1F and S1 Table). This may be the consequence of the comparable size of the structures and recording pipettes [1,37–39], which were similarly small in all recordings. As these parameters can be influenced by instrumental filtering caused by the small pipette required for patching axons, we quantified the integral area of APs. Our analysis showed that the integral area of APs was not correlated with bouton identity or the effective size of the recorded mossy fiber structure, measured by local capacitance (Fig 1G).

Interference between small axons and experimental instruments affects these recordings [1,37–39]. Therefore, in a subset of experiments, we corrected these signals to investigate the native, instrument-free AP shapes by correcting current clamp errors through composite simulation of the morphology, currents, and the recording instruments [38]. Importantly, the corrected APs of sMFs and LMFBs remained indistinguishable (corrected data in Fig 1, S1 Table). The smaller variance of the corrected data compared to the raw data confirms minimal biological variability of APs. In contrast to the models that predicted variable AP decay when active conductances were homogeneously distributed, our results using corrected patch clamp data suggested that despite the complex biophysical consequences of variable axon size, APs in sMFs are similar to LMFB APs. Additionally, the corrected voltage data confirmed that AP area measurements are insensitive to instrumental filtering (Fig 1F).

To test the AP shapes simultaneously in various axonal compartments, we used fast voltage-sensitive dye imaging which allows simultaneous monitoring of APs in different structures of the same axons at sufficient temporal resolution. Voltage imaging of distal axons was challenging because achieving sufficient concentrations of the membrane bound dye at distances of 100 to 1,000 micrometers results in toxically high concentrations at the somatic loading sites. To overcome these limitations, we directly loaded JPW1114 into LMFBs and their neighboring axon segments with sMFs. This dye is fast enough to resolve the rapid time course of axonal APs [1,11]. First, we investigated naturally propagating APs evoked by distal stimulation. The dye-loading pipette was subsequently retracted (Fig 2A). The shapes of the simultaneously imaged APs of sMFs and LMFBs were indistinguishable, and they also matched the previously recorded APs (n = 11; Fig 2B and 2C and S1 Table).

Fig 2. Voltage-sensitive dye imaging confirms similar AP shapes in sMFs and LMFBs.

(A) JPW1114 (50 μM) was loaded via recording of an LMFB. The pipette was retracted and after equilibration (≥1 h), fluorescence signal changes were monitored at 10 kHz in the vicinity of the recording site, while APs were evoked by distal stimulation (>100 μm). (B) Electrophysiological traces were recorded at the beginning of the recordings, independent of the imaging data. Gray traces show individual experiments, with colored average APs from all sMFs and LMFBs (n = 11 experiments). Black trace shows the average signal from pixels right next to the imaged axons. (C) AP parameters from simultaneously imaged LMFBs and sMFs. (D) In the second imaging approach, the loading pipette was kept on the LMFBs allowing the over-sampling of imaged signals by the high-resolution recordings (n = 18 experiments). Amplitudes are not comparable because the presence of the excess dyes in LMFBs reduce signals by increasing non-responding dye fraction (i.e., F₀). (E) Voltage imaging revealed no difference between the local APs of 2 distinct sMF structures, the main axon (main) and the filopodial extensions (filo) of the same axons. Source data are available at https://repo.researchdata.hu/dataset.xhtml?persistentId=hdl:21.15109/ARP/BTK8A4. AP, action potential; LMFB, large mossy fiber bouton; sMF, small mossy fiber.

https://doi.org/10.1371/journal.pbio.3002929.g002

Because this measurement is limited by the 10 kHz imaging rate, in the next experiments, we used higher temporal resolution with the guide of simultaneous electrophysiological signals (Fig 2C). We kept the dye-loading pipette on the LMFBs during imaging and oversampled the JPW1114 signals of locally evoked APs by aligning individual traces to the 100 kHz electrophysiology signals before averaging for distinct axonal compartments. This arrangement reliably reports the temporal profile of APs, although the amplitudes are not comparable due to the presence of the excess, non-responding dye in the pipette on the LMFB (i.e., F₀). Importantly, this measurement also confirmed uniform AP shapes in sMFs and LMFBs (n = 18, S1 Table). Furthermore, simultaneous imaging revealed similar AP shapes in 2 distinct types of sMF structures: the filopodia emanating from LMFBs and main axons with small en passant boutons (Fig 2E and S1 Table). Furthermore, we did not detect differences in the APs of bassoon-positive and -negative small axonal segments (identified by correlated post hoc immunolabeling, S2 Fig) suggesting that AP shape is similar in synaptic and non-synaptic segments. Altogether, we concluded from our independent measurements that AP shape is uniform within individual mossy fibers despite the large intrinsic variabilities of their diameters and biophysical properties.

Next, we tested whether the AP uniformity applies to other cell types. We measured the APs and biophysical properties in diverse types of axons, representing the main cortical axon types, including subcortical and locally originated glutamatergic and GABAergic types. The axons were rigorously identified by using their morphological properties and immunolabeling for 4 to 5 markers on each axon (see Figs 3A, 3B, S3, S4 and S5). First, we confirmed in these axons that the membrane properties and AP shapes are axon type specific (Fig 3C and S2 Table), validating the principle that axonal functions are cell type-specifically tuned. Axons from hypothalamic supramammillary nucleus (SuMa) elicited wider APs than mossy fibers (average AP area: 25.8 ± 1.2 mV*ms, n = 16), while the axonal APs of hilar mossy cells (21.6 ± 3.6 mV*ms, n = 7, MCa) and CB1R-expressing GABAergic axons (18.4 ± 1.8 mV*ms, n = 8, CB1a) were between SuMa and mossy fibers (LMFB: 15.5 ± 0.4 mV*ms, n = 64, sMF: 14.8 ± 0.5 mV*ms, n = 50). The cell type-specific APs also demonstrate that the observed uniformity of mossy fiber APs was not due to the insensitivity of recording methods.

Fig 3. AP uniformity in diverse types of hippocampal axons.

(A) A representative recording from a morphologically identified VGluT2+ SuM axon in the DG (further details of identification are shown in S3 Fig). (B) A representative recording from a morphologically identified VGluT1+ mossy cell axon (see also S4 and S5 Figs). (C) Average electrical properties of axons are cell type dependent (ANOVA: F(4) = 4.45, 7.5, and 27.4, p = 0.002, 1.6*10⁻⁵ and 1*10⁻¹⁶, Bonferroni pairwise comparison is shown in S2 Table). (D) Within cell types, the AP shapes did not show correlation with the local size and membrane time constant of the axons (statistical details of linear fits are shown in S3 Table). Source data are available at https://repo.researchdata.hu/dataset.xhtml?persistentId=hdl:21.15109/ARP/BTK8A4. AP, action potential.

https://doi.org/10.1371/journal.pbio.3002929.g003

These axons, like most in the CNS, have variable diameter due to varicosities. However, within anatomically homogeneous cell types, the AP shape did not depend on the size and passive membrane properties of the recorded axonal structure (Fig 3D and S3 Table). These results suggest that all tested axon types employ uniform APs in spite of their variable size and biophysical properties.

Axonal AP waveforms are not always the same within individual boutons and their shapes exhibit functionally relevant plasticity, as axonal APs typically show activity-dependent broadening during sustained activities influencing their synaptic effects [5,6,8,12–14,30,40,41]. To assess whether LMFB and sMF APs maintain uniformity during various dynamic conditions, we conducted direct recordings and VSD imaging (Fig 4A, 4B, 4D and 4E). We found that sMF APs, similarly to previous data from LMFBs [5], display frequency-dependent broadening during AP trains. Importantly, the extent of AP plasticity was similar in sMFs and LMFBs and did not depend on the size of the structure (Fig 4C and 4F). Thus, AP uniformity persists during dynamic conditions allowing for similar activity-dependent modulation of axonal output.

Fig 4. AP shape plasticity affects sMFs and LMFBs similarly.

(A) AP trains were evoked at 3 different frequencies during direct patch clamp recording of sMFs and LMFBs. The example traces show 40 Hz stimulation, and 3 ms-long current injections pulses were used to avoid the contamination of the repolarization phase by the capacitance artifact. (B) Progressive and frequency-dependent broadening of sMF- and LMFB-APs (see also [5]). (C) Summary data show similar broadening in sMFs and LMFBs at different frequencies (left panel). Furthermore, the broadening of APs did not depend on the functional size of the boutons (right panel). (D) The 100 APs were evoked at 40 Hz in axons during VSD imaging experiments. To avoid photo damage, the axons were illuminated and imaged only during the first 11 and the last 13 APs. (E) Example APs obtained by 2 different imaging approaches with extracellular stimulation (upper panels) and with simultaneous intracellular recording, which allowed oversampling of the imaging signals (see Fig 2). (F) Summary data show similar broadening in sMFs and LMFBs obtained with the 2 approaches. Source data are available at https://repo.researchdata.hu/dataset.xhtml?persistentId=hdl:21.15109/ARP/BTK8A4. AP, action potential; LMFB, large mossy fiber bouton; sMF, small mossy fiber.

https://doi.org/10.1371/journal.pbio.3002929.g004

There must be mechanisms that compensate for the passive biophysical constraints caused by axon size. In the simulations that recreated original recordings of single APs by adjusting the amounts of active currents in the detailed model of an axon with instruments (see Fig 1F), both sMFs and LMFBs required a similar amount of sodium currents (I_Na) on average. However, sMFs needed more potassium currents (I_K) than LMFBs. This predicts a lower I_Na/I_K ratio in sMFs (Fig 5A). To test this prediction, we experimentally measured the I_Na/I_K ratio in outside-out patch recordings, where both I_Na and I_K were measured in each patch using 2 different voltage steps (Fig 5B). Consistent with the model prediction, while I_Na densities were similar, the total I_K were larger in patches pulled from sMFs, resulting in larger I_Na/I_K ratio (n = 46 sMFs and 47 LMFBs, for statistical details see S1 Table and Fig 5C). As outside-out patches sample ionic channels from local membranes only, we concluded that sMFs have more I_K, which speed up their AP repolarization and promote AP uniformity.

Fig 5. Active conductances compensate for the biophysical constraints of smaller axon size.

(A) Recreating native sMF APs (see Fig 1) in simulations required similar I_Na but more I_K than in LMFBs, resulting in larger I_Na/I_K ratio in the latter. (B) Average of recorded I_Na and I_K current densities in membrane patches pulled from sMFs and LMFBs (n = 48 and 40 recordings) using 2 voltage-steps in the same recordings (0 mV for 0.4 ms for I_Na, +70 mV for I_K, from −110 mV). (C) The average I_Na density was similar between LMFB and sMF recordings; however, sMF membranes had larger I_K densities, resulting in larger I_Na/I_K ratio in LMFBs. (D) Selective inhibition of Kv1-mediated I_K by 100 nM DTX had size-dependent effects on axonal APs with larger effects on smaller sMFs. Four representative recordings are shown on the right. (E) In contrast, selective partial Kv3 inhibition by TEA (100 μM) had similar effects on APs of sMFs and LMFBs. Source data are available at https://repo.researchdata.hu/dataset.xhtml?persistentId=hdl:21.15109/ARP/BTK8A4. AP, action potential; DTX, dendrotoxin-I; LMFB, large mossy fiber bouton; sMF, small mossy fiber.

https://doi.org/10.1371/journal.pbio.3002929.g005

Among axonal Kv channels, Kv1s are known to be responsible for fine-tuning APs for specific functions of various axons [4,6–9,13,14,40,42], whereas Kv3 and BK channels usually provide the backbone of repolarization in mossy fibers [43] and Kv7 channels set axonal excitability that also influence spiking properties [44]. However, the contribution of different Kv channels changes during complex firing patterns. Interestingly, electron microscopic studies noted that Kv1.1 channel distribution was not homogeneous in mossy fibers and the expression was more prominent in small axon compartments [45]. Among these channels, we focused on the potential role of Kv1 channels in uniformizing single axonal APs, we inhibited Kv1.1 and Kv1.2 channels with dendrotoxin-I (DTX), which resulted in wider APs in mossy fibers. However, the effects of DTX were larger on AP repolarization in sMFs than on LMFBs APs (38.6% versus 21.5% at the population level, Fig 5D), indicating that sMFs employ more Kv1 channels to achieve fast repolarization. In the presence of DTX, axon size and AP shape showed a similar correlation as predicted in axon models with homogeneous conductances (S1E Fig). This observation suggests the non-uniform distribution of AP-relevant potassium currents explains the difference between the measured and predicted size-dependent behavior of axonal APs. It also suggests an important role for Kv1 channels in accelerating APs in smaller MF compartments. Furthermore, the size-dependent DTX effects on APs independently confirmed our patch data about the contribution of larger I_K to the APs of sMFs. Indeed, in the presence of DTX, the I_K density and I_Na/I_K ratio were similar in LMFBs and sMFs (S6 Fig). The resting membrane potential was not significantly affected by DTX (sMF control versus DTX: −75 ± 0.8 mV versus −72.7 ± 2.6 mV, LMFB control versus DTX: −74.4 ± 1.2 mV versus −75.1 ± 2.5 mV, ANOVA: F(3) = 0.441, p = 0.72, n = 54, 17 and 36, 17), indicating little Kv1 channel activation at resting conditions in MF axons. In contrast to the DTX effects, partial inhibition of Kv3 channels by 100 μM of TEA had similar effects on sMF and LMFB APs (16.9% and 19.5%, Fig 5E). These results show that the contributions of at least 2 AP-relevant channels are differently related to axon size. While Kv3s have similar contributions to single APs, the contribution of Kv1 correlates with axon size compensating the biophysical consequences of small and variable axon size.

For the measurement of the local electrical parameters of axons, 100 ms-long pulses from −70 mV to −90 mV were used in voltage clamp. First, we recorded the signals in cell-attached configuration, which allowed the estimation of the seal resistance in each measurement (12.1 ± 0.6 GΩ for sMF, 13.5 ± 0.6 GΩ for LMFBs, and 12.5 ± 0.9 GΩ for other axons). For the quantification of local axonal capacitance, the average of the cell-attached signal was subtracted from the whole-cell recorded trace to eliminate residual uncompensated instrumental capacitance. We fitted the capacitive current transients with the sum of 2 exponential functions in a 3 to 7 ms time window after the peak assuming that a two-compartmental electrical equivalent circuit is an adequate representation of recorded axons [66,67]. In this model, the faster exponential describes the electrical behavior of the local membrane at the recording site, whereas the slower one is the composite representation of the entire axonal arbor. To validate this two-compartmental simplification, we systematically fitted the traces with mono-, bi-, or tri-exponential functions in a subset of the experiments. The two-compartmental model significantly outperformed the fit of the mono-exponential model assessed (sum of squared error: sMF: 7.81 nA² versus 2.37 nA²; LMFB: 10.58 nA² versus 2.18 nA² for mono- and bi-exponential fits, respectively). Furthermore, fitting the traces with the sum of 3 exponentials resulted in only marginal improvement compared to the biexponential model (sMF: 2.37 nA² versus 2.16 nA²; LMFB: 2.18 nA² versus 2.04 nA² for bi- and tri-exponential fits, respectively) indicating that this simplified two-compartmental model is necessary and sufficient to characterize the passive electrical properties of the recorded axons. Thus, the structure capacitance derived from the fast component of the fit and it represented the biophysically effective size of each recorded bouton. Input resistance was measured both in voltage- and current clamp recordings to check the consistency of the recording, but for quantification we used the voltage clamp data. The membrane time constant data derived from independent current clamp recordings. To calculate the AP area in electrophysiological recording data, we first determined the start of the AP at the voltage value where the upstroke velocity reached 100 mV/ms. Then, we computed the AP area within the region between the start of the AP and the point where the membrane potential returned to the same voltage value.

Modeling of axonal recordings with realistic pipettes and amplifier circuits (Fig 1F)

Computer simulations were performed in the NEURON simulation environment (v7.5) [68] using a detailed model that captures the experimentally observed behavior of the measuring system as described in Olah and colleagues [38]. Pipette parameters and the compensatory mechanisms of the amplifier were set according to the actual measurements using modified model-cell circuits or short-circuiting components of the amplifier. Furthermore, the pipette parameters were quantified using partial submerging, tip-breaking, and direct microscopic measurements of their physical dimensions. The pipette models were adjusted for each recording pipette to recreate capacitive signals obtained in open and on-cell situations. The amplifier and adjusted pipette models allowed to recreate the characteristic capacitive signals during each current clamp recording.

To incorporate realistic morphologies in the model, we used a 140 μm-long detailed reconstruction of the recorded part for each axon. The reconstruction was performed semi-automatically by the Vaa3D software [69] using the confocal images taken right after the recordings. Remote axonal parts were implemented as simplified dummy compartments. To obtain the passive background of the axon, we fitted model responses to the experimentally recorded subthreshold voltage signals by optimizing axonal passive parameters and the access resistance of the recording. These fundamental parameters were similar for models which were based on LMFBs and sMFs (C_m = 0.90 ± 0.08 and 0.89 ± 0.05 μF*cm^-2, R_a = 151.49 ± 18.81 and 134.45 ± 15.66 Ω*cm and R_access = 117.81 ± 7.63 and 185.26 ± 34.31 MΩ). R_m was held constant at 50 kΩ*cm².

NEURON codes are available at Zenodo: https://zenodo.org/records/13977231 and Github: https://github.com/brunnerjanos/axonal-AP/tree/1.0.

The tip of the pipettes was backfilled with normal intracellular solution (see above) and the voltage sensitive dye (JPW1114 also called di-2-ANEPEQ, 10 to 50 μM [70]) containing intracellular solution was carefully loaded thereafter. LMFBs were patched within 4 min after the loading of the pipette. After forming whole cell configuration, the dye was allowed to diffuse into the axon at least for 30 min before starting the imaging experiment. The upright microscope (Nikon FN-1) was equipped with a 1.1 numerical aperture 25× water-immersion objective and a 1.5× magnifier lens in front of the camera. For imaging voltage signal, we used a single mode 532 nm laser source (CNI Changchun MSL-FN-532S-400mW), which was coupled via a bifurcated SMA-905 fiber guide (0.4 mm, NA 0.39) to the epifluorecent attachment of the microscope, which was equipped a filter cube (ZT532rdc dichroic mirror and 542 nm long-pass emission filter). When the axonal objects needed to be illuminated for longer time, for example during focusing and searching, we used a diode laser illuminator (89North LDI-7) via the second branch of the fiber guide. The excitation intensity was regulated by the direct control of the output power and/or by the use of ND filters. Optical signals were acquired with a CMOS camera (Redshirt Imaging, Da Vinci-1K) with a frame rate of 10 kHz (64 × 46 pixels, pixel size: 0.79 μm) and digitized simultaneously with the electrophysiological signals by the AD board of the imaging system. At the end of the experiment, the VSD fluorescence was used also for morphological identification.

Data were discarded if the half-width of the APs showed more than 20% increase of its initial value. A custom Fiji macro was used to correct for photo-bleaching in individual pixels of the image stacks using independent double exponential fits. The pixels were clustered into 8 bins for the fitting. To select the active axonal compartments within bleach corrected image stacks, we generated a ΔF/F₀ image, where the intensities around (±0.2 ms) the AP peaks were subtracted and divided with the baseline values of each pixel on the image. The identification was helped by the multifocal morphological images that were recorded after the imaging session. In the first imaging approach in which the naturally propagating APs were imaged, the 10 kHz imaging traces were segmented and aligned with custom Python scripts. For the second imaging approach that intended to increase the temporal resolution of the imaging signals, we implemented a shift and mean algorithm (written in Python) to increase the temporal resolution of the recorded signals (adopted from [71]). In brief, the higher sampling rate of the electrophysiology signals registered simultaneously on the DigiData AD-board allowed us to align the spikes with 250 kHz temporal resolution. The oversampled imaging signals were pooled, aligned according to these more precise AP peaks and then resampled by averaging multiple (typically 8) data points resulting in 24.5 to 27.5 kHz final resolution. For demonstration purposes, signals were low-pass filtered using a bidirectional digital Chebyshev-II lowpass filter (f_stop = 8 kHz, Microcal OriginPro). If the imaging experiment included longer axons, VSD signals were averaged in short axonal segments (Fig 2B) was selected 3 to 7 pixels distance from the imaged LMFB, which had the brightest emission. Because of the lack of AP signals and intensity changes in the background area, we concluded that neighboring structures (i.e., LMFB and sMF) can be independently analyzed, which were selected with similar distances. AP area was determined as the integral area in a 0.6 ms window starting from 0.05 or 0.1 ms from the peak of peak-normalized AP signals. Normalization was needed because VSD signal amplitude depends on the background intensity, which is influenced by other factors in some cases (e.g., pipette dye load).

Modeling of axonal APs, Ca²⁺ influx, and release rate (Fig 1A and S1 Fig)

To model the relationship between axonal morphology and the AP properties and the evoked synaptic release, a propagating AP was simulated in a complete granule cell reconstruction that had intact mossy fiber trajectory in the CA3 field. This morphology was used previously [38], but here we implemented a more complete electrical simulation on this structure. Both the passive parameters (C_m = 1 μF*cm^-2, R_a = 150 Ω*cm, and 50 kΩ*cm²) and active conductances (290 mS*cm^-2 and 17 mS*cm^-2 for the Hodgkin–Huxley type sodium and potassium channels, respectively) were distributed homogeneously in the entire cell. Equilibrium potentials for the leak, I_K and I_Na were set to −80 mV, −90 mV, and 70 mV, respectively; whereas, voltage dependence of the Ca²⁺ current followed the Goldman–Hodgkin–Katz [72]. Ca²⁺ influx was modeled as a compound current produced by the mixture of P/Q, N, and R-type channels with a ratio of 6.5:2.5:1, respectively, as described in LMFBs [73]. Ca²⁺ channel kinetics were adopted with a temperature coefficient of Q₁₀ = 2.5 to account for the higher temperature used in this model (35°C). Release was calculated from the Ca²⁺ influx assuming a conservative 2.5-power relationship. A single AP was triggered through somatic current injection and parameters related to the propagating AP and the evoked Ca²⁺ influx was quantified at every micrometer along the axon. As there is no explicit voltage threshold for a propagating AP, the duration of the AP was quantified as the width at −20 mV. This simulation was performed with a temporal resolution of 250 kHz.