Axonal Na+ channels ensure fast spike activation and back-propagation in cerebellar granule cells

Abstract

In most neurons, Na+ channels in the axon are complemented by others localized in the soma and dendrites to ensure spike back-propagation. However, cerebellar granule cells are neurons with simplified architecture in which the dendrites are short and unbranched and a single thin ascending axon travels toward the molecular layer before bifurcating into parallel fibers. Here we show that in cerebellar granule cells, Na+ channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. The impact of this channel distribution on neuronal electroresponsiveness was investigated by multi-compartmental modeling. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing excitatory postsynaptic potentials to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock the activation of which promoted spike back-propagation with marginal delay (<200 micros) and attenuation (<20 mV) into the somato-dendritic compartment. These properties allow granule cells to perform sub-millisecond coincidence detection of pre- and postsynaptic activity and to rapidly activate Purkinje cells contacted by the axonal ascending branch.

FIG. 1.

Concentration of sodium channels and fibroblast growth factor homologous factor (FHF) at the axon initial segment of P20 granule cells. Saggital cryosections of P20 cerebellum were incubated with mouse monoclonal antibody to voltage-gated sodium channel alpha subunits (A) or to FHF-4 monoclonal antibody (B), followed by treatment with goat anti-mouse IgG-ALEXA488 and with TO-PRO3 as a nuclear stain. Confocal images were captured at ×4,000 magnification. An individual granule cell nucleus (]) and its axon initial segment (▴) are indicated for each image.

FIG. 2.

Transient Na⁺ currents in granule cells in situ. A: properties of I-Na_t recorded in 2 typical granule cells (the voltage-clamp protocol is shown at the top). The experimental tracings recorded at –75 to –40 mV and at –35 to +20 mV have been split in 2 different subpanels. A1 provides an example of the currents recorded in group-1 neurons, in which an unclamped and a well-clamped I-Na_t component coexist. A2 provides an example of the currents recorded in group-2 neurons, in which the well-clamped I-Na_t component was observed in isolation. Insets: the current-voltage (I-V) relationships for I-Na_t peak amplitude in the same 2 cells. Note the notch in the I-V relationship of the group-1 cell (arrow). B: capacitive currents (the transient has been truncated: tildes) recorded in the cells illustrated in A1 and A2 (B1 and B2, respectively) in response to a –10-mV voltage pulse from −80 to −90 mV. The decay phase of capacitive transients was fitted with a double-exponential function. Fitting parameters for B1: A₁ = −188.6 pA, τ₁ = 97.3 μs, A₂ = −13.7 pA, τ₂ = 0.708 ms, C = −3.2 pA. Fitting parameters for B2: A₁ = −195.59 pA, τ₁ = 65.8 μs, A₂ = −3.4 pA, τ₂ = 1.17 ms, C = −1.2 pA. The gray lines correspond to the sum of the slow exponential component plus offset of each fitting. C: average values of fast time constant (τ₁), slow time constant (τ₂), and relative amplitude coefficient [A₂/(A₁ + A₂)] obtained from exponential fittings of capacitive transients in group-1 cells (white columns; n = 58) and group-2 cells (gray columns; n = 15). Double asterisk: P < 0.003, unpaired t-test).

FIG. 3.

Na⁺ currents in isolated granule cells. The figure documents how the absence of I-Na_t in the majority of acutely dissociated granule cells correlates with a reduction of total membrane but not somatic membrane surface. A: an example of the I-Na_t that could be recorded in a minority of acutely dissociated granule cells (n = 3 of 32). The voltage protocol is shown at the top (only sweeps in 10-mV increments are shown). The corresponding I-V relationship is shown on the right. B: examples of the capacitive currents recorded in a representative granule cell in situ and in a representative dissociated granule cell in response to a –10-mV voltage pulse (the transient has been truncated: tildes). The gray line is the double-exponential fitting of the transient's decay phase. The single-exponential functions are shown as dotted lines. Fitting parameters for the group-1 cell recorded in slice: A₁ = −260.8 pA, τ₁ = 77.5 μs, A₂ = −18.5 pA, τ₂ = 1.26 ms, C = −1.7 pA. Fitting parameters for the acutely isolated cell: A₁ = −420.4 pA, τ₁ = 38.6 μs, A₂ = −5.0 pA, τ₂ = 1.11 ms, C = −1.6 pA. C, left: percentage of cells showing a measurable I-Na_t (n = 91 in situ and n = 32 in dissociated granule cells) and maximal peak amplitude of I-Na_t, when present, in granule cells in situ (n = 84) and acutely dissociated granule cells (n = 3; *, P < 0.05, unpaired t-test). Right: average total charge transferred with capacitive current transients evoked by –10-mV voltage pulses and somatic capacitance (C_sm) in granule cells in situ (n = 83) and acutely dissociated granule cells (n = 32; triple asterisk, P < 0.001, unpaired t-test).

FIG. 4.

Cell-attached single-channel recordings in granule cell somata in situ. The figure shows consecutive current tracings recorded in 2 cell-attached patches in response to the voltage protocol illustrated at the top of each panel. Left traces: representative of 9 patches; right traces: representative of 3 patches. Note the absence of detectable Na⁺-channel activity in the patch at the left and the presence of transient Na⁺-channel activity in the patch at the right. The lowermost tracing in each panel is the ensemble-average current obtained from 40 sweeps.

FIG. 5.

Granule cell multi-compartmental model. A: Schematics of the compartmental structure and ion channel distribution in the model (the axon is only partly represented). All compartments are modeled as cylinders (Rall 1968) and their length and diameter (in μm) are indicated. Inset: the voltage transient elicited by a short current pulse (arrow) injected into the soma. Note the biphasic voltage decay (gray trace), from which the time constants τ_m and τ₁ were estimated through bi-exponential fitting (dashed black trace). B: the plots show average firing frequency (left) and 1st-spike latency (right) during injection of depolarizing current steps in the soma. Inset traces: the response of the model to 10-, 15-, and 20-pA current injection.

FIG. 6.

Na⁺ currents in the model. A: Na⁺ current generated in the model by stepping from −80 to 20 mV in 10-mV steps. Note the marked clamp escape around activation threshold (the −45-mV trace is indicated). Inset: the current transient elicited by a short voltage pulse injected into the soma either in the presence (black trace) or in the absence (gray trace) of the axon. The axon adds a slow component to the transient. B: I-V plots with different sodium channel distributions. The I-V plots are obtained either with control channel distribution (H/A_Na = 0.5, H/A_KV = 0.5, see Fig. 7), or with channels only in the hillock, or with channels only in the axon. In these panels, the simulated currents have been filtered to suit the typical response frequency of voltage-clamp recordings (−3 dB low-pass filtering at 1.6 kHz, see methods).

FIG. 7.

Effects of Na⁺ and K⁺ channel localization. A: spike firing with different axonal sodium channel distributions. Leftmost plot: irregular spikelets when all channels are in the axon (H/A_Na = 0). Central plot: the case when H/A_Na = 0.5: this model generates regular repetitive firing with almost no adaptation. Rightmost plot: the model response when all channels are in hillock (H/A_Na = 1). All the traces were obtained by injecting a 10-pA current pulse in the soma. B, left: variation of spike amplitude vs. H/A_Na ratio. The dotted line corresponds to the control case where H/A_Na = 0.5. Right: variation of spike propagation velocity vs. H/A_Na ratio. The data correspond to spikes elicited by a 10-pA current pulse in the soma. The drawings illustrate the direction of axonal spike transmission, which is active for H/A_Na< 0.5 and passive for H/A_Na> 0.6. C, left: variation of spike amplitude vs. H/A_KV ratio. The dotted line corresponds to the control case where H/A_KV = 0.5. Right: variation of spike propagation velocity vs. H/A_KV ratio. The data correspond to spikes elicited by a 10-pA current pulse in the soma. The drawings illustrate the direction of axonal spike transmission, which is active for all H/A_KV values.

FIG. 8.

Action potential generation and propagation. A spike was elicited by synchronously activating 3 excitatory synapses (initial potential = −70 mV) and membrane potential was recorded at different locations. A: the whole somato-dendritic compartment charged almost simultaneously before a spike was elicited in the axon. Then the spike back-propagated into the somato-dendritic compartment. The axonal spike was larger than in the rest of the neuron. Inset: the spike upstroke on an enlarged scale. A very similar picture could be drawn for spikes elicited by step current injection (not shown). B: the model was implemented with parallel fibers demonstrating that the initiation site remains in the ascending axon. Then the spike actively propagates along the parallel fibers and toward the soma and dendrites. The distance from spike initiation site and the conduction time are indicated.

FIG. 9.

Excitatory and inhibitory postsynaptic potential (EPSP and IPSP) transmission. A: EPSPs shown at the left were generated by activating 2 excitatory synaptic inputs (dendrite 1 and 2). To represent a more natural condition, the traces at the right show model responses to a combination of excitatory (dendrite 1 and 2) and inhibitory (dendrite 2) synaptic inputs. The inhibitory synapse is activated 4 ms after the excitatory synapses to respect the delay in the feed-forward Golgi cell–granule cell loop. Both in the absence and presence of inhibition, the model depolarization in dendrite 2 is almost indistinguishable from that in dendrite 4 (that was inactive) and in the soma, hillock and axonal compartments. Superimposition of traces demonstrates their remarkable similarity and absence of relevant electrotonic decay. B: EPSPs were elicited by activating 2 excitatory synapses. Selective conductance switch-off shows that EPSPs are indeed amplified and protracted by Na⁺ and N-methyl-d-aspartate currents activating in the immediate subthreshold region. However, EPSP amplification was of little effect on potential transmission into the axon.

FIG. 10.

Synaptic integration. The traces show model responses to bursts of spikes in the mossy fibers (5 impulses at 300 Hz). Release probability at the excitatory synapses (from 0.1 to 0.8) and synaptic inhibition (1 to 3 spikes at 200 Hz) regulated the duration and intensity of the discharge. In the simulations, 3 excitatory and 3 inhibitory synapses are activated. All simulations were done from the initial potential of −70 mV.