Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells

Abstract

The Golgi cells have been recently shown to beat regularly in vitro (Forti et al., 2006. J. Physiol. 574, 711-729). Four main currents were shown to be involved, namely a persistent sodium current (I(Na-p)), an h current (I(h)), an SK-type calcium-dependent potassium current (I(K-AHP)), and a slow M-like potassium current (I(K-slow)). These ionic currents could take part, together with others, also to different aspects of neuronal excitability like responses to depolarizing and hyperpolarizing current injection. However, the ionic mechanisms and their interactions remained largely hypothetical. In this work, we have investigated the mechanisms of Golgi cell excitability by developing a computational model. The model predicts that pacemaking is sustained by subthreshold oscillations tightly coupled to spikes. I(Na-p) and I(K-slow) emerged as the critical determinants of oscillations. I(h) also played a role by setting the oscillatory mechanism into the appropriate membrane potential range. I(K-AHP), though taking part to the oscillation, appeared primarily involved in regulating the ISI following spikes. The combination with other currents, in particular a resurgent sodium current (I(Na-r)) and an A-current (I(K-A)), allowed a precise regulation of response frequency and delay. These results provide a coherent reconstruction of the ionic mechanisms determining Golgi cell intrinsic electroresponsiveness and suggests important implications for cerebellar signal processing, which will be fully developed in a companion paper (Solinas et al., 2008. Front. Neurosci. 2:4).

Keywords: Golgi cell; cerebellum; granular layer; modeling; pacemaking.

Figure 1

Passive Golgi cell properties. (A) Schematics of the minimal model built to reproduce cerebellar Golgi cell electroresponsiveness. The model has a spherical soma and processes representing the dendrites and axon. The soma is connected to a micropipette to simulate realistic recording conditions. (B) The recording (black trace) shows a current transient elicited in a Golgi cell by a 50-ms voltage step from −70 to −80 mV. The model (gray trace) faithfully matches the response. The plot shows the relationship between input resistance (R_in ) and input capacitance (C_in) in 39 Golgi cells (black circles, the larger one corresponding to the trace shown on top). The model prediction (large gray dot) falls in the middle of the experimental data distribution (p > 0.8, t-test).

Figure 2

Pacemaking. (A) Pacemaker activity during Golgi cell WCR (black) and in the model (gray). (B) Enlarged view of interspike interval (ISI) taken from A. The model (leakage reversal potential −62 mV) faithfully follows the membrane potential of this specific Golgi cell. (C) Distribution of the ISI of spontaneously firing Golgi cells (mean of 20–50 ISI per cell; n = 32) during WCR. Note that the ISI in the model (gray bar) falls on the mode of the experimental data distribution. (D) Relationships among ISI parameters. Note that the model data points (large gray dots) fall within the distribution of spike amplitude versus spike threshold and within the distribution of AHP trough versus AHP rise-time measured experimentally (black circles, the larger ones corresponding to the trace in A–B). The model did not significantly differ from the data (p > 0.12, t-test). (E) The experimental relationship between CV_ISI and firing rate (n = 47 WCR) showed a negative correlation. The model was injected with a noisy current (32 pA SD, see Methods) and the spontaneous frequency was varied among the values observed during WCRs by changing the leakage reversal potential from −67 to −55 mV. Simulations (gray line) show that the model could appropriately fit the experimental measurements.

Figure 3

The response to hyperpolarization and rebound excitation. (A) The WCR from a Golgi cell shows sagging inward rectification in response to hyperpolarizing current injection and, at the end of the hyperpolarization, rebound excitation with an early and a protracted phase of intensified firing. Simulations of this specific experiment (parameters were adjusted to mimic the experimental trace in detail: leakage reversal potential −64.5 mV, I_K-slow 90%, I_h-HCN1 60 %, I_h-HCN2 12.5 % of their value in the canonical model) show that the model could faithfully reproduce sagging inward rectification and rebound excitation (gray trace). The step-current protocol is shown at the bottom. (B) The plots report the time to first spike and the first ISI during rebound excitation as a function of sag amplitude in 10 Golgi cells (black circles, the larger one corresponding to the trace in A) stimulated using the protocol shown in A. Note that the canonical model (large gray dots) did not significantly differ from the data (p > 0.13, t-test). Even the model adjusted to match the specific trace shown in A (large gray circle, see details reported in A) falls within the experimental data scatter.

Figure 4

The response to depolarization. (A) The traces taken from a WCR in a Golgi cell show that firing frequency and adaptation increase with the intensity of current injection (from top to bottom: 150, 250, 350 pA). Simulations show that the model could faithfully reproduce this behavior (gray traces). Both the real cell and the model were held at −70 mV by injecting a hyperpolarizing current to prevent spontaneous firing (the step-current protocol is shown at the bottom). (B) In the plots, the response of the model (solid gray line) to current injection is compared to the data collected in experimental recordings (dots; n = 10 Golgi cells). Simulations (gray lines) show that the model could appropriately fit the experimental measurements of:

1. first spike delay versus injected current (left: p > 0.1, t-test)

2. instantaneous and steady-state frequency (the inverse of the first and last ISI, experimental data correspond to black dots and diamonds, modeling data correspond to solid and dashed gray lines, respectively) versus injected current (middle plot: p > 0.1, t-test)

3. the adaptation factor (last ISI/first ISI) versus initial firing rate (p > 0.9, t-test).

Figure 5

Pharmacology of pacemaking. The model predicted the effect of ionic channel blockage (Forti et al., 2006) on autorhythmic firing. (A) In these simulations, the control trace shows autorhythmic firing (same as in Figure 1A, firing rate 5 Hz, CV_ISI = 0.0027), a 50% block of I_h (mimicking the effect of ZD7288) reduces the pacemaker frequency by 27%, and the partial block of I_Na-p prevents spontaneous firing. (B) In order to simulate retigabine effects on I_K-slow reported by Forti et al., (2006), I_K-slow was modified by shifting its activation by −6.5 mV (from Tatulian et al., 2001). The model was then stimulated with 1-second current steps (100 pA) from -70 mV. The traces show that, following I_K-slow changes, the model fires less action potentials than in control. The model response to current injection is shown for control (full squares) and I_K-slow -shift conditions (empty squares). (C) The effect of membrane noise on firing was simulated by injecting Gaussian noise into the canonical model. In control conditions, the mean firing rate was unaffected, but CV_ISI was increased from 0.002 to 0.16. When I_K-AHP was blocked, the mean firing rate did not significantly change (from 5 to 5.7 Hz, p > 0.05, t-test). Conversely, CV_ISI changed from 0.16 to 0.36 (cf. Forti et al., 2006). The traces show that pacemaker irregularity is markedly increased by I_K-AHP blockage (the dashed lines indicate the −70 mV level).

Figure 6

Ionic currents and intracellular calcium changes. (A) The traces show the model response during alternated phases of pacemaking, depolarization, and hyperpolarization (the injected current is shown at the bottom). The voltage trace (Vm) shows the membrane potential change. The current traces (Im) show the ionic currents in the ISI. It should be noted that I_Na-p, I_K-AHP, and I_Kslow, but not I_h, show a marked voltage-dependent modulation during the pacemaker cycle. The calcium ([Ca²⁺]_i ) trace shows that [Ca²⁺]_i is promptly reset to its background level of 50 nM following a transient increase during the spike. The inset shows the [Ca²⁺]_i accumulation in coincidence with the high-frequency bursts and spike frequency adaptation. (B) The traces enlarge the model response during a single action potential (Vm). The ionic currents primarily responsible for action potential generation (Im) and the Ca²⁺currents (I_Ca-HVA) are shown along with the [Ca ²⁺] _i transient. Note the delayed activation of the repolarizing mechanisms and of the slow time course of [Ca²⁺]_i transient. I_Na-t, I_K-C, and I_K-V are much larger than currents governing the ISI (cf. panel A).

Figure 7

Ionic currents controlling response intensity and latency. (A) Effect of I_Na-r on the first two spikes elicited by a depolarizing current step. The model was hyperpolarized to −70 mV by tonic current injection and a step current injection of 600 pA elicited an initial firing rate of 200 Hz. I_Na-r block (middle trace) increased the first ISI (2 ms increase) reducing the initial firing rate to 142 Hz. I_Na-r did not affect the 1st spike latency but its activation after the 1st spike could accelerate membrane depolarization and generation of the 2nd spike. (B) The model was hyperpolarized to −70 mV by tonic current injection and then injected with a step current of 100 pA. The 1st spike latency was 18 ms and was reduced by I_KA blockage to 12 ms. The lower traces show the stimulus protocols.

Figure 8

Robustness of the model. Tests of robustness of the model against changes in individual parameters. Polar plot: The maximum conductance of I_K-slow, I_Na-p, I_KA, I_K-AHP, I_Ca-HVA, and I_h, as well as β_Ca, were modified in turn. The changes covered (in 30 steps) the range from total block (center of the polar plot) to threefold increase (outer solid circle) in the canonical model value (thick gray line). Model simulations were obtained using the protocols described in Figures 2–4. The thin black lines delimiting the light gray area show the minimum and maximum parameter changes (percentage of canonical model values), which maintained the model within the boundaries of Golgi cell characteristic response. Lower panels: Results were considered to conform to Golgi cell behavior on the base of five criteria. (i) The pacemaker frequency had to fall in the range 0.5–9 Hz. (ii) The first spike latency triggered by the rebound excitation had to fall in the range 30–100 ms. (iii–v) The response to current injection had to show first spike latency, initial firing rate, and spike frequency adaptation within the boundaries reported in the panels. Thin black lines are boundaries derived from the envelope of data points in Figure 4B and the thick gray line shows the canonical model behavior.

Figure 9

Subthreshold oscillations and spike coupling. In order to investigate the mechanisms of subthreshold oscillations, simulations were performed after blocking the currents generating the spike (I_Na-t, I_K-V, and I_K-C ). (A) The simulated traces show that preventing action potentials lead to the emergence of subthreshold pacemaker oscillations slightly slower than in the spiking regime (4.46 vs. 5 Hz). Upon 100% I_h blockage, the oscillation frequency is reduced (3.3 Hz) but the effect is reversed with the injection of a tonic depolarizing current (dashed trace). (B) The simulated traces (all voltage-dependent currents blocked except for I_Na-p, I_K-AHP, I_Ca-HVA, and I_K-slow) show that subthreshold pacemaker oscillations are interrupted by blocking I_Na-p and that only marginal recovery is obtained by injecting a tonic depolarizing current (dashed trace). Either blocking I_K-AHP or I_K-slow deforms the oscillation trajectory, while their simultaneous block causes the oscillation to cease. (C) The voltage and current traces are shown as a function of time during a full oscillation cycle (all voltage-dependent currents blocked except for I_Na-p, I_K-AHP, I_Ca-HVA, and I_K-slow ). (D) Schematic showing the cascade of processes that generate pacemaking in the Golgi model.