Fast-reset of pacemaking and theta-frequency resonance patterns in cerebellar golgi cells: simulations of their impact in vivo

Abstract

The Golgi cells are inhibitory interneurons of the cerebellar granular layer, which respond to afferent stimulation in vivo with a burst-pause sequence interrupting their irregular background low-frequency firing (Vos et al., 1999a. Eur. J. Neurosci. 11, 2621-2634). However, Golgi cells in vitro are regular pacemakers (Forti et al., 2006. J. Physiol. 574, 711-729), raising the question how their ionic mechanisms could impact on responses during physiological activity. Using patch-clamp recordings in cerebellar slices we show that the pacemaker cycle can be suddenly reset by spikes, making the cell highly sensitive to input variations. Moreover, the neuron resonates around the pacemaker frequency, making it specifically sensitive to patterned stimulation in the theta-frequency band. Computational analysis based on a model developed to reproduce Golgi cell pacemaking (Solinas et al., 2008Front. Neurosci., 2:2) predicted that phase-reset required spike-triggered activation of SK channels and that resonance was sustained by a slow voltage-dependent potassium current and amplified by a persistent sodium current. Adding balanced synaptic noise to mimic the irregular discharge observed in vivo, we found that pacemaking converts into spontaneous irregular discharge, that phase-reset plays an important role in generating the burst-pause pattern evoked by sensory stimulation, and that repetitive stimulation at theta-frequency enhances the time-precision of spike coding in the burst. These results suggest that Golgi cell intrinsic properties exert a profound impact on time-dependent signal processing in the cerebellar granular layer.

Keywords: cerebellum; golgi cell; granular layer; modeling; phase-reset; resonance.

Figure 1

Phase reset of pacemaking. (A1 and B1) A Golgi cell recorded in LCA (black trace) shows autorhythmic firing when a single (A1) or four antidromic spikes at 50 Hz (B1) are elicited by axonal electrical stimulation (arrows). In different sweeps the stimulus was delivered at different phases of the pacemaker cycle. Nonetheless, following stimulation the Golgi cell is phase reset, i.e., restarts firing almost without memory of the preceding phase. The same behavior is observed in the model (gray traces) stimulated with 0.5 ms-long current pulses delivered at varying times during the ISI (the stimulus size is tuned as to inject the minimal charge required to elicit an AP according to the plot in Figure 2B). (A2 and B2) The plots show summary data from 13 and 6 Golgi cells, respectively, to which antidromic stimulation was applied. The time interval between the resetting stimuli and the subsequent spike (ISI_post ) is compared to the time interval preceding the stimulus (ISI_pre). Both ISI_pre and ISI_post were normalized by the average ISI of pacemaking (ISI_pace). ISI_post /ISI_pace was independent from ISI_pre . With 1 stimulus (B1) the correlation coefficient was −0.11 (not significantly different from 0, p > 0.18, t-test; average ISI_post/ISI_pace = 1.05). With four stimuli (B2) the correlation coefficient was 0.08 (not significantly different from 0, p > 0.7, t-test; average ISI_post /ISI_pace = 1.15). In either case, the model (gray traces) predicted the experimental results (p > 0.1, t-test). The experimental data were fitted using a single exponential function (solid black trace, dashed black traces show the 95% confidence limits).

Figure 2

The mechanisms of phase-reset. (A) Phase-reset simulations were performed on subthreshold oscillations after blocking all voltage-dependent currents except for I_Na-p, I_CaHVA, I_K-AHP, and I_K-slow . The simulations show that small current pulses (2 nA for 0.5 ms) do not alter the cycle, while larger perturbations (6.8 nA for 0.5 ms) reset the cycle of the subthreshold oscillation. The currents involved are shown at the bottom, revealing that currents comparable to those observed during spikes are generated only with the larger pulse. (B) The same protocol used in A was repetitively applied to the model by varying pulse width (Δt = 0.1-3 ms) and amplitude (ΔI = 0.1-2 nA). The plot shows ISI_post-pre /ISI_pace (cf. Figure 1) as a function of charge Q = ΔI · Δt. A sudden step in the plot indicates a sharp phase reset threshold. The EPSC and spike charges are also reported. The inset shows that one point in the plot corresponds to a hyperbolic trajectory in a stimulus strength-duration graph. (C) The phase-reset mechanism was explored by simulating block of specific ionic currents (control is with all ionic currents active, spikes are truncated for clarity). While in control simulations (upper trace) a spike-like perturbation resets the pacemaker phase, this does not occur after I_K-AHP blockage (note that in this condition the model fires short spike bursts). However, blocking I_K-slow or I_K-A (lower traces) does not alter the phase reset. It should be noted that the absence of noise in these simulations prevented the ISI irregularity that would have been introduced by I_K-AHP blockage in real cells (see Forti et al., ; Solinas et al., 2007).

Figure 3

Intrinsic theta-frequency resonance. Intrinsic resonance was investigated by injecting short (40 ms) current steps at frequencies between 0.3 and 15 Hz. (A) A Golgi cell (WCR) in the pacemaking regime is repetitively driven to fire bursts of action potentials by injecting sequences of short (40 ms) current pulses. The pulses are repeated 10 times at each frequency (from 0.3 to 15 Hz). (B) Responses are intensified and show a shorter latency around 3 Hz. This experimental observation as also the resonance effects shown in panels C and D are reproduced by the model. (C) The initial firing rate (the inverse of the first ISI) is shown for three Golgi cell WCRs. The curves show resonance at 2.6 Hz. (D) The response speed (the inverse of first spike latency) is shown for the same three Golgi cells reported in C. The curves show resonance at around 3 Hz.

Figure 4

The mechanisms of resonance. (A) I_K-AHP, I_K-slow, and I_Na-p were measured in the model during the resonance protocol shown in Figure 3(the mean values of I_K-AHP and I_K-slow were measured over the inter-pulse interval, the mean value of I_Na-p was measured over the first 5 ms of each depolarizing pulse). Note that I_K-slow decreases while I_Na-p increases in the resonance region (since I_Na-p has fast activation dynamics, its measure is disturbed by spikes) while I_K-AHP increases linearly with frequency. (B) In model simulations, resonance could be explored in the immediate subthreshold range (−65 mV) after blocking spike mechanisms (I_Na-t, I_K-V, and I_K-C ). The simulations show the ZAP response with all ionic current except for I_K-slow and I_Nap and after reintroducing I_K-slow and I_Na-p (50% for graphical reasons) in sequence. The corresponding impedance profiles are shown at the right. The simulations show that I_K-slow generates and I_Na-p amplifies resonance in the theta-frequency range.

Figure 5

The effect of noise on pacemaking. (A) Pacemaking in the model was perturbed by injecting random balanced synaptic currents causing a marked ISI irregularity. (B) The autocorrelogram of a 60-second long simulation shows that the random synaptic input cancels the regularity of the pacemaker cycle.

Figure 6

The effect of noise on phase-reset. (A) The model perturbed with balanced synaptic noise was stimulated by either 5-ms long or 30-ms long current pulses of 800 pA (lower traces show the stimulation protocols) to elicit a singlet or a triplet of spikes, respectively. Visual inspection shows an evident silent pause with the triplet but not with the singlet. (B) The PSTH for singlet shows a brief pause partly populated by spikes. The PSTH for triplets shows a pause roughly corresponding to the average pacemaker cycle free from any spikes. The insets show that the silent pause is short and unreliable with a singlet but not with a triplet. The bottom panel shows data recorded in vivo following vibrissal stimulation in the anaesthetized rat, which cause a brief spike sequence followed by a silent pause. Note the remarkable similarity between in vivo recordings and the model (triplet).

Figure 7

The effect of noise on resonance.(A) The resonance protocol reported in Figure 3 was also applied to the model perturbed with synaptic noise. The traces show the response to 800 pA current pulses taken from a sequence in which stimuli are delivered at increasing frequency. The traces at 6.2 Hz show greater precision of spike timing. (B) The plots show data from four simulations with different random seeds (there are four black circles for each tested stimulation frequency). The initial firing rate and the first spike delay do no longer show a clear resonance. However, the standard deviation of the first spike delay is clearly resonant with a peak at stimulation frequencies around 6 Hz.