Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum

Abstract

The functional properties of cerebellar stellate cells and the way they regulate molecular layer activity are still unclear. We have measured stellate cells electroresponsiveness and their activation by parallel fiber bursts. Stellate cells showed intrinsic pacemaking, along with characteristic responses to depolarization and hyperpolarization, and showed a marked short-term facilitation during repetitive parallel fiber transmission. Spikes were emitted after a lag and only at high frequency, making stellate cells to operate as delay-high-pass filters. A detailed computational model summarizing these physiological properties allowed to explore different functional configurations of the parallel fiber-stellate cell-Purkinje cell circuit. Simulations showed that, following parallel fiber stimulation, Purkinje cells almost linearly increased their response with input frequency, but such an increase was inhibited by stellate cells, which leveled the Purkinje cell gain curve to its 4 Hz value. When reciprocal inhibitory connections between stellate cells were activated, the control of stellate cells over Purkinje cell discharge was maintained only at very high frequencies. These simulations thus predict a new role for stellate cells, which could endow the molecular layer with low-pass and band-pass filtering properties regulating Purkinje cell gain and, along with this, also burst delay and the burst-pause responses pattern.

Figure 1

Stellate cell morphological reconstruction. (A) Confocal microscopy imaging of four mouse SCs filled with Lucifer yellow (scale bar 10 μm) are shown along with the corresponding digital reconstruction with Neurolucida (visualization with Vaa3D simulator; right). The 3D morphological reconstructions of SCs include dendrites (blue), soma (black), AIS (green) and axon (red). (B) The SC model is divided into five electrotonic compartments and endowed with specific ionic mechanisms according to immunohistochemical data. The proximal and distal dendrites are distinguished at the cut-off diameter of 0.6 µm. Ionic channels include Na⁺, K⁺ and Ca²⁺ channels and a Ca²⁺ buffering system.

Figure 2

Pacemaking activity. (A) Pacemaker activity during SC WCR (n = 9; black) and in the model (n = 4; blue) taken at different times (traces taken starting at 2 s and 6 s). The inset shows a simulated and an experimental spike superimposed. (B) Distribution of the ISI of spontaneously firing SCs in WCR over 10 s. Note that the ISI in the model (blue bar; n = 4) falls within the experimental data distribution (black bar; n = 9, p = 0.8). (C) Relationships among ISI parameters. Note that the model data points (blue circles; n = 4) fall within the distribution of spike amplitude vs. spike threshold measured experimentally (black circles; n = 9). The model did not significantly differ from the experimental data (p = 0.64). Data are reported as mean ± SEM.

Figure 3

Response to hyperpolarization and depolarization. (A) A WCR from a SC 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 show that the model could faithfully reproduce sagging inward rectification and rebound excitation (blue trace). The enlarged trace on top shows how the first spike delay and the first ISI were determined. At the bottom, the time course of instantaneous spike frequency for a − 16 pA current pulse. The box-and-whisker plot compares the sag decay time constant obtained in experiments (n = 6) and simulations (n = 4) without revealing statistically significant difference (unpaired t-test, p = 0.4) (B) The plots report the time to first spike and the first ISI during rebound excitation as a function of sag amplitude (black circles; n = 5). Note that the model (blue circles; n = 4) did not significantly differ from the experimental data (p = 0.32). Data are reported as mean ± SEM. (C) A WCR from a SC shows the firing frequency and the pause following depolarizing current step (16 pA). The time course of instantaneous spike frequency for the 16-pA current pulse is shown below. Simulations show that the model could faithfully reproduce this behavior (blue traces). (D) In the plots, the response of the model (blue circles; n = 4) to current injections (from -16 to 20 pA) is compared to experimental data (black circles; n = 5). Simulations show that the model could appropriately fit the experimental measurements of spike frequency versus injected current (16 pA: p = 0.097) and of pause versus injected current (16 pA: p = 0.69). Data are reported as mean ± SEM.

Figure 4

Short-term plasticity at PF-SC synapses. (A) EPSCs recorded from the SC during 50, 100 and 200 Hz parallel fiber stimulations (n = 6). Cells were voltage-clamped at − 70 mV and in the presence of gabazine. Each trace (black) is an average of 10 sweeps. Note that EPSC trains showed first facilitation and then depression. Simulations show that the model could faithfully reproduce the same behavior (blue traces; n = 4). (B) Comparison of peak amplitudes of experimental and simulated EPSCs during high-frequency parallel fiber stimulation. Amplitudes are normalized to the first EPSC in the train (correlation coefficient R² @ 50 Hz = 0.80; @ 100 Hz = 0.90; @ 200 Hz = 0.84). Data are reported as mean ± SEM.

Figure 5

Burst currents at PF-SC and PF-PC cell synapses. (A) The traces show simulated SC EPSCs during trains of 20 stimuli delivered to PFs at different frequencies (4, 10, 20, 50, 100, 200 and 500 Hz; n = 4). Inset, NMDA, AMPA and NMDA + AMPA currents at 200 Hz. (B) The traces show simulated PC EPSCs during trains of 20 stimuli delivered to PFs at different frequencies (4, 10, 20, 50, 100, 200 and 500 Hz). (C) Gain curve for SC (blue circles; n = 4 for each frequency) and PC (red squares) responses with respect to input burst frequency. Gain is the ratio between the maximum response obtained at a certain frequency and the first EPSC. The gain curves show a sigmoidal shape with 50% amplitude around 50 Hz for the SC and around 10 Hz for the PC. Data in C corresponds to the cells in A and B.

Figure 6

Frequency-dependence of SC input–output gain function. (A) The traces show a SC burst in response to 10 pulses @ 100 Hz-delivered to PFs (black trace) and the corresponding simulation (blue trace). Inset (left), calibration of the number of PF-SC synapses required to obtain a given burst frequency (3 in the example). Inset (right), the synaptic current (AMPA + NMDA) corresponding to the simulated burst. (B) The histogram shows the time course of the SC burst shown in A in response to 10 pulses @ 100 Hz-delivered to PFs (black trace) and the corresponding simulation (blue trace). Note the about 50 ms delay to burst response. (C) The array of PSTHs shows the SC responses to PF bursts at different frequencies (10 pulses @ 4 Hz, 10 Hz, 20 Hz, 50 Hz, 100 Hz, 200 Hz, 500 Hz). Note that pronounced spike bursts were generated at high frequencies (e.g. at 100 Hz). (D) Input/output SC gain for experimental (black, n = 5) and simulated bursts (blue, n = 4). SCs did not increase their spike output frequency until about 10 Hz, then their responses increased and tended to saturate beyond 100 Hz. Note the superposition of the single experimental data point and simulated data (asterisk). The simulation was repeated after the switch-off of STF (τ_facil = 10 times the original) and STD (τ_rec = 0), revealing their critical role for the frequency-dependence of the input–output function. Data in B and D are reported as mean ± SEM (n = 4).

Figure 7

Regulation of SC gain function by NMDA and GABA_A receptors. (A) The traces show simulated SC response to 10 pulses @ 100 Hz-delivered to PFs. NMDA receptor switch-off and activation of inhibitory (32) synapses activated simultaneously with the PF burst reduced SC firing rate. Black bar indicates the stimulus duration. (B) Input/output SC gain regulation. Note that the NMDA current block reduced the spike output frequency mostly during high-frequency bursts (200–500 Hz), while a sufficient number of inhibitory synapses (activated simultaneously with PF bursts) shifted SC excitation toward higher input frequencies. Data are reported as mean ± SEM (n = 4).

Figure 8

Prediction of SC filtering of PC responses along the PFs. (A) Schematics of the afferent connections to a PC activated by PF stimulation. Granule cell (GrC); parallel fiber (PF); stellate cell (SC); Purkinje cell (PC). The figure highlights the interactions of elements in the cerebellar molecular layer and the location of afferent PC synapses. (B) The traces show simulated PC response to 10 pulses at different frequencies (10, 200 and 500 Hz) delivered to 100 PFs in which (i) SCs were not activated (SC off), (ii) 100 SC synapses were activated (SC – > PC) and (iii) 100 SC synapses received inhibition from 32 SC synapses (SC – > SC – > PC). Black bar indicates the stimulus duration. (C) Input/output PC burst frequency gain (top) and pause length (bottom). Different curves are obtained using PF trains at different frequency (10 pulses @ 4 Hz, 10 Hz, 20 Hz, 50 Hz, 100 Hz, 200 Hz, 500 Hz) and an increasing number of inhibitory synapses. Dotted traces also include the case of SC-SC inhibition. Note that PC burst and pause showed an almost opposite modulation by SCs. (D) The histogram shows the regulation of PC firing frequency when SCs are off, on and reciprocally inhibited. Note that reciprocal SC inhibition can abolish the effect of SCs on PCs.