Table 1.
The parameters of single cell models.
Fig 1.
PC dynamics controlled by excitation and inhibition.
(A) Schematic illustration of feedforward excitatory GC-PC short-term plasticity (STP) pathway and inhibitory GC-MLI-PC pathway on a PC. Granular cells (GCs, red), molecular intermediate neurons (MLIs, blue) and Purkinje cells (PCs, black). (B) Postsynaptic currents of four types of synapses from experimental data fitted by models. (C) The PC network with 50 PCs (black), 1000 GCs (red), and 500 MLIs (blue). For illustration, only 3 PCs are shown. (D) PC in response to the GC-PC input. (Left) EPSPs triggered by a single GC spike by varying GC-PC synaptic STP amplitudes Uexc (0.05–0.75 with a 0.05 increment). (Middle) EPSPs triggered by a train of 10 spikes at 200 Hz at two different values of U: Uexc = 0.06 for facilitation and Uexc = 0.42 for depression, with (light blue) and without (purple) STP switched on. (Right) STP described by the ratio EPSPn/EPSP1 showing facilitation or depression in a train of a varying number of burst spikes under different U (0.02-0.7, fixed burst frequency at 200 Hz). (E) Similar to D but for IPSPs triggered by the MLI-PC input. Single IPSPs induced by different strengths WMLI (0.5–7 with a 0.5 increment).
Table 2.
Synaptic parameters for each synapse in the model.
Fig 2.
Inhibition-mediated gain modulation of PC firing dynamics enhanced by excitatory short-term plasticity.
(A) (Top) Sum of excitatory conductance Gexc onto a PC in the baseline condition (STP off) and a test condition with STP. The input is 100 independent synaptic trains using Poisson stimulation at 50 Hz. (Bottom) PC membrane potential traces with and without STP. Vertical ticks indicate spike times. (B) Average Gexc changing over a range of GC rates with and without STP. Gexc was averaged over the time course and all GCs connected to a PC. (C) PC input-output relationship in four conditions, with/without STP and/or MLI. Each point is mean±SD (n = 50). Poisson stimulation was used. Lines in (B) and (C) are fits to a Hill function. (D) Heterogeneous gain and offset changes due to STP (±STD) and MLI (±MLI) from fits in (C).
Fig 3.
The gain change of PC firing significantly depending on GC-PC STP.
(A) PC firing modulated by different levels of MLI inhibition strength without STP (top) and with STP (bottom) at Uexc = 0.4. (B) Excitatory conductance modulated by different levels of GC-PC synaptic efficacy Uexc without STP (top) and with STP (bottom).
Fig 4.
PC phase modulation affected by MLI and STP.
(A) PC population firing rate (n = 50) in response to GC inputs sinusoidally-modulated with 1, 10, 20 and 30 Hz, from 100 independent input spike trains. Solid color lines are fitted with sinusoidal functions. (B) Normalized fitting curves from (A) show phase shifts relative to the input. (C) Phase shift as a function of input frequency in four different conditions (left), and the corresponding changes of phase shifts relative to the baseline (right). (D) Phase shift changed over a range of excitation Uexc and inhibition WMLI. (Left) Phase shift over a sequence of input frequencies with different levels of excitation and inhibition in three conditions. (Right) Phase shift changed by combined MLI and STP, where each inner rectangle represents a PC phase shift spectrum over the same sequence of input frequencies (0-30 Hz).
Fig 5.
PC phase modulated by timescales of short-term dynamics of GC-PC synapses.
(A) Histograms of spikes in GCs (top) and PCs (bottom) in response to an input spike train sinusoidally-modulated at 10 Hz, with three examples of time constants of recovery τrec (fixed τfac = 400 ms) and facilitation τfac (fixed τrec = 50 ms). (B) Phase shift as a function of input frequency for (left) τrec and (right) τfac, with similar settings as in (A). (C) Phase shift in the parameter space of τrec and τfac. Each inner rectangle represents a PC phase shift spectrum changing over different modulation frequencies (0-30 Hz).
Fig 6.
PC temporal spike patterns affected by MLI and STP.
(A) Schematic illustration of feedforward MLI inhibition and GC excitation when GC-PC STP is off. (B) PC membrane potential traces gradually delayed by different levels of MLI inhibition with an input of 10 Hz Poisson spikes. (C, D) Similar to (A, B) but for MLI off and STP on with varying excitation at different levels of Uexc. (E) Interspike interval (ISI) distribution of the population PC spikes under four different settings with/without excitatory STP and/or MLI (left). (Right) The change of ISI, CV (coefficient of variation), and CoV2 (local regularity) over a range of GC inputs, averaged over the population of PCs (mean±SD, n = 50).
Fig 7.
PC network dynamics in response to burst input.
(A) Schematic illustration of GC-PC and GC-MLI-PC pathways receiving burst inputs. (Left) GCs stimulated by bursts with 3 and 7 spikes at 100 Hz. (Right) EPSPs and EPSCs recorded from PCs for different burst inputs in the baseline condition (red) and with STP on (green). (B) GC spike raster triggered by a burst input of 5 spikes at 200 Hz, only 50 GCs are shown (top). (Bottom) The corresponding spike rasters of 50 PCs (left), and averaged PC population firing profiles in different conditions. Note that the pause response indicated as the time interval between two arrows in the condition of +STP+MLI only.
Fig 8.
PC synchronization controlled by excitation and inhibition.
(A) PC population firing rate in different conditions. (Right) The corresponding MLI population firing rate when MLIs are triggered by GCs. The burst input here is 10 spikes at 50Hz. (B) Time course of PC network synchronization computed from the population PC firing rate, in response to input bursts with 10 spikes at 50, 100, 200 and 300 Hz under different conditions. (Right) The corresponding time course of MLI population synchronization. (C) Similar to (B) but for burst inputs at 200 Hz with 2, 5 and 7 spikes, respectively. Colored shadows indicate burst duration. The background noise are Poisson spikes at 20Hz. The time scale bar in (A) applied in all the plots.
Fig 9.
The change of PC synchronization and pause response in the parameter space of excitation and inhibition.
(A) The gain of synchronization changed in different ways with WMLI and Uexc under bursts with different spikes and frequencies. Each inner rectangle in each panel represents a single gain value of synchronization under one burst protocol. (Top) Bursts with 2, 5 and 7 spikes at 200 Hz. (Bottom) Bursts with 10 spikes at 50, 100, 200 and 300 Hz. In all plots, note that there is no STP but static excitation with Uexc = 0.4 in the last row of the matrix. Similarly, there is no MLI inhibition in the first column of the matrix. Thus the first point at the left-bottom corner of the matrix is the baseline. The gain was defined as the relative change calculated by the average Knet compared to that in the baseline. (B) Similar to (A) but for pause response induced by bursts.
Fig 10.
PC synchronization is controlled by STP of both excitation and inhibition, whereas PC pause response is less dependent on STP of inhibition.
(A) The gain of synchronization regulated differently by STP of ML-PC inhibition Uinh and excitation GC-PC Uexc under bursts with different spikes and frequencies. Each inner rectangle in each panel represents the gain of network synchronization under one burst protocol. (Top) Bursts with 2, 5 and 7 spikes at fixed 200 Hz. (Bottom) Bursts with 10 spikes at 50, 100, 200 and 300 Hz. Note that the gain was defined as the relative change calculated by the average Knet with STP subtracted by that without STP. (B) Similar to (A) but for pause duration induced by bursts.
Fig 11.
PC synchronization and pause response controlled by MLI inhibition.
(A) PC network with no recurrent MLI inhibition. (Left) Illustration of the PC network receiving different numbers of MLIs. PC synchronization (top) and pause response (bottom) affected by MLI inhibition with stronger weight or more number of MLI-PC synaptic connections per PC, under burst inputs with different spikes and frequencies. Inner rectangles in each panel represent the gain of synchronization under one burst protocol. The gain of synchronization was defined as the relative change of the average Knet. (B) Similar to (A) but for the PC network with recurrent MLIs included, such that each MLI receives 1-8 MLIs recurrently. Here in all plots, each PC receives 8 MLIs.