For synaptic currents, Isyn of MLIs represents the total excitatory input arriving from GCs. Isyn of PCs receives excitatory input from GCs and inhibition input from MLIs. Isyn of GCs represents excitatory input from mossy fibers (MFs). All the synaptic currents were modeled with a similar form as:

where Esyn = 0 mV is for excitatory AMPA and NMDA synapses, and Esyn = −80 mV is for inhibitory GABA synapses. The scaling factor Y is a nonlinear voltage-dependent function for NMDA: Y = 1/(1+ exp(−(V − 84)/38)). Otherwise, Y = 1 for other types of synaptic receptors.

The gating variable r was described by

where, Ru is to represent short-term synaptic plasticity with a simple phenomenological model that describes the kinetics of plasticity, such that it treats short-term depression and facilitation as two independent variables, R and u, respectively [20, 28].

Totally, we mainly used four types of synaptic connections between neurons: the excitatory MF-GC, GC-MLI, and GC-PC synapses, and the inhibitory MLI-PC synapse. All types of synapses show a varying heterogeneity of short-term plasticity with mixed fast and slow time scales. When STP is switched off for GC-PC and MLI-PC synapse, the variables R = 1 and u = U are held fixed without dynamic updates. Synaptic delays in all synapse are included as 1 ms. In addition, MLI-PC synaptic delays are heterogeneous with a Gaussian distribution (mean as 1 ms and SD as 0.2 ms). In case of studying the effect of recurrent inhibition, the MLI-MLI inhibitory synapse was also included. Synaptic parameters for each type of synapse in the model were constrained by experimental measurements as shown in Fig 1B [12, 15, 22, 29]. Postsynaptic currents recorded with current clamps at PCs from experimental data were fitted by models. Specifically, we used the following data: the postsynaptic GC-MLI current under a 10-spike stimulation clamped at -60 mV for MLIs [19]; unitary GC-PC current clamped at -70 mV for PCs [22]; unitary MLI-PC current clamped at 0 mV for PCs [12]; unitary MLI-MLI current clamped at -50 mV for MLIs [30]. The parameters values are described in Table 2. Through the study, two key parameters are focused: the MLI-PC synaptic weight WMLI for varying inhibition strength; the initial efficiency Uexc of GC-PC synapses for varying excitation strength. By default, we set WMLI = 3.5 nS and Uexc = 0.4 as guided by experimental data in Fig 1, unless those values mentioned differently in the work below. To further analyze the impact of MLI inhibition on PC network dynamics, we also systematically varied the initial efficiency Uinh for MLI-PC synaptic STP.

(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).

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