Single cell models

PCs and MLIs were modeled as modified integrate-and-fire neurons [25] that were also used for modelling of cerebellar cells [26]. The membrane potential V obeys the equation:

where C_m is membrane capacitance, g_L is leak conductance and E_L is leak resting potential. The sodium current was given by I_Na = −g_LΔT exp[(V − V_T)/ΔT] with ΔT = 3 mV and the firing threshold V_T drawn randomly for each neuron using a Gaussian distribution. When the membrane potential reaches the threshold V_T at the spike t_spk, V is set to 40 mV for a duration of the spike as τ_dur = 0.6 ms. After the spike, at t = t_spk + τ_dur, repolarizing potential is set to V_rest, and an afterhyperpolarization (AHP) conductance is activated. The gating variable z_AHP follows the dynamics dz_AHP/dt = (1 − z_AHP)/x_AHP − z_AHP/τ_AHP. The resource variable x_AHP obeys the dynamics dxAHP/dt=-xAHP/τAHPx+δ(t-tspike-τdur), where τAHPx=1 ms. The refractory period is set as t_ref = 2 ms. To mimic the ongoing activity in our simple point neuron models, a noisy excitatory current I_noise = (V − V_E)g_N was injected with a slowly fluctuating conductance g_N, described by an Ornstein-Uhlenbeck process, τNdgN/dt=-gN+σNτNb(t), where σ_N = 0.12 nS, τ_N = 1000 ms, and b(t) is white noise with unit variance density.

Similarly, GCs were modeled as previously based on experimental data [15], whose membrane potential V obeys the equation:

where the model components have the similar meanings as the PC and MLI model. All the parameters of neural models of PCs, MLIs, and GCs have the same values, except those listed in Table 1, where the adjustment of parameters for individual cell types were based on previous studies [8, 15, 18, 27].