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 Cm is membrane capacitance, gL is leak conductance and EL is leak resting potential. The sodium current was given by INa = −gLΔT exp[(VVT)/ΔT] with ΔT = 3 mV and the firing threshold VT drawn randomly for each neuron using a Gaussian distribution. When the membrane potential reaches the threshold VT at the spike tspk, V is set to 40 mV for a duration of the spike as τdur = 0.6 ms. After the spike, at t = tspk + τdur, repolarizing potential is set to Vrest, and an afterhyperpolarization (AHP) conductance is activated. The gating variable zAHP follows the dynamics dzAHP/dt = (1 − zAHP)/xAHPzAHP/τAHP. The resource variable xAHP obeys the dynamics dxAHP/dt=-xAHP/τAHPx+δ(t-tspike-τdur), where τAHPx=1 ms. The refractory period is set as tref = 2 ms. To mimic the ongoing activity in our simple point neuron models, a noisy excitatory current Inoise = (VVE)gN was injected with a slowly fluctuating conductance gN, described by an Ornstein-Uhlenbeck process, τNdgN/dt=-gN+σNτNb(t), where σN = 0.12 nS, τN = 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].

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