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We consider a cerebellar ring network for the optokinetic response (OKR), andinvestigate the effect of diverse recoding of granule (GR) cells on OKR byvarying the connection probability $p_c$ from Golgi to GR cells. For an optimalvalue of $p_c^*~(=0.06)$, individual GR cells exhibit diverse spiking patternswhich are in-phase, anti-phase, or complex out-of-phase with respect to theirpopulation-averaged firing activity. Then, these diversely-recoded signals viaparallel fibers (PFs) from GR cells are effectively depressed by theerror-teaching signals via climbing fibers from the inferior olive which arealso in-phase ones. Synaptic weights at in-phase PF-Purkinje cell (PC) synapsesof active GR cells are strongly depressed via strong long-term depression(LTD), while those at anti-phase and complex out-of-phase PF-PC synapses areweakly depressed through weak LTD. This kind of "effective" depression (i.e.,strong/weak LTD) at the PF-PC synapses causes a big modulation in firings ofPCs, which then exert effective inhibitory coordination on the vestibularnucleus (VN) neuron (which evokes OKR). For the firing of the VN neuron, thelearning gain degree ${\cal{L}}_g$, corresponding to the modulation gain ratio,increases with increasing the learning cycle, and it saturates at about the300th cycle. By varying $p_c$ from $p_c^*$, we find that a plot of saturatedlearning gain degree ${\cal L}_g^*$ versus $p_c$ forms a bell-shaped curve witha peak at $p_c^*$ (where the diversity degree in spiking patterns of GR cellsis also maximum). Consequently, the more diverse in recoding of GR cells, themore effective in motor learning for the OKR adaptation.

Effect of Diverse Recoding of Granule Cells on Optokinetic Response in A Cerebellar Ring Network with Synaptic Plasticity