In the granular layer of the cerebellum, the population of excitatory neurons (granule cells) is reciprocally connected tot he population of inhibitory neurons (Golgi cells), but there are no synapses between the neurons within either population. In a realistic network model, bth Golgi and granule cells start firing synchronlusly and at very regular time intervals upon stimulation of granule cells with random mossy fiber input ([3]). Because the granule cell population is disproportionately large, we wondered whether the massive convergence from granule to Golgi cells were essential to obtain this regular firing pattern. Here, we demonstrate that only a small, critical number of synapses from granule to Golgi cells is required. The critical number of synapses is largely independent of the size of the granule cell population, but depends on the number of input channels to the network (the number of mossy fibers), on the strength of the input applied (the mossy fiber firing rate), and on its spatial homogeneity.
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