Transient synaptic redundancy in the developing cerebellum and isostatic random stacking of hard spheres

We propose an automaton for the simulation of the distribution of the number of climbing fibers (CF) making synapses on each Purkinje cell (PC) at the maximum of the synaptic redundancy that exists transiently in the newborn cerebellum. This automaton is based on the hypothesis that the synaptic maximum is limited by topological constraints and can be described by an isostatic random stacking of hard spheres. There is convincing agreement between the simulated distribution of the number of CF axons per Purkinje cell and the distribution experimentally obtained by electrophysiological techniques.