Firing rates of neurons with random excitation and inhibition.

Abstract The expectation of the interspike interval for a Stein model neuron receiving Poisson excitation and inhibition is determined by solving a differential difference equation with both forward and backward differences. The method of solution relies on an asymptotic expansion at large initial hyperpolarizations. The asymptotic solution is continued to near threshold depolarization whereupon the boundary condition is employed along with recursion relations to obtain the complete solution. The dependency of the mean firing rate on excitation at fixed inhibition and on inhibition at fixed excitation is investigated as well as the threshold dependence at fixed input rates. The results are discussed in relation to those for intracellular current injection and synaptic input to real neurons.

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