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The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result

Rockefeller University, New York, NY 10021, and Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.

A. Omurtag

Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.

L. Sirovich

Rockefeller University, New York, NY 10021, and Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.

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