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

Authors:
B. W. Knight;A. Omurtag;L. Sirovich
Affiliations:
Rockefeller University, New York, NY 10021, and Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.;Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.;Rockefeller University, New York, NY 10021, and Laboratory of Applied Mathematics, Mount Sinai School of Medicine, New York, NY 10029, U.S.A.
Venue:
Neural Computation
Year:
2000

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Abstract

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.