Efficient evaluation of neuron populations receiving colored-noise current based on a refractory density method

Anton V. Chizhov and Lyle J. Graham
Phys. Rev. E 77, 011910 – Published 17 January 2008

Abstract

The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.

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  • Received 5 June 2007

DOI:https://doi.org/10.1103/PhysRevE.77.011910

©2008 American Physical Society

Authors & Affiliations

Anton V. Chizhov1,2,* and Lyle J. Graham2

  • 1A.F. Ioffe Physico-Technical Institute of RAS, 26 Politekhnicheskaya Street, 194021 St. Petersburg, Russia
  • 2Laboratory of Neurophysics and Physiology, UMR 8119 CNRS, Université René Descartes, 45 rue des Saints Pères, 75006 Paris, France

  • *Anton.Chizhov@mail.ioffe.ru

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Vol. 77, Iss. 1 — January 2008

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