Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tilo Schwalger, Benjamin Lindner

Abstract

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

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Citations

May 6, 2016·Frontiers in Computational Neuroscience·Robert Rosenbaum
Apr 20, 2017·PLoS Computational Biology·Tilo SchwalgerWulfram Gerstner
Jun 15, 2016·Physical Review. E·Romi Mankin, Neeme Lumi
Apr 20, 2019·Physical Review. E·Wilhelm Braun, André Longtin
Jul 16, 2017·Physical Review. E·Yi Ming Lai, Marc de Kamps
Jun 18, 2017·Physical Review. E·Wilhelm BraunAndré Longtin

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