title: Analytical approach to an integrate-and-fire model with spike-triggered adaptation.
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.
authors.affiliation: Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL) Station 15, CH-1015 Lausanne, Switzerland.|Bernstein Center for Computational Neuroscience, Haus 2, Philippstraße 13, 10115 Berlin, Germany.
authors.forename: Tilo
authors.initials: T
authors.lastname: Schwalger
authors.affiliation: Bernstein Center for Computational Neuroscience, Haus 2, Philippstraße 13, 10115 Berlin, Germany.|Department of Physics, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Lindner