title: Statistics of a neuron model driven by asymmetric colored noise.
abstract: Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.
authors.affiliation: Bernstein Center for Computational Neuroscience, Haus 2, Philippstraße 13, 10115 Berlin, Germany.|Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
authors.forename: Finn
authors.initials: F
authors.lastname: Müller-Hansen
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: Felix
authors.initials: F
authors.lastname: Droste
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
mesh_terms: D000200:Action Potentials / Q000502:physiology; D003198:Computer Simulation; D005583:Fourier Analysis; D008390:Markov Chains; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology; D011336:Probability; D013997:Time Factors