Statistics of a neuron model driven by asymmetric colored noise

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Finn Müller-HansenBenjamin Lindner

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.

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Citations

Jul 12, 2018·IEEE Transactions on Nanobioscience·Sudheer Kumar Sharma Karmeshu
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ryosuke Hosaka, Yutaka Sakai
Jun 15, 2016·Physical Review. E·Romi Mankin, Neeme Lumi
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kamil Rajdl, Petr Lansky
Mar 17, 2017·Physical Review. E·Marie LevakovaPetr Lansky
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L A da Silva, R D Vilela
Jul 16, 2017·Physical Review. E·Yi Ming Lai, Marc de Kamps
Jun 20, 2019·Physical Review. E·Cody BakerRobert Rosenbaum

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