A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current

Biological cybernetics
Henry C TuckwellJean-Pierre Rospars

Abstract

We consider a spatial neuron model in which the membrane potential satisfies a linear cable equation with an input current which is a dynamical random process of the Ornstein-Uhlenbeck (OU) type. This form of current may represent an approximation to that resulting from the random opening and closing of ion channels on a neuron's surface or to randomly occurring synaptic input currents with exponential decay. We compare the results for the case of an OU input with those for a purely white-noise-driven cable model. The statistical properties, including mean, variance and covariance of the voltage response to an OU process input in the absence of a threshold are determined analytically. The mean and the variance are calculated as a function of time for various synaptic input locations and for values of the ratio of the time constant of decay of the input current to the time constant of decay of the membrane voltage in the physiological range for real neurons. The limiting case of a white-noise input current is obtained as the correlation time of the OU process approaches zero. The results obtained with an OU input current can be substantially different from those in the white-noise case. Using simulation of the terms in the serie...Continue Reading

Citations

Feb 10, 2004·Mathematical Biosciences·Nicolangelo IannellaShigeru Tanaka
Oct 28, 2003·Neural Computation·M Rudolph, A Destexhe
May 9, 2008·PLoS Computational Biology·Antti SaarinenOlli Yli-Harja
Nov 18, 2005·Journal of Physiology, Paris·Michael Rudolph, Alain Destexhe
Aug 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xuan ZhanC K Chan
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Susanne Ditlevsen, Petr Lansky
May 10, 2019·Frontiers in Neuroscience·Farad KhoyrateeTimothée Levi
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yaming Chen, Wolfram Just

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