Berlin 2012 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 22: Statistical Physics of Biological Systems III (with DY)

BP 22.10: Vortrag

Donnerstag, 29. März 2012, 17:15–17:30, H 1058

Solution of the Fokker-Planck equation for neurons with adaptation — •Tilo Schwalger and Benjamin Lindner — Institute of Physics, Humboldt-University at Berlin; Bernstein Center of Computational Neuroscience, Berlin, Philippstr. 13,10115 Berlin

Firing rate adaptation is an ubiquitous features of neurons throughout the nervous system. Slow adaptation currents that act as a negative feedback give rise to an intricate neuron dynamics leading to a characteristic spiking statistics already in the spontaneous firing activity. A prominent example are negative correlations between interspike intervals, which have been frequently measured in experiments. We have recently derived an analytical expression of the correlation coefficient of a perfect integrate-and-fire neuron with an adaptation current [1]. This result holds in the deterministic limit, where the white-noise driving is infinitesimally small. To extend the result to stronger noise driving, it is necessary to determine self-consistently the stationary distribution of the adaptation current sampled at the spike times. To this end, we solve the associated two-dimensional Fokker-Planck equation about the deterministic limit distribution: this amounts to a WKB approximation for weak noise. Our approximations of the solution are compared with extensive simulations of the adapting neuron model.

[1] Schwalger T, Fisch K, Benda J, Lindner B, Plos Comp Biol., 2010