Distribution of transition times in a stochastic model of excitable cell: Insights into the cell-intrinsic mechanisms of randomness in neuronal interspike intervals.

Abstract

In this paper, we develop an analytical approach to studying random patterns of activity in excitable cells. Our analytical approach uses a two-state stochastic model of excitable system based on the electrophysiological properties of refractoriness and restitution, which characterize cell recovery after excitation. By applying the notion of probability density flux, we derive the distributions of transition times between states and the distribution of interspike interval (ISI) durations for a constant applied stimulus. The derived ISI distribution is unimodal and, provided that the time spent in the excited state is constant, can be approximated by a Rayleigh peak followed by an exponential tail. We then explore the role of the model parameters in determining the shape of the derived distributions and the ISI coefficient of variation. Finally, we use our analytical results to study simulation results from the stochastic Morris-Lecar neuron and from a three-state extension of the proposed stochastic model, which is capable of reproducing multimodal ISI histograms.