Dongju Lim, Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics.

In this talk, we discuss the paper “Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics” by D. F. Anderson, B. Ermentrout and P. J. Thomas, Journal of Computational Neuroscience, 2015.

Abstract

In this paper we provide two representations for stochastic ion channel kinetics, and compare the perfor- mance of exact simulation with a commonly used numer- ical approximation strategy. The first representation we present is a random time change representation, popular- ized by Thomas Kurtz, with the second being analogous to a “Gillespie” representation. Exact stochastic algorithms are provided for the different representations, which are prefer- able to either (a) fixed time step or (b) piecewise constant propensity algorithms, which still appear in the literature. As examples, we provide versions of the exact algorithms for the Morris-Lecar conductance based model, and detail the error induced, both in a weak and a strong sense, by the use of approximate algorithms on this model. We include ready-to-use implementations of the random time change algorithm in both XPP and Matlab. Finally, through the consideration of parametric sensitivity analysis, we show how the representations presented here are useful in the development of further computational methods. The gen- eral representations and simulation strategies provided here are known in other parts of the sciences, but less so in the present setting.