General stochastic hybrid method for the simulation of chemical reaction processes in cells

Abstract

Stochastic approaches are required for the simulation of biochemical systems like signal transduction networks, since high fluctuations and extremely low particle numbers of some species are ubiquitous. Computational problems arise from the huge differences among the timescales on which the reactions occur, causing high cost for stochastically exact simulations. Here, we demonstrate a general hybrid method combining the exact Gillespie algorithm with a system of stochastic differential equations (SDEs). This technique provides a smooth and correct transition between subsets of 'slow' and 'fast' reactions instead of abruptly cutting the stochastic effects above a certain particle number. The method was successfully applied to mitochondrial Cytochrome C release in the CD95-induced apoptosis pathway. Moreover, this approach can also be used for other kinds of Markov processes. © Springer-Verlag Berlin Heidelberg 2005.