Stochastic Simulation of Genetic Regulatory Networks with Delayed Reactions

Abstract

Many important processes in cells are controlled by genetic regulatory networks. To accurately model such networks, it is often necessary to include reactions with delays. In this work I apply the weighted ensemble (WE) method to simulate models of genetic regulatory networks that incorporate delays. In order to accurately capture the discreteness and stochasticity present in small systems, the Gillespie stochastic simulation algorithm (SSA), extended to include delayed reactions, is used to evolve trajectories in time. Tests of this method on two simple model systems show that theWEmethod yields an unbiased estimate of the system’s probability distribution in the presence of delays, despite the SSA’s non-uniform timesteps. I additionally use the extended SSA to investigate the assumptions used in analytical models of the simple delayed-degradation system. The numerical results indicate that a mean-field approximation is not justified near the system’s bifurcation point, but is conditionally justified both in the limit of small and (surprisingly) of large propensity of the delayed reaction.