Title
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.
Suggested Citation
Veit, Max.
(2014).
Stochastic Simulation of Genetic Regulatory Networks with Delayed Reactions.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/166528.