Dynamics of genetic regulatory networks with delays

Time delays are an important aspect in the modeling of genetic regulation due to slow biochemical reactions such as gene transcription and translation. Based on recent developments of the delays stochastic simulation algorithm, the delays chemical master equation and the delays differential equation are developed for describing biological reactions with time delays. Three typical genetic regulatory networks (i.e., positive network, bistable network and oscillatory network) are used to study the impact of intrinsic noise on the system dynamics where there are delays. In this paper we use reduced delays differential equations, simplified by prefactor method from the complex nonlinear differential equations, to describe the time delays in genetic regulatory networks.