Stochastic modelling of gene regulatory networks

Gene regulatory networks are dynamic and stochastic in nature, and exhibit exquisite feedback and feedforward control loops that regulate their biological function at different levels. Modelling of such networks poses new challenges due, in part, to the small number of molecules involved and the stochastic nature of their interactions. In this article, we motivate the stochastic modelling of genetic networks and demonstrate the approach using several examples. We discuss the mathematics of molecular noise models including the chemical master equation, the chemical Langevin equation, and the reaction rate equation. We then discuss numerical simulation approaches using the stochastic simulation algorithm (SSA) and its variants. Finally, we present some recent advances for dealing with stochastic stiffness, which is the key challenge in efficiently simulating stochastic chemical kinetics. Copyright (c) 2005 John Wiley & Sons, Ltd.