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Stochastic Modeling and Analysis of Genetic Networks

Much of the mathematical modeling of genetic networks represents gene expression and regulation as deterministic processes. There is now, however, considerable experimental evidence indicating that significant stochastic fluctuations are present in these processes. Stochasticity is an inherent feature of biological dynamics, and as such, should be the subject of in-depth analysis. The investigation of stochastic properties in genetic systems involves the formulation of a correct representation of molecular noise, followed by the formulation of mathematically sound approximations for these representations. It also involves devising efficient computational algorithms capable of tackling the complexity of the dynamics involved. In this paper we review a number of these techniques and provide compelling examples that illustrate the richness of phenomena that can result from the interaction of dynamics and noise in genetic networks.