Stochastic Simulations in Systems Biology

With the advances in measurement technology for molecular biology, predictive mathematical models of cellular processes come in reach. A large fraction of such models addresses the kinetics of interaction between biomolecules such as proteins, transcription factors, genes and messenger RNA. In contrast to classical chemical kinetics utilizing the reaction-rate equation, the small volume of cellular compartments requires to account for the stochasticity of chemical kinetics. In this chapter we discuss methods to generate sample paths of this underlying stochastic process for situations where the well-stirredness or fast- diffusion assumption holds true. We introduce various approximations to exact simulation algorithms that are more efficient in terms of computational com- plexity. Moreover, we discuss algorithms that account for the multi-scale nature of cellular reaction events