  Many cellular behaviors are regulated by gene regulation networks, kinetics
of which is one of the main subjects in the study of systems biology. Because
of the low number molecules in these reacting systems, stochastic effects are
significant. In recent years, stochasticity in modeling the kinetics of gene
regulation networks have been drawing the attention of many researchers. This
paper is a self contained review trying to provide an overview of stochastic
modeling. I will introduce the derivation of the main equations in modeling the
biochemical systems with intrinsic noise (chemical master equation, Fokker-Plan
equation, reaction rate equation, chemical Langevin equation), and will discuss
the relations between these formulations. The mathematical formulations for
systems with fluctuations in kinetic parameters are also discussed. Finally, I
will introduce the exact stochastic simulation algorithm and the approximate
explicit tau-leaping method for making numerical simulations.
