Stochastic Molecular Networks

Biomolecular networks formed by interacting biomolecules form the basis of regulatory machineries of many cellular processes. Stochasticity plays important roles in many networks. This chapter first discusses the basic theoretical framework of the probability landscape of a stochastic network and the underlying discrete chemical master equation (dCME). It also discusses a computational method that optimally enumerate the state space essential for solving the dCME, as well as methods for calculating the steady state and the dynamically evolving probability landscape. The chapter then describes approaches to simplify the state space. It further reviews the formulation of the continuous chemical master equation (cCME), which approximates the dCME, as well as its further simplifications in the form of Fokker-Planck and Langevin models. This is followed by a discussion of the approach of Monte Carlo simulations to study stochastic network, with the Gillespie algorithm discussed in some detail.