Simulation Methods in Systems Biology

Abstract

This chapter reviews the theory of stochastic chemical kinetics and several simulation methods that are based on that theory. An effort is made to delineate the logical connections among the major elements of the theory, such as the chemical master equation, the stochastic simulation algorithm, tau-leaping, the chemical Langevin equation, the chemical Fokker-Planck equation, and the deterministic reaction rate equation. Focused presentations are given of two approximate simulation strategies that aim to improve simulation efficiency for systems with "multiscale" complications of the kind that are often encountered in cellular systems: The first, explicit tau-leaping, deals with systems that have a wide range of molecular populations. The second, the slow-scale stochastic simulation algorithm, is designed for systems that have a wide range of reaction rates. The latter procedure is shown to provide a stochastic generalization of the Michaelis-Menten analysis of the enzyme-substrate reaction set.