Chemical Master Equation

This is an excerpt from the content

Synonyms

Gillespie algorithm; Stochastic chemical kinetics

Definition

Chemical master equation is the stochastic counterpart of the chemical kinetic equation based on the law of mass action. It describes the kinetics of chemical reactions in a rapidly stirred tank with small volume in terms of stochastic reaction times giving rise to fluctuating copy numbers of reaction species.

Consider a system of fixed volume V at constant temperature T. Let there be well-stirred mixture of N ≥ 1 molecular species {S1, …,SN} and M ≥ 1 reactions {R1, …, RM}. One specifies the dynamical state of this system by X(t) = (X1(t), …, XN(t)), where Xi(t) is the copy number of molecular species Si in the system at time t.

One describes the time evolution of X(t) from some given initial state X(t0) = x0. Both single-molecule experimental measurements and theoretical investigations have shown that X(t) is a stochastic process because the time at which a particular reaction occurs is random.

...