Reference Work Entry

Encyclopedia of Systems Biology

pp 396-399

Chemical Master Equation

  • Hao GeAffiliated withSchool of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University Email author 
  • , Hong QianAffiliated withDepartment of Applied Mathematics, University of Washington


Gillespie algorithm; Stochastic chemical kinetics


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.

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