Moment Closure for Chemical Reactions

We present a systematic procedure for constructing moment closure functions of arbitrary order for the stochastic models of chemical reaction systems. In the stochastic formulation of chemical reactions, the dynamics of the first M-order moments of the species populations generally do not form a closed system of differential equations, in the sense that the time-derivatives of first M-order moments generally depend on moments of order higher than M. However, for analysis purposes, these dynamics are often made to be closed by approximating the needed derivatives of the first M-order moments by nonlinear functions of the same moments. These functions are called the moment closure functions. We will discuss a new approach to construct moment closure functions. Our method is based on calculating the correlation function of individual moments. We use several examples, with linear and nonlinear sets of reactions, to demonstrate the applicability and the limitations of the scheme.