On Reduced Models for the Chemical Master Equation

The chemical master equation plays a fundamental role for the understanding of gene regulatory networks and other discrete stochastic reaction systems. Solving this equation numerically, however, is usually extremely expensive or even impossible due to the huge size of the state space. Thus, the chemical master equation must often be replaced by a reduced model which operates with a considerably smaller number of degrees of freedom but hopefully still provides the essential information about the dynamics of the full system. We prove error bounds for two reduced models which have previously been proposed in the literature. Based on the error analysis, an alternative model reduction approach for the chemical master equation is introduced and discussed, and its advantage is illustrated by numerical examples.