Solving a System of Master Equations for Parallel Chemical Interactions

The stochastic kinetics of a well-stirred mixture of molecular species interacting through different biochemical reactions can modelled by the chemical master equation. Till now the scientific computing community has focussed mostly on the development of numerical techniques to approximate the solution of the chemical master equation many realizations of the associated Markov jump process. Consequeltly, the domain of exact algorithms for directly solving a chemiacl master equation is still an open research area. In this work we present a method to solve analytically a chemical master equation to describe a reversible molecular reaction and we propose a method to solve a system of such equations. In this method molecular populations are considered as time-dependent, integer-valued random variables. Moreover, we developed mathematical procedures for solving a system of chemical master equations referred to a set of parallel and interdependent biochemical interactions. The causal dependence between reactions is modeled on the time scale in the following way: a reaction starts when its antecessor has produced a sufficient quantity of reactants.