A binomial approach to the stochastic kinetics of simple chemical reactions

An approximate solution method is proposed to find the time dependence of the individual state probabilities in the master equation of the continuous time discrete state (CDS) stochastic kinetic approach. In systems where giving the number of a single type of molecule is enough to identify a state, this molecule number is assumed to show a binomial distribution whose expectation is the same as the solution of the corresponding deterministic rate equation. The approximation method is tested in ten different systems. In the first order reaction, it gives the exact solution of the stochastic master equation. In other systems, comparisons of expectations, standard deviations and distributions at selected reaction times with the exact ones at low initial molecule numbers show that the method gives reasonable results, whose precision is improved with an increase of initial molecule numbers. For the zeroth order process, a closed from for the exact solution of the master equation is also reported.