Continuous-time Markov-chain models for reaction systems: fast and slow processes

It is sometimes of interest to identify the fast and slow processes in a reaction system. We present here an approach to this problem which is based on a simple stochastic model, a continuous-time Markov chain on a small number of states. We show how it is possible to use such a stochastic model to find and plot the time-courses of concentrations, and to find simple short-time and long-time approximations to these time-courses; that is, to separate the fast and the slow processes. The most significant computation involved is the exponentiation of many small matrices, which is easily accomplished in the computing environment R.