Solving the chemical master equation using sliding windows

In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy.The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.Experimental studies have reported the presence of stochastic mechanisms in cellular processes [1-9] and therefore, during the last decade, stochasticity has received much attention in systems biology [10-15]. The investigation of stochastic properties requires that computational models take into consideration the inherent randomness of chemical reactions. Stochastic kinetic approaches may give rise to dynamics that differ significantly from those predicted by deterministic models, because a system might follow very different scenarios with non-zero likelihoods.Under the assumption that the system is spatially homogeneous and has fixed volume and temperature, at a each point in time the state of a network of biochemical reactions is given by the population vector of the involved chemical species. The temporal evolution of the system can be described by a Markov process [16], which is usually represented as a system of ordinary differential equations (ODEs), called the chemical master equation (CME).The CME can be analyzed by applying numerical solution algorithms or, indirectly, by generating trajectories of the underlying Markov process, which is the basis of Gillespie's stochastic simulation algorithm [17,18]. In the former case, the methods are usually based on a matrix description of