Efficient exact stochastic simulation of chemical systems with many species and many channels

There are two fundamental ways to view coupled systems of chemical equation s: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more comm on, systems with very small numbers of molecules are important in some appl ications (e.g., in small biological cells or in surface processes). In both views, most complicated systems with multiple reaction channels and multip le chemical species cannot be solved analytically. There are exact numerica l simulation methods to simulate trajectories of discrete, stochastic syste ms, (methods that are rigorously equivalent to the Master Equation approach ) but these do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate cou pled chemical reactions that is also efficient: it (a) uses only a single r andom number per simulation event, and (b) takes time proportional to the-l ogarithm of the number of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include time-dependent rate consta nts and non-Markov processes and is applied to a sample application in biol ogy (the lysis/lysogeny decision circuit of lambda phage). The performance of the Next Reaction Method on this application is compared with one standa rd method and an optimized version of that standard method.