Solving the chemical master equation by a fast adaptive finite state projection based on the stochastic simulation algorithm.

The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included.