Approximating the solution of the chemical master equation by combining finite state projection and stochastic simulation

The advancement of single-cell technologies has shown that stochasticity plays an important role in many biochemical reaction networks. However, our ability to investigate this stochasticity using mathematical models remains rather limited. The reason for this is that computing the time evolution of the probability distribution of such systems requires one to solve the chemical master equation (CME), which is generally impossible. Therefore, many approximate methods for solving the CME have been proposed. Among these one of the most prominent is the finite state projection algorithm (FSP) where a solvable system of equations is obtained by truncating the state space. The main limitation of FSP is that the size of the truncation which is required to obtain accurate approximations is often prohibitively large. Here, we propose a method for approximating the solution of the CME which is based on a combination of FSP and Gillespie's stochastic simulation algorithm. The important advantage of our approach is that the additional stochastic simulations allow us to choose state truncations of arbitrary size without sacrificing accuracy, alleviating some of the limitations of FSP.