A Multiple Time-Step Finite State Projection Algorithm for the Solution to the Chemical Master Equation

At the mesoscopic scale, chemical processes have probability distributions that evolve according to an infinite set of linear ordinary differential equations known as the chemical master equation (CME). It is commonly believed that the CME cannot be solved except for the most trivial of cases, but recent work has raised questions regarding validity of this belief. For many cases, Finite State Projection (FSP) techniques [1] can reduce the order of the CME to a solvable system while retaining any prespecified error tolerance. Even when accuracy demands require a projection that is too large to be solve efficiently, the FSP retains the linearity of the CME, and is open to a host of additional model reductions and computational techniques. In this paper, we develop a new algorithm based upon the linearity property of super-positioning, and we illustrate the benefits of this algorithm on a simplified model of the heat shock mechanism in E. coli. The new algorithm retains the full accuracy of the original FSP algorithm, but with significantly increased efficiency and a greater range of applicability.