A Parallel Implementation of the Finite State Projection Algorithm for the Solution of the Chemical Master Equation

Abstract

Stochastic reaction networks are a popular modeling framework for biochemical processes that treat the molecular copy numbers within a single cell as a continuous time Markov chain, whose forward Chapman-Kolmogorov equation is known in biochemistry literature as the chemical master equation (CME). The solution of the CME contains extremely useful information that can be compared to experimental data in order to improve the quantitative understanding of biochemical reaction networks within the cell. However, this solution is costly to compute as it requires integrating an enormous system of differential equations that grows exponentially with the number of chemical species. To address this issue, we introduce a novel multiple-sinks Finite State Projection algorithm that approximates the CME with an adaptive sequence of reduced-order models with an effecient parallelization based on MPI. The implementation is tested on models of sizable state spaces using a high-performance computing node on Amazon Web Services, showing favorable scalability.