Yun Min Song, A scalable approach for solving chemical master equations based on modularization and filtering

Solving the chemical master equation (CME) that characterizes the probability evolution of stochastically reacting processes is greatly important for analyzing intracellular reaction systems. Conventional methods for solving CMEs include the simulation-based Monte-Carlo methods, the direct approach (e.g., the finite state projection), and so on; however, they usually do not scale very well with the system dimension either in terms of accuracy or efficiency. To mitigate this problem, we propose a new computational method based on modularization and filtering. Our method first divides the whole system into a leader system and several conditionally independent follower subsystems. Then, we solve the CME by applying the Monte Carlo method to the leader system and the direct approach to the filtered CMEs that characterize the conditional probabilities of the follower subsystems. The system decomposition involved in our method is optimized so that all the subproblems above are low dimensional, and, therefore, our approach scales more favorably with the system dimension. Finally, we demonstrate the efficiency and accuracy of our approach in high-dimensional estimation and inference problems using several biologically relevant examples.