Hybrid Numerical Solution of the Chemical Master Equation

TL;DR

This paper introduces a hybrid numerical method combining stochastic and deterministic approaches to efficiently approximate solutions of the chemical master equation in biological systems.

Contribution

It proposes a novel stochastic hybrid model and a numerical algorithm for solving the chemical master equation more efficiently than traditional methods.

Findings

The method effectively approximates biochemical networks.

Demonstrated efficiency on multiple biological case studies.

Provides accurate results with reduced computational cost.

Abstract

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient probability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We implemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.