Hybrid Numerical Solution of the Chemical Master Equation
This work provides a computational tool for stochastic modeling of biochemical networks, but the improvement over existing methods is not quantified.
The authors developed a hybrid numerical method for solving the chemical master equation, approximating some discrete random variables as continuous deterministic variables. They demonstrated its efficiency on systems biology case studies, though no specific numerical gains are reported.
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.