Efficient parametric analysis of the chemical master equation through model order reduction

TL;DR

This paper introduces a parametric model order reduction method to create low-dimensional, efficient surrogate models for the chemical master equation, enabling faster analysis of stochastic biochemical networks with high-dimensional state spaces.

Contribution

The paper presents a novel application of parametric model order reduction to the chemical master equation, significantly reducing computational costs for parametric analysis tasks.

Findings

Reduced computational time for simulations

Accurate low-dimensional models for gene regulation networks

Effective for parameter exploration and sensitivity analysis

Abstract

Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. Results: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. Conclusions: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.