Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

by Davin Lunz, Gregory Batt, Jakob Ruess, J. Fr édéric Bonnans

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately charac terise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework t hat augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

Source: PLoS Computational Biology - July 28, 2021 Category: Biology Authors: Davin Lunz Source Type: research