Conditions for Extinction Events in Chemical Reaction Networks with Discrete State Spaces

TL;DR

This paper establishes structural conditions for chemical reaction networks with discrete states to guarantee extinction events, using a novel domination-expanded network approach that enables algorithmic verification.

Contribution

It introduces a new method involving domination-expanded reaction networks to determine extinction events, facilitating algorithmic analysis of complex biological models.

Findings

Derived sufficient structural conditions for extinction events.

Applied the method to biological signaling pathways.

Proposed an algorithmic framework for analyzing 458 models.

Abstract

We study chemical reaction networks with discrete state spaces, such as the standard continuous time Markov chain model, and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event. The conditions we derive involve creating a modified chemical reaction network called a domination-expanded reaction network and then checking properties of this network. We apply the results to several networks including an EnvZ-OmpR signaling pathway in Escherichia coli. This analysis produces a system of equalities and inequalities which, in contrast to previous results on extinction events, allows algorithmic implementation. Such an implementation will be investigated in a companion paper where the results are applied to 458 models from the European Bioinformatics Institute's BioModels database.