A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems

TL;DR

This paper presents a MILP framework to determine endotacticity in biochemical networks, enabling verification for systems with more than two species, which helps understand their persistence and stability.

Contribution

The authors develop the first algorithms capable of verifying endotacticity in complex biochemical reaction networks with multiple species.

Findings

Algorithms successfully verify endotacticity in complex networks.

Application to biochemical examples demonstrates practical utility.

Framework advances understanding of network persistence and stability.

Abstract

We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same result is conjectured but as yet unproved for general endotactic networks. The algorithms we present are the first capable of verifying endotacticity of chemical reaction networks for systems with greater than two constituent species. We implement the algorithms in the open-source online package CoNtRol and apply them to several well-studied biochemical examples, including the general $n$-site phosphorylation / dephosphorylation networks and a circadian clock mechanism.