A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems
For researchers studying persistence and permanence in biochemical reaction networks, this provides the first computational method to verify endotacticity for multi-species systems.
The paper introduces a MILP framework to determine if a chemical reaction network is endotactic or strongly endotactic, enabling verification for systems with more than two species. The algorithms are implemented in the open-source CoNtRol package and applied to examples like n-site phosphorylation networks and a circadian clock.
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.