On persistence and cascade decompositions of chemical reaction networks

TL;DR

This paper introduces new criteria for the persistence of chemical reaction networks, accommodating time-varying reaction rates and inflows/outflows, with applications to biological systems like hypoxia and apoptosis networks.

Contribution

It extends previous work by providing checkable, parameter-dependent conditions for persistence, including external signals and non-conservative systems.

Findings

New criteria for persistence of reaction networks.

Application to hypoxia and apoptosis biological networks.

Inclusion of time-varying rates and inflows/outflows.

Abstract

New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying, thus incorporating the effects of external signals, and also relax the assumption of existence of global conservation laws, thus allowing for inflows (production) and outflows (degradation). For time-invariant networks parameter-dependent conditions for persistence of certain classes of networks are provided. As an illustration, two networks arising in the systems biology literature are analyzed, namely a hypoxia and an apoptosis network.