Addition of flow reactions preserving multistationarity and bistability

TL;DR

This paper investigates how adding inflow and outflow reactions affects the number and stability of positive steady states in chemical reaction networks, providing a simple criterion based on stoichiometry.

Contribution

It introduces a sufficient, easy-to-verify criterion to determine if multistationarity and bistability are preserved when inflows and outflows are added.

Findings

The criterion is based solely on the stoichiometry of the network.

It applies to models with inflows and outflows common in biological systems.

Examples from systems biology illustrate the criterion's usefulness.

Abstract

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.