Multistationarity in cyclic sequestration-transmutation networks

TL;DR

This paper characterizes the conditions under which cyclic sequestration-transmutation networks can exhibit multiple steady states, providing fundamental insights into the minimal structures capable of multistationarity in reaction networks.

Contribution

It offers a complete characterization of multistationarity capacity in a class of reaction networks involving sequestration and transmutation with feedback cycles.

Findings

Identifies conditions for multistationarity in these networks

Provides minimal network examples capable of multiple steady states

Establishes a theoretical framework for analyzing feedback cycles

Abstract

We consider a natural class of reaction networks which consist of reactions where either two species can inactivate each other (i.e., sequestration), or some species can be transformed into another (i.e., transmutation), in a way that gives rise to a feedback cycle. We completely characterize the capacity of multistationarity of these networks. This is especially interesting because such networks provide simple examples of "atoms of multistationarity", i.e., minimal networks that can give rise to multiple positive steady states