The smallest multistationary mass-preserving chemical reaction network

TL;DR

This paper identifies the smallest reversible, mass-preserving chemical reaction network capable of bistability and characterizes the parameter conditions for multiple steady states, advancing understanding of minimal biochemical systems exhibiting multistationarity.

Contribution

It establishes the minimal network structure that admits bistability and provides a detailed parameter set characterization for multistationarity.

Findings

Identified the smallest reversible, mass-preserving network with bistability

Derived semi-algebraic conditions for multiple steady states

Contributed to understanding minimal biochemical multistationary systems

Abstract

Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the possibility of multiple steady states. Understanding small networks is important because the existence of multiple steady states in a subnetwork of a biochemical model can sometimes be lifted to establish multistationarity in the larger network. This paper establishes the smallest reversible, mass-preserving network that admits bistability and determines the semi-algebraic set of parameters for which more than one steady state exists.