Structural conditions for saddle-node bifurcations in chemical reaction networks

TL;DR

This paper investigates the structural network conditions that lead to saddle-node bifurcations in biochemical systems, providing methods to identify bifurcation parameters and applying these to various biological networks.

Contribution

It introduces structural conditions for saddle-node bifurcations in chemical reaction networks with general kinetics and develops a method to find bifurcation parameters, including for Michaelis-Menten and Hill kinetics.

Findings

Identified structural conditions guaranteeing saddle-node bifurcations.

Developed a method to determine bifurcation parameters.

Applied the method to biological networks like E. coli metabolism.

Abstract

Motivated by investigating multistationarity in biochemical systems, we address saddle-node bifurcations for chemical reaction networks endowed with general kinetics. At positive equilibria, we identify structural network conditions that guarantee the bifurcation behavior, and we develop a method to identify the proper bifurcation parameters. As a relevant example, we explicitly provide such bifurcation parameters for Michaelis-Menten and Hill kinetics. Examples of applications include reversible feedback cycles, the central carbon metabolism of Escherichia coli, and autocatalytic networks.