Concordant Chemical Reaction Networks and the Species-Reaction Graph

TL;DR

This paper links the structural property of concordance in chemical reaction networks to their dynamical stability, showing that certain graph conditions can ensure concordance and its implications without complex computations.

Contribution

It demonstrates that mild conditions on the Species-Reaction Graph can guarantee network concordance and its dynamical consequences, broadening the tools for analyzing biochemical networks.

Findings

Species-Reaction Graph conditions imply network concordance

Concordance prevents multiple and degenerate equilibria

Eigenvalues at equilibria are negative under certain conditions

Abstract

In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural weakly monotonic class. In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network's Species-Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance. Because the Species-Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring signicant dynamical information directly from standard biochemical reaction diagrams.