Topological bounds on the dynamical growth rate of chemical reaction networks

TL;DR

This paper derives topological bounds on the growth rate of chemical reaction networks using stoichiometry, applicable to origin-of-life and synthetic network design.

Contribution

It introduces a novel topological constraint on CRN growth rates based solely on network structure, independent of specific kinetics.

Findings

Bounds are controlled by the maximum amplification factor.

Numerical tests on random CRN ensembles validate the bounds.

Results are relevant for origin-of-life and synthetic chemistry applications.

Abstract

Growth and decay are system-level properties of chemical reaction networks (CRNs) relevant from prebiotic chemistry to cellular metabolism. Their properties are typically analyzed through the kinetics of particular models, which requires specification of the full set of kinetic laws and parameters. In this work, we derive stoichiometry-based constraints on the growth (or shrinkage) rate, in the balanced-growth regime of scalable CRNs. The resulting bounds are controlled by a topological quantity, the maximum amplification factor, defined via a von Neumann max-min problem over feasible fluxes as illustrated by numerical tests on random-network ensembles of CRNs. We argue for the relevance of our results in the context of origin of life studies but also for designing synthetic chemical reaction networks.