Topological bounds on the dynamical growth rate of chemical reaction networks

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, assuming a steady balanced-growth regime, we derive stoichiometry-based constraints on the growth (or shrinkage) rate. 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 origins of life studies and the design of synthetic chemical reaction networks.