Universal Slow Dynamics of Chemical Reaction Networks

Abstract: Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external reservoirs, a range of behaviors is possible, including transition to a new equilibrium state, a non-equilibrium state, or indefinite growth. This study shows that slowly driven CRNs are governed by the conserved quantities of the closed system, which are generally far fewer in number than the species. Considering both deterministic and stochastic dynamics, a universal slow dynamics equation is derived with singular perturbation methods, and is shown to be thermodynamically consistent. The slow dynamics is highly robust against microscopic details of the network, which may be unknown in practical situations. In particular, non-equilibrium states of realistic large CRNs can be sought without knowledge of bulk reaction rates. The framework is successfully tested against a suite of networks of increasing complexity and argued to be relevant in the treatment of open CRNs as chemical machines.