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.

11 pages + 21 pages SI; v2: added references, explanatory text, & examples, revised discussion of stochastic treatment. v3: added discussion of minor generalizations

References in corpus (5)

• Stochastic thermodynamics of chemical reaction networks
• Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
• Circuit Theory for Chemical Reaction Networks
• Dynamical mean-field theory: from ecosystems to reaction networks
• Linear response in large deviations theory: A method to compute non-equilibrium distributions

Cited by in corpus (2)

• Finding Pathways in Reaction Networks guided by Energy Barriers using Integer Linear Programming
• Effective one-dimension reduction of multi-compartment complex systems dynamics