Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks

TL;DR

This paper investigates how fluctuations in molecule numbers and thermodynamic forces constrain the response of nonequilibrium chemical reaction networks, revealing fundamental trade-offs through theoretical proofs and numerical simulations.

Contribution

It establishes quantitative trade-offs between number fluctuations, thermodynamic driving, and response in both linear and certain nonlinear chemical networks.

Findings

Response limited by number fluctuations and thermodynamic force

Trade-offs proven for linear and single-species nonlinear networks

Numerical results support broad applicability of trade-offs

Abstract

We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations as well as the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to depend sensitively on the deficiency of the network.