Reaction networks as systems for resource allocation: A variational principle for their non-equilibrium steady states

TL;DR

This paper derives a variational principle for the non-equilibrium steady states of chemical reaction networks, framing them as resource allocation systems that optimize substrate use, with applications to toy models and human red blood cell metabolism.

Contribution

It introduces a variational principle for reaction networks' steady states, linking them to resource allocation problems and entropy production decay, a novel theoretical framework.

Findings

Reaction networks minimize a Hopfield-like Hamiltonian at steady state.

Reaction networks can be viewed as systems optimizing substrate competition.

Application to red blood cell metabolism demonstrates the framework's relevance.

Abstract

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell.