On non-ideal chemical-reaction networks and phase separation

TL;DR

This paper extends the theory of chemical-reaction networks to include non-ideal interactions, providing new insights into phase separation and steady-state behavior in complex biological and soft-matter systems.

Contribution

It generalizes known results for ideal CRNs to non-ideal cases with arbitrary interactions, including phase diagrams and steady-state distributions.

Findings

Lyapunov functions for complex-balanced networks are adapted to non-ideal interactions.

A phase diagram for reaction-diffusion solutions is derived based on Lyapunov minimization.

Complex-balanced networks do not generate diffusion currents at steady state.

Abstract

Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and soft-matter physics which appear to deviate from the ideal-solution behaviour. Particularly striking is the case of liquid-liquid phase separation, which is typically caused by inter-particle interactions. Here, we revisit a number of known results in the domain of ideal CRNs, and we generalise and adapt them to arbitrary interactions between the solutes which stem from a given free energy. Among these is the form of the steady-state probability distribution and Lyapunov functions for complex-balanced networks, where the creation and annihilation rates are equal for all chemical complexes which appear as reactants or products in the CRN. Finally, we draw a phase diagram for complex-balanced reaction-diffusion solutions based on the minimisation of such Lyapunov function with a rationale similar to that of equilibrium thermodynamics, but for systems that may sustain non-equilibrium chemical currents at steady state. Nevertheless, we find that complex-balanced networks are not sufficient to create diffusion currents at steady state.