On non-ideal chemical-reaction networks and phase separation

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.

38 pages, 7 figures

References in corpus (4)

• Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics
• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Nonequilibrium Thermodynamics of Non-Ideal Chemical Reaction Networks
• Energy and Matter Supply for Active Droplets

Cited by in corpus (5)

• Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability
• Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization
• Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
• Finding Thermodynamically Favorable Pathways in Chemical Reaction Networks Using Flows in Hypergraphs and Mixed-Integer Linear Programming
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields