Simple Calculation of Phase Diagrams for Liquid–Liquid Phase Separation in Solutions of Two Macromolecular Solute Species

A simple method is described for the calculation of two- and three-dimensional phase diagrams describing stability and coexistence curves or surfaces separating one- and two-phase regions in composition/temperature space of a solution containing solute species 1 and 2. The calculation requires a quantitative description of the intermolecular potentials of mean force acting between like (1-1 and 2-2) and unlike (1-2) species. Example calculations are carried out for solutions of species interacting via spherically symmetric square-well potentials as first-order models for protein-protein interaction. When the interaction between species 1 and 2 is more repulsive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in 1 and depleted in 2 and a phase enriched in 2 and depleted in 1. When the interaction between species 1 and 2 is more attractive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in both species and a phase depleted in both species. The latter example provides a first-order description of coacervate formation without postulating specific interactions between the two solute species.