A liquid-state theory approach to modeling solute partitioning in phase-separated solutions

We present a general theoretical framework to model the partitioning behavior of solutes in phase-separated solutions. Our approach makes use of the McMillan-Mayer solution theory to construct a Gibbs free energy model of the solution. This approach has the following desirable features: (i) the molecular structures of the solute species as well as their interactions are explicit inputs, and, therefore, the application of the theory is not restricted to a particular system, and (ii) the accuracy of the theory can be systematically improved, since the various approximations involved in constructing the solution Gibbs free energy model are clearly delineated. We illustrate the practical implementation of the theoretical framework by examining three cases. First, the theory is utilized in the context of a truncated virial expansion in solution concentration to derive an expression for the solute partition coefficient. Second, the theory is utilized to model protein partitioning in two-phase aqueous surfactant solutions. Third, the theory is utilized to qualitatively predict the partitioning behavior of proteins in a model two-phase aqueous polymer solution, accounting explicitly for the semidilute nature of the concentrated polymer solution phase, We find that the theory captures many of the salient experimental trends observed in protein partitioning in two-phase aqueous polymer solutions.