Towards Predicting Partitioning of Enzymes between Macromolecular Phases: Effects of Polydispersity on the Phase Behavior of Nonadditive Hard Spheres in Solution

Abstract

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.

Phase Behavior of Ternary Polymer Mixtures in a Common Solvent

“…17 Polydisperse systems were discussed by Warren, 18 Sear and Frenkel, 19 Sollich, 20 Edelman et al, 21 and Sturtewagen and van der Linden. 22,23 Here, the theory will be presented for systems with three components (N = 3) in a common solvent forming one, two, or three phases (P = 1, 2, or 3), where the common solvent is not explicitly counted as a component. It is noted that this makes these systems de facto quaternary mixtures.…”

“…Mao et al calculated the phase behavior of multicomponent liquid mixtures . Polydisperse systems were discussed by Warren, Sear and Frenkel, Sollich, Edelman et al, and Sturtewagen and van der Linden. , …”

“… 17 Polydisperse systems were discussed by Warren, 18 Sear and Frenkel, 19 Sollich, 20 Edelman et al, 21 and Sturtewagen and van der Linden. 22 , 23 …”

Phase behavior in multicomponent mixtures

“…In a previous numerical work, we predicted the phase behavior of a polydisperse binary mixture of hard spheres in solution using the virial coefficient approach (Sturtewagen and van der Linden, 2021;Sturtewagen and van der Linden, 2022), based on the theory of McMillan and Mayer (1945). Polydispersity was incorporated into the system by means of sub-components.…”

Phase Separation in Complex Mixtures with Many Components: Analytical Expressions for Spinodal Manifolds

“…Phase separation plays a role in classical fields as diverse as polymer and food technology, hematology, wastewater treatment, archeology, and forensics. Considerable effort was invested in experimental and computational work on multicomponent mixtures. − In addition to the abovementioned areas of interest, phase separation in living soft matter is currently a highly active field of research, in particular, in relation to the cytosol of cells containing complex mixtures of thousands of components. − …”