Phase-Separating Binary Polymer Mixtures: The Degeneracy of the Virial Coefficients and Their Extraction from Phase Diagrams

Preserving condensate structure and composition by lowering sequence complexity

Biomolecular condensates play a vital role in organizing cellular chemistry. They selectively partition biomolecules, preventing unwanted cross talk and buffering against chemical noise. Intrinsically disordered proteins (IDPs) serve as primary components of these condensates due to their flexibility and ability to engage in multivalent interactions, leading to spontaneous aggregation. Theoretical advancements are critical at connecting IDP sequences with condensate emergent properties to establish the so-called molecular grammar. We proposed an extension to the stickers and spacers model, incorporating heterogeneous, nonspecific pairwise interactions between spacers alongside specific interactions among stickers. Our investigation revealed that although spacer interactions contribute to phase separation and co-condensation, their nonspecific nature leads to disorganized condensates. Specific sticker-sticker interactions drive the formation of condensates with well-defined networked structures and molecular composition. We discussed how evolutionary pressures might emerge to affect these interactions, leading to the prevalence of low-complexity domains in IDP sequences. These domains suppress spurious interactions and facilitate the formation of biologically meaningful condensates.

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

The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N ≥ 2. Liquid-liquid phase separation is modeled using a virial expansion up to the second order of the concentrations of the components. Formal analytical expressions for the spinodal manifolds in N dimensions are derived, which simplify their calculation (by transforming the original problem into inequalities that can be evaluated numerically using linear programming techniques). In addition, a new expression is obtained to calculate the critical manifold and composition of the coexisting phases. The present analytical procedure complements previous attempts to handle spinodal decomposition for many components using a statistical approach based on random matrix theory. The results are relevant for predicting the effects of polydispersity on phase behavior in fields like polymer or food science and liquid-liquid phase separation in the cytosol of living cells.

Aqueous Two-Phase Systems within Selectively Permeable Vesicles

An aqueous two-phase system (ATPS) encapsulated within a vesicle organizes the vesicle core as two coexisting phases that partition encapsulated solutes. Here, we use microfluidic technologies to produce vesicles that efficiently encapsulate mixtures of macromolecules, providing a versatile platform to determine the phase behavior of ATPSs. Moreover, we use compartmentalized vesicles to investigate how membrane permeability affects the dynamics of the encapsulated ATPS. Designing a membrane selectively permeable to one of the components of the ATPS, we show that out-of-equilibrium phase separations formed by a rapid outflow of water can be spontaneously reversed by a slower outflow of the permeating component across the vesicle membrane. This dynamics may be exploited advantageously by cells to separate and connect metabolic and signaling routes within their nucleoplasm or cytoplasm depending on external conditions.

Phase Behavior of Ternary Polymer Mixtures in a Common Solvent

The Edmond-Ogston model for phase separation is extended to ternary polymer mixtures in a common solvent (de facto a quaternary mixture). The model assumes a truncated virial expansion of the Helmholtz free energy up to the second-order terms in the concentration of the polymers, and the second virial coefficients (B11, B22, B33, B12, B13, B23) are the six parameters of the model. New results from this model are presented in relation to earlier work on binary mixtures: a necessary condition for the virial coefficients for the occurrence of phase separation in two or three phases, an analysis of the different regions of (local) thermodynamic instability using the Descartes sign rule, an expression for the critical curves, a relation between the tangents in points along the critical curve, a relation between the concentration of components in the different phases according to the so-called Lambert-W function, and a consistency check for the composition of coexisting phases in ternary mixtures. The obtained results are evaluated in the maximally symmetric version of the model, where (B11, B22, B33) are equal and (B12, B13, B23) are equal, which leads to two remarkable observations: the concentration range over which two phases are formed is relatively narrow; not all phase separation occurs within a Gibbs triangle, but also, "out-of-Gibbs-triangle" binodals are observed. These results lead to a deeper insight into the phase behavior of ternary mixtures and show promise as a stepping stone toward modeling phase separation in mixtures with many components.

Erratum: Addition to "Phase-Separating Binary Polymer Mixtures: The Degeneracy of the Virial Coefficients and Their Extraction from Phase Diagrams"

[This corrects the article DOI: 10.1021/acsomega.1c00450.].