Interactions in protein mixtures. Part II: A virial approach to predict phase behavior

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.

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.

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

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

The Edmond-Ogston model for phase separation in binary polymer mixtures is based on a truncated virial expansion of the Helmholtz free energy up to the second-order terms in the concentration of the polymers. The second virial coefficients (B ₁₁, B ₁₂, B ₂₂) are the three parameters of the model. Analytical solutions are presented for the critical point and the spinodal in terms of molar concentrations. The calculation of the binodal is simplified by splitting the problem into a part that can be solved analytically and a (two-dimensional) problem that generally needs to be solved numerically, except in some specific cases. The slope of the tie-lines is identified as a suitable parameter that can be varied between two well-defined limits (close to and far away from the critical point) to perform the numerical part of the calculation systematically. Surprisingly, the analysis reveals a degenerate behavior within the model in the sense that a critical point or tie-line corresponds to an infinite set of triplets of second virial coefficients (B ₁₁, B ₁₂, B ₂₂). Since the Edmond-Ogston model is equivalent to the Flory-Huggins model up to the second order of the expansion in the concentrations, this degeneracy is also present in the Flory-Huggins model. However, as long as the virial coefficients predict the correct critical point, the shape of the binodal is relatively insensitive to the specific choice of the virial coefficients, except in a narrow range of values for the cross-virial coefficient B ₁₂.

Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid-liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

Advancement of food-derived mixed protein systems: Interactions, aggregations, and functional properties

Recently, interests in binary protein systems have been developed considerably ascribed to the sustainability, environment-friendly, rich in nutrition, low cost, and tunable mechanical properties of these systems. However, the molecular coalition is challenged by the complex mechanisms of interaction, aggregation, gelation, and emulsifying of the mixed system in which another protein is introduced. To overcome these fundamental difficulties and better modulate the structural and functional properties of binary systems, efforts have been steered to gain basic information regarding the underlying dynamics, theories, and physicochemical characteristics of mixed systems. Therefore, the present review provides an overview of the current studies on the behaviors of proteins in such systems and highlights shortcomings and future challenges when applied in scientific fields.

Gelation of food protein-protein mixtures

Gelation of proteins is one of the principal means to give desirable texture to food products. Gelation of individual proteins in aqueous solution has been investigated intensively in the past, but in most food products the system contains mixtures of different types of proteins. Therefore one needs to consider interaction between different proteins both before and during gelation. Most food proteins can be classified as globular proteins, but casein and gelatin are also important food proteins. In this review the focus is on gelation induced by heating or cooling, which is the most commonly used method. After briefly discussing general features of protein aggregation and gelation, the literature on gelation of mixtures of different types of globular proteins is reviewed as well as that of mixtures of globular proteins with gelatin or with casein. The effect on the gel stiffness and the microstructure of the gelled mixtures will be discussed in terms of different scenarios that can be envisaged: independent aggregation and gelation, co-aggregation and phase separation.

Investigating the effect of sterilisation methods on the physical properties and cytocompatibility of methyl cellulose used in combination with alginate for 3D-bioplotting of chondrocytes

For both the incorporation of cells and future therapeutic applications the sterility of a biomaterial must be ensured. However, common sterilisation techniques are intense and often negatively impact on material physicochemical attributes, which can affect its suitability for tissue engineering and 3D printing. In the present study four sterilisation methods, autoclave, supercritical CO₂ (scCO₂) treatment, UV- and gamma (γ) irradiation were evaluated regarding their impact on material properties and cellular responses. The investigations were performed on methyl cellulose (MC) as a component of an alginate/methyl cellulose (alg/MC) bioink, used for bioprinting embedded bovine primary chondrocytes (BPCs). In contrast to the autoclave, scCO₂ and UV-treatments, the γ-irradiated MC resulted in a strong reduction in alg/MC viscosity and stability after extrusion which made this method unsuitable for precise bioprinting. Gel permeation chromatography analysis revealed a significant reduction in MC molecular mass only after γ-irradiation, which influenced MC chain mobility in the Ca²⁺-crosslinked alginate network as well as gel composition and microstructure. With regard to cell survival and proteoglycan matrix production, the results determined UV-irradiation and autoclaving as the best candidates for sterilisation. The scCO₂-treatment of MC resulted in an unfavourable cell response indicating that this method needs careful optimisation prior to application for cell encapsulation. As proven by consistent FT-IR spectra, chemical alterations could be excluded as a cause for the differences seen between MC treatments on alg/MC behaviour. This investigation provides knowledge for the development of a clinically appropriate 3D-printing-based fabrication process to produce bioengineered tissue for cartilage regeneration.

Chaperone-like food components: from basic concepts to food applications

The significance of chaperones in preventing protein aggregation including amyloid fibril formation has been extensively documented in the biological field, but there is limited research on the potential effect of chaperone-like molecules on food protein functionality and food quality.