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

Dissolution mechanisms of amorphous solid dispersions: Role of polymer molecular weight and identification of a new failure mode

The mechanisms of drug release from amorphous solid dispersions (ASDs) are complex and not fully explored, making it difficult to optimize for in vivo performance. A recurring behavior has been the limit of congruency (LoC), a drug loading above which the ASD surface forms an amorphous drug-rich barrier in the presence of water, which hinders release, especially in non-sink conditions. Drug-polymer interactions and drug glass transition temperature were reported to affect the LoC. However, the effect of polymer molecular weight has not been explored. ASDs of clotrimazole and different molecular weight grades of poly (vinylpyrrolidone) (PVP) were studied for their release to obtain their LoC drug loadings. Failure modes underpinning the LoC were investigated using fluorescence confocal microscopy to analyze the ASD/solution interface and phase behavior of ASD films at high relative humidity. ASDs with good release formed stable drug-rich nanodroplets at the ASD/solution interface, while ASDs with poor release were limited by one of two failure modes, depending on PVP molecular weight. In Failure Mode I the nanodroplets quickly agglomerated, while in Failure Mode II the system underwent phase inversion. This work highlights the importance of identifying the mechanisms underlying the LoC to improve the release of higher drug loading ASDs.

Mechanistic Insights into the c-MYC G-Quadruplex and Berberine Binding inside an Aqueous Two-Phase System Mimicking Biomolecular Condensates

We investigated the binding between the c-MYC G-quadruplex (GQ) and berberine chloride (BCl) in an aqueous two-phase system (ATPS) with 12.3 wt % polyethylene glycol and 5.6 wt % dextran, mimicking the highly crowded intracellular biomolecular condensates formed via liquid-liquid phase separation. We found that in the ATPS, complex formation is significantly altered, leading to an increase in affinity and a change in the stoichiometry of the complex with respect to neat buffer conditions. Thermodynamic studies reveal that binding becomes more thermodynamically favorable in the ATPS due to entropic effects, as the strong excluded volume effect inside ATPS droplets reduces the entropic penalty associated with binding. Finally, the binding affinity of BCl for the c-MYC GQ is higher than those for other DNA structures, indicating potential specific interactions. Overall, these findings will be helpful in the design of potential drugs targeting the c-MYC GQ structures in cancer-related biocondensates.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. In addition, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

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.

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Macromolecular Crowding, Phase Separation, and Homeostasis in the Orchestration of Bacterial Cellular Functions

Macromolecular crowding affects the activity of proteins and functional macromolecular complexes in all cells, including bacteria. Crowding, together with physicochemical parameters such as pH, ionic strength, and the energy status, influences the structure of the cytoplasm and thereby indirectly macromolecular function. Notably, crowding also promotes the formation of biomolecular condensates by phase separation, initially identified in eukaryotic cells but more recently discovered to play key functions in bacteria. Bacterial cells require a variety of mechanisms to maintain physicochemical homeostasis, in particular in environments with fluctuating conditions, and the formation of biomolecular condensates is emerging as one such mechanism. In this work, we connect physicochemical homeostasis and macromolecular crowding with the formation and function of biomolecular condensates in the bacterial cell and compare the supramolecular structures found in bacteria with those of eukaryotic cells. We focus on the effects of crowding and phase separation on the control of bacterial chromosome replication, segregation, and cell division, and we discuss the contribution of biomolecular condensates to bacterial cell fitness and adaptation to environmental stress.

Self-Lubricating and Shape-Stable Phase-Change Materials Based on Epoxy Resin and Vegetable Oils

Palm or coconut oil is capable of dissolving in a mixture of bisphenol A-based epoxy resin and a high-temperature hardener (4,4'-diaminodiphenyl sulfone) when heated and then forms a dispersed phase as a result of cross-linking and molecular weight growth of the epoxy medium. Achieving the temporary miscibility between the curing epoxy matrix and the vegetable oil allows a uniform distribution of vegetable oil droplets in the epoxy medium. This novel approach to creating a dispersed phase-change material made a cured epoxy polymer containing up to 20% oil. The miscibility of epoxy resin and oil was studied by laser interferometry, and phase state diagrams of binary mixtures were calculated according to theory and experiments. A weak effect of oil on the viscosity and kinetics of the epoxy resin curing was demonstrated by rotational rheometry. According to differential scanning calorimetry and dynamic mechanical analysis, the oil plasticizes the epoxy matrix slightly, expanding its glass transition region towards low temperatures and reducing its elastic modulus. In the cured epoxy matrix, oil droplets have a diameter of 3-14 µm and are incapable of complete crystallization due to their multi-component chemical composition and non-disappeared limited miscibility. The obtained phase-change materials have relatively low specific energy capacity but can be used alternatively as self-lubricating low-noise materials due to dispersed oil, high stiffness, and reduced friction coefficient. Palm oil crystallizes more readily, better matching the creation of phase-change materials, whereas coconut oil crystallization is more suppressed, making it better for reducing the friction coefficient of the oil-containing material.

Thermodynamically controlled multiphase separation of heterogeneous liquid crystal colloids

Phase separation is a universal physical transition process whereby a homogeneous mixture splits into two distinct compartments that are driven by the component activity, elasticity, or compositions. In the current work, we develop a series of heterogeneous colloidal suspensions that exhibit both liquid-liquid phase separation of semiflexible binary polymers and liquid crystal phase separation of rigid, rod-like nanocellulose particles. The phase behavior of the multicomponent mixture is controlled by the trade-off between thermodynamics and kinetics during the two transition processes, displaying cholesteric self-assembly of nanocellulose within or across the compartmented aqueous phases. Upon thermodynamic control, two-, three-, and four-phase coexistence behaviors with rich liquid crystal stackings are realized. Among which, each relevant multiphase separation kinetics shows fundamentally different paths governed by nucleation and growth of polymer droplets and nanocellulose tactoids. Furthermore, a coupled multiphase transition can be realized by tuning the composition and the equilibrium temperature, which results in thermotropic behavior of polymers within a lyotropic liquid crystal matrix. Finally, upon drying, the multicomponent mixture undergoes a hierarchical self-assembly of nanocellulose and polymers into stratified cholesteric films, exhibiting compartmentalized polymer distribution and anisotropic microporous structure.

Epoxy Phase-Change Materials Based on Paraffin Wax Stabilized by Asphaltenes

The usual problem of meltable phase-change agents is the instability in their form upon heating, which can be solved by placing them into a continuous polymer matrix. Epoxy resin is a suitable medium for dispersing molten agents, but it is necessary to make the obtained droplets stable during the curing of the formed phase-change material. This work shows that molten paraffin wax forms a Pickering emulsion in an epoxy medium and in the presence of asphaltenes extracted from heavy crude oil. Theoretical calculations revealed the complex equilibrium in the epoxy/wax/asphaltene triple system due to their low mutual solubility. Rheological studies showed the viscoplastic behavior of the obtained dispersions at 25 °C, which disappears upon the heating and melting of the paraffin phase. Wax and asphaltenes increased the viscosity of the epoxy medium during its curing but did not inhibit cross-linking or reduce the glass transition temperature of the cured polymer. As a result of curing, it is possible to obtain phase-change materials containing up to 45% paraffin wax that forms a dispersed phase with a size of 0.2-6.5 μm. The small size of dispersed wax can decrease its degree of crystallinity to 13-29% of its original value, reducing the efficiency of the phase-change material.

Phase Transitions of Associative Biomacromolecules

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. Additionally, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

SIGNIFICANCE

Phase separation has emerged as a process of significant relevance to sorting macromolecules into distinct compartments, thereby enabling spatial and temporal control over cellular matter. Considerable effort is being invested into uncovering the driving forces that enable the separation of macromolecular solutions into coexisting phases. At its heart, this process is governed by the balance of macromolecule-solvent, inter-macromolecule, and solvent-solvent interactions. We show that the driving forces for phase separation, including the coefficients that measure interaction strengths between macromolecules, can be extracted by titrating the concentrations of crowders that enable macromolecules to phase separate at lower concentrations. Our work paves the way to leverage specific categories of measurements for quantitative characterizations of driving forces for phase separation.

Dissolution Mechanisms of Amorphous Solid Dispersions: A Close Look at the Dissolution Interface

Despite the recent success of amorphous solid dispersions (ASDs) at enabling the delivery of poorly soluble small molecule drugs, ASD-based dosage forms are limited by low drug loading. This is partially due to a sharp decline in drug release from the ASD at drug loadings surpassing the 'limit of congruency' (LoC). In some cases, the LoC is as low as 5% drug loading, significantly increasing the risk of pill burden. Despite efforts to understand the mechanism responsible for the LoC, a clear picture of the molecular processes occurring at the ASD/solution interface remains elusive. In this study, the ASD/solution interface was studied for two model compounds formulated as ASDs with copovidone. The evolution of a gel layer and its phase behavior was captured in situ with fluorescence confocal microscopy, where fluorescent probes were added to label the hydrophobic and hydrophilic phases. Phase separation was detected in the gel layer for most of the ASDs. The morphology of the hydrophobic phase was found to correlate with the release behavior, where a discrete phase resulted in good release and a continuous phase formed a barrier leading to poor release. The continuous phase formed at a lower drug loading for the system with stronger drug-polymer interactions. This was due to incorporation of the polymer into the hydrophobic phase. The study highlights the complex molecular and phase behavior at the ASD/solution interface of copovidone-based ASDs and provides a thermodynamic argument for qualitatively predicting the release behavior based on drug-polymer interactions.

Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Non-Solvent- and Temperature-Induced Phase Separations of Polylaurolactam Solutions in Benzyl Alcohol as Methods for Producing Microfiltration Membranes

The possibility of obtaining porous films through solutions of polylaurolactam (PA12) in benzyl alcohol (BA) was considered. The theoretical calculation of the phase diagram showed the presence of the upper critical solution temperature (UCST) for the PA12/BA system at 157 °C. The PA12 completely dissolved in BA at higher temperatures, but the resulting solutions underwent phase separation upon cooling down to 120–140 °C because of the PA12’s crystallization. The viscosity of the 10–40% PA12 solutions increased according to a power law but remained low and did not exceed 5 Pa·s at 160 °C. Regardless of the concentration, PA12 formed a dispersed phase when its solutions were cooled, which did not allow for the obtention of strong films. On the contrary, the phase separation of the 20–30% PA12 solutions under the action of a non-solvent (isopropanol) leads to the formation of flexible microporous films. The measurement of the porosity, wettability, strength, permeability, and rejection of submicron particles showed the best results for a porous film produced from a 30% solution by non-solvent-induced phase separation. This process makes it possible to obtain a membrane material with a 240 nm particle rejection of 99.6% and a permeate flow of 1.5 kg/m2hbar for contaminated water and 69.9 kg/m2hbar for pure water.

Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions

High drug load amorphous solid dispersions (ASDs) have been a challenge to formulate partially because drug release is inhibited at high drug loads. The maximum drug load prior to inhibition of release has been termed the limit of congruency (LoC) and has been most widely studied for copovidone (PVPVA)-based ASDs. The terminology was derived from the observation that below LoC, the polymer controlled the kinetics and the drug and the polymer released congruently, while above LoC, the release rates diverged and were impaired. Recent studies show a correlation between the LoC value and drug-polymer interaction strength, where a lower LoC was observed for systems with stronger interactions. The aim of this study was to investigate the causality between drug-PVPVA interaction strength and LoC. Four chemical analogues with diverse abilities to interact with PVPVA were used as model drugs. The distribution of the polymer between the dilute aqueous phase and the insoluble nanoparticles containing drug was studied with solution nuclear magnetic resonance spectroscopy and traditional separation techniques to understand the thermodynamics of the systems in a dilute environment. Polymer diffusion to and from ASD particles suspended in aqueous solution was monitored for drug loads above the LoC to investigate the thermodynamic driving force for polymer release. The surface composition of ASD compacts before and after exposure to buffer was studied with Fourier transform infrared spectroscopy to capture potential kinetic barriers to release. It was found that ASD compacts with drug loads above the LoC formed an insoluble barrier on the surface that was in pseudo-equilibrium with the aqueous phase and prevented further release of drugs and polymers during dissolution. The insoluble barrier contained a substantial amount of the polymer for the strongly interacting drug-polymer systems. In contrast, a negligible amount was found for the weakly interacting systems. This observation provides an explanation for the ability of strongly interacting systems to form an insoluble barrier at lower drug loads. The study highlights the importance of thermodynamic and kinetic factors on the dissolution behavior of ASDs and provides a potential framework for maximizing the drug load in ASDs.

The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Polyphenol-solubility alters amyloid fibril formation of α-synuclein

Amyloid fibril formation is associated with various amyloidoses, including neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Amyloid fibrils form above the solubility of amyloidogenic proteins or peptides upon breaking supersaturation, followed by a nucleation and elongation mechanism, which is similar to the crystallization of solutes. Many additives, including salts, detergents, and natural compounds, promote or inhibit amyloid formation. However, the underlying mechanisms of the opposing effects are unclear. We examined the effects of two polyphenols, that is, epigallocatechin gallate (EGCG) and kaempferol-7─O─glycoside (KG), with high and low solubilities, respectively, on the amyloid formation of α-synuclein (αSN). EGCG and KG inhibited and promoted amyloid formation of αSN, respectively, when monitored by thioflavin T (ThT) fluorescence or transmission electron microscopy (TEM). Nuclear magnetic resonance (NMR) analysis revealed that, although interactions of αSN with soluble EGCG increased the solubility of αSN, thus inhibiting amyloid formation, interactions of αSN with insoluble KG reduced the solubility of αSN, thereby promoting amyloid formation. Our study suggests that opposing effects of polyphenols on amyloid formation of proteins and peptides can be interpreted based on the solubility of polyphenols.

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.

Breakdown of supersaturation barrier links protein folding to amyloid formation

The thermodynamic hypothesis of protein folding, known as the "Anfinsen's dogma" states that the native structure of a protein represents a free energy minimum determined by the amino acid sequence. However, inconsistent with the Anfinsen's dogma, globular proteins can misfold to form amyloid fibrils, which are ordered aggregates associated with diseases such as Alzheimer's and Parkinson's diseases. Here, we present a general concept for the link between folding and misfolding. We tested the accessibility of the amyloid state for various proteins upon heating and agitation. Many of them showed Anfinsen-like reversible unfolding upon heating, but formed amyloid fibrils upon agitation at high temperatures. We show that folding and amyloid formation are separated by the supersaturation barrier of a protein. Its breakdown is required to shift the protein to the amyloid pathway. Thus, the breakdown of supersaturation links the Anfinsen's intramolecular folding universe and the intermolecular misfolding universe.