Predict Phase Separation Research Articles

Predicting Heteropolymer Interactions: Demixing and Hypermixing of Disordered Protein Sequences

Cells contain multiple condensates which spontaneously form due to the heterotypic interactions between their components. Although the proteins and disordered region sequences that are responsible for condensate formation have been extensively studied, the rule of interactions between the components that allow demixing, i.e., the coexistence of multiple condensates, is yet to be elucidated. Here, we construct an effective theory of the interaction between heteropolymers by fitting it to the molecular dynamics simulation results obtained for more than 200 sequences sampled from the disordered regions of human proteins. We find that the sum of amino acid pair interactions across two heteropolymers predicts the Boyle temperature qualitatively well, which can be quantitatively improved by the dimer pair approximation, where we incorporate the effect of neighboring amino acids in the sequences. The improved theory, combined with the finding of a metric that captures the effective interaction strength between distinct sequences, allowed the selection of up to three disordered region sequences that demix with each other in multicomponent simulations, as well as the generation of artificial sequences that demix with a given sequence. The theory points to a generic sequence design strategy to demix or hypermix thanks to the low-dimensional nature of the space of the interactions that we identify. As a consequence of the geometric arguments in the space of interactions, we find that the number of distinct sequences that can demix with each other is strongly constrained, irrespective of the choice of the coarse-grained model. Altogether, we construct a theoretical basis for methods to estimate the effective interaction between heteropolymers, which can be utilized in predicting phase separation properties as well as rules of assignment in the localization and functions of disordered proteins. Published by the American Physical Society 2024

Physical information-enhanced graph neural network for predicting phase separation

Abstract Although phase separation is a ubiquitous phenomenon, the interactions between multiple components make it difficult to accurately model and predict. In recent years, machine learning has been widely used in physics simulations. Here, we present a physical information-enhanced graph neural network (PIENet) to simulate and predict the evolution of phase separation. The accuracy of our model in predicting particle positions is improved by 40.3% and 51.77% compared with CNN and SVM respectively. Moreover, we design an order parameter based on local density to measure the evolution of phase separation and analyze the systematic changes with different repulsion coefficients and different Schmidt numbers. The results demonstrate that our model can achieve long-term accurate predictions of order parameters without requiring complex handcrafted features. These results prove that graph neural networks can become new tools and methods for predicting the structure and properties of complex physical systems.

Biomolecular phase separation through theoretical and computational microscope

AbstractBiomolecular phase separation is a vital mechanism for orchestrating biomolecules within living cells. This crucial role has spurred an intense pursuit to comprehend the molecular underpinnings governing and regulating these processes. Computational methodologies offer a unique perspective, augmenting experimental techniques by providing detailed information that cannot be obtained otherwise. In this review, we briefly overview the theoretical and computational approaches to investigate biomolecular phase separation. As a short primer, we explain the factors driving and affecting phase separation of biomolecules, and then we delve into analytical and simulation methods used to study phase separation. We explain how analytical methods like the Flory–Huggins theory, random phase approximation, and graph‐based methods have been used to study phase behaviors of various proteins. We also discuss principles and applications of all‐atom simulations, coarse‐grained simulations, and field‐theoretical approaches. Additionally, we explore the recent advances in machine learning approach to predict phase separation of biomolecules.

Phase separation methods for protein purification: A meta-analysis of purification performance and cost-effectiveness.

Protein purifications based on phase separations (e.g., precipitation and liquid-liquid extraction) have seen little adoption in commercial protein drug production. To identify barriers, we analyzed the purification performance and economics of 290 phase separation purifications from 168 publications. First, we found that studies using Design of Experiments for optimization achieved significantly greater mean yield and host cell protein log10 removal values than those optimizing one factor at a time (11.5% and 53% increases, respectively). Second, by modeling each reported purification at scales from 10 to 10,000kg product/year and comparing its cost-effectiveness versus chromatography, we found that cost-effectiveness depends strongly on scale: the fraction of phase separations predicted to be cost-effective at the 10, 100, and 1000kg/year scales was 8%, 15%, and 43%, respectively. Total cost per unit product depends inversely on input purity, with phase separation being cheaper than chromatography at the 100kg/year scale in 100% of cases where input purity was ≤ 1%, compared to about 25% of cases in the dataset as a whole. Finally, we identified a simple factor that strongly predicts phase separation process costs: the mass ratio of reagents versus purified product (the "direct materials usage rate"), which explains up to 58% of variation in cost per unit of purified product among all 290 reports, and up to 98% of variation within particular types of phase separation.

Mechanics Underpinning Phase Separation of Hydrogels.

This paper reveals the underpinning role of mechanical constraints and dynamic loading in triggering volume phase transitions and phase separation of hydrogels. Using the Flory-Rehner free energy that does not predict phase separation of hydrogels under equilibrium free swelling, we show that mechanical constraints can lead to coexistence of multiple phases. We systematically obtain the states of equilibrium for hydrogels under various mechanical constraints and unravel how mechanical constraints change the convexity of the free energy and monotonicity of the stress-stretch curves, leading to phase coexistence. Using a phase-field model, we predict the pattern evolution of phase coexistence and show that many features cannot be captured by the homogeneous states of equilibrium due to large mismatch stretch between the coexisting phases. We further reveal that the system size, quenching rate, and loading rate can significantly influence the phase behavior, which provides insights for experimental studies related to morphological patterns of hydrogels.

How to Predict the Order of Phase Separation of Polyelectrolyte Complexes and Their Miscibility.

The mixture of two oppositely charged polyelectrolyte solutions results in complexation that may lead to an associative phase separation, forming a highly concentrated phase in both polyelectrolytes in equilibrium with a dilute phase. In this work, we aim to investigate what controls the order of complexation when more polyelectrolytes of the same charge are present. For this, the effect of the addition of a third oppositely charged polyelectrolyte in a mixture of two polyelectrolytes with the same charge was studied. Our results show that, under certain conditions, the electrostatic complexation takes place selectively, where one polyanion (or polycation) phase separates first, followed by the other phase separation, with both complexes at their 1:1 charge stoichiometry. Infrared analyses of the phase-separated complexes confirmed that, in a mixture of polyanions, poly(styrenesulfonate) is complexed first, followed by poly(acrylate). For polycations, these analyses showed that poly(diallyldimethylammonium) is preferentially complexed over poly(allylamine). These results suggest that electrostatic complexation occurs following the sequence predicted as in an acid/base titration, where the acidic/basic strength of the involved polyions dictates which one is complexed first. In this respect, the order of complexation can be associated with the equivalence pH for each pair, which we propose can be used as a parameter to predict phase separation in polyelectrolyte mixtures. In addition, we have investigated the miscibility of these complex mixtures, confirming that multiphasic complexes are formed whenever the polyions display ionizable groups with different acid/basic strengths and that this can also be related to their equivalence pH.

Pan-cancer assessment of mutational landscape in intrinsically disordered hotspots reveals potential driver genes.

Large-scale cancer genome sequencing has enabled the catalogs of somatic mutations; however, the mutational impact on intrinsically disordered protein regions (IDRs) has not been systematically investigated to date. Here, we comprehensively characterized the mutational landscapes of IDRs and found that IDRs have higher mutation frequencies across diverse cancers. We thus developed a computational method, ROI-Driver, to identify putative driver genes enriching IDR and domain hotspots in cancer. Numerous well-known cancer-related oncogenes or tumor suppressors that play important roles in cancer signaling regulation, development and immune response were identified at a higher resolution. In particular, the incorporation of IDR structures helps in the identification of novel potential driver genes that play central roles in human protein–protein interaction networks. Interestingly, we found that the putative driver genes with IDR hotspots were significantly enriched with predicted phase separation propensities, suggesting that IDR mutations disrupt phase separation in key cellular pathways. We also identified an appreciable number of clinically relevant genes enriching IDR mutational hotspots that exhibited differential expression patterns and are associated with cancer patient survival. In summary, combinations of mutational effects on IDRs significantly increase the sensitivity of driver detection and are likely to open new therapeutic avenues for various cancers.

The perinuclear region concentrates disordered proteins with predicted phase separation distributed in a 3D network of cytoskeletal filaments and organelles

Membraneless organelles have emerged during the evolution of eukaryotic cells as intracellular domains in which multiple proteins organize into complex structures to perform specialized functions without the need of a lipid bilayer compartment. Here we describe the perinuclear space of eukaryotic cells as a highly organized network of cytoskeletal filaments that facilitates assembly of biomolecular condensates. Using bioinformatic analyses, we show that the perinuclear proteome is enriched in intrinsic disorder with several proteins predicted to undergo liquid-liquid phase separation. We also analyze immunofluorescence and transmission electron microscopy images showing the association between the nucleus and other organelles, such as mitochondria and lysosomes, or the labeling of specific proteins within the perinuclear region of cells. Altogether our data support the existence of a perinuclear dense sub-micron region formed by a well-organized three-dimensional network of structural and signaling proteins, including several proteins containing intrinsically disordered regions with phase behavior. This network of filamentous cytoskeletal proteins extends a few micrometers from the nucleus, contributes to local crowding, and organizes the movement of molecular complexes within the perinuclear space. Our findings take a key step towards understanding how membraneless regions within eukaryotic cells can serve as hubs for biomolecular condensates assembly, in particular the perinuclear space. Finally, evaluation of the disease context of the perinuclear proteins revealed that alterations in their expression can lead to several pathological conditions, and neurological disorders and cancer are among the most frequent.

Solubility Product Constant Governs Multivalent Protein Phase Separations

Liquid-liquid phase separation (LLPS) has emerged as an intriguing phenomenon inside living cells. The phase-separated droplets, where specific biochemical events can take place and which also buffer cytosolic concentrations, are composed of weakly binding multivalent proteins or nucleic acids. Despite the explosion of this field of study, a general purpose quantitative principle to predict phase separation for multicomponent (“heterotypic”) binders has yet to emerge. In this study, we used non-spatial (NFSim) and spatial (SpringSaLaD) network-free rule-based modeling to determine the concentration threshold for LLPS as a function of molecular valencies. Remarkably, the simulations suggest that the phase separation behavior conforms to the solubility product constant (Ksp), familiar for ions in solution in equilibrium with solid salts: as long as the product of monomer concentrations exceeded the Ksp, the system showed phase separation - irrespective of the individual monomer concentrations. The solubility product constant decreases as the molecular valency of binding partners increases, shifting the concentration threshold to lower values. When we mixed molecules with different valencies, penta-valent and tri-valent, for example, Ksp followed an expression determined by ideal stoichiometries, similar to that of a mixed-valent salt like Al2(SO4)3. Spatial simulations revealed the importance of molecular flexibility and inter binding sites distance of the multivalent molecules. When the inter-site distances of a heterotypic tetravalent molecular pair are exactly matched, a prevalence of dimer (“dimeric trap”) was observed. A rigid molecular pair, with equal inter-site distances, produced this “dimeric trap” more prominently, while unequal inter-site distances disrupted the trap and formed large clusters that displayed a Ksp similar to that found in the non-spatial simulations. Thus our study establishes a general principle underlying the concentration threshold for phase separations, the Ksp, and how molecular structure can shape it. (Support: NIH grants R24GM137787 and R01GM132859)

Variational Approach for Many-Body Systems at Finite Temperature.

We introduce an equation for density matrices that ensures a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal. We build a variational approach for many-body systems that can be applied to a broad class of states, including all bosonic and fermionic Gaussian, as well as their generalizations obtained by unitary transformations, such as polaron transformations in electron-phonon systems. We apply it to the Holstein model on 20×20 and 50×50 square lattices, and predict phase separation between the superconducting and charge-density wave phases in the strong interaction regime.

The proline-rich domain promotes Tau liquid-liquid phase separation in cells.

Tau protein in vitro can undergo liquid-liquid phase separation (LLPS); however, observations of this phase transition in living cells are limited. To investigate protein state transitions in living cells, we attached Cry2 to Tau and studied the contribution of each domain that drives the Tau cluster in living cells. Surprisingly, the proline-rich domain (PRD), not the microtubule binding domain (MTBD), drives LLPS and does so under the control of its phosphorylation state. Readily observable, PRD-derived cytoplasmic condensates underwent fusion and fluorescence recovery after photobleaching consistent with the PRD LLPS in vitro. Simulations demonstrated that the charge properties of the PRD predicted phase separation. Tau PRD formed heterotypic condensates with EB1, a regulator of plus-end microtubule dynamic instability. The specific domain properties of the MTBD and PRD serve distinct but mutually complementary roles that use LLPS in a cellular context to implement emergent functionalities that scale their relationship from binding α-beta tubulin heterodimers to the larger proportions of microtubules.

On the use of solubility parameters to investigate phase separation-morphology-mechanical behavior relationships of TPU

This study proposes a thorough investigation, especially based on thermodynamics, to predict phase separation in a linear thermoplastic polyurethane, denoted TPU, prepared from fatty acid-based soft segments and MDI (4,4′-methylene bis(phenyl isocyanate))/BDO (1,4-butanediol) hard segments and specially designed for bitumen modification. Hansen’ solubility parameters (HSP) of both segments are evaluated to predict their compatibility. The later ones are evaluated either individually from the corresponding segment synthesized separately or from a decomposition of the solubility diagram of the TPUs into two distinct spheres. In a second step, phase separation is experimentally analyzed by combining differential scanning calorimetry, microscopy techniques, and small angle X-ray scattering (SAXS). The microstructure of the TPUs is described considering one soft phase made of polyol chains and short miscible hard segments and a hard phase organized as semi-crystalline nanodomains either dispersed or assembled as ramified (nano)objects within the soft phase. The dynamic mechanical properties of the TPUs can be explained by the presence of such well-defined hard domains in the structure of the TPU, acting as reinforcing fillers while maintaining a thermoplastic elastomer mechanical behavior to the TPU above the glass transition of the continuous soft phase.

Numerical simulation on constituents separation of R134a/R600a in a horizontal T-junction

Abstract T-junction, which is regarded as an effective solution to phase separation of air-water, has already been widely applied in industry sector, especially in thermodynamic cycles for improving cycle performance. However, the research on constituent separation of organic refrigerants in the T-junction is just emerging without clear understanding on mechanism, variation and application. In this paper, the constituent separation performance of organic refrigerants, R134a/R600a, in horizontal branch T-junctions is numerically investigated. The computations are conducted based on the Eulerian method with the k-e turbulence model, which has been used to predict phase separation and an agreement is concluded. The inlet mass flux and qualities are 200 kg·m−2·s−1 and from 0.1 to 0.4, respectively. Based on the model, detailed phase and constituent distribution in T-junction are obtained and then discussed. Furthermore, the separation efficiencies of R134a are analysed based on calculation results. The results show that an agreement is observed on the separation efficiency with the inlet quality varying from 0.123 to 0.286 by comparing with the experimental results. When the inlet quality is 0.4, the inconsistency between the simulation results and the theoretical results and the experimental results may be due to two factors: changing of flow patterns and mass transfer of constituents.

Using the Cahn–Hilliard Theory in Metastable Binary Solutions

A solution may be in one of three states: stable, unstable, or metastable. If the solution is unstable, phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, the solution must overcome an activation barrier for phase separation to proceed spontaneously. This mechanism is called nucleation and growth. Manipulating morphology using phase separation has been of great research interest because of its practical use to fabricate functional materials. The Cahn–Hilliard theory, incorporating Flory–Huggins free energy, has been used widely and successfully to model phase separation by spinodal decomposition in the unstable region. This model is used in this paper to mathematically model and numerically simulate the phase separation by nucleation and growth in the metastable state for a binary solution. Our numerical results indicate that Cahn–Hilliard theory is able to predict phase separation in the metastable region but in a region near the spinodal line.

Time-dependent phase separation of amorphous solid dispersions: Implications for accelerated stability studies

Freshly prepared amorphous solid dispersions (ASDs) may not be in an equilibrium mixed state, as high-temperatures and/or solvents are generally used during their preparation. In this study, tolbutamide (TLB) and acetaminophen (AAP) were transformed into ASDs using hydroxypropylmethylcellulose acetate succinate, Eudragit E100 (E100), Soluplus, and Kollidon VA64 using the melt-quench method to observe their phase stability at 5, 25, 40, and 60 °C. Time-dependent phase separation was observed for all the drug and excipient combinations under all investigated storage conditions. The phase separation of the E100/TLB and Soluplus/TLB ASDs was faster under high-temperature storage conditions, whereas the opposite trend was observed with the other ASDs. In the above-mentioned stability studies, phase separation kinetics of the E100/TLB and Soluplus/TLB ASDs appeared to be dominated by molecular mobility due to the low glass transition temperature (Tg) of both the drug and polymer, whereas departure from equilibrium was a dominating factor for the other ASDs. The Tg of the mixed phase just after preparation could be used as an indicator for predicting phase separation after long-term storage, as the mixing ratio calculated from the Tg was in agreement with that after storage for certain ASDs.

AbInitio Calculation of the Miscibility Diagram for Hydrogen-Helium Mixtures.

We use finite-temperature density functional theory coupled to classical molecular dynamics simulation to calculate the miscibility gap of hydrogen-helium mixtures. The van der Waals density functional (vdW-DF) theory is used, which leads to lower demixing temperatures compared to computations using the Perdew-Burke-Ernzerhof functional. Our calculations suggest that current Jupiter models are most likely too hot to allow demixing in the interior. A Jupiter isentrope based on our vdW-DF data is presented. Our demixing phase diagram still predicts phase separation in Saturn, but in a significantly reduced fraction of its volume.

Formation of Nanofibrous Matrices, Three-Dimensional Scaffolds, and Microspheres: From Theory to Practice.

Nanofibrous architecture presents unique biophysical cues to facilitate cellular responses and is considered an indispensable feature of a biomimetic three-dimensional (3D) scaffold and cell carrier. While electrospinning is a widely used method to prepare natural extracellular matrix-like nanofibers, it faces significant challenges to incorporate nanofibrous architecture into well-defined macroporous 3D scaffolds or injectable microspheres. Here we report a nonelectrospinning approach that is effective at generating nanofibers from a variety of synthetic and natural biodegradable polymers and integrating these nanofibers into (1) 3D scaffolds with constructive geometry and designed internal macropore structures; and (2) injectable microspheres. Our approach to generating polymer nanofibers is based on the control of polymer-solvent interaction parameter χp-s. We obtained the χp-s and solvent composition phase diagrams of different temperatures according to the Flory-Huggins classic lattice model and the Hildebrand-Scott solubility parameter equation. A critical polymer-solvent interaction parameter χcrit was introduced as a criterion to predict phase separation and nanofiber formation. To test the effectiveness of our approach, a total of 15 widely used biodegradable polymers were selected and successfully fabricated into nanofibrous matrices. Furthermore, macroporous nanofibrous 3D scaffolds with complex architecture and nanofibrous injectable microspheres were generated from those biodegradable polymers by combining our method with other processes. Our approach is universally effective to fabricate nanofibrous matrices from any polymeric materials. This work, therefore, greatly expands our ability to design appropriate biomimetic 3D scaffolds and injectable cell carriers for advanced regenerative therapies.

Development of Experiment and Theory to Detect and Predict Ligand Phase Separation on Silver Nanoparticles

AbstractMALDI mass‐spectrometry measurements are combined with self‐consistent mean‐field (SCF) calculations to detect and predict ligand phase separation on Ag nanoparticles. The experimental and theoretical techniques complement each other by enabling quantification of the nearest‐neighbor distribution of a ligand mixture in a monolayer shell. By tracking a characteristic metallic fragment family, analysis of a MALDI spectrum produces a frequency distribution corresponding to specific ligand patterning. Inherent to the SCF calculation is the enumeration of local interactions that dictate ligand assembly. Interweaving MALDI and SCF facilitates a comparison between the experimentally and theoretically derived frequency distributions as well as their deviation from a well‐mixed state. Thus, we combine these techniques to detect and predict phase separation in monolayers that mix uniformly or experience varying degrees of de‐mixing, including microphase separation and stripe formation. Definition of MALDI removed as this is a commonly recognized technique.

Development of experiment and theory to detect and predict ligand phase separation on silver nanoparticles.

MALDI mass-spectrometry measurements are combined with self-consistent mean-field (SCF) calculations to detect and predict ligand phase separation on Ag nanoparticles. The experimental and theoretical techniques complement each other by enabling quantification of the nearest-neighbor distribution of a ligand mixture in a monolayer shell. By tracking a characteristic metallic fragment family, analysis of a MALDI spectrum produces a frequency distribution corresponding to specific ligand patterning. Inherent to the SCF calculation is the enumeration of local interactions that dictate ligand assembly. Interweaving MALDI and SCF facilitates a comparison between the experimentally and theoretically derived frequency distributions as well as their deviation from a well-mixed state. Thus, we combine these techniques to detect and predict phase separation in monolayers that mix uniformly or experience varying degrees of de-mixing, including microphase separation and stripe formation. Definition of MALDI removed as this is a commonly recognized technique.

Effective interactions in active Brownian suspensions.

Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase separation becomes suppressed by moderate activity, consistent with recent experiments and simulations, and suggests a mechanism for reentrant cluster formation at high activity.