A Lattice Model of Charge-Pattern-Dependent Polyampholyte Phase Separation

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Direct prediction of intermolecular interactions driven by disordered regions

Intrinsically disordered regions (IDRs) are critical for a wide variety of cellular functions, many of which involve interactions with partner proteins. Molecular recognition is typically considered through the lens of sequence-specific binding events. However, a growing body of work has shown that IDRs often interact with partners in a manner that does not depend on the precise order of the amino acid order, instead driven by complementary chemical interactions leading to disordered bound-state complexes. Despite this emerging paradigm, we lack tools to describe, quantify, predict, and interpret these types of structurally heterogeneous interactions from the underlying amino acid sequences. Here, we repurpose the chemical physics developed originally for molecular simulations to develop an approach for predicting intermolecular interactions between IDRs and partner proteins. Our approach enables the direct prediction of phase diagrams, the identification of chemically-specific interaction hotspots on IDRs, and a route to develop and test mechanistic hypotheses regarding IDR function in the context of molecular recognition. We use our approach to examine a range of systems and questions to highlight its versatility and applicability.

Charge block-driven liquid-liquid phase separation - mechanism and biological roles

Liquid-liquid phase separation (LLPS) has increasingly been found to play pivotal roles in a number of intracellular events and reactions, and has introduced a new paradigm in cell biology to explain protein-protein and enzyme-ligand interactions beyond conventional molecular and biochemical theories. LLPS is driven by the cumulative effects of weak and promiscuous interactions, including electrostatic, hydrophobic and cation-π interactions, among polypeptides containing intrinsically disordered regions (IDRs) and describes the macroscopic behaviours of IDR-containing proteins in an intracellular milieu. Recent studies have revealed that interactions between 'charge blocks' - clusters of like charges along the polypeptide chain - strongly induce LLPS and play fundamental roles in its spatiotemporal regulation. Introducing a new parameter, termed 'charge blockiness', into physicochemical models of disordered polypeptides has yielded a better understanding of how the intrinsic amino acid sequence of a polypeptide determines the spatiotemporal occurrence of LLPS within a cell. Charge blockiness might also explain why some post-translational modifications segregate within IDRs and how they regulate LLPS. In this Review, we summarise recent progress towards understanding the mechanism and biological roles of charge block-driven LLPS and discuss how this new characteristic parameter of polypeptides offers new possibilities in the fields of structural biology and cell biology.

Multiscale Computational Framework for the Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

The reversible assembly of intrinsically disordered proteins (IDPs) to form membraneless organelles (MLOs) is a fundamental process involved in the spatiotemporal regulation in living cells. MLOs formed via liquid-liquid phase separation (LLPS) serve as molecule-enhancing hubs to regulate cell functions. Owing to the complexity and dynamic nature of the protein assembly via a network of weak inter- and intra-molecular interactions, it is challenging to describe and predict the LLPS behavior. We have developed a multiscale computational model for IDPs, using the fused in sarcoma (FUS) protein and its variants as illustrative examples. To simplify the description of protein, FUS is represented as a linear chain of stickers interspaced by spacers, as inspired by the associative polymer theory. Low-complexity aromatic-rich kinked segments (LARKS) available in FUS were identified using LARKSdb and represented as "stickers". The pairwise potential energies of each pair of stickers and their β-sheet-forming propensity were estimated via molecular docking and all atomistic molecular dynamics (AA-MD) simulations. Subsequently, FUS chains were randomly positioned in a cubic lattice as coarse-grained (CG) beads, with the bead assignment based on the Kuhn length estimation of stickers and spacers. Stochastic FUS movements were modeled by Monte Carlo (MC) simulations. In addition to the Metropolis algorithm, discretized pair potential distributions between stickers were considered in the move acceptance criteria. The chosen pair potential represents one of the possible binding energy states, with its probability determined by the frequency of the binding energy distribution histogram. The fluctuations of averaged radial distribution functions (RDFs) in successive MC trial move intervals of equilibrated lattice MC simulations were used to indicate the dynamic nature of assembly/disassembly of the protein chains. This multiscale computational framework provides an economical and efficient way of predicting and describing the LLPS behavior of IDPs.

Liquid-liquid biopolymers aqueous solution segregative phase separation in food: From fundamentals to applications-A review

As a result of the spontaneous movement of molecules, liquid-liquid biopolymer segregative phase separation takes place in an aqueous solution. The efficacy of this type of separation can be optimized under conditions where variables such as pH, temperature, and molecular concentrations have minimal impact on its dynamics. Recently, interest in the applications of biopolymers and their segregative phase separation-associated molecular stratification has increased, particularly in the food industry, where these methods permit the purification of specific particles and the embedding of microcapsules. The present review offers a comprehensive examination of the theoretical mechanisms that regulate the liquid-liquid biopolymers aqueous solution segregative phase separation, the factors that may exert an impact on this procedure, and the importance of this particular separation method in the context of food science. These discussion points also address existing difficulties and future possibilities related to the use of segregative phase separation in food applications. This highlights the potential for the design of novel functional foods and the enhancement of food properties.

RNA regulates cohesiveness and porosity of a biological condensate

Biological condensates have emerged as key elements of a biological cell function, concentrating disparate biomolecules to accomplish specific biological tasks. RNA was identified as a key ingredient of such condensates, however, its effect on the physical properties of the condensate was found to depend on the condensate's composition while its effect on the microstructure has remained elusive. Here, we characterize the physical properties and the microstructure of a protein-RNA condensate by means of large-scale coarse-grained (CG) molecular dynamics simulations. By developing a custom CG model of RNA compatible with a popular CG model of proteins, we systematically investigate the structural, thermodynamic, and kinetic properties of condensate droplets containing thousands of individual protein and RNA molecules over a range of temperatures. While we find RNA to increase the condensate's cohesiveness, its effect on the condensate's fluidity is more nuanced with longer molecules compacting the condensate and making it less fluid. We show that a biological condensate has a sponge-like morphology of interconnected channels of size that increases with temperature and decreases in the presence of RNA. Our results suggest that longer RNA form a dynamic scaffold within a condensate, regulating not only its fluidity but also permeability to intruder molecules.

Cross-Talk of Cation-π Interactions with Electrostatic and Aromatic Interactions: A Salt-Dependent Trade-off in Biomolecular Condensates

Biomolecular condensates are essential for cellular functionality, yet the complex interplay among the diverse molecular interactions that mediate their formation remains poorly understood. Here, using coarse-grained molecular dynamics simulations, we address the contribution of cation-π interactions to the stability of condensates formed via liquid-liquid phase separation. We found greater stabilization of up to 80% via cation-π interactions in condensates formed from peptides with higher aromatic residue content or less charge clustering. The contribution of cation-π interactions to droplet stability increases with increasing ionic strength, suggesting a trade-off between cation-π and electrostatic interactions. Cation-π interactions, therefore, can compensate for reduced electrostatic interactions, such as occurs at higher salt concentrations and in sequences with less charged residue content or clustering. Designing condensates with desired biophysical characteristics therefore requires quantification not only of the individual interactions but also cross-talks involving charge-charge, π-π, and cation-π interactions.

Sequence variations of phase-separating proteins and resources for studying biomolecular condensates

Phase separation (PS) is an important mechanism underlying the formation of biomolecular condensates. Physiological condensates are associated with numerous biological processes, such as transcription, immunity, signaling, and synaptic transmission. Changes in particular amino acids or segments can disturb the protein's phase behavior and interactions with other biomolecules in condensates. It is thus presumed that variations in the phase-separating-prone domains can significantly impact the properties and functions of condensates. The dysfunction of condensates contributes to a number of pathological processes. Pharmacological perturbation of these condensates is proposed as a promising way to restore physiological states. In this review, we characterize the variations observed in PS proteins that lead to aberrant biomolecular compartmentalization. We also showcase recent advancements in bioinformatics of membraneless organelles (MLOs), focusing on available databases useful for screening PS proteins and describing endogenous condensates, guiding researchers to seek the underlying pathogenic mechanisms of biomolecular condensates.

Investigating the Hydrogen Bond-Induced Self-Assembly of Polysulfamides Using Molecular Simulations and Experiments

In this paper, we present a synergistic, experimental, and computational study of the self-assembly of N,N'-disubstituted polysulfamides driven by hydrogen bonds (H-bonds) between the H-bonding donor and acceptor groups present in repeating sulfamides as a function of the structural design of the polysulfamide backbone. We developed a coarse-grained (CG) polysulfamide model that captures the directionality of H-bonds between the sulfamide groups and used this model in molecular dynamics (MD) simulations to study the self-assembly of these polymers in implicit solvent. The CGMD approach was validated by reproducing experimentally observed trends in the extent of crystallinity for three polysulfamides synthesized with aliphatic and/or aromatic repeating units. After validation of our CGMD approach, we computationally predicted the effect of repeat unit bulkiness, length, and uniformity of segment lengths in the polymers on the extent of orientational and positional order among the self-assembled polysulfamide chains, providing key design principles for tuning the extent of crystallinity in polysulfamides in experiments. Those computational predictions were then experimentally tested through the synthesis and characterization of polysulfamide architectures.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions featuring the appropriate sequence grammars can contribute via homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. Experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be measured or computed for individual intrinsically disordered regions in complex milieus. For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary, or binodal. Often, only a few points along the binodal are accessible via measurements. In such cases, and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to mean-field free energies for polymer solutions. The nonlinearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules.

Rational design of phase separating peptides based on phase separating protein sequence of p53

Artificial phase-separating (PS) peptides can be used in various applications such as microreactors and drug delivery; however, the design of artificial PS peptides remains a challenge. This can be attributed to the limitation of PS-relevant residues that drive phase separation by interactions of their pairs in short peptides and the difficulty in the design involving interaction with target PS proteins. In this study, we propose a rational method to design artificial PS peptides that satisfy the requirements of liquid droplet formation and co-phase separation with target PS proteins based on the target PS protein sequence. As a proof of concept, we designed five artificial peptides from the model PS protein p53 using this method and confirmed their PS properties using differential interference contrast and fluorescence microscopy. Single-molecule fluorescent tracking demonstrated rapid diffusion of the designed peptides in their droplets compared to that of p53 in p53 droplets. In addition, size-dependent uptake of p53 oligomers was observed in the designed peptide droplets. Large oligomers were excluded from the droplet voids and localized on the droplet surface. The uptake of high-order p53 oligomers into the droplets was enhanced by the elongated linker of the designed peptides. Furthermore, we found that the designed peptide droplets recruited p53 to suppress gel-like aggregate formation. Finally, we discuss aspects that were crucial in the successful design of the artificial PS peptides.

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.

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.

Molecular Determinants for the Layering and Coarsening of Biological Condensates

Many membraneless organelles, or biological condensates, form through phase separation, and play key roles in signal sensing and transcriptional regulation. While the functional importance of these condensates has inspired many studies to characterize their stability and spatial organization, the underlying principles that dictate these emergent properties are still being uncovered. In this review, we examine recent work on biological condensates, especially multicomponent systems. We focus on connecting molecular factors such as binding energy, valency, and stoichiometry with the interfacial tension, explaining the nontrivial interior organization in many condensates. We further discuss mechanisms that arrest condensate coalescence by lowering the surface tension or introducing kinetic barriers to stabilize the multidroplet state.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

Protein structural transitions critically transform the network connectivity and viscoelasticity of RNA-binding protein condensates but RNA can prevent it

Biomolecular condensates, some of which are liquid-like during health, can age over time becoming gel-like pathological systems. One potential source of loss of liquid-like properties during ageing of RNA-binding protein condensates is the progressive formation of inter-protein β-sheets. To bridge microscopic understanding between accumulation of inter-protein β-sheets over time and the modulation of FUS and hnRNPA1 condensate viscoelasticity, we develop a multiscale simulation approach. Our method integrates atomistic simulations with sequence-dependent coarse-grained modelling of condensates that exhibit accumulation of inter-protein β-sheets over time. We reveal that inter-protein β-sheets notably increase condensate viscosity but does not transform the phase diagrams. Strikingly, the network of molecular connections within condensates is drastically altered, culminating in gelation when the network of strong β-sheets fully percolates. However, high concentrations of RNA decelerate the emergence of inter-protein β-sheets. Our study uncovers molecular and kinetic factors explaining how the accumulation of inter-protein β-sheets can trigger liquid-to-solid transitions in condensates, and suggests a potential mechanism to slow such transitions down.

In this work the authors propose a multiscale computational approach, integrating atomistic and coarse-grained models simulations, to study the thermodynamic and kinetic factors playing a major role in the liquid-to-solid transition of biomolecular condensates. It is revealed how the gradual accumulation of inter-protein β-sheets increases the viscosity of functional liquid-like condensates, transforming them into gel-like pathological aggregates, and it is also shown how high concentrations of RNA can decelerate such transition.

Multi-level analysis of intrinsically disordered protein docking methods

Intrinsically Disordered Proteins (IDPs) are a class of proteins in which at least some region of the protein does not possess any stable structure in solution in the physiological condition but may adopt an ordered structure upon binding to a globular receptor. These IDP-receptor complexes are thus subject to protein complex modeling in which computational techniques are applied to accurately reproduce the IDP ligand-receptor interactions. This often exists in the form of protein docking, in which the 3D structures of both the subunits are known, but the position of the ligand relative to the receptor is not. Here, we evaluate the performance of three IDP-receptor modeling tools with metrics that characterize the IDP-receptor interface at various resolutions. We show that all three methods are able to properly identify the general binding site, as identified by lower resolution metrics, but begin to struggle with higher resolution metrics that capture biophysical interactions.

A Mechanistic Model for Cell Cycle Control in Which CDKs Act as Switches of Disordered Protein Phase Separation

Cyclin-dependent kinases (CDKs) are presumed to control the cell cycle by phosphorylating a large number of proteins involved in S-phase and mitosis, two mechanistically disparate biological processes. While the traditional qualitative model of CDK-mediated cell cycle control relies on differences in inherent substrate specificity between distinct CDK-cyclin complexes, they are largely dispensable according to the opposing quantitative model, which states that changes in the overall CDK activity level promote orderly progression through S-phase and mitosis. However, a mechanistic explanation for how such an activity can simultaneously regulate many distinct proteins is lacking. New evidence suggests that the CDK-dependent phosphorylation of ostensibly very diverse proteins might be achieved due to underlying similarity of phosphorylation sites and of the biochemical effects of their phosphorylation: they are preferentially located within intrinsically disordered regions of proteins that are components of membraneless organelles, and they regulate phase separation. Here, we review this evidence and suggest a mechanism for how a single enzyme’s activity can generate the dynamics required to remodel the cell at mitosis.

Rules of Physical Mathematics Govern Intrinsically Disordered Proteins

In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.

Cell cycle-specific phase separation regulated by protein charge blockiness

Dynamic morphological changes of intracellular organelles are often regulated by protein phosphorylation or dephosphorylation^1–6. Phosphorylation modulates stereospecific interactions among structured proteins, but how it controls molecular interactions among unstructured proteins and regulates their macroscopic behaviours remains unknown. Here we determined the cell cycle-specific behaviour of Ki-67, which localizes to the nucleoli during interphase and relocates to the chromosome periphery during mitosis. Mitotic hyperphosphorylation of disordered repeat domains of Ki-67 generates alternating charge blocks in these domains and increases their propensity for liquid–liquid phase separation (LLPS). A phosphomimetic sequence and the sequences with enhanced charge blockiness underwent strong LLPS in vitro and induced chromosome periphery formation in vivo. Conversely, mitotic hyperphosphorylation of NPM1 diminished a charge block and suppressed LLPS, resulting in nucleolar dissolution. Cell cycle-specific phase separation can be modulated via phosphorylation by enhancing or reducing the charge blockiness of disordered regions, rather than by attaching phosphate groups to specific sites.

Yamazaki et al. show that cell cycle-regulated changes in hyperphosphorylation of Ki-67 and NPM1 modulate alternating charge blocks in these proteins, which defines their propensity for liquid–liquid phase separation at chromatin.

Field theory description of ion association in re-entrant phase separation of polyampholytes

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion-pairs through an association reaction. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion-association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

Intrinsically disordered proteins (IDPs) and multidomain proteins with flexible linkers show a high level of structural heterogeneity and are best described by ensembles consisting of multiple conformations with associated thermodynamic weights. Determining conformational ensembles usually involves the integration of biophysical experiments and computational models. In this review, we discuss current approaches to determine conformational ensembles of IDPs and multidomain proteins, including the choice of biophysical experiments, computational models used to sample protein conformations, models to calculate experimental observables from protein structure, and methods to refine ensembles against experimental data. We also provide examples of recent applications of integrative conformational ensemble determination to study IDPs and multidomain proteins and suggest future directions for research in the field.

RNA length has a non-trivial effect in the stability of biomolecular condensates formed by RNA-binding proteins

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) play a crucial role in the spatiotemporal organization of the cell material. Nucleic acids can act as critical modulators in the stability of these protein condensates. To unveil the role of RNA length in regulating the stability of RNA binding protein (RBP) condensates, we present a multiscale computational strategy that exploits the advantages of a sequence-dependent coarse-grained representation of proteins and a minimal coarse-grained model wherein proteins are described as patchy colloids. We find that for a constant nucleotide/protein ratio, the protein fused in sarcoma (FUS), which can phase separate on its own-i.e., via homotypic interactions-only exhibits a mild dependency on the RNA strand length. In contrast, the 25-repeat proline-arginine peptide (PR25), which does not undergo LLPS on its own at physiological conditions but instead exhibits complex coacervation with RNA-i.e., via heterotypic interactions-shows a strong dependence on the length of the RNA strands. Our minimal patchy particle simulations suggest that the strikingly different effect of RNA length on homotypic LLPS versus RBP-RNA complex coacervation is general. Phase separation is RNA-length dependent whenever the relative contribution of heterotypic interactions sustaining LLPS is comparable or higher than those stemming from protein homotypic interactions. Taken together, our results contribute to illuminate the intricate physicochemical mechanisms that influence the stability of RBP condensates through RNA inclusion.

Limitations of field-theory simulation for exploring phase separation: The role of repulsion in a lattice protein model

Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding

The assembly of functional biomolecular condensates often involves liquid-liquid phase separation (LLPS) of proteins with multiple modular domains, which can be folded or conformationally disordered to various degrees. To understand the LLPS-driving domain-domain interactions, a fundamental question is how readily the interactions in the condensed phase can be inferred from interdomain interactions in dilute solutions. In particular, are the interactions leading to LLPS exclusively those underlying the formation of discrete interdomain complexes in homogeneous solutions? We address this question by developing a mean-field LLPS theory of two stoichiometrically constrained solute species. The theory is applied to the neuronal proteins SynGAP and PSD-95, whose complex coacervate serves as a rudimentary model for neuronal postsynaptic densities (PSDs). The predicted phase behaviors are compared with experiments. Previously, a three SynGAP/two PSD-95 ratio was determined for SynGAP/PSD-95 complexes in dilute solutions. However, when this 3:2 stoichiometry is uniformly imposed in our theory encompassing both dilute and condensed phases, the tie-line pattern of the predicted SynGAP/PSD-95 phase diagram differs drastically from that obtained experimentally. In contrast, theories embodying alternate scenarios postulating auxiliary SynGAP-PSD-95 as well as SynGAP-SynGAP and PSD-95-PSD-95 interactions, in addition to those responsible for stoichiometric SynGAP/PSD-95 complexes, produce tie-line patterns consistent with experiment. Hence, our combined theoretical-experimental analysis indicates that weaker interactions or higher-order complexes beyond the 3:2 stoichiometry, but not yet documented, are involved in the formation of SynGAP/PSD-95 condensates, imploring future efforts to ascertain the nature of these auxiliary interactions in PSD-like LLPS and underscoring a likely general synergy between stoichiometric, structurally specific binding and stochastic, multivalent "fuzzy" interactions in the assembly of functional biomolecular condensates.

Motif-pattern dependence of biomolecular phase separation driven by specific interactions

Eukaryotic cells partition a wide variety of important materials and processes into biomolecular condensates—phase-separated droplets that lack a membrane. In addition to nonspecific electrostatic or hydrophobic interactions, phase separation also depends on specific binding motifs that link together constituent molecules. Nevertheless, few rules have been established for how these ubiquitous specific, saturating, motif-motif interactions drive phase separation. By integrating Monte Carlo simulations of lattice-polymers with mean-field theory, we show that the sequence of heterotypic binding motifs strongly affects a polymer’s ability to phase separate, influencing both phase boundaries and condensate properties (e.g. viscosity and polymer diffusion). We find that sequences with large blocks of single motifs typically form more inter-polymer bonds, which promotes phase separation. Notably, the sequence of binding motifs influences phase separation primarily by determining the conformational entropy of self-bonding by single polymers. This contrasts with systems where the molecular architecture primarily affects the energy of the dense phase, providing a new entropy-based mechanism for the biological control of phase separation.

Cells need to concentrate biomolecules in the right place at the right time in order to function. Many important intracellular compartments are liquid droplets formed by phase separation, the same process that separates oil from vinegar. The properties of such “biomolecular condensates” depend on the component molecules, such as proteins and RNAs. These molecules are polymers made of many interacting monomers, often organized into “motifs,” and the sequence of motifs shapes the properties of the condensates. Recent work has revealed important principles governing phase separation when the motifs are charged and interact across long distances, but many phase-separating molecules form specific interactions that are short-range and one-to-one. How does the sequence of specifically-interacting motifs affect phase separation? Using a combination of simulations and theoretical calculations, we show that the sequence has profound effects on both the formation and properties of condensates. Sequences with large blocks of identical motifs are better at phase separating but more viscous and solid-like. Importantly, we find that sequence controls phase separation via the proclivity to form self-bonds instead of forming bonds with other polymers. Thus the sequence of specifically-interacting motifs provides a control point for the formation and properties of phase-separated intracellular compartments.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

'RNA modulation of transport properties and stability in phase-separated condensates

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

Clustering of Aromatic Residues in Prion-like Domains Can Tune the Formation, State, and Organization of Biomolecular Condensates

In immature oocytes, Balbiani bodies are conserved membraneless condensates implicated in oocyte polarization, the organization of mitochondria, and long-term organelle and RNA storage. In Xenopus laevis, Balbiani body assembly is mediated by the protein Velo1. Velo1 contains an N-terminal prion-like domain (PLD) that is essential for Balbiani body formation. PLDs have emerged as a class of intrinsically disordered regions that can undergo various different types of intracellular phase transitions and are often associated with dynamic, liquid-like condensates. Intriguingly, the Velo1 PLD forms solid-like assemblies. Here we sought to understand why Velo1 phase behavior appears to be biophysically distinct from that of other PLD-containing proteins. Through bioinformatic analysis and coarse-grained simulations, we predict that the clustering of aromatic residues and the amino acid composition of residues between aromatics can influence condensate material properties, organization, and the driving forces for assembly. To test our predictions, we redesigned the Velo1 PLD to test the impact of targeted sequence changes in vivo. We found that the Velo1 design with evenly spaced aromatic residues shows rapid internal dynamics, as probed by fluorescent recovery after photobleaching, even when recruited into Balbiani bodies. Our results suggest that Velo1 might have been selected in evolution for distinctly clustered aromatic residues to maintain the structure of Balbiani bodies in long-lived oocytes. In general, our work identifies several tunable parameters that can be used to augment the condensate material state, offering a road map for the design of synthetic condensates.

Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions

Multivalent proteins and nucleic acids can self-assemble into biomolecular condensates that contribute to compartmentalize the cell interior. Computer simulations offer a unique view to elucidate the mechanisms and key intermolecular interactions behind the dynamic formation and dissolution of these condensates. In this work, we present a novel approach to include explicit water and salt in sequence-dependent coarse-grained (CG) models for proteins and RNA, enabling the study of biomolecular condensate formation in a salt-dependent manner. Our framework combines a reparameterized version of the HPS protein force field with the monoatomic mW water model and the mW-ion potential for NaCl. We show how our CG model qualitatively captures the experimental radius of the gyration trend of a subset of intrinsically disordered proteins and reproduces the experimental protein concentration and water percentage of the human fused in sarcoma (FUS) low-complexity-domain droplets at physiological salt concentration. Moreover, we perform seeding simulations as a function of salt concentration for two antagonist systems: the engineered peptide PR₂₅ and poly-uridine/poly-arginine mixtures, finding good agreement with their reported in vitro phase behavior with salt concentration in both cases. Taken together, our work represents a step forward towards extending sequence-dependent CG models to include water and salt, and to consider their key role in biomolecular condensate self-assembly.

Sequence Determines the Switch in the Fibril Forming Regions in the Low-Complexity FUS Protein and Its Variants

Residues spanning distinct regions of the low-complexity domain of the RNA-binding protein, Fused in Sarcoma (FUS-LC), form fibril structures with different core morphologies. Solid-state NMR experiments show that the 214-residue FUS-LC forms a fibril with an S-bend (core-1, residues 39-95), while the rest of the protein is disordered. In contrast, the fibrils of the C-terminal variant (FUS-LC-C; residues 111-214) have a U-bend topology (core-2, residues 112-150). Absence of the U-bend in FUS-LC implies that the two fibril cores do not coexist. Computer simulations show that these perplexing findings could be understood in terms of the population of sparsely populated fibril-like excited states in the monomer. The propensity to form core-1 is higher compared to core-2. We predict that core-2 forms only in truncated variants that do not contain the core-1 sequence. At the monomer level, sequence-dependent enthalpic effects determine the relative stabilities of the core-1 and core-2 topologies.

Dissecting the complexity of biomolecular condensates

Biomolecular condensates comprise a diverse and ubiquitous class of membraneless organelles. Condensate assembly is often described by liquid-liquid phase separation. While this process explains many key features, it cannot account for the compositional or architectural complexity that condensates display in cells. Recent work has begun to dissect the rich network of intermolecular interactions that give rise to biomolecular condensates. Here, we review the latest results from theory, simulations and experiments, and discuss what they reveal about the structure-function relationship of condensates.

How Do Flaviviruses Hijack Host Cell Functions by Phase Separation?

Viral proteins interact with different sets of host cell components throughout the viral life cycle and are known to localize to the intracellular membraneless organelles (MLOs) of the host cell, where formation/dissolution is regulated by phase separation of intrinsically disordered proteins and regions (IDPs/IDRs). Viral proteins are rich in IDRs, implying that viruses utilize IDRs to regulate phase separation of the host cell organelles and augment replication by commandeering the functions of the organelles and/or sneaking into the organelles to evade the host immune response. This review aims to integrate current knowledge of the structural properties and intracellular localizations of viral IDPs to understand viral strategies in the host cell. First, the properties of viral IDRs are reviewed and similarities and differences with those of eukaryotes are described. The higher IDR content in viruses with smaller genomes suggests that IDRs are essential characteristics of viral proteins. Then, the interactions of the IDRs of flaviviruses with the MLOs of the host cell are investigated with emphasis on the viral proteins localized in the nucleoli and stress granules. Finally, the possible roles of viral IDRs in regulation of the phase separation of organelles and future possibilities for antiviral drug development are discussed.

Finite-size shifts in simulated protein droplet phase diagrams

Computer simulation can provide valuable insight into the forces driving biomolecular liquid-liquid phase separation. However, the simulated systems have a limited size, which makes it important to minimize and control finite-size effects. Here, using a phenomenological free-energy ansatz, we investigate how the single-phase densities observed in a canonical system under coexistence conditions depend on the system size and the total density. We compare the theoretical expectations with results from Monte Carlo simulations based on a simple hydrophobic/polar protein model. We consider both cubic systems with spherical droplets and elongated systems with slab-like droplets. The results presented suggest that the slab simulation method greatly facilitates the estimation of the coexistence densities in the large-system limit.

Protein Phase Separation Arising from Intrinsic Disorder: First-Principles to Bespoke Applications

The phase separation of biomolecules has become the focus of intense research in the past decade, with a growing body of research implicating this phenomenon in essentially all biological functions, including but not limited to homeostasis, stress responses, gene regulation, cell differentiation, and disease. Excellent reviews have been published previously on the underlying physical basis of liquid-liquid phase separation (LLPS) of biological molecules (Nat. Phys. 2015, 11, 899-904) and LLPS as it occurs natively in physiology and disease (Science 2017, 357, eaaf4382; Biochemistry 2018, 57, 2479-2487; Chem. Rev. 2014, 114, 6844-6879). Here, we review how the theoretical physical basis of LLPS has been used to better understand the behavior of biomolecules that undergo LLPS in natural systems and how this understanding has also led to the development of novel synthetic systems that exhibit biomolecular phase separation, and technologies that exploit these phenomena. In part 1 of this Review, we explore the theory behind the phase separation of biomolecules and synthetic macromolecules and introduce a few notable phase-separating biomolecules. In part 2, we cover experimental and computational methods used to study phase-separating proteins and how these techniques have uncovered the mechanisms underlying phase separation in physiology and disease. Finally, in part 3, we cover the development and applications of engineered phase-separating polypeptides, ranging from control of their self-assembly to create defined supramolecular architectures to reprogramming biological processes using engineered IDPs that exhibit LLPS.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.

Thermodynamic and sequential characteristics of phase separation and droplet formation for an intrinsically disordered region/protein ensemble

Liquid–liquid phase separation (LLPS) of some IDPs/IDRs can lead to the formation of the membraneless organelles in vitro and in vivo, which are essential for many biological processes in the cell. Here we select three different IDR segments of chaperon Swc5 and develop a polymeric slab model at the residue-level. By performing the molecular dynamics simulations, LLPS can be observed at low temperatures even without charge interactions and disappear at high temperatures. Both the sequence length and the charge pattern of the Swc5 segments can influence the critical temperature of LLPS. The results suggest that the effects of the electrostatic interactions on the LLPS behaviors can change significantly with the ratios and distributions of the charged residues, especially the sequence charge decoration (SCD) values. In addition, three different forms of swc conformation can be distinguished on the phase diagram, which is different from the conventional behavior of the free IDP/IDR. Both the packed form (the condensed-phase) and the dispersed form (the dilute-phase) of swc chains are found to be coexisted when LLPS occurs. They change to the fully-spread form at high temperatures. These findings will be helpful for the investigation of the IDP/IDR ensemble behaviors as well as the fundamental mechanism of the LLPS process in bio-systems.

The membraneless organelles caused by liquid–liquid phase separation (LLPS) of IDPs/IDRs are involved in a wide range of biological functions such as RNA processing, ribosome biogenesis, and sequestration of mRNA, proteins, and compacted chromatin. In this study, we focus on the histone H2A-H2B binding partner, Swc5 and investigate the effects of the temperature, sequence length and number of charged residues on the LLPS behaviors. Moreover, we proposed three forms of swc conformation in ensemble according to the phase diagram. These characteristics of conformational changes (from LLPS to no LLPS, from condensed-phase to dilute-phase) are observed in the swc chains with different sequence length and charge pattern, which may be the general property for the IDP/IDR ensembles.

Biophysics of Phase Separation of Disordered Proteins Is Governed by Balance between Short- And Long-Range Interactions

Intrinsically disordered proteins play a crucial role in cellular phase separation, yet the diverse molecular forces driving phase separation are not fully understood. It is of utmost importance to understand how peptide sequence, and particularly the balance between the peptides’ short- and long-range interactions with other peptides, may affect the stability, structure, and dynamics of liquid–liquid phase separation in protein condensates. Here, using coarse-grained molecular dynamics simulations, we studied the liquid properties of the condensate in a series of polymers in which the ratio of short-range dispersion interactions to long-range electrostatic interactions varied. As the fraction of mutations that participate in short-range interactions increases at the expense of long-range electrostatic interactions, a significant decrease in the critical temperature of phase separation is observed. Nevertheless, sequences with a high fraction of short-range interactions exhibit stabilization, which suggests compensation for the loss of long-range electrostatic interactions. Decreased condensate stability is coupled with decreased translational diffusion of the polymers in the condensate, which may result in the loss of liquid characteristics in the presence of a high fraction of uncharged residues. The effect of exchanging long-range electrostatic interactions for short-range interactions can be explained by the kinetics of breaking intermolecular contacts with neighboring polymers and the kinetics of intramolecular fluctuations. While both time scales are coupled and increase as electrostatic interactions are lost, for sequences that are dominated by short-range interactions, the kinetics of intermolecular contact breakage significantly slows down. Our study supports the contention that different types of interactions can maintain protein condensates, however, long-range electrostatic interactions enhance its liquid-like behavior.

Fundamental Challenges and Outlook in Simulating Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) populate an ensemble of dynamic conformations, making their structural characterization by experiments challenging. Many IDPs undergo liquid-liquid phase separation into dense membraneless organelles with myriad cellular functions. Multivalent interactions in low-complexity IDPs promote the formation of these subcellular coacervates. While solution NMR, Förster resonance energy transfer (FRET), and small-angle X-ray scattering (SAXS) studies on IDPs have their own challenges, recent computational methods draw a rational trade-off to characterize the driving forces underlying phase separation. In this Perspective, we critically evaluate the scope of approximation-free field theoretic simulations, well-tempered ensemble methods, enhanced sampling techniques, coarse-grained force fields, and slab simulation approaches to offer an improved understanding of phase separation. A synergy between simulation length scale and model resolution would reduce the existing caveats and enable theories of polymer physics to elucidate finer details of liquid-liquid phase separation (LLPS). These computational advances offer promise for rigorous characterization of the IDP proteome and designing peptides with tunable material and self-assembly properties.

Cavin1 intrinsically disordered domains are essential for fuzzy electrostatic interactions and caveola formation

Caveolae are spherically shaped nanodomains of the plasma membrane, generated by cooperative assembly of caveolin and cavin proteins. Cavins are cytosolic peripheral membrane proteins with negatively charged intrinsically disordered regions that flank positively charged α-helical regions. Here, we show that the three disordered domains of Cavin1 are essential for caveola formation and dynamic trafficking of caveolae. Electrostatic interactions between disordered regions and α-helical regions promote liquid-liquid phase separation behaviour of Cavin1 in vitro, assembly of Cavin1 oligomers in solution, generation of membrane curvature, association with caveolin-1, and Cavin1 recruitment to caveolae in cells. Removal of the first disordered region causes irreversible gel formation in vitro and results in aberrant caveola trafficking through the endosomal system. We propose a model for caveola assembly whereby fuzzy electrostatic interactions between Cavin1 and caveolin-1 proteins, combined with membrane lipid interactions, are required to generate membrane curvature and a metastable caveola coat.

Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.

Simulation of FUS Protein Condensates with an Adapted Coarse-Grained Model

Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01-0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625-0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.

Finite-size scaling analysis of protein droplet formation

The formation of biomolecular condensates inside cells often involve intrinsically disordered proteins (IDPs), and several of these IDPs are also capable of forming dropletlike dense assemblies on their own, through liquid-liquid phase separation. When modeling thermodynamic phase changes, it is well known that finite-size scaling analysis can be a valuable tool. However, to our knowledge, this approach has not been applied before to the computationally challenging problem of modeling sequence-dependent biomolecular phase separation. Here we implement finite-size scaling methods to investigate the phase behavior of two 10-bead sequences in a continuous hydrophobic-polar protein model. Combined with reversible explicit-chain Monte Carlo simulations of these sequences, finite-size scaling analysis turns out to be both feasible and rewarding, despite relying on theoretical results for asymptotically large systems. While both sequences form dense clusters at low temperature, this analysis shows that only one of them undergoes liquid-liquid phase separation. Furthermore, the transition temperature at which droplet formation sets in is observed to converge slowly with system size, so that even for our largest systems the transition is shifted by about 8%. Using finite-size scaling analysis, this shift can be estimated and corrected for.

Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Microfluidic characterization of macromolecular liquid-liquid phase separation

Liquid-liquid phase separation plays important roles in the compartmentalization of cells. Developing an understanding of how phase separation is encoded in biomacromolecules requires quantitative mapping of their phase behavior. Given that such experiments require large quantities of the biomolecule of interest, these efforts have been lagging behind the recent breadth of biological insights. Herein, we present a microfluidic phase chip that enables the measurement of saturation concentrations over at least three orders of magnitude for a broad spectrum of biomolecules and solution conditions. The phase chip consists of five units, each made of twenty individual sample chambers to allow the measurement of five sample conditions simultaneously. The analytes are slowly concentrated via evaporation of water, which is replaced by oil, until the sample undergoes phase separation into a dilute and dense phase. We show that the phase chip lowers the required sample quantity by 98% while offering six-fold better statistics in comparison to standard manual experiments that involve centrifugal separation of dilute and dense phases. We further show that the saturation concentrations measured in chips are in agreement with previously reported data for a variety of biomolecules. Concomitantly, time-dependent changes of the dense phase morphology and potential off-pathway processes, including aggregation, can be monitored microscopically. In summary, the phase chip is suited to exploring sequence-to-binodal relationships by enabling the determination of a large number of saturation concentrations at low protein cost.

How do intrinsically disordered protein regions encode a driving force for liquid-liquid phase separation?

Liquid-liquid phase separation is the mechanism underlying the formation of biomolecular condensates. Disordered protein regions often drive phase separation, but the molecular interactions mediating this phenomenon are not well understood, sometimes leading to the conflation that all disordered protein regions drive phase separation. Given the critical role of phase separation in many cellular processes, and that dysfunction of phase separation can lead to debilitating diseases, it is important that we understand the interactions and sequence properties underlying phase behavior. A conceptual framework that divides IDRs into interacting and solvating regions has proven particularly useful, and analytical instantiations and coarse-grained models can test our understanding of the driving forces against experimental phase behavior. Validated simulation paradigms enable the exploration of sequence space to help our understanding of how disordered protein regions can encode phase behavior, which IDRs may mediate phase separation in cells, and which IDRs are highly soluble.

Analytical Theory for Sequence-Specific Binary Fuzzy Complexes of Charged Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed by the interacting IDPs' amino acid sequences, while their assembled conformations remain largely disordered. To help elucidate a basic aspect of this fascinating yet poorly understood phenomenon, the binding of a homo or heterodimeric pair of polyampholytic IDPs is modeled statistical mechanically using cluster expansion. We find that the binding affinities of binary fuzzy complexes in the model correlate strongly with a newly derived simple "joint sequence charge decoration" parameter readily calculable from the pair of IDPs' sequence charge patterns. Predictions by our analytical theory are in essential agreement with coarse-grained explicit-chain simulations. This computationally efficient theoretical framework is expected to be broadly applicable to rationalizing and predicting sequence-specific IDP-IDP polyelectrostatic interactions.