Decoding the physical principles of two-component biomolecular phase separation

Sequence complexity and monomer rigidity control the morphologies and aging dynamics of protein aggregates

Understanding the biophysical basis of protein aggregation is important in biology because of the potential link to several misfolding diseases. Although experiments have shown that protein aggregates adopt a variety of morphologies, the dynamics of their formation are less well characterized. Here, we introduce a minimal model to explore the dependence of the aggregation dynamics on the structural and sequence features of the monomers. Using simulations, we demonstrate that sequence complexity (codified in terms of word entropy) and monomer rigidity profoundly influence the dynamics and morphology of the aggregates. Flexible monomers with low sequence complexity (corresponding to repeat sequences) form liquid-like droplets that exhibit ergodic behavior. Strikingly, these aggregates abruptly transition to more ordered structures, reminiscent of amyloid fibrils, when the monomer rigidity is increased. In contrast, aggregates resulting from monomers with high sequence complexity are amorphous and display nonergodic glassy dynamics. The heterogeneous dynamics of the low and high-complexity sequences follow stretched exponential kinetics, which is one of the characteristics of glassy dynamics. Importantly, at nonzero values of the bending rigidities, the aggregates age with the relaxation times that increase with the waiting time. Informed by these findings, we provide insights into aging dynamics in protein condensates and contrast the behavior with the dynamics expected in RNA repeat sequences. Our findings underscore the influence of the monomer characteristics in shaping the morphology and dynamics of protein aggregates, thus providing a foundation for deciphering the general rules governing the behavior of protein condensates.

Nonspecific Yet Selective Interactions Contribute to Small Molecule Condensate Binding

Biomolecular condensates are essential in various cellular processes, and their misregulation has been demonstrated to underlie disease. Small molecules that modulate condensate stability and material properties offer promising therapeutic approaches, but mechanistic insights into their interactions with condensates remain largely lacking. We employ a multiscale approach to enable long-time, equilibrated all-atom simulations of various condensate-ligand systems. Systematic characterization of the ligand binding poses reveals that condensates can form diverse and heterogeneous chemical environments with one or multiple chains to bind small molecules. Unlike traditional protein-ligand interactions, these chemical environments are dominated by nonspecific hydrophobic interactions. Nevertheless, the chemical environments feature unique amino acid compositions and physicochemical properties that favor certain small molecules over others, resulting in varied ligand partitioning coefficients within condensates. Notably, different condensates share similar sets of chemical environments but at different populations. This population shift drives ligand selectivity toward specific condensates. Our approach can enhance the interpretation of experimental screening data and may assist in the rational design of small molecules targeting specific condensates.

Selectivity of Complex Coacervation in Multiprotein Mixtures

Liquid-liquid phase separation of biomolecules is increasingly recognized as being relevant to various cellular functions, and complex coacervation of biomacromolecules, particularly proteins, is emerging as a key mechanism for this phenomenon. Complex coacervation is also being explored as a potential protein purification method due to its potential scalability, aqueous operation, and ability to produce a highly concentrated product. However, to date, most studies of complex coacervation have evaluated the phase behavior of a binary mixture of two oppositely charged macromolecules. Therefore, a comprehensive understanding of the phase behavior of complex biological mixtures is yet to be established. To address this, a panel of engineered proteins was designed to allow for quantitative analysis of the complex coacervation of individual proteins within a multicomponent mixture. The behavior of individual proteins was evaluated using a defined mixture of proteins that mimics the charge profile of the Escherichia coli proteome. To allow for the direct quantification of proteins in each phase, spectrally separated fluorescent proteins were used to construct the protein mixture. From this quantitative analysis, we observed that protein coacervation was synchronized in the mixture, which was distinctive from the behavior when each protein was evaluated in a single-protein system. Subtle differences in biophysical properties between the proteins, such as the ionization of individual charged residues and overall charge density, became noticeable in the mixture, which allowed us to elucidate parameters for protein complex coacervation. With this understanding, we successfully designed methods to enrich a range of proteins of interest from a mixture of proteins.

The exchange dynamics of biomolecular condensates

A hallmark of biomolecular condensates formed via liquid-liquid phase separation is that they dynamically exchange material with their surroundings, and this process can be crucial to condensate function. Intuitively, the rate of exchange can be limited by the flux from the dilute phase or by the mixing speed in the dense phase. Surprisingly, a recent experiment suggests that exchange can also be limited by the dynamics at the droplet interface, implying the existence of an 'interface resistance'. Here, we first derive an analytical expression for the timescale of condensate material exchange, which clearly conveys the physical factors controlling exchange dynamics. We then utilize sticker-spacer polymer models to show that interface resistance can arise when incident molecules transiently touch the interface without entering the dense phase, i.e., the molecules 'bounce' from the interface. Our work provides insight into condensate exchange dynamics, with implications for both natural and synthetic systems.

Measurement of solubility product reveals the interplay of oligomerization and self-association for defining condensate formation

Cellular condensates often consist of 10s to 100s of distinct interacting molecular species. Because of the complexity of these interactions, predicting the point at which they will undergo phase separation is daunting. Using experiments and computation, we therefore studied a simple model system consisting of polySH3 and polyPRM designed for pentavalent heterotypic binding. We tested whether the peak solubility product, or the product of the dilute phase concentration of each component, is a predictive parameter for the onset of phase separation. Titrating up equal total concentrations of each component showed that the maximum solubility product does approximately coincide with the threshold for phase separation in both experiments and models. However, we found that measurements of dilute phase concentration include small oligomers and monomers; therefore, a quantitative comparison of the experiments and models required inclusion of small oligomers in the model analysis. Even with the inclusion of small polyPRM and polySH3 oligomers, models did not predict experimental results. This led us to perform dynamic light scattering experiments, which revealed homotypic binding of polyPRM. Addition of this interaction to our model recapitulated the experimentally observed asymmetry. Thus, comparing experiments with simulation reveals that the solubility product can be predictive of the interactions underlying phase separation, even if small oligomers and low affinity homotypic interactions complicate the analysis.

Mechanistic insights into condensate formation of human liver-type phosphofructokinase by stochastic modeling approaches

Human liver-type phosphofructokinase 1 (PFKL) has been shown to regulate glucose flux as a scaffolder arranging glycolytic and gluconeogenic enzymes into a multienzyme metabolic condensate, the glucosome. However, it has remained elusive of how phase separation of PFKL is governed and initiates glucosome formation in living cells, thus hampering to understand a mechanism of glucosome formation and its functional contribution to human cells. In this work, we developed a stochastic model in silico using the principle of Langevin dynamics to investigate how biological properties of PFKL contribute to the condensate formation. The significance of an intermolecular interaction between PFKLs, an effective concentration of PFKL at a region of interest, and its own self-assembled filaments in formation of PFKL condensates and control of their sizes were demonstrated by molecular dynamics simulation using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Such biological properties that define intracellular dynamics of PFKL appear to be essential for phase separation of PFKL, which may represent an initiation step for the formation of glucosome condensates. Collectively, our computational study provides mechanistic insights of glucosome formation, particularly an initial stage through the formation of PFKL condensates in living human cells.

Non-specific yet selective interactions contribute to small molecule condensate partitioning behavior

Biomolecular condensates are essential in various cellular processes, and their misregulation has been demonstrated to be underly disease. Small molecules that modulate condensate stability and material properties offer promising therapeutic approaches, but mechanistic insights into their interactions with condensates remain largely lacking. We employ a multiscale approach to enable long-time, equilibrated all-atom simulations of various condensate-ligand systems. Systematic characterization of the ligand binding poses reveals that condensates can form diverse and heterogeneous chemical environments with one or multiple chains to bind small molecules. Unlike traditional protein-ligand interactions, these chemical environments are dominated by non-specific hydrophobic interactions. Nevertheless, the chemical environments feature unique amino acid compositions and physicochemical properties that favor certain small molecules over others, resulting in varied ligand partitioning coefficients within condensates. Notably, different condensates share similar sets of chemical environments but at different populations. This population shift drives ligand selectivity towards specific condensates. Our approach can enhance the interpretation of experimental screening data and may assist in the rational design of small molecules targeting specific condensates.

Rapid and reversible dissolution of biomolecular condensates using light-controlled recruitment of a solubility tag

Biomolecular condensates are broadly implicated in both normal cellular regulation and disease. Consequently, several chemical biology and optogenetic approaches have been developed to induce phase separation of a protein of interest. However, few tools are available to perform the converse function - dissolving a condensate of interest on demand. Such a tool would aid in testing whether the condensate plays specific functional roles. Here we show that light-gated recruitment of a solubilizing domain, maltose-binding protein (MBP), results in rapid and controlled dissolution of condensates formed from proteins of interest. Our optogenetic MBP-based dissolution strategy (OptoMBP) is rapid, reversible, and can be spatially controlled with subcellular precision. We also provide a proof-of-principle application of OptoMBP by disrupting condensation of the oncogenic fusion protein FUS-CHOP and reverting FUS-CHOP driven transcriptional changes. We envision that the OptoMBP system could be broadly useful for disrupting constitutive protein condensates to probe their biological functions.

Preserving condensate structure and composition by lowering sequence complexity

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

Determinants that enable disordered protein assembly into discrete condensed phases

Cells harbour numerous mesoscale membraneless compartments that house specific biochemical processes and perform distinct cellular functions. These protein- and RNA-rich bodies are thought to form through multivalent interactions among proteins and nucleic acids, resulting in demixing via liquid-liquid phase separation. Proteins harbouring intrinsically disordered regions (IDRs) predominate in membraneless organelles. However, it is not known whether IDR sequence alone can dictate the formation of distinct condensed phases. We identified a pair of IDRs capable of forming spatially distinct condensates when expressed in cells. When reconstituted in vitro, these model proteins do not co-partition, suggesting condensation specificity is encoded directly in the polypeptide sequences. Through computational modelling and mutagenesis, we identified the amino acids and chain properties governing homotypic and heterotypic interactions that direct selective condensation. These results form the basis of physicochemical principles that may direct subcellular organization of IDRs into specific condensates and reveal an IDR code that can guide construction of orthogonal membraneless compartments.

Aromatic and arginine content drives multiphasic condensation of protein-RNA mixtures

Multiphasic architectures are found ubiquitously in biomolecular condensates and are thought to have important implications for the organization of multiple chemical reactions within the same compartment. Many of these multiphasic condensates contain RNA in addition to proteins. Here, we investigate the importance of different interactions in multiphasic condensates comprising two different proteins and RNA using computer simulations with a residue-resolution coarse-grained model of proteins and RNA. We find that in multilayered condensates containing RNA in both phases, protein-RNA interactions dominate, with aromatic residues and arginine forming the key stabilizing interactions. The total aromatic and arginine content of the two proteins must be appreciably different for distinct phases to form, and we show that this difference increases as the system is driven toward greater multiphasicity. Using the trends observed in the different interaction energies of this system, we demonstrate that we can also construct multilayered condensates with RNA preferentially concentrated in one phase. The "rules" identified can thus enable the design of synthetic multiphasic condensates to facilitate further study of their organization and function.

Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase

The condensation of Rubisco holoenzymes and linker proteins into "pyrenoids," a crucial supercharger of photosynthesis in algae, is qualitatively understood in terms of "sticker-and-spacer" theory. We derive semianalytical partition sums for small Rubisco-linker aggregates, which enable the calculation of both dilute-phase titration curves and dimerization diagrams. By fitting the titration curves to surface plasmon resonance and single-molecule fluorescence microscopy data, we extract the molecular properties needed to predict dimerization diagrams. We use these to estimate typical concentrations for condensation, and successfully compare these to microscopy observations.

Selectivity of Complex Coacervation in Multi-Protein Mixtures

Liquid-liquid phase separation of biomolecules is increasingly recognized as relevant to various cellular functions, and complex coacervation of biomacromolecules, particularly proteins, is emerging as a key mechanism for this phenomenon. Complex coacervation is also being explored as a potential protein purification method due to its potential scalability, aqueous operation, and ability to produce a highly concentrated product. However, to date most studies of complex coacervation have evaluated the phase behavior of a binary mixture of two oppositely charged macromolecules. Therefore, a comprehensive understanding of the phase behavior of complex biological mixtures has yet to be established. To address this, a panel of engineered proteins was designed to allow for quantitative analysis of the complex coacervation of individual proteins within a multi-component mixture. The behavior of individual proteins was evaluated using a defined mixture of proteins that mimics the charge profile of the E. coli proteome. To allow for direct quantification of proteins in each phase, spectrally separated fluorescent proteins were used to construct the protein mixture. From this quantitative analysis, we observed that the coacervation behavior of individual proteins in the mixture was consistent with each other, which was distinctive from the behavior when each protein was evaluated in a single-protein system. Subtle differences in biophysical properties between the proteins became noticeable in the mixture, which allowed us to elucidate parameters for protein complex coacervation. With this understanding, we successfully designed methods to enrich a range of proteins of interest from a mixture of proteins.

Measurement of solubility product in a model condensate reveals the interplay of small oligomerization and self-association

Cellular condensates often consist of 10s to 100s of distinct interacting molecular species. Because of the complexity of these interactions, predicting the point at which they will undergo phase separation into discrete compartments is daunting. Using experiments and computation, we therefore studied a simple model system consisting of 2 proteins, polySH3 and polyPRM, designed for pentavalent heterotypic binding. We tested whether the peak solubility product, the product of dilute phase monomer concentrations, is a predictive parameter for the onset of phase separation. Titrating up equal total concentrations of each component showed that the maximum solubility product does approximately coincide with the threshold for phase separation in both the experiments and models. However, we found that measurements of dilute phase concentration include contributions from small oligomers, not just monomers; therefore, a quantitative comparison of the experiments and models required inclusion of small oligomers in the model analysis. We also examined full phase diagrams where the model results were almost symmetric along the diagonal, but the experimental results were highly asymmetric. This led us to perform dynamic light scattering experiments, where we discovered a weak homotypic interaction for polyPRM; when this was added to the computational model, it was able to recapitulate the experimentally observed asymmetry. Thus, comparing experiments to simulation reveals that the solubility product can be predictive of phase separation, even if small oligomers and low affinity homotypic interactions preclude experimental measurement of monomer concentration.

SAGA1 and SAGA2 promote starch formation around proto-pyrenoids in Arabidopsis chloroplasts

The pyrenoid is a chloroplastic microcompartment in which most algae and some terrestrial plants condense the primary carboxylase, Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase) as part of a CO2-concentrating mechanism that improves the efficiency of CO2 capture. Engineering a pyrenoid-based CO2-concentrating mechanism (pCCM) into C3 crop plants is a promising strategy to enhance yield capacities and resilience to the changing climate. Many pyrenoids are characterized by a sheath of starch plates that is proposed to act as a barrier to limit CO2 diffusion. Recently, we have reconstituted a phase-separated "proto-pyrenoid" Rubisco matrix in the model C3 plant Arabidopsis thaliana using proteins from the alga with the most well-studied pyrenoid, Chlamydomonas reinhardtii [N. Atkinson, Y. Mao, K. X. Chan, A. J. McCormick, Nat. Commun. 11, 6303 (2020)]. Here, we describe the impact of introducing the Chlamydomonas proteins StArch Granules Abnormal 1 (SAGA1) and SAGA2, which are associated with the regulation of pyrenoid starch biogenesis and morphology. We show that SAGA1 localizes to the proto-pyrenoid in engineered Arabidopsis plants, which results in the formation of atypical spherical starch granules enclosed within the proto-pyrenoid condensate and adjacent plate-like granules that partially cover the condensate, but without modifying the total amount of chloroplastic starch accrued. Additional expression of SAGA2 further increases the proportion of starch synthesized as adjacent plate-like granules that fully encircle the proto-pyrenoid. Our findings pave the way to assembling a diffusion barrier as part of a functional pCCM in vascular plants, while also advancing our understanding of the roles of SAGA1 and SAGA2 in starch sheath formation and broadening the avenues for engineering starch morphology.

Rapid and reversible dissolution of biomolecular condensates using light-controlled recruitment of a solubility tag

Biomolecular condensates are broadly implicated in both normal cellular regulation and disease. Consequently, several chemical biology and optogenetic approaches have been developed to induce phase separation of a protein of interest. However, few tools are available to perform the converse function-dissolving a condensate of interest on demand. Such a tool would aid in testing whether the condensate plays specific functional roles, a major question in cell biology and drug development. Here we report an optogenetic approach to selectively dissolve a condensate of interest in a reversible and spatially controlled manner. We show that light-gated recruitment of maltose-binding protein (MBP), a commonly used solubilizing domain in protein purification, results in rapid and controlled dissolution of condensates formed from proteins of interest. Our optogenetic MBP-based dissolution strategy (OptoMBP) is rapid, reversible, and can be spatially controlled with subcellular precision. We also provide a proof-of-principle application of OptoMBP, showing that disrupting condensation of the oncogenic fusion protein FUS-CHOP results in reversion of FUS-CHOP driven transcriptional changes. We envision that the OptoMBP system could be broadly useful for disrupting constitutive protein condensates to probe their biological functions.

Preserving condensate structure and composition by lowering sequence complexity

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

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Effects of linker length on phase separation: lessons from the Rubisco-EPYC1 system of the algal pyrenoid

Biomolecular condensates are membraneless organelles formed via phase separation of macromolecules, typically consisting of bond-forming "stickers" connected by flexible "linkers". Linkers have diverse roles, such as occupying space and facilitating interactions. To understand how linker length relative to other lengths affects condensation, we focus on the pyrenoid, which enhances photosynthesis in green algae. Specifically, we apply coarse-grained simulations and analytical theory to the pyrenoid proteins of Chlamydomonas reinhardtii: the rigid holoenzyme Rubisco and its flexible partner EPYC1. Remarkably, halving EPYC1 linker lengths decreases critical concentrations by ten-fold. We attribute this difference to the molecular "fit" between EPYC1 and Rubisco. Varying Rubisco sticker locations reveals that the native sites yield the poorest fit, thus optimizing phase separation. Surprisingly, shorter linkers mediate a transition to a gas of rods as Rubisco stickers approach the poles. These findings illustrate how intrinsically disordered proteins affect phase separation through the interplay of molecular length scales.

Theory and Simulation of Multiphase Coexistence in Biomolecular Mixtures

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase behavior of heterogeneous biomolecular mixtures are only beginning to be explored. Theory and simulation provide invaluable tools for probing the relationship between molecular determinants, such as protein and RNA sequences, and the emergence of phase-separated condensates in such complex environments. This review covers recent advances in the prediction and computational design of biomolecular mixtures that phase-separate into many coexisting phases. First, we review efforts to understand the phase behavior of mixtures with hundreds or thousands of species using theoretical models and statistical approaches. We then describe progress in developing analytical theories and coarse-grained simulation models to predict multiphase condensates with the molecular detail required to make contact with biophysical experiments. We conclude by summarizing the challenges ahead for modeling the inhomogeneous spatial organization of biomolecular mixtures in living cells.

Role of Strong Localized vs Weak Distributed Interactions in Disordered Protein Phase Separation

Interaction strength and localization are critical parameters controlling the single-chain and condensed-state properties of intrinsically disordered proteins (IDPs). Here, we decipher these relationships using coarse-grained heteropolymers comprised of hydrophobic (H) and polar (P) monomers as model IDPs. We systematically vary the fraction of P monomers XP and employ two distinct particle-based models that include either strong localized attractions between only H-H pairs (HP model) or weak distributed attractions between both H-H and H-P pairs (HP+ model). To compare different sequences and models, we first carefully tune the attraction strength for all sequences to match the single-chain radius of gyration. Interestingly, we find that this procedure produces similar conformational ensembles, nonbonded potential energies, and chain-level dynamics for single chains of almost all sequences in both models, with some deviations for the HP model at large XP. However, we observe a surprisingly rich phase behavior for the sequences in both models that deviates from the expectation that similarity at the single-chain level will translate to a similar phase-separation propensity. Coexistence between dilute and dense phases is only observed up to a model-dependent XP, despite the presence of favorable interchain interactions, which we quantify using the second virial coefficient. Instead, the limited number of attractive sites (H monomers) leads to the self-assembly of finite-sized clusters of different sizes depending on XP. Our findings strongly suggest that models with distributed interactions favor the formation of liquid-like condensates over a much larger range of sequence compositions compared to models with localized interactions.

The maximum solubility product marks the threshold for condensation of multivalent biomolecules

Clustering of weakly interacting multivalent biomolecules underlies the formation of membraneless compartments known as condensates. As opposed to single-component (homotypic) systems, the concentration dependence of multicomponent (heterotypic) condensate formation is not well understood. We previously proposed the solubility product (SP), the product of monomer concentrations in the dilute phase, as a tool for understanding the concentration dependence of multicomponent systems. In this study, we further explore the limits of the SP concept using spatial Langevin dynamics and rule-based stochastic simulations. We show, for a variety of idealized molecular structures, how the maximum SP coincides with the onset of the phase transition, i.e., the formation of large clusters. We reveal the importance of intracluster binding in steering the free and cluster phase molecular distributions. We also show how structural features of biomolecules shape the SP profiles. The interplay of flexibility, length, and steric hindrance of linker regions controls the phase transition threshold. Remarkably, when SPs are normalized to nondimensional variables and plotted against the concentration scaled to the threshold for phase transition, the curves all coincide independent of the structural features of the binding partners. Similar coincidence is observed for the normalized clustering versus concentration plots. Overall, the principles derived from these systematic models will help guide and interpret in vitro and in vivo experiments on the biophysics of biomolecular condensates.

Detecting Liquid-Liquid Phase Separations Using Molecular Dynamics Simulations and Spectral Clustering

A stringent test of the accuracy of empirical force fields is reproducing the phase diagram of bulk phases and mixtures. Exploring the phase diagram of mixtures requires the detection of phase boundaries and critical points. In contrast to most solid-liquid transitions, in which a global order parameter (average density) can be used to discriminate between two phases, some demixing transitions entail relatively subtle changes in the local environment of each molecule. In such cases, finite sampling errors and finite-size effects make the identification of trends in local order parameters extremely challenging. Here we analyze one such example, namely a methanol/hexane mixture, and compute several local and global structural properties. We simulate the system at various temperatures and study the structural changes associated with demixing. We show that despite a seemingly continuous transformation between mixed and demixed states, the topological properties of the H-bond network change abruptly as the system crosses the demixing line. In particular, by using spectral clustering, we show that the distribution of cluster sizes develops a fat tail (as expected from percolation theory) in the vicinity of the critical point. We illustrate a simple criterion to identify this behavior, which results from the emergence of large system-spanning clusters from a collection of aggregates. We further tested the spectral clustering analysis on a Lennard-Jones system as a standard example of a system with no H-bonds, and also, in this case, we were able to detect the demixing transition.

Compartmentalization of the SUMO/RNF4 pathway by SLX4 drives DNA repair

SLX4, disabled in the Fanconi anemia group P, is a scaffolding protein that coordinates the action of structure-specific endonucleases and other proteins involved in the replication-coupled repair of DNA interstrand cross-links. Here, we show that SLX4 dimerization and SUMO-SIM interactions drive the assembly of SLX4 membraneless compartments in the nucleus called condensates. Super-resolution microscopy reveals that SLX4 forms chromatin-bound clusters of nanocondensates. We report that SLX4 compartmentalizes the SUMO-RNF4 signaling pathway. SENP6 and RNF4 regulate the assembly and disassembly of SLX4 condensates, respectively. SLX4 condensation per se triggers the selective modification of proteins by SUMO and ubiquitin. Specifically, SLX4 condensation induces ubiquitylation and chromatin extraction of topoisomerase 1 DNA-protein cross-links. SLX4 condensation also induces the nucleolytic degradation of newly replicated DNA. We propose that the compartmentalization of proteins by SLX4 through site-specific interactions ensures the spatiotemporal control of protein modifications and nucleolytic reactions during DNA repair.

Thermodynamic origins of two-component multiphase condensates of proteins

Intracellular condensates are highly multi-component systems in which complex phase behaviour can ensue, including the formation of architectures comprising multiple immiscible condensed phases. Relying solely on physical intuition to manipulate such condensates is difficult because of the complexity of their composition, and systematically learning the underlying rules experimentally would be extremely costly. We address this challenge by developing a computational approach to design pairs of protein sequences that result in well-separated multilayered condensates and elucidate the molecular origins of these compartments. Our method couples a genetic algorithm to a residue-resolution coarse-grained protein model. We demonstrate that we can design protein partners to form multiphase condensates containing naturally occurring proteins, such as the low-complexity domain of hnRNPA1 and its mutants, and show how homo- and heterotypic interactions must differ between proteins to result in multiphasicity. We also show that in some cases the specific pattern of amino-acid residues plays an important role. Our findings have wide-ranging implications for understanding and controlling the organisation, functions and material properties of biomolecular condensates.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Uncovering the mechanism for aggregation in repeat expanded RNA reveals a reentrant transition

RNA molecules aggregate under certain conditions. The resulting condensates are implicated in human neurological disorders, and can potentially be designed towards specified bulk properties in vitro. However, the mechanism for aggregation-including how aggregation properties change with sequence and environmental conditions-remains poorly understood. To address this challenge, we introduce an analytical framework based on multimer enumeration. Our approach reveals the driving force for aggregation to be the increased configurational entropy associated with the multiplicity of ways to form bonds in the aggregate. Our model uncovers rich phase behavior, including a sequence-dependent reentrant phase transition, and repeat parity-dependent aggregation. We validate our results by comparison to a complete computational enumeration of the landscape, and to previously published molecular dynamics simulations. Our work unifies and extends published results, both explaining the behavior of CAG-repeat RNA aggregates implicated in Huntington's disease, and enabling the rational design of programmable RNA condensates.

Effective simulations of interacting active droplets

Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn-Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using approximate analytical solutions obtained from a sharp interface limit and linearized equations in the bulk phases. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells.

Phase-separating pyrenoid proteins form complexes in the dilute phase

While most studies of biomolecular phase separation have focused on the condensed phase, relatively little is known about the dilute phase. Theory suggests that stable complexes form in the dilute phase of two-component phase-separating systems, impacting phase separation; however, these complexes have not been interrogated experimentally. We show that such complexes indeed exist, using an in vitro reconstitution system of a phase-separated organelle, the algal pyrenoid, consisting of purified proteins Rubisco and EPYC1. Applying fluorescence correlation spectroscopy (FCS) to measure diffusion coefficients, we found that complexes form in the dilute phase with or without condensates present. The majority of these complexes contain exactly one Rubisco molecule. Additionally, we developed a simple analytical model which recapitulates experimental findings and provides molecular insights into the dilute phase organization. Thus, our results demonstrate the existence of protein complexes in the dilute phase, which could play important roles in the stability, dynamics, and regulation of condensates.

Stress granule assembly in vivo is deficient in the CNS of mutant TDP-43 ALS mice

Responding effectively to external stress is crucial for neurons. Defective stress granule dynamics has been hypothesized as one of the pathways that renders motor neurons in amyotrophic lateral sclerosis (ALS) more prone to early death. Specifically, it is thought that stress granules seed the cytoplasmic TDP-43 inclusions that are observed in the neurons of most ALS patients, as well as ~50% of all frontotemporal dementia (FTD) patients. In this study, we tested this hypothesis in an intact mammalian nervous system. We established an in vivo heat stress paradigm in mice that effectively triggers the eIF2α pathway and the formation of stress granules in the CNS. In non-transgenic mice, we report an age-dependent decline in the formation of heat-induced stress granules, with 18-month-old animals showing a significant impairment. Furthermore, although neuronal stress granules were robustly observed in non-transgenic mice and SOD1G93A mice, they were largely absent in age-matched TDP-43M337V animals. The observed defect in stress granule formation in TDP-43M337V mice correlated with deficits in expression of key protein components typically required for phase separation. Lastly, while TDP-43 was not localized to stress granules, we observed complete nuclear depletion of TDP-43 in a subset of neurons, with the highest proportion being in the TDP-43M337V mice. Overall, our results indicate that mutant TDP-43 expression is associated with defective stress granule assembly and increased TDP-43 nuclear depletion in the mammalian nervous system, which could be relevant to ALS/FTD pathogenesis.

An Introduction to the Stickers-and-Spacers Framework as Applied to Biomolecular Condensates

Cellular organization is determined by a combination of membrane-bound and membrane-less biomolecular assemblies that range from clusters of tens of molecules to micrometer-sized cellular bodies. Over the last decade, membrane-less assemblies have come to be referred to as biomolecular condensates, reflecting their ability to condense specific molecules with respect to the remainder of the cell. In many cases, the physics of phase transitions provides a conceptual framework and a mathematical toolkit to describe the assembly, maintenance, and dissolution of biomolecular condensates. Among the various quantitative and qualitative models applied to understand intracellular phase transitions, the stickers-and-spacers framework offers an intuitive yet rigorous means to map biomolecular sequences and structure to the driving forces needed for higher-order assembly. This chapter introduces the fundamental concepts behind the stickers-and-spacers model, considers its application to different biological systems, and discusses limitations and misconceptions around the model.

Dynamics of protein condensates in weak-binding regime

Weak complementary interactions between proteins and nucleic acids are the main driving forces of intracellular liquid-liquid phase separation. The sticker-spacer model has emerged as a unifying principle for understanding the phase behavior of these multivalent molecules. It remains elusive how specific interactions mediated by stickers contribute to the rheological properties of the liquid condensates. Previous studies have revealed that for strong binding strength ɛ_{b}, the bulk diffusivity D depends on the effective bond lifetime τ, viz., D∝τ^{-1}. Consequently, equal concentrations of the complementary stickers induce a slow down in the dynamics of the condensates D∝e^{-1.5ɛ_{b}}. However, for weak-binding strength, it is expected that the resulting condensates are dynamic, loose network liquids rather than kinetically arrested, compact clusters. We develop a mean-field theory using the thermodynamics of the associative polymers and perform molecular-dynamics simulations based on the sticker-spacer model to study the controlling factors in the structure and dynamics of such condensates in the weak-binding regime. Through scaling analysis, we delineate how the free sticker fraction W_{f} and the bulk diffusivity D decrease with increasing binding energy and find that the internal dynamics of such network liquids are controlled by the free sticker fraction D∝W_{f}∝e^{-0.5ɛ_{b}} rather than the effective bond lifetime. Referred to as the free-sticker-dominated diffusivity, the microscopic slowdown due to a gradual loss of the free stickers affects the viscosity of the condensates as well, with the scaling of the zero-shear viscosity η∝e^{0.5ɛ_{b}}. Therefore, the way of controlling the structure, diffusivity, and viscosity of the condensates through the binding energy can be tested experimentally.

Uncovering the molecular mechanism for dual effect of ATP on phase separation in FUS solution

Recent studies reported that adenosine triphosphate (ATP) could inhibit and enhance the phase separation in prion-like proteins. The molecular mechanism underlying such a puzzling phenomenon remains elusive. Here, taking the fused in sarcoma (FUS) solution as an example, we comprehensively reveal the underlying mechanism by which ATP regulates phase separation by combining the semiempirical quantum mechanical method, mean-field theory, and molecular simulation. At the microscopic level, ATP acts as a bivalent or trivalent binder; at the macroscopic level, the reentrant phase separation occurs in dilute FUS solutions, resulting from the ATP concentration-dependent binding ability under different conditions. The ATP concentration for dissolving the protein condensates is about 10 mM, agreeing with experimental results. Furthermore, from a dynamic point of view, the effect of ATP on phase separation is also nonmonotonic. This work provides a clear physical description of the microscopic interaction and macroscopic phase diagram of the ATP-modulated phase separation.

The mechanobiology of nuclear phase separation

The cell nucleus can be thought of as a complex, dynamic, living material, which functions to organize and protect the genome and coordinate gene expression. These functions are achieved via intricate mechanical and biochemical interactions among its myriad components, including the nuclear lamina, nuclear bodies, and the chromatin itself. While the biophysical organization of the nuclear lamina and chromatin have been thoroughly studied, the concept that liquid-liquid phase separation and related phase transitions play a role in establishing nuclear structure has emerged only recently. Phase transitions are likely to be intimately coupled to the mechanobiology of structural elements in the nucleus, but their interplay with one another is still not understood. Here, we review recent developments on the role of phase separation and mechanics in nuclear organization and discuss the functional implications in cell physiology and disease states.

Controlling cluster size in 2D phase-separating binary mixtures with specific interactions

By varying the concentration of molecules in the cytoplasm or on the membrane, cells can induce the formation of condensates and liquid droplets, similar to phase separation. Their thermodynamics, much studied, depends on the mutual interactions between microscopic constituents. Here, we focus on the kinetics and size control of 2D clusters, forming on membranes. Using molecular dynamics of patchy colloids, we model a system of two species of proteins, giving origin to specific heterotypic bonds. We find that concentrations, together with valence and bond strength, control both the size and the growth time rate of the clusters. In particular, if one species is in large excess, it gradually saturates the binding sites of the other species; the system then becomes kinetically arrested and cluster coarsening slows down or stops, thus yielding effective size selection. This phenomenology is observed both in solid and fluid clusters, which feature additional generic homotypic interactions and are reminiscent of the ones observed on biological membranes.

Inhibitory postsynaptic density from the lens of phase separation

To faithfully transmit and decode signals released from presynaptic termini, postsynaptic compartments of neuronal synapses deploy hundreds of various proteins. In addition to distinct sets of proteins, excitatory and inhibitory postsynaptic apparatuses display very different organization features and regulatory properties. Decades of extensive studies have generated a wealth of knowledge on the molecular composition, assembly architecture and activity-dependent regulatory mechanisms of excitatory postsynaptic compartments. In comparison, our understanding of the inhibitory postsynaptic apparatus trails behind. Recent studies have demonstrated that phase separation is a new paradigm underlying the formation and plasticity of both excitatory and inhibitory postsynaptic molecular assemblies. In this review, we discuss molecular composition, organizational and regulatory features of inhibitory postsynaptic densities through the lens of the phase separation concept and in comparison with the excitatory postsynaptic densities.

Single-stranded nucleic acid binding and coacervation by linker histone H1

The H1 linker histone family is the most abundant group of eukaryotic chromatin-binding proteins. However, their contribution to chromosome structure and function remains incompletely understood. Here we use single-molecule fluorescence and force microscopy to directly visualize the behavior of H1 on various nucleic acid and nucleosome substrates. We observe that H1 coalesces around single-stranded DNA generated from tension-induced DNA duplex melting. Using a droplet fusion assay controlled by optical tweezers, we find that single-stranded nucleic acids mediate the formation of gel-like H1 droplets, whereas H1-double-stranded DNA and H1-nucleosome droplets are more liquid-like. Molecular dynamics simulations reveal that multivalent and transient engagement of H1 with unpaired DNA strands drives their enhanced phase separation. Using eGFP-tagged H1, we demonstrate that inducing single-stranded DNA accumulation in cells causes an increase in H1 puncta that are able to fuse. We further show that H1 and Replication Protein A occupy separate nuclear regions, but that H1 colocalizes with the replication factor Proliferating Cell Nuclear Antigen, particularly after DNA damage. Overall, our results provide a refined perspective on the diverse roles of H1 in genome organization and maintenance, and indicate its involvement at stalled replication forks.

Surface tension and super-stoichiometric surface enrichment in two-component biomolecular condensates

Cells can achieve internal organization by exploiting liquid-liquid phase separation to form biomolecular condensates. Here we focus on the surface properties of condensates composed of two multivalent associative polymers held together by one-to-one "sticker" bonds. Using coarse-grained molecular-dynamics simulations, we study the influence of component stoichiometry on condensate surface properties. We find that unequal stoichiometry results in enrichment of the majority species at the interface and a sharp reduction of surface tension. To relate these two effects, we show that the reduction in surface tension scales linearly with the excess concentration of free binding sites at the interface. Our results imply that each excess free site contributes an approximately fixed additional energy and entropy to the interface, with the latter dominating such that enrichment of free majority sites lowers the surface tension. Our work provides insight into novel physical mechanisms by which cells can regulate condensate surface properties.

Stoichiometry Controls the Dynamics of Liquid Condensates of Associative Proteins

Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such "bond-network" condensates comprising two complementary proteins via scaling analysis and molecular dynamics. We find that when stoichiometry is balanced, relaxation slows down dramatically due to a scarcity of alternative binding partners following bond breakage. This microscopic slow-down strongly affects the bulk diffusivity, viscosity, and mixing, which provides a means to experimentally test this prediction.

Role of Solvent Compatibility in the Phase Behavior of Binary Solutions of Weakly Associating Multivalent Polymers

Condensate formation of biopolymer solutions, prominently those of various intrinsically disordered proteins (IDPs), is often driven by "sticky" interactions between associating residues, multivalently present along the polymer backbone. Using a ternary mean-field "stickers-and-spacers" model, we demonstrate that if sticker association is of the order of a few times the thermal energy, a delicate balance between specific binding and nonspecific polymer-solvent interactions gives rise to a particularly rich ternary phase behavior under physiological circumstances. For a generic system represented by a solution comprising multiassociative scaffold and client polymers, the difference in solvent compatibility between the polymers modulates the nature of isothermal liquid-liquid phase separation (LLPS) between associative and segregative. The calculations reveal regimes of dualistic phase behavior, where both types of LLPS occur within the same phase diagram, either associated with the presence of multiple miscibility gaps or a flip in the slope of the tie-lines belonging to a single coexistence region.

Single-Molecule Microscopy Meets Molecular Dynamics Simulations for Characterizing the Molecular Action of Proteins on DNA and in Liquid Condensates

DNA-binding proteins trigger various cellular functions and determine cellular fate. Before performing functions such as transcription, DNA repair, and DNA recombination, DNA-binding proteins need to search for and bind to their target sites in genomic DNA. Under evolutionary pressure, DNA-binding proteins have gained accurate and rapid target search and binding strategies that combine three-dimensional search in solution, one-dimensional sliding along DNA, hopping and jumping on DNA, and intersegmental transfer between two DNA molecules. These mechanisms can be achieved by the unique structural and dynamic properties of these proteins. Single-molecule fluorescence microscopy and molecular dynamics simulations have characterized the molecular actions of DNA-binding proteins in detail. Furthermore, these methodologies have begun to characterize liquid condensates induced by liquid-liquid phase separation, e.g., molecular principles of uptake and dynamics in droplets. This review discusses the molecular action of DNA-binding proteins on DNA and in liquid condensate based on the latest studies that mainly focused on the model protein p53.

Liquid-Liquid Phase Separation: Unraveling the Enigma of Biomolecular Condensates in Microbial Cells

Numerous examples of microbial phase-separated biomolecular condensates have now been identified following advances in fluorescence imaging and single molecule microscopy technologies. The structure, function, and potential applications of these microbial condensates are currently receiving a great deal of attention. By neatly compartmentalizing proteins and their interactors in membrane-less organizations while maintaining free communication between these macromolecules and the external environment, microbial cells are able to achieve enhanced metabolic efficiency. Typically, these condensates also possess the ability to rapidly adapt to internal and external changes. The biological functions of several phase-separated condensates in small bacterial cells show evolutionary convergence with the biological functions of their eukaryotic paralogs. Artificial microbial membrane-less organelles are being constructed with application prospects in biocatalysis, biosynthesis, and biomedicine. In this review, we provide an overview of currently known biomolecular condensates driven by liquid-liquid phase separation (LLPS) in microbial cells, and we elaborate on their biogenesis mechanisms and biological functions. Additionally, we highlight the major challenges and future research prospects in studying microbial LLPS.

Phase separation vs aggregation behavior for model disordered proteins

Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. Although the LLPS of proteins is known to occur in a sequence-dependent manner, it is unclear how sequence properties dictate the nature of the phase transition and thereby influence condensed phase morphology. In this work, we have utilized grand canonical Monte Carlo simulations for a simple coarse-grained model of disordered proteins to systematically investigate how sequence distribution, sticker fraction, and chain length impact the formation of finite-size aggregates, which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Additionally, we find that this order parameter is strongly correlated with the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase density. Results obtained from an analysis of the order parameter reveal that at sufficiently long chain lengths, the vast majority of sequences are likely to phase separate. Our results suggest that classical LLPS should be the primary phase transition for disordered proteins when short-ranged attractive interactions dominate and suggest a possible reason behind recent findings of widespread phase separation throughout living cells.