Consistent Force Field Captures Homologue-Resolved HP1 Phase Separation

Toward Predictive Coarse-Grained Simulations of Biomolecular Condensates

Phase separation is a fundamental process that enables cellular organization by forming biomolecular condensates. These assemblies regulate diverse functions by creating distinct environments, influencing reaction kinetics, and facilitating processes such as genome organization, signal transduction, and RNA metabolism. Recent studies highlight the complexity of condensate properties, shaped by intrinsic molecular features and external factors such as temperature and pH. Molecular simulations serve as an effective approach to establishing a comprehensive framework for analyzing these influences, offering high-resolution insights into condensate stability, dynamics, and material properties. This review evaluates recent advancements in biomolecular condensate simulations, with a particular focus on coarse-grained 1-bead-per-amino-acid (1BPA) protein models, and emphasizes OpenABC, a tool designed to simplify and streamline condensate simulations. OpenABC supports the implementation of various coarse-grained force fields, enabling their performance evaluation. Our benchmarking identifies inconsistencies in phase behavior predictions across force fields, even though these models accurately capture single-chain statistics. This finding underscores the need for enhanced force field accuracy, achievable through enriched training data sets, many-body potentials, and advanced optimization techniques. Such refinements could significantly improve the predictive capacity of coarse-grained models, bridging molecular details with emergent condensate behaviors.

Prediction of phase-separation propensities of disordered proteins from sequence

Phase separation is one possible mechanism governing the selective cellular enrichment of biomolecular constituents for processes such as transcriptional activation, mRNA regulation, and immune signaling. Phase separation is mediated by multivalent interactions of macromolecules including intrinsically disordered proteins and regions (IDRs). Despite considerable advances in experiments, theory, and simulations, the prediction of the thermodynamics of IDR phase behavior remains challenging. We combined coarse-grained molecular dynamics simulations and active learning to develop a fast and accurate machine learning model to predict the free energy and saturation concentration for phase separation directly from sequence. We validate the model using computational and previously measured experimental data, as well as new experimental data for six proteins. We apply our model to all 27,663 IDRs of chain length up to 800 residues in the human proteome and find that 1,420 of these (5%) are predicted to undergo homotypic phase separation with transfer free energies < -2 kBT. We use our model to understand the relationship between single-chain compaction and phase separation and find that changes from charge- to hydrophobicity-mediated interactions can break the symmetry between intra- and intermolecular interactions. We also provide proof of principle for how the model can be used in force field refinement. Our work refines and quantifies the established rules governing the connection between sequence features and phase-separation propensities, and our prediction models will be useful for interpreting and designing cellular experiments on the role of phase separation, and for the design of IDRs with specific phase-separation propensities.

Microphase separation produces interfacial environment within diblock biomolecular condensates

The phase separation of intrinsically disordered proteins is emerging as an important mechanism for cellular organization. However, efforts to connect protein sequences to the physical properties of condensates, that is, the molecular grammar, are hampered by a lack of effective approaches for probing high-resolution structural details. Using a combination of multiscale simulations and fluorescence lifetime imaging microscopy experiments, we systematically explored a series of systems consisting of diblock elastin-like polypeptides (ELPs). The simulations succeeded in reproducing the variation of condensate stability upon amino acid substitution and revealed different microenvironments within a single condensate, which we verified with environmentally sensitive fluorophores. The interspersion of hydrophilic and hydrophobic residues and a lack of secondary structure formation result in an interfacial environment, which explains both the strong correlation between ELP condensate stability and interfacial hydrophobicity scales, as well as the prevalence of protein-water hydrogen bonds. Our study uncovers new mechanisms for condensate stability and organization that may be broadly applicable.

Machine learning methods to study sequence-ensemble-function relationships in disordered proteins

Recent years have seen tremendous developments in the use of machine learning models to link amino-acid sequence, structure, and function of folded proteins. These methods are, however, rarely applicable to the wide range of proteins and sequences that comprise intrinsically disordered regions. We here review developments in the study of sequence-ensemble-function relationships of disordered proteins that exploit or are used to train machine learning models. These include methods for generating conformational ensembles and designing new sequences, and for linking sequences to biophysical properties and biological functions. We highlight how these developments are built on a tight integration between experiment, theory and simulations, and account for evolutionary constraints, which operate on sequences of disordered regions differently than on those of folded domains.

Coarse-Grained Model of Disordered RNA for Simulations of Biomolecular Condensates

Protein-RNA condensates are involved in a range of cellular activities. Coarse-grained molecular models of intrinsically disordered proteins have been developed to shed light on and predict single-chain properties and phase separation. An RNA model compatible with such models for disordered proteins would enable the study of complex biomolecular mixtures involving RNA. Here, we present a sequence-independent coarse-grained, two-beads-per-nucleotide model of disordered, flexible RNA based on a hydropathy scale. We parametrize the model, which we term CALVADOS-RNA, using a combination of bottom-up and top-down approaches to reproduce local RNA geometry and intramolecular interactions based on atomistic simulations and in vitro experiments. The model semiquantitatively captures several aspects of RNA-RNA and RNA-protein interactions. We examined RNA-RNA interactions by comparing calculated and experimental virial coefficients and nonspecific RNA-protein interaction by studying the reentrant phase behavior of protein-RNA mixtures. We demonstrate the utility of the model by simulating the formation of mixed condensates consisting of the disordered region of MED1 and RNA chains and the selective partitioning of disordered regions from transcription factors into these and compare the results to experiments. Despite the simplicity of our model, we show that it captures several key aspects of protein-RNA interactions and may therefore be used as a baseline model to study several aspects of the biophysics and biology of protein-RNA condensates.

Accurate prediction of thermoresponsive phase behavior of disordered proteins

Protein responses to environmental stress, particularly temperature fluctuations, have long been a subject of investigation, with a focus on how proteins maintain homeostasis and exhibit thermoresponsive properties. While UCST-type (upper critical solution temperature) phase behavior has been studied extensively and can now be predicted reliably using computational models, LCST-type (lower critical solution temperature) phase transitions remain less explored, with a lack of computational models capable of accurate prediction. This gap limits our ability to probe fully how proteins undergo phase transitions in response to temperature changes. Here, we introduce Mpipi-T, a residue-level coarse-grained model designed to predict LCST-type phase behavior of proteins. Parametrized using both atomistic simulations and experimental data, Mpipi-T accounts for entropically driven protein phase separation that occurs upon heating. Accordingly, Mpipi-T predicts temperature-driven protein behavior quantitatively in both single- and multi-chain systems. Beyond its predictive capabilities, we demonstrate that Mpipi-T provides a framework for uncovering the molecular mechanisms underlying heat stress responses, offering new insights into how proteins sense and adapt to thermal changes in biological systems.

Chemically Informed Coarse-Graining of Electrostatic Forces in Charge-Rich Biomolecular Condensates

Biomolecular condensates composed of highly charged biomolecules, such as DNA, RNA, chromatin, and nucleic-acid binding proteins, are ubiquitous in the cell nucleus. The biophysical properties of these charge-rich condensates are largely regulated by electrostatic interactions. Residue-resolution coarse-grained models that describe solvent and ions implicitly are widely used to gain mechanistic insights into the biophysical properties of condensates, offering transferability, computational efficiency, and accurate predictions for multiple systems. However, their predictive accuracy diminishes for charge-rich condensates due to the implicit treatment of solvent and ions. Here, we present Mpipi-Recharged, a residue-resolution coarse-grained model that improves the description of charge effects in biomolecular condensates containing disordered proteins, multidomain proteins, and/or disordered single-stranded RNAs. Mpipi-Recharged introduces a pair-specific asymmetric Yukawa electrostatic potential, informed by atomistic simulations. We show that this asymmetric coarse-graining of electrostatic forces captures intricate effects, such as charge blockiness, stoichiometry variations in complex coacervates, and modulation of salt concentration, without requiring explicit solvation. Mpipi-Recharged provides excellent agreement with experiments in predicting the phase behavior of highly charged condensates. Overall, Mpipi-Recharged improves the computational tools available to investigate the physicochemical mechanisms regulating biomolecular condensates, enhancing the scope of computer simulations in this field.

Amino Acid Transfer Free Energies Reveal Thermodynamic Driving Forces in Biomolecular Condensate Formation

The self-assembly of intrinsically disordered proteins into biomolecular condensates shows a dependence on the primary sequence of the protein, leading to sequence-dependent phase separation. Methods to investigate this sequence-dependent phase separation rely on effective residue-level interaction potentials that quantify the propensity for the residues to remain in the dilute phase versus the dense phase. The most direct measure of these effective potentials are the distribution coefficients of the different amino acids between the two phases, but due to the lack of availability of these coefficients, proxies, most notably hydropathy, have been used. However, recent work has demonstrated the limitations of the assumption of hydropathy-driven phase separation. In this work, we address this fundamental gap by calculating the transfer free energies associated with transferring each amino acid side chain analog from the dilute phase to the dense phase of a model biomolecular condensate. We uncover an interplay between favorable protein-mediated and unfavorable water-mediated contributions to the overall free energies of transfer. We further uncover an asymmetry between the contributions of positive and negative charges in the driving forces for condensate formation. The results presented in this work provide an explanation for several non-trivial trends observed in the literature and will aid in the interpretation of experiments aimed at elucidating the sequence-dependent driving forces underlying the formation of biomolecular 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.

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.

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

Microphase Separation Produces Interfacial Environment within Diblock Biomolecular Condensates

The phase separation of intrinsically disordered proteins is emerging as an important mechanism for cellular organization. However, efforts to connect protein sequences to the physical properties of condensates, i.e., the molecular grammar, are hampered by a lack of effective approaches for probing high-resolution structural details. Using a combination of multiscale simulations and fluorescence lifetime imaging microscopy experiments, we systematically explored a series of systems consisting of diblock elastin-like polypeptides (ELP). The simulations succeeded in reproducing the variation of condensate stability upon amino acid substitution and revealed different microenvironments within a single condensate, which we verified with environmentally sensitive fluorophores. The interspersion of hydrophilic and hydrophobic residues and a lack of secondary structure formation result in an interfacial environment, which explains both the strong correlation between ELP condensate stability and interfacial hydrophobicity scales, as well as the prevalence of protein-water hydrogen bonds. Our study uncovers new mechanisms for condensate stability and organization that may be broadly applicable.

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.

Dynamical phase transition in models that couple chromatin folding with histone modifications

Genomic regions can acquire heritable epigenetic states through unique histone modifications, which lead to stable gene expression patterns without altering the underlying DNA sequence. However, the relationship between chromatin conformational dynamics and epigenetic stability is poorly understood. In this paper, we propose kinetic models to investigate the dynamic fluctuations of histone modifications and the spatial interactions between nucleosomes. Our model explicitly incorporates the influence of chemical modifications on the structural stability of chromatin and the contribution of chromatin contacts to the cooperative nature of chemical reactions. Through stochastic simulations and analytical theory, we have discovered distinct steady-state outcomes in different kinetic regimes, resembling a dynamical phase transition. Importantly, we have validated that the emergence of this transition, which occurs on biologically relevant timescales, is robust against variations in model design and parameters. Our findings suggest that the viscoelastic properties of chromatin and the timescale at which it transitions from a gel-like to a liquidlike state significantly impact dynamic processes that occur along the one-dimensional DNA sequence.

Interplay between charge distribution and DNA in shaping HP1 paralog phase separation and localization

The heterochromatin protein 1 (HP1) family is a crucial component of heterochromatin with diverse functions in gene regulation, cell cycle control, and cell differentiation. In humans, there are three paralogs, HP1α, HP1β, and HP1γ, which exhibit remarkable similarities in their domain architecture and sequence properties. Nevertheless, these paralogs display distinct behaviors in liquid-liquid phase separation (LLPS), a process linked to heterochromatin formation. Here, we employ a coarse-grained simulation framework to uncover the sequence features responsible for the observed differences in LLPS. We highlight the significance of the net charge and charge patterning along the sequence in governing paralog LLPS propensities. We also show that both highly conserved folded and less-conserved disordered domains contribute to the observed differences. Furthermore, we explore the potential co-localization of different HP1 paralogs in multicomponent assemblies and the impact of DNA on this process. Importantly, our study reveals that DNA can significantly reshape the stability of a minimal condensate formed by HP1 paralogs due to competitive interactions of HP1α with HP1β and HP1γ versus DNA. In conclusion, our work highlights the physicochemical nature of interactions that govern the distinct phase-separation behaviors of HP1 paralogs and provides a molecular framework for understanding their role in chromatin organization.

Micropolarity governs the structural organization of biomolecular condensates

Membraneless organelles within cells have unique microenvironments that play a critical role in their functions. However, how microenvironments of biomolecular condensates affect their structure and function remains unknown. In this study, we investigated the micropolarity and microviscosity of model biomolecular condensates by fluorescence lifetime imaging coupling with environmentally sensitive fluorophores. Using both in vitro and in cellulo systems, we demonstrated that sufficient micropolarity difference is key to forming multilayered condensates, where the shells present more polar microenvironments than the cores. Furthermore, micropolarity changes were shown to be accompanied by conversions of the layered structures. Decreased micropolarities of the granular components, accompanied by the increased micropolarities of the dense fibrillar components, result in the relocation of different nucleolus subcompartments in transcription-stalled conditions. Our results demonstrate the central role of the previously overlooked micropolarity in the regulation of structures and functions of membraneless organelles.

Submillisecond Atomistic Molecular Dynamics Simulations Reveal Hydrogen Bond-Driven Diffusion of a Guest Peptide in Protein-RNA Condensate

Liquid-liquid phase separation mediated by proteins and/or nucleic acids is believed to underlie the formation of many distinct condensed phases, or membraneless organelles, within living cells. These condensates have been proposed to orchestrate a variety of important processes. Despite recent advances, the interactions that regulate the dynamics of molecules within a condensate remain poorly understood. We performed accumulated 564.7 μs all-atom molecular dynamics (MD) simulations (system size ∼200k atoms) of model condensates formed by a scaffold RNA oligomer and a scaffold peptide rich in arginine (Arg). These model condensates contained one of three possible guest peptides: the scaffold peptide itself or a variant in which six Arg residues were replaced by lysine (Lys) or asymmetric dimethyl arginine (ADMA). We found that the Arg-rich peptide can form the largest number of hydrogen bonds and bind the strongest to the scaffold RNA in the condensate, relative to the Lys- and ADMA-rich peptides. Our MD simulations also showed that the Arg-rich peptide diffused more slowly in the condensate relative to the other two guest peptides, which is consistent with a recent fluorescence microscopy study. There was no significant increase in the number of cation-π interactions between the Arg-rich peptide and the scaffold RNA compared to the Lys-rich and ADMA-rich peptides. Our results indicate that hydrogen bonds between the peptides and the RNA backbone, rather than cation-π interactions, play a major role in regulating peptide diffusion in the condensate.

Backbone interactions and secondary structures in phase separation of disordered proteins

Intrinsically disordered proteins (IDPs) are one of the major drivers behind the formation and characteristics of biomolecular condensates. Due to their inherent flexibility, the backbones of IDPs are significantly exposed, rendering them highly influential and susceptible to biomolecular phase separation. In densely packed condensates, exposed backbones have a heightened capacity to interact with neighboring protein chains, which might lead to strong coupling between the secondary structures and phase separation and further modulate the subsequent transitions of the condensates, such as aging and fibrillization. In this mini-review, we provide an overview of backbone-mediated interactions and secondary structures within biomolecular condensates to underscore the importance of protein backbones in phase separation. We further focus on recent advances in experimental techniques and molecular dynamics simulation methods for probing and exploring the roles of backbone interactions and secondary structures in biomolecular phase separation involving IDPs.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Optimizing the Martini 3 Force Field Reveals the Effects of the Intricate Balance between Protein-Water Interaction Strength and Salt Concentration on Biomolecular Condensate Formation

Condensation/dissolution has become a widely acknowledged biological macromolecular assembly phenomenon in subcellular compartmentalization. The MARTINI force field offers a coarse-grained protein model with a resolution that preserves molecular details with an explicit (CG) solvent. Despite its relatively higher resolution, it can still achieve condensate formation in a reasonable computing time with explicit solvent and ionic species. Therefore, it is highly desirable to tune this force field to be able to reproduce the experimentally observed properties of the condensate formation. In this work, we studied the condensate formation of the low-sequence complexity domain of fused in sarcoma protein using a MARTINI 3 force field by systematically modifying (increasing) the protein-water interaction strength and varying the salt concentration. We found that the condensate formation is sensitive both to the protein-water interaction strength and the presence of salt. While the unmodified MARTINI force field yields a complete collapse of proteins into one dense phase (i.e., no dilute phase), we reported a range of modified protein-water interaction strength that is capable of capturing the experimentally found transfer free energy between dense and dilute phases. We also found that the condensates lose their spherical shape upon the addition of salt, especially when the protein-water interactions are weak. Interchain amino acid contact map analysis showed one explanation for this observation: the protein-protein contact fraction reduces as salt is added to systems (when the protein-water interactions are weak), consistent with electrostatic screening effects. This reduction might be responsible for the condensates becoming nonspherical upon the addition of salt by reducing the need for minimizing the interfacial area. However, as the protein-water interactions become stronger to the extent that makes the transfer free energy agree well with experimentally observed transfer free energy, we found an increase in the protein-protein contact fraction upon the addition of salt, consistent with the salting-out effects. Therefore, we concluded that there is an intricate balance between screening effects and salting-out effects upon the addition of salt and this balance is highly sensitive to the strength of protein-water interactions.

Explicit ion modeling predicts physicochemical interactions for chromatin organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono- and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Toward Accurate Simulation of Coupling between Protein Secondary Structure and Phase Separation

Intrinsically disordered proteins (IDPs) frequently mediate phase separation that underlies the formation of a biomolecular condensate. Together with theory and experiment, efficient coarse-grained (CG) simulations have been instrumental in understanding the sequence-specific phase separation of IDPs. However, the widely used Cα-only models are limited in capturing the peptide nature of IDPs, particularly backbone-mediated interactions and effects of secondary structures, in phase separation. Here, we describe a hybrid resolution (HyRes) protein model toward a more accurate description of the backbone and transient secondary structures in phase separation. With an atomistic backbone and coarse-grained side chains, HyRes can semiquantitatively capture the residue helical propensity and overall chain dimension of monomeric IDPs. Using GY-23 as a model system, we show that HyRes is efficient enough for the direct simulation of spontaneous phase separation and, at the same time, appears accurate enough to resolve the effects of single His to Lys mutations. HyRes simulations also successfully predict increased β-structure formation in the condensate, consistent with available experimental CD data. We further utilize HyRes to study the phase separation of TPD-43, where several disease-related mutants in the conserved region (CR) have been shown to affect residual helicities and modulate the phase separation propensity as measured by the saturation concentration. The simulations successfully recapitulate the effect of these mutants on the helicity and phase separation propensity of TDP-43 CR. Analyses reveal that the balance between backbone and side chain-mediated interactions, but not helicity itself, actually determines phase separation propensity. These results support that HyRes represents an effective protein model for molecular simulation of IDP phase separation and will help to elucidate the coupling between transient secondary structures and phase separation.

Transferable Implicit Solvation via Contrastive Learning of Graph Neural Networks

Implicit solvent models are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. Efforts are underway to develop accurate and transferable implicit solvent models and coarse-grained (CG) force fields in general, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to the lack of analytical expressions for the PMF and algorithmic limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent the solvation free energy and potential contrasting for parameter optimization. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside of the training data. Our study offers valuable insights for deriving systematically improvable implicit solvent models and CG force fields from a bottom-up perspective.

Interplay between charge distribution and DNA in shaping HP1 paralog phase separation and localization

The heterochromatin protein 1 (HP1) family is a crucial component of heterochromatin with diverse functions in gene regulation, cell cycle control, and cell differentiation. In humans, there are three paralogs, HP1α, HP1β, and HP1γ, which exhibit remarkable similarities in their domain architecture and sequence properties. Nevertheless, these paralogs display distinct behaviors in liquid-liquid phase separation (LLPS), a process linked to heterochromatin formation. Here, we employ a coarse-grained simulation framework to uncover the sequence features responsible for the observed differences in LLPS. We highlight the significance of the net charge and charge patterning along the sequence in governing paralog LLPS propensities. We also show that both highly conserved folded and less-conserved disordered domains contribute to the observed differences. Furthermore, we explore the potential co-localization of different HP1 paralogs in multicomponent assemblies and the impact of DNA on this process. Importantly, our study reveals that DNA can significantly reshape the stability of a minimal condensate formed by HP1 paralogs due to competitive interactions of HP1α with HP1β and HP1γ versus DNA. In conclusion, our work highlights the physicochemical nature of interactions that govern the distinct phase-separation behaviors of HP1 paralogs and provides a molecular framework for understanding their role in chromatin organization.

Explicit Ion Modeling Predicts Physicochemical Interactions for Chromatin Organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Transferable Coarse Graining via Contrastive Learning of Graph Neural Networks

Coarse-grained (CG) force fields are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. These simulations employ simplified models grouping atoms into interaction sites, enabling the study of complex biomolecular systems over biologically relevant timescales. Efforts are underway to develop accurate and transferable CG force fields, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to many-body effects, lack of analytical expressions for the PMF, and limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent CG force fields and potential contrasting for parameterization from atomistic simulation data. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside the training data. Our study offers valuable insights for building accurate coarse-grained models bottom-up.

Efficient Hi-C inversion facilitates chromatin folding mechanism discovery and structure prediction

Genome-wide chromosome conformation capture (Hi-C) experiments have revealed many structural features of chromatin across multiple length scales. Further understanding genome organization requires relating these discoveries to the mechanisms that establish chromatin structures and reconstructing these structures in three dimensions, but both objectives are difficult to achieve with existing algorithms that are often computationally expensive. To alleviate this challenge, we present an algorithm that efficiently converts Hi-C data into contact energies, which measure the interaction strength between genomic loci brought into proximity. Contact energies are local quantities unaffected by the topological constraints that correlate Hi-C contact probabilities. Thus, extracting contact energies from Hi-C contact probabilities distills the biologically unique information contained in the data. We show that contact energies reveal the location of chromatin loop anchors, support a phase separation mechanism for genome compartmentalization, and parameterize polymer simulations that predict three-dimensional chromatin structures. Therefore, we anticipate that contact energy extraction will unleash the full potential of Hi-C data and that our inversion algorithm will facilitate the widespread adoption of contact energy analysis.

OpenABC enables flexible, simplified, and efficient GPU accelerated simulations of biomolecular condensates

Biomolecular condensates are important structures in various cellular processes but are challenging to study using traditional experimental techniques. In silico simulations with residue-level coarse-grained models strike a balance between computational efficiency and chemical accuracy. They could offer valuable insights by connecting the emergent properties of these complex systems with molecular sequences. However, existing coarse-grained models often lack easy-to-follow tutorials and are implemented in software that is not optimal for condensate simulations. To address these issues, we introduce OpenABC, a software package that greatly simplifies the setup and execution of coarse-grained condensate simulations with multiple force fields using Python scripting. OpenABC seamlessly integrates with the OpenMM molecular dynamics engine, enabling efficient simulations with performance on a single GPU that rivals the speed achieved by hundreds of CPUs. We also provide tools that convert coarse-grained configurations to all-atom structures for atomistic simulations. We anticipate that OpenABC will significantly facilitate the adoption of in silico simulations by a broader community to investigate the structural and dynamical properties of condensates.

Accurate Simulation of Coupling between Protein Secondary Structure and Liquid-Liquid Phase Separation

Intrinsically disordered proteins (IDPs) frequently mediate liquid-liquid phase separation (LLPS) that underlies the formation of membraneless organelles. Together with theory and experiment, efficient coarse-grained (CG) simulations have been instrumental in understanding sequence-specific phase separation of IDPs. However, the widely-used Cα-only models are severely limited in capturing the peptide nature of IDPs, including backbone-mediated interactions and effects of secondary structures, in LLPS. Here, we describe a hybrid resolution (HyRes) protein model for accurate description of the backbone and transient secondary structures in LLPS. With an atomistic backbone and coarse-grained side chains, HyRes accurately predicts the residue helical propensity and chain dimension of monomeric IDPs. Using GY-23 as a model system, we show that HyRes is efficient enough for direct simulation of spontaneous phase separation, and at the same time accurate enough to resolve the effects of single mutations. HyRes simulations also successfully predict increased beta-sheet formation in the condensate, consistent with available experimental data. We further utilize HyRes to study the phase separation of TPD-43, where several disease-related mutants in the conserved region (CR) have been shown to affect residual helicities and modulate LLPS propensity. The simulations successfully recapitulate the effect of these mutants on the helicity and LLPS propensity of TDP-43 CR. Analyses reveal that the balance between backbone and sidechain-mediated interactions, but not helicity itself, actually determines LLPS propensity. We believe that the HyRes model represents an important advance in the molecular simulation of LLPS and will help elucidate the coupling between IDP transient secondary structures and phase separation.

HP1-driven phase separation recapitulates the thermodynamics and kinetics of heterochromatin condensate formation

The spatial segregation of pericentromeric heterochromatin (PCH) into distinct, membrane-less nuclear compartments involves the binding of Heterochromatin Protein 1 (HP1) to H3K9me2/3-rich genomic regions. While HP1 exhibits liquid-liquid phase separation properties in vitro, its mechanistic impact on the structure and dynamics of PCH condensate formation in vivo remains largely unresolved. Here, using a minimal theoretical framework, we systematically investigate the mutual coupling between self-interacting HP1-like molecules and the chromatin polymer. We reveal that the specific affinity of HP1 for H3K9me2/3 loci facilitates coacervation in nucleo and promotes the formation of stable PCH condensates at HP1 levels far below the concentration required to observe phase separation in purified protein assays in vitro. These heterotypic HP1-chromatin interactions give rise to a strong dependence of the nucleoplasmic HP1 density on HP1-H3K9me2/3 stoichiometry, consistent with the thermodynamics of multicomponent phase separation. The dynamical cross talk between HP1 and the viscoelastic chromatin scaffold also leads to anomalously slow equilibration kinetics, which strongly depend on the genomic distribution of H3K9me2/3 domains and result in the coexistence of multiple long-lived, microphase-separated PCH compartments. The morphology of these complex coacervates is further found to be governed by the dynamic establishment of the underlying H3K9me2/3 landscape, which may drive their increasingly abnormal, aspherical shapes during cell development. These findings compare favorably to 4D microscopy measurements of HP1 condensate formation in live Drosophila embryos and suggest a general quantitative model of PCH formation based on the interplay between HP1-based phase separation and chromatin polymer mechanics.

Theoretical and Data-Driven Approaches for Biomolecular Condensates

Biomolecular condensation processes are increasingly recognized as a fundamental mechanism that living cells use to organize biomolecules in time and space. These processes can lead to the formation of membraneless organelles that enable cells to perform distinct biochemical processes in controlled local environments, thereby supplying them with an additional degree of spatial control relative to that achieved by membrane-bound organelles. This fundamental importance of biomolecular condensation has motivated a quest to discover and understand the molecular mechanisms and determinants that drive and control this process. Within this molecular viewpoint, computational methods can provide a unique angle to studying biomolecular condensation processes by contributing the resolution and scale that are challenging to reach with experimental techniques alone. In this Review, we focus on three types of dry-lab approaches: theoretical methods, physics-driven simulations and data-driven machine learning methods. We review recent progress in using these tools for probing biomolecular condensation across all three fields and outline the key advantages and limitations of each of the approaches. We further discuss some of the key outstanding challenges that we foresee the community addressing next in order to develop a more complete picture of the molecular driving forces behind biomolecular condensation processes and their biological roles in health and disease.

Efficient Hi-C inversion facilitates chromatin folding mechanism discovery and structure prediction

Genome-wide chromosome conformation capture (Hi-C) experiments have revealed many structural features of chromatin across multiple length scales. Further understanding genome organization requires relating these discoveries to the mechanisms that establish chromatin structures and reconstructing these structures in three dimensions, but both objectives are difficult to achieve with existing algorithms that are often computationally expensive. To alleviate this challenge, we present an algorithm that efficiently converts Hi-C data into contact energies, which measure the interaction strength between genomic loci brought into proximity. Contact energies are local quantities unaffected by the topological constraints that correlate Hi-C contact probabilities. Thus, extracting contact energies from Hi-C contact probabilities distills the biologically unique information contained in the data. We show that contact energies reveal the location of chromatin loop anchors, support a phase separation mechanism for genome compartmentalization, and parameterize polymer simulations that predict three-dimensional chromatin structures. Therefore, we anticipate that contact energy extraction will unleash the full potential of Hi-C data and that our inversion algorithm will facilitate the widespread adoption of contact energy analysis.

A coarse-grained DNA model to study protein-DNA interactions and liquid-liquid phase separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define non-bonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), that is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond timescale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micron-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

OpenABC Enables Flexible, Simplified, and Efficient GPU Accelerated Simulations of Biomolecular Condensates

Biomolecular condensates are important structures in various cellular processes but are challenging to study using traditional experimental techniques. In silico simulations with residue-level coarse-grained models strike a balance between computational efficiency and chemical accuracy. They could offer valuable insights by connecting the emergent properties of these complex systems with molecular sequences. However, existing coarse-grained models often lack easy-to-follow tutorials and are implemented in software that is not optimal for condensate simulations. To address these issues, we introduce OpenABC, a software package that greatly simplifies the setup and execution of coarse-grained condensate simulations with multiple force fields using Python scripting. OpenABC seamlessly integrates with the OpenMM molecular dynamics engine, enabling efficient simulations with performances on a single GPU that rival the speed achieved by hundreds of CPUs. We also provide tools that convert coarse-grained configurations to all-atom structures for atomistic simulations. We anticipate that Open-ABC will significantly facilitate the adoption of in silico simulations by a broader community to investigate the structural and dynamical properties of condensates. Open-ABC is available at https://github.com/ZhangGroup-MITChemistry/OpenABC.

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.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

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.

Principles Governing the Phase Separation of Multidomain Proteins

A variety of membraneless organelles, often termed "biological condensates", play an important role in the regulation of cellular processes such as gene transcription, translation, and protein quality control. On the basis of experimental and theoretical investigations, liquid-liquid phase separation (LLPS) has been proposed as a possible mechanism for the origin of biological condensates. LLPS requires multivalent macromolecules that template the formation of long-range, intermolecular interaction networks and results in the formation of condensates with defined composition and material properties. Multivalent interactions driving LLPS exhibit a wide range of modes from highly stereospecific to nonspecific and involve both folded and disordered regions. Multidomain proteins serve as suitable macromolecules for promoting phase separation and achieving disparate functions due to their potential for multivalent interactions and regulation. Here, we aim to highlight the influence of the domain architecture and interdomain interactions on the phase separation of multidomain protein condensates. First, the general principles underlying these interactions are illustrated on the basis of examples of multidomain proteins that are predominantly associated with nucleic acid binding and protein quality control and contain both folded and disordered regions. Next, the examples showcase how LLPS properties of folded and disordered regions can be leveraged to engineer multidomain constructs that form condensates with the desired assembly and functional properties. Finally, we highlight the need for improvements in coarse-grained computational models that can provide molecular-level insights into multidomain protein condensates in conjunction with experimental efforts.

Contrastive Learning of Coarse-Grained Force Fields

Coarse-grained models have proven helpful for simulating complex systems over long time scales to provide molecular insights into various processes. Methodologies for systematic parametrization of the underlying energy function or force field that describes the interactions among different components of the system are of great interest for ensuring simulation accuracy. We present a new method, potential contrasting, to enable efficient learning of force fields that can accurately reproduce the conformational distribution produced with all-atom simulations. Potential contrasting generalizes the noise contrastive estimation method with umbrella sampling to better learn the complex energy landscape of molecular systems. When applied to the Trp-cage protein, we found that the technique produces force fields that thoroughly capture the thermodynamics of the folding process despite the use of only α-carbons in the coarse-grained model. We further showed that potential contrasting could be applied over large data sets that combine the conformational ensembles of many proteins to improve force field transferability. We anticipate potential contrasting as a powerful tool for building general-purpose coarse-grained force fields.

Toward Accurate Coarse-Grained Simulations of Disordered Proteins and Their Dynamic Interactions

Intrinsically disordered proteins (IDPs) play crucial roles in cellular regulatory networks and are now recognized to often remain highly dynamic even in specific interactions and assemblies. Accurate description of these dynamic interactions is extremely challenging using atomistic simulations because of the prohibitive computational cost. Efficient coarse-grained approaches could offer an effective solution to overcome this bottleneck if they could provide an accurate description of key local and global properties of IDPs in both unbound and bound states. The recently developed hybrid-resolution (HyRes) protein model has been shown to be capable of providing a semiquantitative description of the secondary structure propensities of IDPs. Here, we show that greatly improved description of global structures and transient interactions can be achieved by introducing a solvent-accessible surface area-based implicit solvent term followed by reoptimization of effective interaction strengths. The new model, termed HyRes II, can semiquantitatively reproduce a wide range of local and global structural properties of a set of IDPs of various lengths and complexities. It can also distinguish the level of compaction between folded proteins and IDPs. In particular, applied to the disordered N-terminal transactivation domain (TAD) of tumor suppressor p53, HyRes II is able to recapitulate various nontrivial structural properties compared to experimental results, some of them to a level of accuracy that is almost comparable to results from atomistic explicit solvent simulations. Furthermore, we demonstrate that HyRes II can be used to simulate the dynamic interactions of TAD with the DNA-binding domain of p53, generating structural ensembles that are highly consistent with existing NMR data. We anticipate that HyRes II will provide an efficient and relatively reliable tool toward accurate coarse-grained simulations of dynamic protein interactions.

Chromatin fiber breaks into clutches under tension and crowding

The arrangement of nucleosomes inside chromatin is of extensive interest. While in vitro experiments have revealed the formation of 30 nm fibers, most in vivo studies have failed to confirm their presence in cell nuclei. To reconcile the diverging experimental findings, we characterized chromatin organization using a residue-level coarse-grained model. The computed force–extension curve matches well with measurements from single-molecule experiments. Notably, we found that a dodeca-nucleosome in the two-helix zigzag conformation breaks into structures with nucleosome clutches and a mix of trimers and tetramers under tension. Such unfolded configurations can also be stabilized through trans interactions with other chromatin chains. Our study suggests that unfolding from chromatin fibers could contribute to the irregularity of in vivo chromatin configurations. We further revealed that chromatin segments with fibril or clutch structures engaged in distinct binding modes and discussed the implications of these inter-chain interactions for a potential sol–gel phase transition.

Phase Separation and Correlated Motions in Motorized Genome

The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation-dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.

On the stability and layered organization of protein-DNA condensates

Multi-component phase separation is emerging as a key mechanism for the formation of biological condensates that play essential roles in signal sensing and transcriptional regulation. The molecular factors that dictate these condensates' stability and spatial organization are not fully understood, and it remains challenging to predict their microstructures. Using a near-atomistic, chemically accurate force field, we studied the phase behavior of chromatin regulators that are crucial for heterochromatin organization and their interactions with DNA. Our computed phase diagrams recapitulated previous experimental findings on different proteins. They revealed a strong dependence of condensate stability on the protein-DNA mixing ratio as a result of balancing protein-protein interactions and charge neutralization. Notably, a layered organization was observed in condensates formed by mixing HP1, histone H1, and DNA. This layered organization may be of biological relevance, as it enables cooperative DNA packaging between the two chromatin regulators: histone H1 softens the DNA to facilitate the compaction induced by HP1 droplets. Our study supports near-atomistic models as a valuable tool for characterizing the structure and stability of biological condensates.

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.

Kinetic interplay between droplet maturation and coalescence modulates shape of aged protein condensates

Biomolecular condensates formed by the process of liquid-liquid phase separation (LLPS) play diverse roles inside cells, from spatiotemporal compartmentalisation to speeding up chemical reactions. Upon maturation, the liquid-like properties of condensates, which underpin their functions, are gradually lost, eventually giving rise to solid-like states with potential pathological implications. Enhancement of inter-protein interactions is one of the main mechanisms suggested to trigger the formation of solid-like condensates. To gain a molecular-level understanding of how the accumulation of stronger interactions among proteins inside condensates affect the kinetic and thermodynamic properties of biomolecular condensates, and their shapes over time, we develop a tailored coarse-grained model of proteins that transition from establishing weak to stronger inter-protein interactions inside condensates. Our simulations reveal that the fast accumulation of strongly binding proteins during the nucleation and growth stages of condensate formation results in aspherical solid-like condensates. In contrast, when strong inter-protein interactions appear only after the equilibrium condensate has been formed, or when they accumulate slowly over time with respect to the time needed for droplets to fuse and grow, spherical solid-like droplets emerge. By conducting atomistic potential-of-mean-force simulations of NUP-98 peptides-prone to forming inter-protein [Formula: see text]-sheets-we observe that formation of inter-peptide [Formula: see text]-sheets increases the strength of the interactions consistently with the loss of liquid-like condensate properties we observe at the coarse-grained level. Overall, our work aids in elucidating fundamental molecular, kinetic, and thermodynamic mechanisms linking the rate of change in protein interaction strength to condensate shape and maturation during ageing.

Unifying coarse-grained force fields for folded and disordered proteins

Liquid-liquid phase separation drives the formation of biological condensates that play essential roles in transcriptional regulation and signal sensing. Computational modeling could provide high-resolution structural characterizations of these condensates and help uncover physicochemical interactions that dictate their stability. However, many protein molecules involved in phase separation often contain multiple ordered domains connected with flexible, structureless linkers. Simulating such proteins necessitates force fields with consistent accuracy for both folded and disordered proteins. We provide a critical review of existing coarse-grained force fields for disordered proteins and highlight the challenges in their application to folded proteins. After discussing existing algorithms for force field parameterization, we propose an optimization strategy that should lead to computer models with improved transferability across protein types.

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy

Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π-π and hybrid cation-π/π-π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in-vitro phase diagrams; Mpipi predictions agree well with experiment on both fronts. Moreover, it can account for protein-RNA interactions, correctly predicts the multiphase behaviour of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental LLPS trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.

Size conservation emerges spontaneously in biomolecular condensates formed by scaffolds and surfactant clients

Biomolecular condensates are liquid-like membraneless compartments that contribute to the spatiotemporal organization of proteins, RNA, and other biomolecules inside cells. Some membraneless compartments, such as nucleoli, are dispersed as different condensates that do not grow beyond a certain size, or do not present coalescence over time. In this work, using a minimal protein model, we show that phase separation of binary mixtures of scaffolds and low-valency clients that can act as surfactants-i.e., that significantly reduce the droplet surface tension-can yield either a single drop or multiple droplets that conserve their sizes on long timescales (herein 'multidroplet size-conserved' scenario'), depending on the scaffold to client ratio. Our simulations demonstrate that protein connectivity and condensate surface tension regulate the balance between these two scenarios. The multidroplet size-conserved scenario spontaneously arises at increasing surfactant-to-scaffold concentrations, when the interfacial penalty for creating small liquid droplets is sufficiently reduced by the surfactant proteins that are preferentially located at the interface. In contrast, low surfactant-to-scaffold concentrations enable continuous growth and fusion of droplets without restrictions. Overall, our work proposes one thermodynamic mechanism to help rationalize how size-conserved coexisting condensates can persist inside cells-shedding light on the roles of protein connectivity, binding affinity, and droplet composition in this process.