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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., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Polycomb repressive complex 1 (PRC1) undergoes phase separation to form Polycomb condensates that are multi-component hubs for silencing Polycomb target genes. In this study, we demonstrate that formation and regulation of PRC1 condensates are consistent with the scaffold-client model, where the Chromobox 2 (CBX2) protein behaves as the scaffold while the other PRC1 proteins are clients. Such clients induce a re-entrant phase transition of CBX2 condensates. The composition of the multi-component PRC1 condensates (1) determines the dynamic properties of the scaffold protein; (2) selectively promotes the formation of CBX4-PRC1 condensates while dissolving condensates of CBX6-, CBX7-, and CBX8-PRC1; and (3) controls the enrichment of CBX4-, CBX7-, and CBX8-PRC1 in CBX2-PRC1 condensates and the exclusion of CBX6-PRC1 from CBX2-PRC1 condensates. Our findings uncover how multi-component PRC1 condensates are assembled via an intricate scaffold-client mechanism whereby the properties of the PRC1 condensates are sensitively regulated by its composition and stoichiometry., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 The Authors. Published by Elsevier Inc. All rights reserved.)

Phase separation plays an important role in the formation of membraneless compartments within the cell and intrinsically disordered proteins with low-complexity sequences can drive this compartmentalisation. Various intermolecular forces, such as aromatic-aromatic and cation-aromatic interactions, promote phase separation. However, little is known about how the ability of proteins to phase separate under physiological conditions is encoded in their energy landscapes and this is the focus of the present investigation. Our results provide a first glimpse into how the energy landscapes of minimal peptides that contain - and cation- interactions differ from the peptides that lack amino acids with such interactions. The peaks in the heat capacity () as a function of temperature report on alternative low-lying conformations that differ significantly in terms of their enthalpic and entropic contributions. The analysis and subsequent quantification of frustration of the energy landscape suggest that the interactions that promote phase separation lead to features (peaks or inflection points) at low temperatures in . More features may occur for peptides containing residues with better phase separation propensity and the energy landscape is more frustrated for such peptides. Overall, this work links the features in the underlying single-molecule potential energy landscapes to their collective phase separation behaviour and identifies quantities ( and frustration metric) that can be utilised in soft material design., Competing Interests: The authors declare no competing interest exists., (© The Author(s) 2023.)

Maturation of functional liquid-like biomolecular condensates into solid-like aggregates has been linked to the onset of several neurodegenerative disorders. Low-complexity aromatic-rich kinked segments (LARKS) contained in numerous RNA-binding proteins can promote aggregation by forming inter-protein β-sheet fibrils that accumulate over time and ultimately drive the liquid-to-solid transition of the condensates. Here, atomistic molecular dynamics simulations are combined with sequence-dependent coarse-grained models of various resolutions to investigate the role of LARKS abundance and position within the amino acid sequence in the maturation of condensates. Remarkably, proteins with tail-located LARKS display much higher viscosity over time than those in which the LARKS are placed toward the center. Yet, at very long timescales, proteins with a single LARKS-independently of its location-can still relax and form high viscous liquid condensates. However, phase-separated condensates of proteins containing two or more LARKS become kinetically trapped due to the formation of percolated β-sheet networks that display gel-like behavior. Furthermore, as a work case example, they demonstrate how shifting the location of the LARKS-containing low-complexity domain of FUS protein toward its center effectively precludes the accumulation of β-sheet fibrils in FUS-RNA condensates, maintaining functional liquid-like behavior without ageing., (© 2023 The Authors. Advanced Science published by Wiley-VCH GmbH.)

A wide range of macromolecules can undergo phase separation, forming biomolecular condensates in living cells. These membraneless organelles are typically highly dynamic, formed reversibly, and carry out essential functions in biological systems. Crucially, however, a further liquid-to-solid transition of the condensates can lead to irreversible pathological aggregation and cellular dysfunction associated with the onset and development of neurodegenerative diseases. Despite the importance of this liquid-to-solid transition of proteins, the mechanism by which it is initiated in normally functional condensates is unknown. Here we show, by measuring the changes in structure, dynamics, and mechanics in time and space, that single-component FUS condensates do not uniformly convert to a solid gel, but rather that liquid and gel phases coexist simultaneously within the same condensate, resulting in highly inhomogeneous structures. Furthermore, our results show that this transition originates at the interface between the condensate and the dilute continuous phase, and once initiated, the gelation process propagates toward the center of the condensate. To probe such spatially inhomogeneous rheology during condensate aging, we use a combination of established micropipette aspiration experiments together with two optical techniques, spatial dynamic mapping and reflective confocal dynamic speckle microscopy. These results reveal the importance of the spatiotemporal dimension of the liquid-to-solid transition and highlight the interface of biomolecular condensates as a critical element in driving pathological protein aggregation.

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.

Biomolecular condensates, thought to form via liquid-liquid phase separation of intracellular mixtures, are multicomponent systems that can include diverse types of proteins and RNAs. RNA is a critical modulator of RNA-protein condensate stability, as it induces an RNA concentration-dependent reentrant phase transition-increasing stability at low RNA concentrations and decreasing it at high concentrations. Beyond concentration, RNAs inside condensates can be heterogeneous in length, sequence, and structure. Here, we use multiscale simulations to understand how different RNA parameters interact with one another to modulate the properties of RNA-protein condensates. To do so, we perform residue/nucleotide resolution coarse-grained molecular dynamics simulations of multicomponent RNA-protein condensates containing RNAs of different lengths and concentrations, and either FUS or PR 25 proteins. Our simulations reveal that RNA length regulates the reentrant phase behavior of RNA-protein condensates: increasing RNA length sensitively rises the maximum value that the critical temperature of the mixture reaches, and the maximum concentration of RNA that the condensate can incorporate before beginning to become unstable. Strikingly, RNAs of different lengths are organized heterogeneously inside condensates, which allows them to enhance condensate stability via two distinct mechanisms: shorter RNA chains accumulate at the condensate's surface acting as natural biomolecular surfactants, while longer RNA chains concentrate inside the core to saturate their bonds and enhance the density of molecular connections in the condensate. Using a patchy particle model, we additionally demonstrate that the combined impact of RNA length and concentration on condensate properties is dictated by the valency, binding affinity, and polymer length of the various biomolecules involved. Our results postulate that diversity on RNA parameters within condensates allows RNAs to increase condensate stability by fulfilling two different criteria: maximizing enthalpic gain and minimizing interfacial free energy; hence, RNA diversity should be considered when assessing the impact of RNA on biomolecular condensates regulation., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Biomolecular condensates are important contributors to the internal organization of the cell material. While initially described as liquid-like droplets, the term biomolecular condensates is now used to describe a diversity of condensed phase assemblies with material properties extending from low to high viscous liquids, gels, and even glasses. Because the material properties of condensates are determined by the intrinsic behavior of their molecules, characterizing such properties is integral to rationalizing the molecular mechanisms that dictate their functions and roles in health and disease. Here, we apply and compare three distinct computational methods to measure the viscoelasticity of biomolecular condensates in molecular simulations. These methods are the Green-Kubo (GK) relation, the oscillatory shear (OS) technique, and the bead tracking (BT) method. We find that, although all of these methods provide consistent results for the viscosity of the condensates, the GK and OS techniques outperform the BT method in terms of computational efficiency and statistical uncertainty. We thus apply the GK and OS techniques for a set of 12 different protein/RNA systems using a sequence-dependent coarse-grained model. Our results reveal a strong correlation between condensate viscosity and density, as well as with protein/RNA length and the number of stickers vs spacers in the amino acid protein sequence. Moreover, we couple the GK and the OS technique to nonequilibrium molecular dynamics simulations that mimic the progressive liquid-to-gel transition of protein condensates due to the accumulation of interprotein β-sheets. We compare the behavior of three different protein condensates, i.e., those formed by either hnRNPA1, FUS, or TDP-43 proteins, whose liquid-to-gel transitions are associated with the onset of amyotrophic lateral sclerosis and frontotemporal dementia. We find that both the GK and OS techniques successfully predict the transition from functional liquid-like behavior to kinetically arrested states once the network of interprotein β-sheets has percolated through the condensates. Overall, our work provides a comparison of different modeling rheological techniques to assess the viscosity of biomolecular condensates, a critical magnitude that provides information on the behavior of biomolecules inside condensates.

Singlet fission (SF), an exciton-doubling process observed in certain molecular semiconductors where two triplet excitons are generated from one singlet exciton, requires correctly tuned intermolecular coupling to allow separation of the two triplets to different molecular units. We explore this using DNA-encoded assembly of SF-capable pentacenes into discrete π-stacked constructs of defined size and geometry. Precise structural control is achieved via a combination of the DNA duplex formation between complementary single-stranded DNA and the local molecular geometry that directs the SF chromophores into a stable and predictable slip-stacked configuration, as confirmed by molecular dynamics (MD) modeling. Transient electron spin resonance spectroscopy revealed that within these DNA-assembled pentacene stacks, SF evolves via a bound triplet pair quintet state, which subsequently converts into free triplets. SF evolution via a long-lived quintet state sets specific requirements on intermolecular coupling, rendering the quintet spectrum and its zero-field-splitting parameters highly sensitive to intermolecular geometry. We have found that the experimental spectra and zero-field-splitting parameters are consistent with a slight systematic strain relative to the MD-optimized geometry. Thus, the transient electron spin resonance analysis is a powerful tool to test and refine the MD-derived structure models. DNA-encoded assembly of coupled semiconductor molecules allows controlled construction of electronically functional structures, but brings with it significant dynamic and polar disorders. Our findings here of efficient SF through quintet states demonstrate that these conditions still allow efficient and controlled semiconductor operation and point toward future opportunities for constructing functional optoelectronic systems.

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., Competing Interests: The authors declare no competing interests., (This journal is © The Royal Society of Chemistry.)

The protein high mobility group A1 (HMGA1) is an important regulator of chromatin organization and function. However, the mechanisms by which it exerts its biological function are not fully understood. Here, we report that the HMGA isoform, HMGA1a, nucleates into foci that display liquid-like properties in the nucleus, and that the protein readily undergoes phase separation to form liquid condensates in vitro. By bringing together machine-leaning modelling, cellular and biophysical experiments and multiscale simulations, we demonstrate that phase separation of HMGA1a is promoted by protein-DNA interactions, and has the potential to be modulated by post-transcriptional effects such as phosphorylation. We further show that the intrinsically disordered C-terminal tail of HMGA1a significantly contributes to its phase separation through electrostatic interactions via AT hooks 2 and 3. Our work sheds light on HMGA1 phase separation as an emergent biophysical factor in regulating chromatin structure., (© 2022 The Authors. ChemBioChem published by Wiley-VCH GmbH.)

Biomolecular condensates, some of which are liquid-like during health, can age over time becoming gel-like pathological systems. One potential source of loss of liquid-like properties during ageing of RNA-binding protein condensates is the progressive formation of inter-protein β-sheets. To bridge microscopic understanding between accumulation of inter-protein β-sheets over time and the modulation of FUS and hnRNPA1 condensate viscoelasticity, we develop a multiscale simulation approach. Our method integrates atomistic simulations with sequence-dependent coarse-grained modelling of condensates that exhibit accumulation of inter-protein β-sheets over time. We reveal that inter-protein β-sheets notably increase condensate viscosity but does not transform the phase diagrams. Strikingly, the network of molecular connections within condensates is drastically altered, culminating in gelation when the network of strong β-sheets fully percolates. However, high concentrations of RNA decelerate the emergence of inter-protein β-sheets. Our study uncovers molecular and kinetic factors explaining how the accumulation of inter-protein β-sheets can trigger liquid-to-solid transitions in condensates, and suggests a potential mechanism to slow such transitions down., (© 2022. The Author(s).)

Phase-separated biomolecular condensates that contain multiple coexisting phases are widespread in vitro and in cells. Multiphase condensates emerge readily within multicomponent mixtures of biomolecules (e.g., proteins and nucleic acids) when the different components present sufficient physicochemical diversity (e.g., in intermolecular forces, structure, and chemical composition) to sustain separate coexisting phases. Because such diversity is highly coupled to the solution conditions (e.g., temperature, pH, salt, composition), it can manifest itself immediately from the nucleation and growth stages of condensate formation, develop spontaneously due to external stimuli or emerge progressively as the condensates age. Here, we investigate thermodynamic factors that can explain the progressive intrinsic transformation of single-component condensates into multiphase architectures during the nonequilibrium process of aging. We develop a multiscale model that integrates atomistic simulations of proteins, sequence-dependent coarse-grained simulations of condensates, and a minimal model of dynamically aging condensates with nonconservative intermolecular forces. Our nonequilibrium simulations of condensate aging predict that single-component condensates that are initially homogeneous and liquid like can transform into gel-core/liquid-shell or liquid-core/gel-shell multiphase condensates as they age due to gradual and irreversible enhancement of interprotein interactions. The type of multiphase architecture is determined by the aging mechanism, the molecular organization of the gel and liquid phases, and the chemical makeup of the protein. Notably, we predict that interprotein disorder to order transitions within the prion-like domains of intracellular proteins can lead to the required nonconservative enhancement of intermolecular interactions. Our study, therefore, predicts a potential mechanism by which the nonequilibrium process of aging results in single-component multiphase condensates.

The three-dimensional organisation of the genome modulates biological processes and is, in turn, transformed by the activity in the nucleus. Not surprisingly, understanding how the genome operates requires uncovering the fundamental biophysical and molecular mechanisms that establish and regulate its organisation. Genome organisation starts with the formation of chromatin: a polymer of nucleoprotein complexes, termed nucleosomes, that carry variable chemical signatures according to their biological context. The physicochemical heterogeneity of chromatin, the stochastic organisation it fosters, and the multiscale nature of genome organisation pose great technical challenges. Excitingly, advances in imaging and molecular biology techniques are addressing chromatin organisation at increasing resolutions. In tandem, computer models are testing and postulating hypotheses, interpreting the experimental data, and linking molecular properties of nucleosomes to the mesoscale organisation of chromatin. We discuss how coarse-grained models at varying resolutions are expanding our mechanistic understanding of chromatin organisation, and the challenges still remaining in the field., Competing Interests: Conflict of interest statement Nothing declared., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

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., (© 2022. The Author(s).)

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) play a crucial role in the spatiotemporal organization of the cell material. Nucleic acids can act as critical modulators in the stability of these protein condensates. To unveil the role of RNA length in regulating the stability of RNA binding protein (RBP) condensates, we present a multiscale computational strategy that exploits the advantages of a sequence-dependent coarse-grained representation of proteins and a minimal coarse-grained model wherein proteins are described as patchy colloids. We find that for a constant nucleotide/protein ratio, the protein fused in sarcoma (FUS), which can phase separate on its own-i.e., via homotypic interactions-only exhibits a mild dependency on the RNA strand length. In contrast, the 25-repeat proline-arginine peptide (PR25), which does not undergo LLPS on its own at physiological conditions but instead exhibits complex coacervation with RNA-i.e., via heterotypic interactions-shows a strong dependence on the length of the RNA strands. Our minimal patchy particle simulations suggest that the strikingly different effect of RNA length on homotypic LLPS versus RBP-RNA complex coacervation is general. Phase separation is RNA-length dependent whenever the relative contribution of heterotypic interactions sustaining LLPS is comparable or higher than those stemming from protein homotypic interactions. Taken together, our results contribute to illuminate the intricate physicochemical mechanisms that influence the stability of RBP condensates through RNA inclusion., Competing Interests: The authors have declared that no competing interests exist.

Liquid-liquid phase separation underlies the formation of biological condensates. Physically, such systems are microemulsions that in general have a propensity to fuse and coalesce; however, many condensates persist as independent droplets in the test tube and inside cells. This stability is crucial for their function, but the physicochemical mechanisms that control the emulsion stability of condensates remain poorly understood. Here, by combining single-condensate zeta potential measurements, optical microscopy, tweezer experiments, and multiscale molecular modeling, we investigate how the nanoscale forces that sustain condensates impact their stability against fusion. By comparing peptide-RNA (PR 25 :PolyU) and proteinaceous (FUS) condensates, we show that a higher condensate surface charge correlates with a lower fusion propensity. Moreover, measurements of single condensate zeta potentials reveal that such systems can constitute classically stable emulsions. Taken together, these results highlight the role of passive stabilization mechanisms in protecting biomolecular condensates against coalescence.

Natural photosystems use protein scaffolds to control intermolecular interactions that enable exciton flow, charge generation, and long-range charge separation. In contrast, there is limited structural control in current organic electronic devices such as OLEDs and solar cells. We report here the DNA-encoded assembly of π-conjugated perylene diimides (PDIs) with deterministic control over the number of electronically coupled molecules. The PDIs are integrated within DNA chains using phosphoramidite coupling chemistry, allowing selection of the DNA sequence to either side, and specification of intermolecular DNA hybridization. In this way, we have developed a "toolbox" for construction of any stacking sequence of these semiconducting molecules. We have discovered that we need to use a full hierarchy of interactions: DNA guides the semiconductors into specified close proximity, hydrophobic-hydrophilic differentiation drives aggregation of the semiconductor moieties, and local geometry and electrostatic interactions define intermolecular positioning. As a result, the PDIs pack to give substantial intermolecular π wave function overlap, leading to an evolution of singlet excited states from localized excitons in the PDI monomer to excimers with wave functions delocalized over all five PDIs in the pentamer. This is accompanied by a change in the dominant triplet forming mechanism from localized spin-orbit charge transfer mediated intersystem crossing for the monomer toward a delocalized excimer process for the pentamer. Our modular DNA-based assembly reveals real opportunities for the rapid development of bespoke semiconductor architectures with molecule-by-molecule precision.

Chromatin in eukaryotic cells is a negatively charged long polymer consisting of DNA, histones, and various associated proteins. With its highly charged and heterogeneous nature, chromatin structure varies greatly depending on various factors (e.g. chemical modifications and protein enrichment) and the surrounding environment (e.g. cations): from a 10-nm fiber, a folded 30-nm fiber, to chromatin condensates/droplets. Recent advanced imaging has observed that chromatin exhibits a dynamic liquid-like behavior and undergoes structural variations within the cell. Current computational modeling has made it possible to reconstruct the liquid-like chromatin in the cell by dealing with a number of nucleosomes on multiscale levels and has become a powerful technique to inspect the molecular mechanisms giving rise to the observed behavior, which imaging methods cannot do on their own. Based on new findings from both imaging and modeling studies, we discuss the dynamic aspect of chromatin in living cells and its functional relevance., Competing Interests: Conflict of interest statement Nothing declared., (Copyright © 2021 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The structure of B-DNA, the physiological form of the DNA molecule, has been a central topic in biology, chemistry and physics. Far from uniform and rigid, the double helix was revealed as a flexible and structurally polymorphic molecule. Conformational changes that lead to local and global changes in the helix geometry are mediated by a complex choreography of base and backbone rearrangements affecting the ability of the B-DNA to recognize ligands and consequently on its functionality. In this sense, the knowledge obtained from the sequence-dependent structural properties of B-DNA has always been thought crucial to rationalize how ligands and, most notably, proteins recognize B-DNA and modulate its activity, i.e. the structural basis of gene regulation. Honouring the anniversary of the first high-resolution X-ray structure of a B-DNA molecule, in this contribution, we present the most important discoveries of the last 40 years on the sequence-dependent structural and dynamical properties of B-DNA, from the early beginnings to the current frontiers in the field., Competing Interests: Conflict of interestThe authors declare no competing interests., (© International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany, part of Springer Nature 2021.)

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., Competing Interests: Competing Interests Statement The authors declare no competing interests.

Rationally and efficiently modifying the amino-acid sequence of proteins to control their ability to undergo liquid-liquid phase separation (LLPS) on demand is not only highly desirable, but can also help to elucidate which protein features are important for LLPS. Here, we propose a computational method that couples a genetic algorithm to a sequence-dependent coarse-grained protein model to evolve the amino-acid sequences of phase-separating intrinsically disordered protein regions (IDRs), and purposely enhance or inhibit their capacity to phase-separate. We validate the predicted critical solution temperatures of the mutated sequences with ABSINTH, a more accurate all-atom model. We apply the algorithm to the phase-separating IDRs of three naturally occurring proteins, namely FUS, hnRNPA1 and LAF1, as prototypes of regions that exist in cells and undergo homotypic LLPS driven by different types of intermolecular interaction, and we find that the evolution of amino-acid sequences towards enhanced LLPS is driven in these three cases, among other factors, by an increase in the average size of the amino acids. However, the direction of change in the molecular driving forces that enhance LLPS (such as hydrophobicity, aromaticity and charge) depends on the initial amino-acid sequence. Finally, we show that the evolution of amino-acid sequences to modulate LLPS is strongly coupled to the make-up of the medium (e.g. the presence or absence of RNA), which may have significant implications for our understanding of phase separation within the many-component mixtures of biological systems., Competing Interests: The authors have declared that no competing interests exist.

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., (© 2021. The Author(s).)

Liquid-liquid phase separation (LLPS) is an important mechanism that helps explain the membraneless compartmentalization of the nucleus. Because chromatin compaction and LLPS are collective phenomena, linking their modulation to the physicochemical features of nucleosomes is challenging. Here, we develop an advanced multiscale chromatin model-integrating atomistic representations, a chemically-specific coarse-grained model, and a minimal model-to resolve individual nucleosomes within sub-Mb chromatin domains and phase-separated systems. To overcome the difficulty of sampling chromatin at high resolution, we devise a transferable enhanced-sampling Debye-length replica-exchange molecular dynamics approach. We find that nucleosome thermal fluctuations become significant at physiological salt concentrations and destabilize the 30-nm fiber. Our simulations show that nucleosome breathing favors stochastic folding of chromatin and promotes LLPS by simultaneously boosting the transient nature and heterogeneity of nucleosome-nucleosome contacts, and the effective nucleosome valency. Our work puts forward the intrinsic plasticity of nucleosomes as a key element in the liquid-like behavior of nucleosomes within chromatin, and the regulation of chromatin LLPS.

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules., (Copyright © 2021. Published by Elsevier Inc.)

Liquid-liquid phase separation of proteins underpins the formation of membraneless compartments in living cells. Elucidating the molecular driving forces underlying protein phase transitions is therefore a key objective for understanding biological function and malfunction. Here we show that cellular proteins, which form condensates at low salt concentrations, including FUS, TDP-43, Brd4, Sox2, and Annexin A11, can reenter a phase-separated regime at high salt concentrations. By bringing together experiments and simulations, we demonstrate that this reentrant phase transition in the high-salt regime is driven by hydrophobic and non-ionic interactions, and is mechanistically distinct from the low-salt regime, where condensates are additionally stabilized by electrostatic forces. Our work thus sheds light on the cooperation of hydrophobic and non-ionic interactions as general driving forces in the condensation process, with important implications for aberrant function, druggability, and material properties of biomolecular condensates.

Biomolecular condensates, which assemble via the process of liquid-liquid phase separation (LLPS), are multicomponent compartments found ubiquitously inside cells. Experiments and simulations have shown that biomolecular condensates with many components can exhibit multilayered organizations. Using a minimal coarse-grained model for interacting multivalent proteins, we investigate the thermodynamic parameters governing the formation of multilayered condensates through changes in protein valency and binding affinity. We focus on multicomponent condensates formed by scaffold proteins (high-valency proteins that can phase separate on their own via homotypic interactions) and clients (proteins recruited to condensates via heterotypic scaffold-client interactions). We demonstrate that higher valency species are sequestered to the center of the multicomponent condensates, while lower valency proteins cluster towards the condensate interface. Such multilayered condensate architecture maximizes the density of LLPS-stabilizing molecular interactions, while simultaneously reducing the surface tension of the condensates. In addition, multilayered condensates exhibit rapid exchanges of low valency proteins in and out, while keeping higher valency proteins-the key biomolecules involved in condensate nucleation-mostly within. We also demonstrate how modulating the binding affinities among the different proteins in a multicomponent condensate can significantly transform its multilayered structure, and even trigger fission of a condensate into multiple droplets with different compositions.

Proteins containing intrinsically disordered regions (IDRs) are ubiquitous within biomolecular condensates, which are liquid-like compartments within cells formed through liquid-liquid phase separation (LLPS). The sequence of amino acids of a protein encodes its phase behaviour, not only by establishing the patterning and chemical nature (e.g., hydrophobic, polar, charged) of the various binding sites that facilitate multivalent interactions, but also by dictating the protein conformational dynamics. Besides behaving as random coils, IDRs can exhibit a wide-range of structural behaviours, including conformational switching, where they transition between alternate conformational ensembles. Using Molecular Dynamics simulations of a minimal coarse-grained model for IDRs, we show that the role of protein conformation has a non-trivial effect in the liquid-liquid phase behaviour of IDRs. When an IDR transitions to a conformational ensemble enriched in disordered extended states, LLPS is enhanced. In contrast, IDRs that switch to ensembles that preferentially sample more compact and structured states show inhibited LLPS. This occurs because extended and disordered protein conformations facilitate LLPS-stabilising multivalent protein-protein interactions by reducing steric hindrance; thereby, such conformations maximize the molecular connectivity of the condensed liquid network. Extended protein configurations promote phase separation regardless of whether LLPS is driven by homotypic and/or heterotypic protein-protein interactions. This study sheds light on the link between the dynamic conformational plasticity of IDRs and their liquid-liquid phase behaviour.

One of the key mechanisms used by cells to control the spatiotemporal organization of their many components is the formation and dissolution of biomolecular condensates through liquid-liquid phase separation (LLPS). Using a minimal coarse-grained model that allows us to simulate thousands of interacting multivalent proteins, we investigate the physical parameters dictating the stability and composition of multicomponent biomolecular condensates. We demonstrate that the molecular connectivity of the condensed-liquid network-i.e., the number of weak attractive protein-protein interactions per unit of volume-determines the stability (e.g., in temperature, pH, salt concentration) of multicomponent condensates, where stability is positively correlated with connectivity. While the connectivity of scaffolds (biomolecules essential for LLPS) dominates the phase landscape, introduction of clients (species recruited via scaffold-client interactions) fine-tunes it by transforming the scaffold-scaffold bond network. Whereas low-valency clients that compete for scaffold-scaffold binding sites decrease connectivity and stability, those that bind to alternate scaffold sites not required for LLPS or that have higher-than-scaffold valencies form additional scaffold-client-scaffold bridges increasing stability. Proteins that establish more connections (via increased valencies, promiscuous binding, and topologies that enable multivalent interactions) support the stability of and are enriched within multicomponent condensates. Importantly, proteins that increase the connectivity of multicomponent condensates have higher critical points as pure systems or, if pure LLPS is unfeasible, as binary scaffold-client mixtures. Hence, critical points of accessible systems (i.e., with just a few components) might serve as a unified thermodynamic parameter to predict the composition of multicomponent condensates., Competing Interests: The authors declare no competing interest.

Intrinsically disordered proteins are crucial elements of chromatin heterogenous organization. While disorder in the histone tails enables a large variation of inter-nucleosome arrangements, disorder within the chromatin-binding proteins facilitates promiscuous binding to a wide range of different molecular targets, consistent with structural heterogeneity. Among the partially disordered chromatin-binding proteins, the H1 linker histone influences a myriad of chromatin characteristics including compaction, nucleosome spacing, transcription regulation, and the recruitment of other chromatin regulating proteins. Although it is now established that the long C-terminal domain (CTD) of H1 remains disordered upon nucleosome binding and that such disorder favours chromatin fluidity, the structural behaviour and thereby the role/function of the N-terminal domain (NTD) within chromatin is yet unresolved. On the basis of microsecond-long parallel-tempering metadynamics and temperature-replica exchange atomistic molecular dynamics simulations of different H1 NTD subtypes, we demonstrate that the NTD is completely unstructured in solution but undergoes an important disorder-to-order transition upon nucleosome binding: it forms a helix that enhances its DNA binding ability. Further, we show that the helical propensity of the H1 NTD is subtype-dependent and correlates with the experimentally observed binding affinity of H1 subtypes, suggesting an important functional implication of this disorder-to-order transition., (© The Author(s) 2020. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Protein flexibility and disorder is emerging as a crucial modulator of chromatin structure. Histone tail disorder enables transient binding of different molecules to the nucleosomes, thereby promoting heterogeneous and dynamic internucleosome interactions and making possible recruitment of a wide-range of regulatory and remodeling proteins. On the basis of extensive multiscale modeling we reveal the importance of linker histone H1 protein disorder for chromatin hierarchical looping. Our multiscale approach bridges microsecond-long bias-exchange metadynamics molecular dynamics simulations of atomistic 211-bp nucleosomes with coarse-grained Monte Carlo simulations of 100-nucleosome systems. We show that the long C-terminal domain (CTD) of H1-a ubiquitous nucleosome-binding protein-remains disordered when bound to the nucleosome. Notably, such CTD disorder leads to an asymmetric and dynamical nucleosome conformation that promotes chromatin structural flexibility and establishes long-range hierarchical loops. Furthermore, the degree of condensation and flexibility of H1 can be fine-tuned, explaining chromosomal differences of interphase versus metaphase states that correspond to partial and hyperphosphorylated H1, respectively. This important role of H1 protein disorder in large-scale chromatin organization has a wide range of biological implications., Competing Interests: The authors declare no competing interest.

The phase diagram of molecular or colloidal systems depends strongly on the range and angular dependence of the interactions between the constituent particles. For instance, it is well known that the critical density of particles with "patchy" interactions shifts to lower values as the number of patches is decreased [see Bianchi et al. Phys. Rev. Lett. 97, 168301 (2006)]. Here, we present simulations that show that the phase behavior of patchy particles is even more interesting than had been appreciated. In particular, we find that, upon cooling below the critical point, the width of the liquid-vapor coexistence region of a system of particles with tetrahedrally arranged patches first increases, then decreases, and finally increases again. In other words, this system exhibits a doubly re-entrant liquid-vapor transition. As a consequence, the system exhibits a very large deviation from the law of rectilinear diameter, which assumes that the critical density can be obtained by linear extrapolation of the averages of the densities of the coexisting liquid and vapor phases. We argue that the unusual behavior of this system has the same origin as the density maximum in liquid water and is not captured by the Wertheim theory. The Wertheim theory also cannot account for our observation that the phase diagram of particles with three patches depends strongly on the geometrical distribution of the patches and on the degree to which their position on the particle surface is rigidly constrained. However, the phase diagram is less sensitive to small angular spreads in the patch locations. We argue that the phase behavior reported in this paper should be observable in experiments on patchy colloids and may be relevant for the liquid-liquid equilibrium in solutions of properly functionalized dendrimers.

Histone tails and their epigenetic modifications play crucial roles in gene expression regulation by altering the architecture of chromatin. However, the structural mechanisms by which histone tails influence the interconversion between active and inactive chromatin remain unknown. Given the technical challenges in obtaining detailed experimental characterizations of the structure of chromatin, multiscale computations offer a promising alternative to model the effect of histone tails on chromatin folding. Here we combine multimicrosecond atomistic molecular dynamics simulations of dinucleosomes and histone tails in explicit solvent and ions, performed with three different state-of-the-art force fields and validated by experimental NMR measurements, with coarse-grained Monte Carlo simulations of 24-nucleosome arrays to describe the conformational landscape of histone tails, their roles in chromatin compaction, and the impact of lysine acetylation, a widespread epigenetic change, on both. We find that while the wild-type tails are highly flexible and disordered, the dramatic increase of secondary-structure order by lysine acetylation unfolds chromatin by decreasing tail availability for crucial fiber-compacting internucleosome interactions. This molecular level description of the effect of histone tails and their charge modifications on chromatin folding explains the sequence sensitivity and underscores the delicate connection between local and global structural and functional effects. Our approach also opens new avenues for multiscale processes of biomolecular complexes.

The chromatin fiber undergoes significant structural changes during the cell's life cycle to modulate DNA accessibility. Detailed mechanisms of such structural transformations of chromatin fibers as affected by various internal and external conditions such as the ionic conditions of the medium, the linker DNA length, and the presence of linker histones, constitute an open challenge. Here we utilize Monte Carlo (MC) simulations of a coarse grained model of chromatin with nonuniform linker DNA lengths as found in vivo to help explain some aspects of this challenge. We investigate the unfolding mechanisms of chromatin fibers with alternating linker lengths of 26-62 bp and 44-79 bp using a series of end-to-end stretching trajectories with and without linker histones and compare results to uniform-linker-length fibers. We find that linker histones increase overall resistance of nonuniform fibers and lead to fiber unfolding with superbeads-on-a-string cluster transitions. Chromatin fibers with nonuniform linker DNA lengths display a more complex, multi-step yet smoother process of unfolding compared to their uniform counterparts, likely due to the existence of a more continuous range of nucleosome-nucleosome interactions. This finding echoes the theme that some heterogeneity in fiber component is biologically advantageous.

RNA hairpins play a pivotal role in a diverse range of cellular functions, and are integral components of ribozymes, mRNA, and riboswitches. However, the mechanistic and kinetic details of RNA hairpin folding, which are key determinants of most of its biological functions, are poorly understood. In this work, we use the discrete path sampling (DPS) approach to explore the energy landscapes of two RNA tetraloop hairpins, and provide insights into their folding mechanisms and kinetics in atomistic detail. Our results show that the potential energy landscapes have a distinct funnel-like bias toward the folded hairpin state, consistent with efficient structure-seeking properties. Mechanistic and kinetic information is analyzed in terms of kinetic transition networks. We find microsecond folding times, consistent with temperature jump experiments, for hairpin folding initiated from relatively compact unfolded states. This process is essentially driven by an initial collapse, followed by rapid zippering of the helix stem in the final phase. Much lower folding rates are predicted when the folding is initiated from extended chains, which undergo longer excursions on the energy landscape before nucleation events can occur. Our work therefore explains recent experiments and coarse-grained simulations, where the folding kinetics exhibit precisely this dependency on the initial conditions.