Energy landscapes and heat capacity signatures for peptides correlate with phase separation propensity.

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.

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.

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.

The Chromatin Regulator HMGA1a Undergoes Phase Separation in the Nucleus.

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.

Aging can transform single-component protein condensates into multiphase architectures.

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.

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.

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

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

Surface Electrostatics Govern the Emulsion Stability of Biomolecular Condensates.

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 (PR25: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.

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.

Nucleosome plasticity is a critical element of chromatin liquid-liquid phase separation and multivalent nucleosome interactions.

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.

Valency and Binding Affinity Variations Can Regulate the Multilayered Organization of Protein Condensates with Many Components.

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.

Reentrant liquid condensate phase of proteins is stabilized by hydrophobic and non-ionic interactions.

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.

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

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

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.

Liquid network connectivity regulates the stability and composition of biomolecular condensates with many components.

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.

Energy Landscape for Fold-Switching in Regulatory Protein RfaH.

The C-terminal domain (CTD) of bacterial regulatory protein RfaH undergoes a dramatic structural rearrangement from an α-helical hairpin to a ß-barrel. We employ a quasi-continuous interpolation scheme and geometry optimization techniques to construct a kinetic transition network for this process. The computed free energy landscape at 310 K is multifunneled, and the predicted free energy ensembles are in good agreement with experiment and other simulation studies. We find that rearrangement from the α-helical conformer to the ß-sheet proceeds via an essentially unstructured state. The techniques refined for the present system should be transferable to other protein conformational switches, with the potential to advance our understanding of such systems.

Intrinsically Disordered Landscapes for Human CD4 Receptor Peptide.

Because of their inherent structural plasticity, intrinsically disordered proteins (IDPs) are generally difficult to characterize, both experimentally and via simulations. In this work, an approach for studying IDPs within the potential energy landscape framework is implemented and tested. Specifically, human CD4 receptor peptide, a disordered region implicated in HIV-1 infection, is characterized via basin-hopping parallel tempering and discrete path sampling. We also investigate the effects of three state-of-the-art AMBER force fields (ff99SB-ILDN, ff14ipq, and ff14SB) on the energy landscape. The results for ff99SB-ILDN exhibit the best agreement with experiment. Metastable states identified on the free energy surface help to unify, and are consistent with, several earlier predictions, and may serve as starting points for probing the reaction interface between CD4 and HIV-1 accessory proteins.

Exploring biomolecular energy landscapes.

The potential energy landscape perspective provides both a conceptual and a computational framework for predicting, understanding and designing molecular properties. In this Feature Article, we highlight some recent advances that greatly facilitate structure prediction and analysis of global thermodynamics and kinetics in proteins and nucleic acids. The geometry optimisation procedures, on which these calculations are based, can be accelerated significantly using local rigidification of selected degrees of freedom, and through implementations on graphics processing units. Results of progressive local rigidification are first summarised for trpzip1, including a systematic analysis of the heat capacity and rearrangement rates. Benchmarks for all the essential optimisation procedures are then provided for a variety of proteins. Applications are then illustrated from a study of how mutation affects the energy landscape for a coiled-coil protein, and for transitions in helix morphology for a DNA duplex. Both systems exhibit an intrinsically multifunnel landscape, with the potential to act as biomolecular switches.

Structure, Thermodynamics, and Folding Pathways for a Tryptophan Zipper as a Function of Local Rigidification.

We investigate how the underlying potential energy landscape for a tryptophan zipper changes as indole rings, peptide bonds, termini, and trigonal planar centers are systematically grouped into local rigid bodies. The local rigid body framework results in a substantial computational speedup by effectively reducing the total number of degrees of freedom. Benchmarks are presented for the thermodynamics and folding mechanism. In general, the melting transition, as well as the precise sequence of folding events, is accurately reproduced with conservative local rigidification. However, aggressive rigidification leads to increased topological frustration and a concomitant slowing down of the global kinetics. Our results suggest that an optimal choice of local rigidification, and perhaps a hierarchical approach, could be very useful for investigating complex pathways in biomolecules.

Comparative computational study of model halogen-bonded complexes of FKrCl.

Quantum chemical calculations for the FKrCl molecule at various levels of theory were performed and suggest that this molecule is metastable and may be amenable to experimental synthesis under cryogenic conditions. The FKrCl molecule forms weak halogen-bonded complexes FKrCl···Y with small molecules like FH and H2O and its computed properties were compared with those for analogous complexes of its precursor, FCl, and its rare gas hydride counterpart, FKrH. The cooperative effect of additional noncovalent interactions introduced at the F atom in the FKrCl···Y dimer (to give Z···FKrCl···Y trimers) showed a general strengthening of the intermolecular interactions in the order halogen bond < hydrogen bond < beryllium bond < lithium bond.