Challenges in studying the liquid-to-solid phase transitions of proteins using computer simulations

“Membraneless organelles,” also referred to as biomolecular condensates, perform a variety of cellular functions and their dysregulation is implicated in cancer and neurodegeneration. In the last two decades, liquid-liquid phase separation (LLPS) of intrinsically disordered and multidomain proteins has emerged as a plausible mechanism underlying the formation of various biomolecular condensates. Further, the occurrence of liquid-to-solid transitions within liquid-like condensates may give rise to amyloid structures, implying a biophysical link between phase separation and protein aggregation. Despite significant advances, uncovering the microscopic details of liquid-to-solid phase transitions using experiments remains a considerable challenge and presents an exciting opportunity for the development of computational models which provide valuable, complementary insights into the underlying phenomenon. In this review, we first highlight recent biophysical studies which provide new insights into the molecular mechanisms underlying liquid-to-solid (fibril) phase transitions of folded, disordered and multi-domain proteins. Next, we summarize the range of computational models used to study protein aggregation and phase separation. Finally, we discuss recent computational approaches which attempt to capture the underlying physics of liquid-to-solid transitions along with their merits and shortcomings.     

Interplay of folded domains and the disordered low-complexity domain in mediating hnRNPA1 phase separation

Liquid–liquid phase separation underlies the membrane-less compartmentalization of cells. Intrinsically disordered low-complexity domains (LCDs) often mediate phase separation, but how their phase behavior is modulated by folded domains is incompletely understood. Here, we interrogate the interplay between folded and disordered domains of the RNA-binding protein hnRNPA1. The LCD of hnRNPA1 is sufficient for mediating phase separation in vitro. However, we show that the folded RRM domains and a folded solubility-tag modify the phase behavior, even in the absence of RNA. Notably, the presence of the folded domains reverses the salt dependence of the driving force for phase separation relative to the LCD alone. Small-angle X-ray scattering experiments and coarse-grained MD simulations show that the LCD interacts transiently with the RRMs and/or the solubility-tag in a salt-sensitive manner, providing a mechanistic explanation for the observed salt-dependent phase separation. These data point to two effects from the folded domains: (i) electrostatically-mediated interactions that compact hnRNPA1 and contribute to phase separation and (ii) increased solubility at higher ionic strengths mediated by the folded domains. The interplay between disordered and folded domains can modify the dependence of phase behavior on solution conditions and can obscure signatures of physicochemical interactions underlying phase separation.     

ATP regulates RNA‐driven cold inducible RNA binding protein phase separation

Intrinsically disordered proteins and proteins containing intrinsically disordered regions are highly abundant in the proteome of eukaryotes and are extensively involved in essential biological functions. More recently, their role in the organization of biomolecular condensates has become evident and along with their misregulation in several neurologic disorders. Currently, most studies involving these proteins are carried out in vitro and using purified proteins. Given that in cells, condensate‐forming proteins are exposed to high, millimolar concentrations of cellular metabolites, we aimed to reveal the interactions of cellular metabolites and a representative condensate‐forming protein. Here, using the arginine–glycine/arginine–glycine–glycine (RG/RGG)‐rich cold inducible RNA binding protein (CIRBP) as paradigm, we studied binding of the cellular metabolome to CIRBP. We found that most of the highly abundant cellular metabolites, except nucleotides, do not directly bind to CIRBP. ATP, ADP, and AMP as well as NAD⁺, NADH, NADP⁺, and NADPH directly interact with CIRBP, involving both the folded RNA‐recognition motif and the disordered RG/RGG region. ATP binding inhibited RNA‐driven phase separation of CIRBP. Thus, it might be beneficial to include cellular metabolites in in vitro liquid–liquid phase separation studies of RG/RGG and other condensate‐forming proteins in order to better mimic the cellular environment in the future.     

The key role of solvent in condensation: Mapping water in liquid-liquid phase-separated FUS

Formation of biomolecular condensates through liquid-liquid phase separation (LLPS) has emerged as a pervasive principle in cell biology, allowing compartmentalization and spatiotemporal regulation of dynamic cellular processes. Proteins that form condensates under physiological conditions often contain intrinsically disordered regions with low-complexity domains. Among them, the RNA-binding proteins FUS and TDP-43 have been a focus of intense investigation because aberrant condensation and aggregation of these proteins is linked to neurodegenerative diseases such as amyotrophic lateral sclerosis and frontotemporal dementia. LLPS occurs when protein-rich condensates form surrounded by a dilute aqueous solution. LLPS is per se entropically unfavorable. Energetically favorable multivalent protein-protein interactions are one important aspect to offset entropic costs. Another proposed aspect is the release of entropically unfavorable preordered hydration water into the bulk. We used attenuated total reflection spectroscopy in the terahertz frequency range to characterize the changes in the hydrogen bonding network accompanying the FUS enrichment in liquid-liquid phase-separated droplets to provide experimental evidence for the key role of the solvent as a thermodynamic driving force. The FUS concentration inside LLPS droplets was determined to be increased to 2.0 mM independent of the initial protein concentration (5 or 10 μM solutions) by fluorescence measurements. With terahertz spectroscopy, we revealed a dewetting of hydrophobic side chains in phase-separated FUS. Thus, the release of entropically unfavorable water populations into the bulk goes hand in hand with enthalpically favorable protein-protein interaction. Both changes are energetically favorable, and our study shows that both contribute to the thermodynamic driving force in phase separation.     

The pairwise energy content estimated from amino acid composition discriminates between folded and intrinsically unstructured proteins

The structural stability of a protein requires a large number of interresidue interactions. The energetic contribution of these can be approximated by low-resolution force fields extracted from known structures, based on observed amino acid pairing frequencies. The summation of such energies, however, cannot be carried out for proteins whose structure is not known or for intrinsically unstructured proteins. To overcome these limitations, we present a novel method for estimating the total pairwise interaction energy, based on a quadratic form in the amino acid composition of the protein. This approach is validated by the good correlation of the estimated and actual energies of proteins of known structure and by a clear separation of folded and disordered proteins in the energy space it defines. As the novel algorithm has not been trained on unstructured proteins, it substantiates the concept of protein disorder, i.e. that the inability to form a well-defined 3D structure is an intrinsic property of many proteins and protein domains. This property is encoded in their sequence, because their biased amino acid composition does not allow sufficient stabilizing interactions to form. By limiting the calculation to a predefined sequential neighborhood, the algorithm was turned into a position-specific scoring scheme that characterizes the tendency of a given amino acid to fall into an ordered or disordered region. This application we term IUPred and compare its performance with three generally accepted predictors, PONDR VL3H, DISOPRED2 and GlobPlot on a database of disordered proteins.     

On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations

Solution techniques such as small-angle X-ray scattering (SAXS) play a central role in structural studies of intrinsically disordered proteins (IDPs); yet, due to low resolution, it is generally necessary to combine SAXS with additional experimental sources of data and to use molecular simulations. Computational methods for the calculation of theoretical SAXS intensity profiles can be separated into two groups, depending on whether the solvent is modeled implicitly as continuous electron density or considered explicitly. The former offers reduced computational cost but requires the definition of a number of free parameters to account for, for example, the excess density of the solvation layer. Overfitting can thus be an issue, particularly when the structural ensemble is unknown. Here, we investigate and show how small variations of the contrast of the hydration shell, δρ, severely affect the outcome, analysis and interpretation of computed SAXS profiles for folded and disordered proteins. For both the folded and disordered proteins studied here, using a default δρ may, in some cases, result in the calculation of non-representative SAXS profiles, leading to an overestimation of their size and a misinterpretation of their structural nature. The solvation layer of the different IDP simulations also impacts their size estimates differently, depending on the protein force field used. The same is not true for the folded protein simulations, suggesting differences in the solvation of the two classes of proteins, and indicating that different force fields optimized for IDPs may cause expansion of the polypeptide chain through different physical mechanisms.     

Beta turn propensity and a model polymer scaling exponent identify intrinsically disordered phase-separating proteins

The complex cellular milieu can spontaneously demix, or phase separate, in a process controlled in part by intrinsically disordered (ID) proteins. A protein''s propensity to phase separate is thought to be driven by a preference for protein–protein over protein–solvent interactions. The hydrodynamic size of monomeric proteins, as quantified by the polymer scaling exponent (v), is driven by a similar balance. We hypothesized that mean v, as predicted by protein sequence, would be smaller for proteins with a strong propensity to phase separate. To test this hypothesis, we analyzed protein databases containing subsets of proteins that are folded, disordered, or disordered and known to spontaneously phase separate. We find that the phase-separating disordered proteins, on average, had lower calculated values of v compared with their non-phase-separating counterparts. Moreover, these proteins had a higher sequence-predicted propensity for β-turns. Using a simple, surface area-based model, we propose a physical mechanism for this difference: transient β-turn structures reduce the desolvation penalty of forming a protein-rich phase and increase exposure of atoms involved in π/sp² valence electron interactions. By this mechanism, β-turns could act as energetically favored nucleation points, which may explain the increased propensity for turns in ID regions (IDRs) utilized biologically for phase separation. Phase-separating IDRs, non-phase-separating IDRs, and folded regions could be distinguished by combining v and β-turn propensity. Finally, we propose a new algorithm, ParSe (partition sequence), for predicting phase-separating protein regions, and which is able to accurately identify folded, disordered, and phase-separating protein regions based on the primary sequence.     

A User’s Guide for Phase Separation Assays with Purified Proteins

The formation of membrane-less organelles and compartments by protein phase separation is an important way in which cells organize their cytoplasm and nucleoplasm. In vitro phase separation assays with purified proteins have become the standard way to investigate proteins that form membrane-less compartments. By now, various proteins have been purified and tested for their ability to phase separate and form liquid condensates in vitro. However, phase-separating proteins are often aggregation-prone and difficult to purify and handle. As a consequence, the results from phase separation assays often differ between labs and are not easily reproduced. Thus, there is an urgent need for high-quality proteins, standardized procedures, and generally agreed-upon practices for protein purification and conducting phase separation assays. This paper provides protocols for protein purification and guides the user through the practicalities of in vitro protein phase separation assays, including best-practice approaches and pitfalls to avoid. We believe that this compendium of protocols and practices will provide a useful resource for scientists studying the phase behavior of proteins.     

A predictive coarse-grained model for position-specific effects of post-translational modifications

Biomolecules undergo liquid-liquid phase separation (LLPS), resulting in the formation of multicomponent protein-RNA membraneless organelles in cells. However, the physiological and pathological role of post-translational modifications (PTMs) on the biophysics of phase behavior is only beginning to be probed. To study the effect of PTMs on LLPS in silico, we extend our transferable coarse-grained model of intrinsically disordered proteins to include phosphorylated and acetylated amino acids. Using the parameters for modified amino acids available for fixed-charge atomistic force fields, we parameterize the size and atomistic hydropathy of the coarse-grained-modified amino acid beads and, hence, the interactions between the modified and natural amino acids. We then elucidate how the number and position of phosphorylated and acetylated residues alter the protein’s single-chain compactness and its propensity to phase separate. We show that both the number and the position of phosphorylated threonines/serines or acetylated lysines can serve as a molecular on/off switch for phase separation in the well-studied disordered regions of Fused in Sarcoma (FUS) and DDX3X, respectively. We also compare modified residues to their commonly used PTM mimics for their impact on chain properties. Importantly, we show that the model can predict and capture experimentally measured differences in the phase behavior for position-specific modifications, showing that the position of modifications can dictate phase separation. In sum, this model will be useful for studying LLPS of post-translationally modified intrinsically disordered proteins and predicting how modifications control phase behavior with position-specific resolution.     

Liquid–liquid phase separation of tau: From molecular biophysics to physiology and disease

Biomolecular condensation via liquid–liquid phase separation (LLPS) of intrinsically disordered proteins/regions (IDPs/IDRs), with and without nucleic acids, has drawn widespread interest due to the rapidly unfolding role of phase‐separated condensates in a diverse range of cellular functions and human diseases. Biomolecular condensates form via transient and multivalent intermolecular forces that sequester proteins and nucleic acids into liquid‐like membrane‐less compartments. However, aberrant phase transitions into gel‐like or solid‐like aggregates might play an important role in neurodegenerative and other diseases. Tau, a microtubule‐associated neuronal IDP, is involved in microtubule stabilization, regulates axonal outgrowth and transport in neurons. A growing body of evidence indicates that tau can accomplish some of its cellular activities via LLPS. However, liquid‐to‐solid transition resulting in the abnormal aggregation of tau is associated with neurodegenerative diseases. The physical chemistry of tau is crucial for governing its propensity for biomolecular condensation which is governed by various intermolecular and intramolecular interactions leading to simple one‐component and complex multi‐component condensates. In this review, we aim at capturing the current scientific state in unveiling the intriguing molecular mechanism of phase separation of tau. We particularly focus on the amalgamation of existing and emerging biophysical tools that offer unique spatiotemporal resolutions on a wide range of length‐ and time‐scales. We also discuss the link between quantitative biophysical measurements and novel biological insights into biomolecular condensation of tau. We believe that this account will provide a broad and multidisciplinary view of phase separation of tau and its association with physiology and disease.     

Quantifying viscosity and surface tension of multicomponent protein-nucleic acid condensates

Living cells organize their internal space into dynamic condensates through liquid-liquid phase separation of multivalent proteins in association with cellular nucleic acids. Here, we study how variations in nucleic acid (NA)-to-protein stoichiometry modulate the condensed phase organization and fluid dynamics in a model system of multicomponent heterotypic condensates. Employing a multiparametric approach comprised of video particle tracking microscopy and optical tweezer-induced droplet fusion, we show that the interfacial tension, but not viscosity, of protein-NA condensates is controlled by the NA/protein ratio across the two-phase regime. In parallel, we utilize fluorescence correlation spectroscopy to quantify protein and NA diffusion in the condensed phase. Fluorescence correlation spectroscopy measurements reveal that the diffusion of the component protein and NA within the condensate core is governed by the viscosity, and hence, also remains insensitive to the changes in NA-to-protein stoichiometry. Collectively, our results provide insights into the regulation of multicomponent heterotypic liquid condensates, reflecting how the bulk mixture composition affects their core versus surface organization and dynamical properties.     

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.     

Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions

Biomolecular force fields optimized for globular proteins fail to properly reproduce properties of intrinsically disordered proteins. In particular, parameters of the water model need to be modified to improve applicability of the force fields to both ordered and disordered proteins. Here, we compared performance of force fields recommended for intrinsically disordered proteins in molecular dynamics simulations of three proteins differing in the content of ordered and disordered regions (two proteins consisting of a well-structured domain and of a disordered region with and without a transient helical motif and one disordered protein containing a region of increased helical propensity). The obtained molecular dynamics trajectories were used to predict measurable parameters, including radii of gyration of the proteins and chemical shifts, residual dipolar couplings, paramagnetic relaxation enhancement, and NMR relaxation data of their individual residues. The predicted quantities were compared with experimental data obtained within this study or published previously. The results showed that the NMR relaxation parameters, rarely used for benchmarking, are particularly sensitive to the choice of force-field parameters, especially those defining the water model. Interestingly, the TIP3P water model, leading to an artificial structural collapse, also resulted in unrealistic relaxation properties. The TIP4P-D water model, combined with three biomolecular force-field parameters for the protein part, significantly improved reliability of the simulations. Additional analysis revealed only one particular force field capable of retaining the transient helical motif observed in NMR experiments. The benchmarking protocol used in our study, being more sensitive to imperfections than the commonly used tests, is well suited to evaluate the performance of newly developed force fields.     

Previously uncharacterized interactions between the folded and intrinsically disordered domains impart asymmetric effects on UBQLN2 phase separation

Shuttle protein UBQLN2 functions in protein quality control (PQC) by binding to proteasomal receptors and ubiquitinated substrates via its N‐terminal ubiquitin‐like (UBL) and C‐terminal ubiquitin‐associated (UBA) domains, respectively. Between these two folded domains are low‐complexity STI1‐I and STI1‐II regions, connected by disordered linkers. The STI1 regions bind other components, such as HSP70, that are important to the PQC functions of UBQLN2. We recently determined that the STI1‐II region enables UBQLN2 to undergo liquid–liquid phase separation (LLPS) to form liquid droplets in vitro and biomolecular condensates in cells. However, how the interplay between the folded (UBL/UBA) domains and the intrinsically disordered regions mediates phase separation is largely unknown. Using engineered domain deletion constructs, we found that removing the UBA domain inhibits UBQLN2 LLPS while removing the UBL domain enhances LLPS, suggesting that UBA and UBL domains contribute asymmetrically in modulating UBQLN2 LLPS. To explain these differential effects, we interrogated the interactions that involve the UBA and UBL domains across the entire UBQLN2 molecule using nuclear magnetic resonance spectroscopy. To our surprise, aside from well‐studied canonical UBL:UBA interactions, there also exist moderate interactions between the UBL and several disordered regions, including STI1‐I and residues 555–570, the latter of which is a known contributor to UBQLN2 LLPS. Our findings are essential for the understanding of both the molecular driving forces of UBQLN2 LLPS and the effects of ligand binding to UBL, UBA, or disordered regions on the phase behavior and physiological functions of UBQLN2.     

Ubiquitin-Modulated Phase Separation of Shuttle Proteins: Does Condensate Formation Promote Protein Degradation?

Liquid-liquid phase separation (LLPS) has recently emerged as a possible mechanism that enables ubiquitin-binding shuttle proteins to facilitate the degradation of ubiquitinated substrates via distinct protein quality control (PQC) pathways. Shuttle protein LLPS is modulated by multivalent interactions among their various domains as well as heterotypic interactions with polyubiquitin chains. Here, the properties of three different shuttle proteins (hHR23B, p62, and UBQLN2) are closely examined, unifying principles for the molecular determinants of their LLPS are identified, and how LLPS is connected to their functions is discussed. Evidence supporting LLPS of other shuttle proteins is also found. In this review, it is proposed that shuttle protein LLPS leads to spatiotemporal regulation of PQC activities by mediating the recruitment of PQC machinery (including proteasomes or autophagic components) to biomolecular condensates, assembly/disassembly of condensates, selective enrichment of client proteins, and extraction of ubiquitinated proteins from condensates in cells.     

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding

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

Crowding-induced phase separation and gelling by co-condensation of PEG in NPM1-rRNA condensates

The crowdedness of the cell calls for adequate intracellular organization. Biomolecular condensates, formed by liquid-liquid phase separation of intrinsically disordered proteins and nucleic acids, are important organizers of cellular fluids. To underpin the molecular mechanisms of protein condensation, cell-free studies are often used where the role of crowding is not investigated in detail. Here, we investigate the effects of macromolecular crowding on the formation and material properties of a model heterotypic biomolecular condensate, consisting of nucleophosmin (NPM1) and ribosomal RNA (rRNA). We studied the effect of the macromolecular crowding agent poly(ethylene glycol) (PEG), which is often considered an inert crowding agent. We observed that PEG could induce both homotypic and heterotypic phase separation of NPM1 and NPM1-rRNA, respectively. Crowding increases the condensed concentration of NPM1 and decreases its equilibrium dilute phase concentration, although no significant change in the concentration of rRNA in the dilute phase was observed. Interestingly, the crowder itself is concentrated in the condensates, suggesting that co-condensation rather than excluded volume interactions underlie the enhanced phase separation by PEG. Fluorescence recovery after photobleaching measurements indicated that both NPM1 and rRNA become immobile at high PEG concentrations, indicative of a liquid-to-gel transition. Together, these results provide more insight into the role of synthetic crowding agents in phase separation and demonstrate that condensate properties determined in vitro depend strongly on the addition of crowding agents.