The physics of liquid-to-solid transitions in multi-domain protein condensates

Surface-catalyzed liquid-liquid phase separation and amyloid-like assembly in microscale compartments

Liquid-liquid phase separation is a key phenomenon in the formation of membrane-less structures within the cell, appearing as liquid biomolecular condensates. Protein condensates are the most studied for their biological relevance, and their tendency to evolve, resulting in the formation of aggregates with a high level of order called amyloid. In this study, it is demonstrated that Human Insulin forms micrometric, round amyloid-like structures at room temperature within sub-microliter scale aqueous compartments. These distinctive particles feature a solid core enveloped by a fluid-like corona and form at the interface between the aqueous compartment and the glass coverslip upon which they are cast. Quantitative fluorescence microscopy is used to study in real-time the formation of amyloid-like superstructures. Their formation results driven by liquid-liquid phase separation process that arises from spatially heterogeneous distribution of nuclei at the glass-water interface. The proposed experimental setup allows modifying the surface-to-volume ratio of the aqueous compartments, which affects the aggregation rate and particle size, while also inducing fine alterations in the molecular structures of the final assemblies. These findings enhance the understanding of the factors governing amyloid structure formation, shedding light on the catalytic role of surfaces in this process.

Separation of sticker-spacer energetics governs the coalescence of metastable biomolecular condensates

Biological condensates often emerge as a multi-droplet state and never coalesce into one large droplet within the experimental timespan. Previous work revealed that the sticker-spacer architecture of biopolymers may dynamically stabilize the multi-droplet state. Here, we simulate the condensate coalescence using metadynamics approach and reveal two distinct physical mechanisms underlying the fusion of droplets. Condensates made of sticker-spacer polymers readily undergo a kinetic arrest when stickers exhibit slow exchange while fast exchanging stickers at similar levels of saturation allow merger to equilibrium states. On the other hand, condensates composed of homopolymers fuse readily until they reach a threshold density. Increase in entropy upon inter-condensate mixing of chains drives the fusion of sticker-spacer chains. We map the range of mechanisms of kinetic arrest from slow sticker exchange dynamics to density mediated in terms of energetic separation of stickers and spacers. Our predictions appear to be in excellent agreement with recent experiments probing dynamic nature of protein-RNA condensates.

Direct computations of viscoelastic moduli of biomolecular condensates

In vitro facsimiles of biomolecular condensates are formed by different types of intrinsically disordered proteins including prion-like low complexity domains (PLCDs). PLCD condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model and information regarding intra- and inter-chain contacts that is extracted from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations. The key ingredient of the generalized Rouse model is the Zimm matrix that we compute from equilibrium MMC simulations. We compute two flavors of Zimm matrices, one referred to as the single-chain model that accounts only for intra-chain contacts, and the other referred to as a collective model, that accounts for inter-chain interactions. The single-chain model systematically overestimates the storage and loss moduli, whereas the collective model reproduces the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two models proves to be most accurate. In line with the theory of Rouse, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic versus dominantly viscous behaviors is influenced by the totality of the relaxation modes. Hence, our analysis suggests that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain distributions of relaxation times that underlie the dynamics within condensates.

Ensemble structure of the N-terminal domain (1-267) of FUS in a biomolecular condensate

Solutions of some proteins phase separate into a condensed state of high protein concentration and a dispersed state of low concentration. Such behavior is observed in living cells for a number of RNA-binding proteins that feature intrinsically disordered domains. It is relevant for cell function via the formation of membraneless organelles and transcriptional condensates. On a basic level, the process can be studied in vitro on protein domains that are necessary and sufficient for liquid-liquid phase separation (LLPS). We have performed distance distribution measurements by electron paramagnetic resonance for 13 sections in an N-terminal domain (NTD) construct of the protein fused in sarcoma (FUS), consisting of the QGSY-rich domain and the RGG1 domain, in the denatured, dispersed, and condensed state. Using 10 distance distribution restraints for ensemble modeling and three such restraints for model validation, we have found that FUS NTD behaves as a random-coil polymer under good-solvent conditions in both the dispersed and condensed state. Conformation distribution in the biomolecular condensate is virtually indistinguishable from the one in an unrestrained ensemble, with the latter one being based on only residue-specific Ramachandran angle distributions. Over its whole length, FUS NTD is slightly more compact in the condensed than in the dispersed state, which is in line with the theory for random coils in good solvent proposed by de Gennes, Daoud, and Jannink. The estimated concentration in the condensate exceeds the overlap concentration resulting from this theory. The QGSY-rich domain is slightly more extended, slightly more hydrated, and has slightly higher propensity for LLPS than the RGG1 domain. Our results support previous suggestions that LLPS of FUS is driven by multiple transient nonspecific hydrogen bonding and π-sp2 interactions.

Conformational fluctuations and phases in fused in sarcoma (FUS) low-complexity domain

The well-known phenomenon of phase separation in synthetic polymers and proteins has become a major topic in biophysics because it has been invoked as a mechanism of compartment formation in cells, without the need for membranes. Most of the coacervates (or condensates) are composed of Intrinsically Disordered Proteins (IDPs) or regions that are structureless, often in interaction with RNA and DNA. One of the more intriguing IDPs is the 526-residue RNA-binding protein, Fused in Sarcoma (FUS), whose monomer conformations and condensates exhibit unusual behavior that are sensitive to solution conditions. By focussing principally on the N-terminus low-complexity domain (FUS-LC comprising residues 1-214) and other truncations, we rationalize the findings of solid-state NMR experiments, which show that FUS-LC adopts a non-polymorphic fibril structure (core-1) involving residues 39-95, flanked by fuzzy coats on both the N- and C-terminal ends. An alternate structure (core-2), whose free energy is comparable to core-1, emerges only in the truncated construct (residues 110-214). Both core-1 and core-2 fibrils are stabilized by a Tyrosine ladder as well as hydrophilic interactions. The morphologies (gels, fibrils, and glass-like) adopted by FUS seem to vary greatly, depending on the experimental conditions. The effect of phosphorylation is site-specific. Simulations show that phosphorylation of residues within the fibril has a greater destabilization effect than residues that are outside the fibril region, which accords well with experiments. Many of the peculiarities associated with FUS may also be shared by other IDPs, such as TDP43 and hnRNPA2. We outline a number of problems for which there is no clear molecular explanation.

Phase behaviour of semiflexible lattice polymers in poor-solvent solution: Mean-field theory and Monte Carlo simulations

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d = 3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.

Fibrils Emerging from Droplets: Molecular Guiding Principles behind Phase Transitions of a Short Peptide-Based Condensate Studied by Solid-State NMR

Biochemical reactions occurring in highly crowded cellular environments require different means of control to ensure productivity and specificity. Compartmentalization of reagents by liquid-liquid phase separation is one of these means. However, extremely high local protein concentrations of up to 400 mg/ml can result in pathological aggregation into fibrillar amyloid structures, a phenomenon that has been linked to various neurodegenerative diseases. Despite its relevance, the process of liquid-to-solid transition inside condensates is still not well understood at the molecular level. We thus herein use small peptide derivatives that can undergo both liquid-liquid and subsequent liquid-to-solid phase transition as model systems to study both processes. Using solid-state nuclear magnetic resonance (NMR) and transmission electron microscopy (TEM), we compare the structure of condensed states of leucine, tryptophan and phenylalanine containing derivatives, distinguishing between liquid-like condensates, amorphous aggregates and fibrils, respectively. A structural model for the fibrils formed by the phenylalanine derivative was obtained by an NMR-based structure calculation. The fibrils are stabilised by hydrogen bonds and side-chain π-π interactions, which are likely much less pronounced or absent in the liquid and amorphous state. Such noncovalent interactions are equally important for the liquid-to-solid transition of proteins, particularly those related to neurodegenerative diseases.

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.

Modeling the effects of phosphorylation on phase separation of the FUS low-complexity domain

Aggregation of the RNA-binding protein fused in sarcoma (FUS) is a hallmark of neurodegenerative diseases. Phosphorylation of Ser/Thr in the FUS low-complexity domain (FUS-LC) may regulate phase separation of FUS and prevent pathological aggregation in cells. However, many details of this process remain elusive to date. In this work, we systematically investigated the phosphorylation of FUS-LC and the underlying molecular mechanism by molecular dynamics (MD) simulations and free energy calculations. The results clearly show that phosphorylation can destroy the fibril core structure of FUS-LC by breaking interchain interactions, particularly contacts involving residues like Tyr, Ser, and Gln. Among the six phosphorylation sites, Ser61 and Ser84 may have more important effects on the stability of the fibril core. Our study reveals structural and dynamic details of FUS-LC phase separation modulated by phosphorylation.

Dissecting the Effect of ALS Mutation G335D on the Early Aggregation of the TDP-43 Amyloidogenic Core Peptide: Helix-to-β-Sheet Transition and Conformational Shift

The aggregation of TAR DNA-binding protein of 43 kDa (TDP-43) into fibrillary deposits is associated with amyotrophic lateral sclerosis (ALS). The 311-360 fragment of TDP-43 (TDP-43311-360), the amyloidogenic core region, can spontaneously aggregate into fibrils, and the ALS-associated mutation G335D has an enhanced effect on TDP-43311-360 fibrillization. However, the molecular mechanism underlying G335D-enhanced aggregation at atomic level remains largely unknown. By utilizing all-atom molecular dynamics (MD) and replica exchange with solute tempering 2 (REST2) simulations, we investigated influences of G335D on the dimerization (the first step of aggregation) and conformational ensemble of the TDP-43311-360 peptide. Our simulations show that G335D mutation increases inter-peptide interactions, especially inter-peptide hydrogen-bonding interactions in which the mutant site has a relatively large contribution, and enhances the dimerization of TDP-43311-360 peptides. The α-helix regions in the NMR-resolved conformation of the TDP-43311-360 monomer (321-330 and 335-343) play an essential role in the formation of the dimer. G335D mutation induces helix unfolding and promotes α-to-β conversion. G335D mutation alters the conformational distribution of TDP-43311-360 dimers and causes population shift from helix-rich to β-sheet-rich conformations, which facilitates the fibrillization of the TDP-43311-360 peptide. Our MD and REST2 simulation results suggest that the 321-330 region is of paramount importance to α-to-β transition and could be the initiation site for TDP-43311-360 fibrillization. Our work reveals the mechanism underlying the enhanced aggregation propensity of the G335D TDP-43311-360 peptide, which provides atomistic insights into the G335D mutation-caused pathogenicity of TDP-43 protein.

Phosphorylation sites are evolutionary checkpoints against liquid-solid transition in protein condensates

Assemblies of multivalent RNA-binding protein fused in sarcoma (FUS) can exist in the functional liquid-like state as well as less dynamic and potentially toxic amyloid- and hydrogel-like states. How could then cells form liquid-like condensates while avoiding their transformation to amyloids? Here, we show how posttranslational phosphorylation can provide a "handle" that prevents liquid-solid transition of intracellular condensates containing FUS. Using residue-specific coarse-grained simulations, for 85 different mammalian FUS sequences, we show how the number of phosphorylation sites and their spatial arrangement affect intracluster dynamics preventing conversion to amyloids. All atom simulations further confirm that phosphorylation can effectively reduce the β-sheet propensity in amyloid-prone fragments of FUS. A detailed evolutionary analysis shows that mammalian FUS PLDs are enriched in amyloid-prone stretches compared to control neutrally evolved sequences, suggesting that mammalian FUS proteins evolved to self-assemble. However, in stark contrast to proteins that do not phase-separate for their function, mammalian sequences have phosphosites in close proximity to these amyloid-prone regions. These results suggest that evolution uses amyloid-prone sequences in prion-like domains to enhance phase separation of condensate proteins while enriching phosphorylation sites in close proximity to safeguard against liquid-solid transitions.

Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Biophysics of biomolecular condensates

The formation of biomolecular condensates has emerged as a new biophysical principle for subcellular compartmentalization within cells to facilitate the spatiotemporal regulation of a multitude of complex biomolecular reactions. In this Research Highlight, we summarize the findings that were published in Biophysical Journal during the past two years (2021 and 2022). These papers provided biophysical insights into the formation of biomolecular condensates via phase separation of proteins with or without nucleic acids.

Macromolecular Crowding Is Surprisingly Unable to Deform the Structure of a Model Biomolecular Condensate

The crowded interior of a living cell makes performing experiments on simpler in vitro systems attractive. Although these reveal interesting phenomena, their biological relevance can be questionable. A topical example is the phase separation of intrinsically disordered proteins into biomolecular condensates, which is proposed to underlie the membrane-less compartmentalization of many cellular functions. How a cell reliably controls biochemical reactions in compartments open to the compositionally-varying cytoplasm is an important question for understanding cellular homeostasis. Computer simulations are often used to study the phase behavior of model biomolecular condensates, but the number of relevant parameters increases as the number of protein components increases. It is unfeasible to exhaustively simulate such models for all parameter combinations, although interesting phenomena are almost certainly hidden in their high-dimensional parameter space. Here, we have studied the phase behavior of a model biomolecular condensate in the presence of a polymeric crowding agent. We used a novel compute framework to execute dozens of simultaneous simulations spanning the protein/crowder concentration space. We then combined the results into a graphical representation for human interpretation, which provided an efficient way to search the model's high-dimensional parameter space. We found that steric repulsion from the crowder drives a near-critical system across the phase boundary, but the molecular arrangement within the resulting biomolecular condensate is rather insensitive to the crowder concentration and molecular weight. We propose that a cell may use the local cytoplasmic concentration to assist the formation of biomolecular condensates, while relying on the dense phase to reliably provide a stable, structured, fluid milieu for cellular biochemistry despite being open to its changing environment.

Formation of dissipative structures in microscopic models of mixtures with species interconversion

The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation is one of the simplest examples of dissipative structures in condensed matter. In this work, we investigate the formation of such mesoscale steady-state structures through Monte Carlo and molecular dynamics simulations of three physically distinct microscopic models of binary mixtures that exhibit both equilibrium (natural) interconversion and a nonequilibrium source of forced interconversion. We show that this source can be introduced through an internal imbalance of intermolecular forces or an external flux of energy that promotes molecular interconversion, possible manifestations of which could include the internal nonequilibrium environment of living cells or a flux of photons. The main trends and observations from the simulations are well captured by a nonequilibrium thermodynamic theory of phase transitions affected by interconversion. We show how a nonequilibrium bicontinuous microemulsion or a spatially modulated state may be generated depending on the interplay between diffusion, natural interconversion, and forced interconversion.

Different states and the associated fates of biomolecular condensates

Biomolecular condensates are functional assemblies, which can enrich intrinsically disordered proteins (IDPs) and/or RNAs at concentrations that are orders of magnitude higher than the bulk. In their native functional state, these structures can exist in multiple physical states including liquid-droplet phase, hydrogels, and solid assemblies. On the other hand, an aberrant transition between these physical states can result in loss-of-function or a gain-of-toxic-function. A prime example of such an aberrant transition is droplet aging—a phenomenon where some condensates may progressively transition into less dynamic material states at biologically relevant timescales. In this essay, we review structural and viscoelastic roots of aberrant liquid–solid transitions. Also, we highlight the different checkpoints and experimentally tunable handles, both active (ATP-dependent enzymes, post-translational modifications) and passive (colocalization of RNA molecules), that could alter the material state of assemblies.

Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Phase-separating RNA-binding proteins form heterogeneous distributions of clusters in subsaturated solutions

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion-like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs.