Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior

We introduce a lattice framework that incorporates elements of Flory-Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory-Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory-Huggins-Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil-globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.

Molecular insights into the interaction between a disordered protein and a folded RNA

Intrinsically disordered protein regions (IDRs) are well-established as contributors to intermolecular interactions and the formation of biomolecular condensates. In particular, RNA-binding proteins (RBPs) often harbor IDRs in addition to folded RNA-binding domains that contribute to RBP function. To understand the dynamic interactions of an IDR-RNA complex, we characterized the RNA-binding features of a small (68 residues), positively charged IDR-containing protein, SERF. At high concentrations, SERF and RNA undergo charge-driven associative phase separation to form a protein- and RNA-rich dense phase. A key advantage of this model system is that this threshold for demixing is sufficiently high that we could use solution-state biophysical methods to interrogate the stoichiometric complexes of SERF with RNA in the one-phase regime. Herein, we describe our comprehensive characterization of SERF alone and in complex with a small fragment of the HIV-1 TAR RNA (TAR) with complementary biophysical methods and molecular simulations. We find that this binding event is not accompanied by the acquisition of structure by either molecule; however, we see evidence for a modest global compaction of the SERF ensemble when bound to RNA. This behavior likely reflects attenuated charge repulsion within SERF via binding to the polyanionic RNA and provides a rationale for the higher-order assembly of SERF in the context of RNA. We envision that the SERF-RNA system will lower the barrier to accessing the details that support IDR-RNA interactions and likewise deepen our understanding of the role of IDR-RNA contacts in complex formation and liquid-liquid phase separation.

SIGNIFICANCE

Subcellular organization through the formation of biomolecular condensates has emerged as an important contributor to myriad cellular functions, with implications in homeostasis, stress response, and disease. To understand the general and specific principles that support condensate formation, we must interrogate the interactions and assembly of their constituent biomolecules. To this end, this study introduces a simple model system comprised of a small, disordered protein and small RNA that undergo charge-driven, associative phase separation. In addition to extensive biophysical characterization of these molecules and their complex, we also generate new insights into mode of interaction and assembly between an unstructured protein and a structured RNA.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Microtubule specialization by +TIP networks: from mechanisms to functional implications

To fulfill their actual cellular role, individual microtubules become functionally specialized through a broad range of mechanisms. The 'search and capture' model posits that microtubule dynamics and functions are specified by cellular targets that they capture (i.e., a posteriori), independently of the microtubule-organizing center (MTOC) they emerge from. However, work in budding yeast indicates that MTOCs may impart a functional identity to the microtubules they nucleate, a priori. Key effectors in this process are microtubule plus-end tracking proteins (+TIPs), which track microtubule tips to regulate their dynamics and facilitate their targeted interactions. In this review, we discuss potential mechanisms of a priori microtubule specialization, focusing on recent findings indicating that +TIP networks may undergo liquid biomolecular condensation in different cell types.

Backbone interactions and secondary structures in phase separation of disordered proteins

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

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

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

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

RNAs undergo phase transitions with lower critical solution temperatures

Co-phase separation of RNAs and RNA-binding proteins drives the biogenesis of ribonucleoprotein granules. RNAs can also undergo phase transitions in the absence of proteins. However, the physicochemical driving forces of protein-free, RNA-driven phase transitions remain unclear. Here we report that various types of RNA undergo phase separation with system-specific lower critical solution temperatures. This entropically driven phase separation is an intrinsic feature of the phosphate backbone that requires Mg2+ ions and is modulated by RNA bases. RNA-only condensates can additionally undergo enthalpically favourable percolation transitions within dense phases. This is enabled by a combination of Mg2+-dependent bridging interactions between phosphate groups and RNA-specific base stacking and base pairing. Phase separation coupled to percolation can cause dynamic arrest of RNAs within condensates and suppress the catalytic activity of an RNase P ribozyme. Our work highlights the need to incorporate RNA-driven phase transitions into models for ribonucleoprotein granule biogenesis.

Multi-scale molecular simulation of random peptide phase separation and its extended-to-compact structure transition driven by hydrophobic interactions

Intrinsically disordered proteins (IDPs) often undergo liquid-liquid phase separation (LLPS) and form membraneless organelles or protein condensates. One of the core problems is how do electrostatic repulsion and hydrophobic interactions in peptides regulate the phase separation process? To answer this question, this study uses random peptides composed of positively charged arginine (Arg, R) and hydrophobic isoleucine (Ile, I) as the model systems, and conduct large-scale simulations using all atom and coarse-grained model multi-scale simulation methods. In this article, we investigate the phase separation of different sequences using a coarse-grained model. It is found that the stronger the electrostatic repulsion in the system, the more extended the single-chain structure, and the more likely the system forms a low-density homogeneous phase. In contrast, the stronger the hydrophobic effect of the system, the more compact the single-chain structure, the easier phase separation, and the higher the critical temperature of phase separation. Overall, by taking the random polypeptides composed of two types of amino acid residues as model systems, this study discusses the relationship between the protein sequence and phase behaviour, and provides theoretical insights into the interactions within or between proteins. It is expected to provide essential physical information for the sequence design of functional IDPs, as well as data to support the diagnosis and treatment of the LLPS-associated diseases.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these are in turn determined by the multiscale structural features within condensates. However, structural characterizations of condensates are challenging, and hence rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and bespoke coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that mimic nucleolar granular components (GCs). We show that facsimiles of GCs are network fluids featuring spatial inhomogeneities across hierarchies of length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights, extracted from a combination of approaches, suggest that condensates formed by multivalent proteins share features with network fluids formed by associative systems such as patchy or hairy colloids.

ParSe 2.0: A web tool to identify drivers of protein phase separation at the proteome level

We have developed an algorithm, ParSe, which accurately identifies from the primary sequence those protein regions likely to exhibit physiological phase separation behavior. Originally, ParSe was designed to test the hypothesis that, for flexible proteins, phase separation potential is correlated to hydrodynamic size. While our results were consistent with that idea, we also found that many different descriptors could successfully differentiate between three classes of protein regions: folded, intrinsically disordered, and phase-separating intrinsically disordered. Consequently, numerous combinations of amino acid property scales can be used to make robust predictions of protein phase separation. Built from that finding, ParSe 2.0 uses an optimal set of property scales to predict domain-level organization and compute a sequence-based prediction of phase separation potential. The algorithm is fast enough to scan the whole of the human proteome in minutes on a single computer and is equally or more accurate than other published predictors in identifying proteins and regions within proteins that drive phase separation. Here, we describe a web application for ParSe 2.0 that may be accessed through a browser by visiting https://stevewhitten.github.io/Parse_v2_FASTA to quickly identify phase-separating proteins within large sequence sets, or by visiting https://stevewhitten.github.io/Parse_v2_web to evaluate individual protein sequences.

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

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

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Regulation of Biomolecular Condensates by Poly(ADP-ribose)

Biomolecular condensates are reversible compartments that form through a process called phase separation. Post-translational modifications like ADP-ribosylation can nucleate the formation of these condensates by accelerating the self-association of proteins. Poly(ADP-ribose) (PAR) chains are remarkably transient modifications with turnover rates on the order of minutes, yet they can be required for the formation of granules in response to oxidative stress, DNA damage, and other stimuli. Moreover, accumulation of PAR is linked with adverse phase transitions in neurodegenerative diseases, including Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. In this review, we provide a primer on how PAR is synthesized and regulated, the diverse structures and chemistries of ADP-ribosylation modifications, and protein-PAR interactions. We review substantial progress in recent efforts to determine the molecular mechanism of PAR-mediated phase separation, and we further delineate how inhibitors of PAR polymerases may be effective treatments for neurodegenerative pathologies. Finally, we highlight the need for rigorous biochemical interrogation of ADP-ribosylation in vivo and in vitro to clarify the exact pathway from PARylation to condensate formation.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions featuring the appropriate sequence grammars can contribute via homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. Experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be measured or computed for individual intrinsically disordered regions in complex milieus. For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary, or binodal. Often, only a few points along the binodal are accessible via measurements. In such cases, and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to mean-field free energies for polymer solutions. The nonlinearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules.

FUS fibrillation occurs through a nucleation-based process below the critical concentration required for liquid-liquid phase separation

FUS is an RNA-binding protein involved in familiar forms of ALS and FTLD that also assembles into fibrillar cytoplasmic aggregates in some neurodegenerative diseases without genetic causes. The self-adhesive prion-like domain in FUS generates reversible condensates via the liquid-liquid phase separation process (LLPS) whose maturation can lead to the formation of insoluble fibrillar aggregates in vitro, consistent with the appearance of cytoplasmic inclusions in ageing neurons. Using a single-molecule imaging approach, we reveal that FUS can assemble into nanofibrils at concentrations in the nanomolar range. These results suggest that the formation of fibrillar aggregates of FUS could occur in the cytoplasm at low concentrations of FUS, below the critical ones required to trigger the liquid-like condensate formation. Such nanofibrils may serve as seeds for the formation of pathological inclusions. Interestingly, the fibrillation of FUS at low concentrations is inhibited by its binding to mRNA or after the phosphorylation of its prion-like domain, in agreement with previous models.

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.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions (IDRs) featuring the appropriate sequence grammar can contribute homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. At this juncture, experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be quantified for individual IDRs in complex milieus both in vitro and in vivo . For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary or binodal. Often, only a few points along the binodal, especially in the dense phase, are accessible for measurement. In such cases and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to well-known mean-field free energies for polymer solutions. Unfortunately, the non-linearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules. Here, we emphasize the ease-of-use and utility of FIREBALL using examples based on data for two different IDRs.

Statement of Significance

Macromolecular phase separation drives the assembly of membraneless bodies known as biomolecular condensates. Measurements and computer simulations can now be brought to bear to quantify how the concentrations of macromolecules in coexisting dilute and dense phases vary with changes to solution conditions. These mappings can be fit to analytical expressions for free energies of solution to extract information regarding parameters that enable comparative assessments of the balance of macromolecule-solvent interactions across different systems. However, the underlying free energies are non-linear and fitting them to actual data is non-trivial. To enable comparative numerical analyses, we introduce FIREBALL, a user-friendly suite of computational tools that allows one to generate, analyze, and fit phase diagrams and coil-to-globule transitions using well-known theories.

Phase Transitions of Associative Biomacromolecules

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Determining the Physico-Chemical Composition of Biomolecular Condensates from Spatially-Resolved NMR

Liquid-Liquid phase separation has emerged as fundamental process underlying the formation of biomolecular condensates. Insights into the composition and structure of biomolecular condensates is, however, complicated by their molecular complexity and dynamics. Here, we introduce an improved spatially-resolved NMR experiment that enables quantitative analysis of the physico-chemical composition of multi-component biomolecular condensates in equilibrium and label-free. Application of spatially-resolved NMR to condensates formed by the Alzheimer's disease-associated protein Tau demonstrates decreased water content, exclusion of the molecular crowding agent dextran, presence of a specific chemical environment of the small molecule DSS, and ≈150-fold increased concentration of Tau inside the condensate. The results suggest that spatially-resolved NMR can have a major impact in understanding the composition and physical chemistry of biomolecular condensates.

An Introduction to the Stickers-and-Spacers Framework as Applied to Biomolecular Condensates

Cellular organization is determined by a combination of membrane-bound and membrane-less biomolecular assemblies that range from clusters of tens of molecules to micrometer-sized cellular bodies. Over the last decade, membrane-less assemblies have come to be referred to as biomolecular condensates, reflecting their ability to condense specific molecules with respect to the remainder of the cell. In many cases, the physics of phase transitions provides a conceptual framework and a mathematical toolkit to describe the assembly, maintenance, and dissolution of biomolecular condensates. Among the various quantitative and qualitative models applied to understand intracellular phase transitions, the stickers-and-spacers framework offers an intuitive yet rigorous means to map biomolecular sequences and structure to the driving forces needed for higher-order assembly. This chapter introduces the fundamental concepts behind the stickers-and-spacers model, considers its application to different biological systems, and discusses limitations and misconceptions around the model.

Intrinsically disordered regions that drive phase separation form a robustly distinct protein class

Protein phase separation is thought to be a primary driving force for the formation of membrane-less organelles, which control a wide range of biological functions from stress response to ribosome biogenesis. Among phase-separating (PS) proteins, many have intrinsically disordered regions (IDRs) that are needed for phase separation to occur. Accurate identification of IDRs that drive phase separation is important for testing the underlying mechanisms of phase separation, identifying biological processes that rely on phase separation, and designing sequences that modulate phase separation. To identify IDRs that drive phase separation, we first curated datasets of folded, ID, and PS ID sequences. We then used these sequence sets to examine how broadly existing amino acid property scales can be used to distinguish between the three classes of protein regions. We found that there are robust property differences between the classes and, consequently, that numerous combinations of amino acid property scales can be used to make robust predictions of protein phase separation. This result indicates that multiple, redundant mechanisms contribute to the formation of phase-separated droplets from IDRs. The top-performing scales were used to further optimize our previously developed predictor of PS IDRs, ParSe. We then modified ParSe to account for interactions between amino acids and obtained reasonable predictive power for mutations that have been designed to test the role of amino acid interactions in driving protein phase separation. Collectively, our findings provide further insight into the classification of IDRs and the elements involved in protein phase separation.

Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations

Biomolecular condensates form via coupled associative and segregative phase transitions of multivalent associative macromolecules. Phase separation coupled to percolation is one example of such transitions. Here, we characterize molecular and mesoscale structural descriptions of condensates formed by intrinsically disordered prion-like low complexity domains (PLCDs). These systems conform to sticker-and-spacers architectures. Stickers are cohesive motifs that drive associative interactions through reversible crosslinking and spacers affect the cooperativity of crosslinking and overall macromolecular solubility. Our computations reproduce experimentally measured sequence-specific phase behaviors of PLCDs. Within simulated condensates, networks of reversible inter-sticker crosslinks organize PLCDs into small-world topologies. The overall dimensions of PLCDs vary with spatial location, being most expanded at and preferring to be oriented perpendicular to the interface. Our results demonstrate that even simple condensates with one type of macromolecule feature inhomogeneous spatial organizations of molecules and interfacial features that likely prime them for biochemical activity.

Sequence Context and Complex Hofmeister Salt Interactions Dictate Phase Separation Propensity of Resilin-like Polypeptides

Resilin is an elastic material found in insects with exceptional durability, resilience, and extensibility, making it a promising biomaterial for tissue engineering. The monomeric precursor, pro-resilin, undergoes thermo-responsive self-assembly through liquid-liquid phase separation (LLPS). Understanding the molecular details of this assembly process is critical to developing complex biomaterials. The present study investigates the interplay between the solvent, sequence syntax, structure, and dynamics in promoting LLPS of resilin-like-polypeptides (RLPs) derived from domains 1 and 3 of Drosophila melanogaster pro-resilin. NMR, UV-vis, and microscopy data demonstrate that while kosmotropic salts and low pH promote LLPS, the effects of chaotropic salts with increasing pH are more complex. Subtle variations between the repeating amino acid motifs of resilin domain 1 and domain 3 lead to significantly different salt and pH dependence of LLPS, with domain 3 sequence motifs more strongly favoring phase separation under most conditions. These findings provide new insight into the molecular drivers of RLP phase separation and the complex roles of both RLP sequence and solution composition in fine-tuning assembly conditions.

SpiDec: Computing binodals and interfacial tension of biomolecular condensates from simulations of spinodal decomposition

Phase separation of intrinsically disordered proteins (IDPs) is a phenomenon associated with many essential cellular processes, but a robust method to compute the binodal from molecular dynamics simulations of IDPs modeled at the all-atom level in explicit solvent is still elusive, due to the difficulty in preparing a suitable initial dense configuration and in achieving phase equilibration. Here we present SpiDec as such a method, based on spontaneous phase separation via spinodal decomposition that produces a dense slab when the system is initiated at a homogeneous, low density. After illustrating the method on four model systems, we apply SpiDec to a tetrapeptide modeled at the all-atom level and solvated in TIP3P water. The concentrations in the dense and dilute phases agree qualitatively with experimental results and point to binodals as a sensitive property for force-field parameterization. SpiDec may prove useful for the accurate determination of the phase equilibrium of IDPs.

Uncovering the molecular mechanism for dual effect of ATP on phase separation in FUS solution

Recent studies reported that adenosine triphosphate (ATP) could inhibit and enhance the phase separation in prion-like proteins. The molecular mechanism underlying such a puzzling phenomenon remains elusive. Here, taking the fused in sarcoma (FUS) solution as an example, we comprehensively reveal the underlying mechanism by which ATP regulates phase separation by combining the semiempirical quantum mechanical method, mean-field theory, and molecular simulation. At the microscopic level, ATP acts as a bivalent or trivalent binder; at the macroscopic level, the reentrant phase separation occurs in dilute FUS solutions, resulting from the ATP concentration-dependent binding ability under different conditions. The ATP concentration for dissolving the protein condensates is about 10 mM, agreeing with experimental results. Furthermore, from a dynamic point of view, the effect of ATP on phase separation is also nonmonotonic. This work provides a clear physical description of the microscopic interaction and macroscopic phase diagram of the ATP-modulated phase separation.

Sequence grammar underlying the unfolding and phase separation of globular proteins

Aberrant phase separation of globular proteins is associated with many diseases. Here, we use a model protein system to understand how the unfolded states of globular proteins drive phase separation and the formation of unfolded protein deposits (UPODs). We find that for UPODs to form, the concentrations of unfolded molecules must be above a threshold value. Additionally, unfolded molecules must possess appropriate sequence grammars to drive phase separation. While UPODs recruit molecular chaperones, their compositional profiles are also influenced by synergistic physicochemical interactions governed by the sequence grammars of unfolded proteins and cellular proteins. Overall, the driving forces for phase separation and the compositional profiles of UPODs are governed by the sequence grammars of unfolded proteins. Our studies highlight the need for uncovering the sequence grammars of unfolded proteins that drive UPOD formation and cause gain-of-function interactions whereby proteins are aberrantly recruited into UPODs.

Shelterin Components Modulate Nucleic Acids Condensation and Phase Separation in the Context of Telomeric DNA

Telomeres are nucleoprotein complexes that protect the ends of chromosomes and are essential for chromosome stability in Eukaryotes. In cells, individual telomeres form distinct globules of finite size that appear to be smaller than expected for bare DNA. Moreover, telomeres can cluster together, form telomere-induced-foci or co-localize with promyelocytic leukemia (PML) nuclear bodies. The physical basis for collapse of individual telomeres and coalescence of multiple ones remains unclear, as does the relationship between these two phenomena. By combining single-molecule force spectroscopy measurements, optical microscopy, turbidity assays, and simulations, we show that the telomere scaffolding protein TRF2 can condense individual DNA chains and drives coalescence of multiple DNA molecules, leading to phase separation and the formation of liquid-like droplets. Addition of the TRF2 binding protein hRap1 modulates phase boundaries and tunes the specificity of solution demixing while simultaneously altering the degree of DNA compaction. Our results suggest that the condensation of single telomeres and formation of biomolecular condensates containing multiple telomeres are two different outcomes driven by the same set of molecular interactions. Moreover, binding partners, such as other telomere components, can alter those interactions to promote single-chain DNA compaction over multiple-chain phase separation.

Biomolecular condensates: new opportunities for drug discovery and RNA therapeutics

Biomolecular condensates organize cellular functions in the absence of membranes. These membraneless organelles can form through liquid-liquid phase separation coalescing RNA and proteins into well-defined, yet dynamic, structures distinct from the surrounding cellular milieu. Numerous physiological and disease-causing processes link to biomolecular condensates, which could impact drug discovery in several ways. First, disruption of pathological condensates seeded by mutated proteins or RNAs may provide new opportunities to treat disease. Second, condensates may be leveraged to tackle difficult-to-drug targets lacking binding pockets whose function depends on phase separation. Third, condensate-resident small molecules and RNA therapeutics may display unexpected pharmacology. We discuss the potential impact of phase separation on drug discovery and RNA therapeutics, leveraging concrete examples, towards novel clinical opportunities.

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.

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.

Rules of Physical Mathematics Govern Intrinsically Disordered Proteins

In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.

RNA chain length and stoichiometry govern surface tension and stability of protein-RNA condensates

Proteomic studies have shown that cellular condensates are frequently enriched in diverse RNA molecules, which is suggestive of mechanistic links between phase separation and transcriptional activities. Here, we report a systematic experimental and computational study of thermodynamic landscapes and interfacial properties of protein-RNA condensates. We have studied the affinity of protein-RNA condensation as a function of variable RNA sequence length and RNA-protein stoichiometry under different ionic environments and external crowding. We have chosen the PolyU sequences for RNA and arginine/glycine-rich intrinsically disordered peptide (RGG) for proteins as a model system of RNA-protein condensates, which we then investigate through in vitro microscopy measurements and coarse-grained molecular dynamics simulations. We find that crowding and RNA chain length can have a major stabilizing effect on the condensation. We also find that the RNA-protein charge ratio is a crucial variable controlling stability, interfacial properties, and the reentrant phase behavior of RGG-RNA mixtures.

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LLPS with long RNAs is favored because of the lower entropic penalty of dissociation

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RNA chain length modulates interfacial and material properties of condensates

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Crowding can stabilize condensates with shorter RNAs

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Salt reduces the reentrant LLPS window but does not change the optimal stoichiometry

Dilute phase oligomerization can oppose phase separation and modulate material properties of a ribonucleoprotein condensate

SignificanceA large subclass of biomolecular condensates are linked to RNA regulation and are known as ribonucleoprotein (RNP) bodies. While extensive work has identified driving forces for biomolecular condensate formation, relatively little is known about forces that oppose assembly. Here, using a fungal RNP protein, Whi3, we show that a portion of its intrinsically disordered, glutamine-rich region modulates phase separation by forming transient alpha helical structures that promote the assembly of dilute phase oligomers. These oligomers detour Whi3 proteins from condensates, thereby impacting the driving forces for phase separation, the protein-to-RNA ratio in condensates, and the material properties of condensates. Our findings show how nanoscale conformational and oligomerization equilibria can influence mesoscale phase equilibria.

Modeling the Structure and Interactions of Intrinsically Disordered Peptides with Multiple Replica, Metadynamics-Based Sampling Methods and Force-Field Combinations

Intrinsically disordered proteins play a key role in many biological processes, including the formation of biomolecular condensates within cells. A detailed characterization of their configurational ensemble and structure-function paradigm is crucial for understanding their biological activity and for exploiting them as building blocks in material sciences. In this work, we incorporate bias-exchange metadynamics and parallel-tempering well-tempered metadynamics with CHARMM36m and CHARMM22* to explore the structural and thermodynamic characteristics of a short archetypal disordered sequence derived from a DEAD-box protein. The conformational landscapes emerging from our simulations are largely congruent across methods and force fields. Nevertheless, differences in fine details emerge from varying combinations of force-fields and sampling methods. For this protein, our analysis identifies features that help to explain the low propensity of this sequence to undergo self-association in vitro, which are common to all force-field/sampling method combinations. Overall, our work demonstrates the importance of using multiple force-field and sampling method combinations for accurate structural and thermodynamic information in the study of disordered proteins.

Mechanisms of DNA Mobilization and Sequestration

The entire genome becomes mobilized following DNA damage. Understanding the mechanisms that act at the genome level requires that we embrace experimental and computational strategies to capture the behavior of the long-chain DNA polymer, which is the building block for the chromosome. Long-chain polymers exhibit constrained, sub-diffusive motion in the nucleus. Cross-linking proteins, including cohesin and condensin, have a disproportionate effect on genome organization in their ability to stabilize transient interactions. Cross-linking proteins can segregate the genome into sub-domains through polymer–polymer phase separation (PPPS) and can drive the formation of gene clusters through small changes in their binding kinetics. Principles from polymer physics provide a means to unravel the mysteries hidden in the chains of life.

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

A method to estimate the size of single-chain nanoparticles under severe crowding conditions

Single-chain nanoparticles (SCNPs) result from the folding of isolated polymer chains via intramolecular interactions. Currently, there is no theory able to rationalize the astonishing conformational behaviour of SCNPs under severe crowding conditions (e.g., highly concentrated solutions, all-polymer nanocomposites) and, specifically, the significant size reduction observed in highly crowded solutions of covalent-bonded SCNPs and all-polymer nanocomposites containing SCNPs. Herein, we propose a valuable method to estimate the size of SCNPs under crowding. The method – which is based on combining MD simulations results with scaling concepts – is also useful for ring polymers and nanostructured Janus-shaped SCNPs.

A method to estimate the size of single-chain nanoparticles (SCNPs), ring polymers and nanostructured Janus-shaped SCNPs under crowding.

What are the distinguishing features and size requirements of biomolecular condensates and their implications for RNA-containing condensates?

Exciting recent work has highlighted that numerous cellular compartments lack encapsulating lipid bilayers (often called "membraneless organelles"), and that their structure and function are central to the regulation of key biological processes, including transcription, RNA splicing, translation, and more. These structures have been described as "biomolecular condensates" to underscore that biomolecules can be significantly concentrated in them. Many condensates, including RNA granules and processing bodies, are enriched in proteins and nucleic acids. Biomolecular condensates exhibit a range of material states from liquid- to gel-like, with the physical process of liquid-liquid phase separation implicated in driving or contributing to their formation. To date, in vitro studies of phase separation have provided mechanistic insights into the formation and function of condensates. However, the link between the often micron-sized in vitro condensates with nanometer-sized cellular correlates has not been well established. Consequently, questions have arisen as to whether cellular structures below the optical resolution limit can be considered biomolecular condensates. Similarly, the distinction between condensates and discrete dynamic hub complexes is debated. Here we discuss the key features that define biomolecular condensates to help understand behaviors of structures containing and generating RNA.

Clustering of Aromatic Residues in Prion-like Domains Can Tune the Formation, State, and Organization of Biomolecular Condensates

In immature oocytes, Balbiani bodies are conserved membraneless condensates implicated in oocyte polarization, the organization of mitochondria, and long-term organelle and RNA storage. In Xenopus laevis, Balbiani body assembly is mediated by the protein Velo1. Velo1 contains an N-terminal prion-like domain (PLD) that is essential for Balbiani body formation. PLDs have emerged as a class of intrinsically disordered regions that can undergo various different types of intracellular phase transitions and are often associated with dynamic, liquid-like condensates. Intriguingly, the Velo1 PLD forms solid-like assemblies. Here we sought to understand why Velo1 phase behavior appears to be biophysically distinct from that of other PLD-containing proteins. Through bioinformatic analysis and coarse-grained simulations, we predict that the clustering of aromatic residues and the amino acid composition of residues between aromatics can influence condensate material properties, organization, and the driving forces for assembly. To test our predictions, we redesigned the Velo1 PLD to test the impact of targeted sequence changes in vivo. We found that the Velo1 design with evenly spaced aromatic residues shows rapid internal dynamics, as probed by fluorescent recovery after photobleaching, even when recruited into Balbiani bodies. Our results suggest that Velo1 might have been selected in evolution for distinctly clustered aromatic residues to maintain the structure of Balbiani bodies in long-lived oocytes. In general, our work identifies several tunable parameters that can be used to augment the condensate material state, offering a road map for the design of synthetic condensates.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

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.

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.