Biophysics of Phase Separation of Disordered Proteins Is Governed by Balance between Short- And Long-Range Interactions

Peptide diffusion in biomolecular condensates

Diffusion determines the turnover of biomolecules in liquid-liquid phase-separated condensates. We considered the mean square displacement and thus the diffusion constant for simple model systems of peptides GGGGG, GGQGG, and GGVGG in aqueous solutions after phase separation by simulating atomic-level models. These solutions readily separate into aqueous and peptide-rich droplet phases. We noted the effect of the peptides being in a solvated, surface, or droplet state on the peptide's diffusion coefficients. Both sequence and peptide conformational distribution were found to influence diffusion and condensate turnover in these systems, with sequence dominating the magnitude of the differences. We found that the most compact structures for each sequence diffused the fastest in the peptide-rich condensate phase. This model result may have implications for turnover dynamics in signaling systems.

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.

Direct prediction of intermolecular interactions driven by disordered regions

Intrinsically disordered regions (IDRs) are critical for a wide variety of cellular functions, many of which involve interactions with partner proteins. Molecular recognition is typically considered through the lens of sequence-specific binding events. However, a growing body of work has shown that IDRs often interact with partners in a manner that does not depend on the precise order of the amino acid order, instead driven by complementary chemical interactions leading to disordered bound-state complexes. Despite this emerging paradigm, we lack tools to describe, quantify, predict, and interpret these types of structurally heterogeneous interactions from the underlying amino acid sequences. Here, we repurpose the chemical physics developed originally for molecular simulations to develop an approach for predicting intermolecular interactions between IDRs and partner proteins. Our approach enables the direct prediction of phase diagrams, the identification of chemically-specific interaction hotspots on IDRs, and a route to develop and test mechanistic hypotheses regarding IDR function in the context of molecular recognition. We use our approach to examine a range of systems and questions to highlight its versatility and applicability.

The emerging role of receptor tyrosine kinase phase separation in cancer

Receptor tyrosine kinase (RTK)-mediated signal transduction is fundamental to cell function and drives important cellular outcomes which, when dysregulated, can lead to malignant tumour growth and metastasis. The initiation of signals from plasma membrane-bound RTKs is subjected to multiple regulatory mechanisms that control downstream effector protein recruitment and function. The high propensity of RTKs to condense via liquid-liquid phase separation (LLPS) into membraneless organelles with downstream effector proteins provides a further fundamental mechanism for signal regulation. Herein we highlight how this phenomenon contributes to cancer signalling and consider the potential impact of LLPS on outcomes for cancer patients.

Vibrational Dipole-Dipole Coupling and Long-Range Forces between Macromolecules

Long-range interactions between biomacromolecules are considered important for directing intracellular processes. Recent studies have posited that interactions between oscillating dipoles are well-suited to mediating long-range forces because they are weakly screened by a dielectric environment. Here, we extend these studies and present a quantum electrodynamic mechanism for resonant interactions between vibrational transition dipole moments of molecules. We explicitly consider the molecular charge density oscillations as IR transition dipoles. This gives a physical, molecular assignment to the idea of oscillating dipoles and allows us to develop explicit expressions for the interactions that can be quantified using parameters known from experiment. Moreover, in the same framework, we can describe van der Waals forces. We use numerical calculations to estimate the strength of resonant vibrational dipole-dipole interactions over long distances and compare these estimates to the van der Waals interaction. We find that the resonant vibrational dipole-dipole interactions dominate over the long range.

Active learning of the thermodynamics-dynamics trade-off in protein condensates

Phase-separated biomolecular condensates exhibit a wide range of dynamic properties, which depend on the sequences of the constituent proteins and RNAs. However, it is unclear to what extent condensate dynamics can be tuned without also changing the thermodynamic properties that govern phase separation. Using coarse-grained simulations of intrinsically disordered proteins, we show that the dynamics and thermodynamics of homopolymer condensates are strongly correlated, with increased condensate stability being coincident with low mobilities and high viscosities. We then apply an "active learning" strategy to identify heteropolymer sequences that break this correlation. This data-driven approach and accompanying analysis reveal how heterogeneous amino acid compositions and nonuniform sequence patterning map to a range of independently tunable dynamic and thermodynamic properties of biomolecular condensates. Our results highlight key molecular determinants governing the physical properties of biomolecular condensates and establish design rules for the development of stimuli-responsive biomaterials.

Ultrafast Spectroscopy Reveals Slow Water Dynamics in Biocondensates

Cells achieve high spatiotemporal control over biochemical processes through compartmentalization to membrane-bound as well as membraneless organelles that assemble by liquid-liquid phase separation. Characterizing the balance of forces within these environments is essential to understanding their stability and function, and water is an integral part of the condensate, playing an important role in mediating electrostatic and hydrogen-bonding interactions. Here, we investigate the ultrafast, picosecond hydrogen-bond dynamics of a model biocondensate consisting of a peptide poly-l-arginine (Poly-R) and the nucleic acid adenosine monophosphate (AMP) using coherent two-dimensional infrared (2D IR) spectroscopy. We investigated three vibrational modes: the arginine side-chain C═N stretches, an AMP ring mode, and the amide backbone carbonyl stretching modes. Dynamics slow considerably between the dilute phase and the condensate phase for each vibrational probe. For example, the arginine side-chain C═N modes slow from 0.38 to 2.26 ps due to strong electrostatic interactions. All-atom molecular dynamics simulations provide an atomistic interpretation of the H-bond network disruption resulting from electrostatic contributions as well as collapse within the condensate. Simulations predict that a fraction of water molecules are highly constrained within the condensate, explaining the observed slowdown in the H-bond dynamics.

Single-molecule-binding studies of antivirals targeting the hepatitis C virus core protein

IMPORTANCE

The hepatitis C virus is associated with nearly 300,000 deaths annually. At the core of the virus is an RNA-protein complex called the nucleocapsid, which consists of the viral genome and many copies of the core protein. Because the assembly of the nucleocapsid is a critical step in viral replication, a considerable amount of effort has been devoted to identifying antiviral therapeutics that can bind to the core protein and disrupt assembly. Although several candidates have been identified, little is known about how they interact with the core protein or how those interactions alter the structure and thus the function of this viral protein. Our work biochemically characterizes several of these binding interactions, highlighting both similarities and differences as well as strengths and weaknesses. These insights bolster the notion that this viral protein is a viable target for novel therapeutics and will help to guide future developments of these candidate antivirals.

Cross-Talk of Cation-π Interactions with Electrostatic and Aromatic Interactions: A Salt-Dependent Trade-off in Biomolecular Condensates

Biomolecular condensates are essential for cellular functionality, yet the complex interplay among the diverse molecular interactions that mediate their formation remains poorly understood. Here, using coarse-grained molecular dynamics simulations, we address the contribution of cation-π interactions to the stability of condensates formed via liquid-liquid phase separation. We found greater stabilization of up to 80% via cation-π interactions in condensates formed from peptides with higher aromatic residue content or less charge clustering. The contribution of cation-π interactions to droplet stability increases with increasing ionic strength, suggesting a trade-off between cation-π and electrostatic interactions. Cation-π interactions, therefore, can compensate for reduced electrostatic interactions, such as occurs at higher salt concentrations and in sequences with less charged residue content or clustering. Designing condensates with desired biophysical characteristics therefore requires quantification not only of the individual interactions but also cross-talks involving charge-charge, π-π, and cation-π interactions.

Not Only Expansion: Proline Content and Density Also Induce Disordered Protein Conformation Compaction

Intrinsically disordered proteins (IDPs) adopt a wide array of different conformations that can be constrained by the presence of proline residues, which are frequently found in IDPs. To assess the effects of proline, we designed a series of peptides that differ with respect to the number of prolines in the sequence and their organization. Using high-resolution atomistic molecular dynamics simulations, we found that accounting for whether the proline residues are clustered or isolated contributed significantly to explaining deviations in the experimentally-determined gyration radii of IDPs from the values expected based on the Flory scaling-law. By contrast, total proline content makes smaller contribution to explaining the effect of prolines on IDP conformation. Proline residues exhibit opposing effects depending on their organizational pattern in the IDP sequence. Clustered prolines (i.e., prolines with ≤2 intervening non-proline residues) result in expanded peptide conformations whereas isolated prolines (i.e., prolines with >2 intervening non-proline residues) impose compacted conformations. Clustered prolines were estimated to induce an expansion of ∼20% in IDP dimension (via formation of PPII structural elements) whereas isolated prolines were estimated to induce a compaction of ∼10% in IDP dimension (via the formation of backbone turns). This dual role of prolines provides a mechanism for conformational switching that does not rely on the kinetically much slower isomerization of cis proline to the trans form. Bioinformatic analysis demonstrates high populations of both isolated and clustered prolines and implementing them in coarse-grained molecular dynamics models illustrates that they improve the characterization of the conformational ensembles of IDPs.

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.

Conformational Analysis of Charged Homo-Polypeptides

Many proteins have intrinsically disordered regions (IDRs), which are often characterized by a high fraction of charged residues with polyampholytic (i.e., mixed charge) or polyelectrolytic (i.e., uniform charge) characteristics. Polyelectrolytic IDRs include consecutive positively charged Lys or Arg residues (K/R repeats) or consecutive negatively charged Asp or Glu residues (D/E repeats). In previous research, D/E repeats were found to be about five times longer than K/R repeats and to be much more common in eukaryotes. Within these repeats, a preference is often observed for E over D and for K over R. To understand the greater prevalence of D/E over K/R repeats and the higher abundance of E and K, we simulated the conformational ensemble of charged homo-polypeptides (polyK, polyR, polyD, and polyE) using molecular dynamics simulations. The conformational preferences and dynamics of these polyelectrolytic polypeptides change with changes in salt concentration. In particular, polyD and polyE are more sensitive to salt than polyK and polyR, as polyD and polyE tend to adsorb more divalent cations, which leads to their having more compact conformations. We conclude with a discussion of biophysical explanations for the relative abundance of charged amino acids and particularly for the greater abundance of D/E repeats over K/R repeats.

Biomolecular condensates formed by designer minimalistic peptides

Inspired by the role of intracellular liquid-liquid phase separation (LLPS) in formation of membraneless organelles, there is great interest in developing dynamic compartments formed by LLPS of intrinsically disordered proteins (IDPs) or short peptides. However, the molecular mechanisms underlying the formation of biomolecular condensates have not been fully elucidated, rendering on-demand design of synthetic condensates with tailored physico-chemical functionalities a significant challenge. To address this need, here we design a library of LLPS-promoting peptide building blocks composed of various assembly domains. We show that the LLPS propensity, dynamics, and encapsulation efficiency of compartments can be tuned by changes to the peptide composition. Specifically, with the aid of Raman and NMR spectroscopy, we show that interactions between arginine and aromatic amino acids underlie droplet formation, and that both intra- and intermolecular interactions dictate droplet dynamics. The resulting sequence-structure-function correlation could support the future development of compartments for a variety of applications.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

The formation and viscoelastic properties of condensates of intrinsically disordered proteins (IDPs) is dictated by amino acid sequence and solution conditions. Because of the involvement of biomolecular condensates in cell physiology and disease, advancing our understanding of the relationship between protein sequence and phase separation (PS) may have important implications in the formulation of new therapeutic hypotheses. Here, we present CALVADOS 2, a coarse-grained model of IDPs that accurately predicts conformational properties and propensities to undergo PS for diverse sequences and solution conditions. In particular, we systematically study the effect of varying the range of the nonionic interactions and use our findings to improve the temperature scale of the model. We further optimize the residue-specific model parameters against experimental data on the conformational properties of 55 proteins, while also leveraging 70 hydrophobicity scales from the literature to avoid overfitting the training data. Extensive testing shows that the model accurately predicts chain compaction and PS propensity for sequences of diverse length and charge patterning, as well as at different temperatures and salt concentrations.

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.

Phase-Separation Kinetics in the Two-Dimensional Long-Range Ising Model

Using Monte Carlo computer simulations, we investigate the kinetics of phase separation in the two-dimensional conserved Ising model with power-law decaying long-range interactions, the prototypical model for many long-range interacting systems. A long-standing analytical prediction for the characteristic length is shown to be applicable. In the simulation, we relied on our novel algorithm which provides a massive speedup for long-range interacting systems.

Protein conformation and biomolecular condensates

Protein conformation and cell compartmentalization are fundamental concepts and subjects of vast scientific endeavors. In the last two decades, we have witnessed exciting advances that unveiled the conjunction of these concepts. An avalanche of studies highlighted the central role of biomolecular condensates in membraneless subcellular compartmentalization that permits the spatiotemporal organization and regulation of myriads of simultaneous biochemical reactions and macromolecular interactions. These studies have also shown that biomolecular condensation, driven by multivalent intermolecular interactions, is mediated by order-disorder transitions of protein conformation and by protein domain architecture. Conceptually, protein condensation is a distinct level in protein conformational landscape in which collective folding of large collections of molecules takes place. Biomolecular condensates arise by the physical process of phase separation and comprise a variety of bodies ranging from membraneless organelles to liquid condensates to solid-like conglomerates, spanning lengths from mesoscopic clusters (nanometers) to micrometer-sized objects. In this review, we summarize and discuss recent work on the assembly, composition, conformation, material properties, thermodynamics, regulation, and functions of these bodies. We also review the conceptual framework for future studies on the conformational dynamics of condensed proteins in the regulation of cellular processes.

Multi-level analysis of intrinsically disordered protein docking methods

Intrinsically Disordered Proteins (IDPs) are a class of proteins in which at least some region of the protein does not possess any stable structure in solution in the physiological condition but may adopt an ordered structure upon binding to a globular receptor. These IDP-receptor complexes are thus subject to protein complex modeling in which computational techniques are applied to accurately reproduce the IDP ligand-receptor interactions. This often exists in the form of protein docking, in which the 3D structures of both the subunits are known, but the position of the ligand relative to the receptor is not. Here, we evaluate the performance of three IDP-receptor modeling tools with metrics that characterize the IDP-receptor interface at various resolutions. We show that all three methods are able to properly identify the general binding site, as identified by lower resolution metrics, but begin to struggle with higher resolution metrics that capture biophysical interactions.

Affinity of disordered protein complexes is modulated by entropy-energy reinforcement

Intrinsically disordered proteins (IDPs), which are very common and essential to many biological activities, sometimes function via interaction with another IDP and form a fuzzy complex, which can be highly stable. It is unclear what the biophysical forces are that govern their thermodynamics and specificity, which are essential for de novo fuzzy complex design. Here, we explored the fuzzy complex formed between ProTα and H1, which are oppositely charged IDPs, by swapping the charges between them, generating variants that have either greater polyampholytic or polyelectrolytic nature as well as different charge patterns. Charge swapping and shuffling dramatically change the affinity of the fuzzy complex, which is contributed to by both enthalpy and entropy, where the latter is dominated by counterion release.

The association between two intrinsically disordered proteins (IDPs) may produce a fuzzy complex characterized by a high binding affinity, similar to that found in the ultrastable complexes formed between two well-structured proteins. Here, using coarse-grained simulations, we quantified the biophysical forces driving the formation of such fuzzy complexes. We found that the high-affinity complex formed between the highly and oppositely charged H1 and ProTα proteins is sensitive to electrostatic interactions. We investigated 52 variants of the complex by swapping charges between the two oppositely charged proteins to produce sequences whose negatively or positively charged residue content was more homogeneous or heterogenous (i.e., polyelectrolytic or polyampholytic, having higher or lower absolute net charges, respectively) than the wild type. We also changed the distributions of oppositely charged residues within each participating sequence to produce variants in which the charges were segregated or well mixed. Both types of changes significantly affect binding affinity in fuzzy complexes, which is governed by both enthalpy and entropy. The formation of H1–ProTa is supported by an increase in configurational entropy and by entropy due to counterion release. The latter can be twice as large as the former, illustrating the dominance of counterion entropy in modulating the binding thermodynamics. Complexes formed between proteins with greater absolute net charges are more stable, both enthalpically and entropically, indicating that enthalpy and entropy have a mutually reinforcing effect. The sensitivity of the thermodynamics of the complex to net charge and the charge pattern within each of the binding constituents may provide a means to achieve binding specificity between IDPs.

Negatively Charged Disordered Regions are Prevalent and Functionally Important Across Proteomes

Intrinsically disordered regions (IDRs) of proteins are often characterized by a high fraction of charged residues, but differ in their overall net charge and in the organization of the charged residues. The function-encoding information stored via IDR charge composition and organization remains elusive. Here, we aim to decipher the sequence-function relationship in IDRs by presenting a comprehensive bioinformatic analysis of the charge properties of IDRs in the human, mouse, and yeast proteomes. About 50% of the proteins comprise at least a single IDR, which is either positively or negatively charged. Highly negatively charged IDRs are longer and possess greater net charge per residue compared with highly positively charged IDRs. A striking difference between positively and negatively charged IDRs is the characteristics of the repeated units, specifically, of consecutive Lys or Arg residues (K/R repeats) and Asp or Glu (D/E repeats) residues. D/E repeats are found to be about five times longer than K/R repeats, with the longest found containing 49 residues. Long stretches of consecutive D and E are found to be more prevalent in nucleic acid-related proteins. They are less common in prokaryotes, and in eukaryotes their abundance increases with genome size. The functional role of D/E repeats and the profound differences between them and K/R repeats are discussed.

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

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.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Single-Molecule Microscopy Meets Molecular Dynamics Simulations for Characterizing the Molecular Action of Proteins on DNA and in Liquid Condensates

DNA-binding proteins trigger various cellular functions and determine cellular fate. Before performing functions such as transcription, DNA repair, and DNA recombination, DNA-binding proteins need to search for and bind to their target sites in genomic DNA. Under evolutionary pressure, DNA-binding proteins have gained accurate and rapid target search and binding strategies that combine three-dimensional search in solution, one-dimensional sliding along DNA, hopping and jumping on DNA, and intersegmental transfer between two DNA molecules. These mechanisms can be achieved by the unique structural and dynamic properties of these proteins. Single-molecule fluorescence microscopy and molecular dynamics simulations have characterized the molecular actions of DNA-binding proteins in detail. Furthermore, these methodologies have begun to characterize liquid condensates induced by liquid-liquid phase separation, e.g., molecular principles of uptake and dynamics in droplets. This review discusses the molecular action of DNA-binding proteins on DNA and in liquid condensate based on the latest studies that mainly focused on the model protein p53.

Molecular principles of recruitment and dynamics of guest proteins in liquid droplets

Despite the continuous discovery of host and guest proteins in membraneless organelles, complex host–guest interactions hinder the understanding of the molecular grammar governing liquid–liquid phase separation. In this study, we characterized the localization and dynamic properties of guest proteins in liquid droplets using single-molecule fluorescence microscopy. Eighteen guest proteins of different sizes, structures, and oligomeric states were examined in host p53 liquid droplets. Recruitment did not significantly depend on the structural properties of the guest proteins, but was moderately correlated with their length, total charge, and number of R and Y residues. In contrast, the diffusion of disordered guest proteins was comparable to that of host p53, whereas that of folded proteins varied widely. Molecular dynamics simulations suggest that folded proteins diffuse within the voids of the liquid droplet while interacting weakly with neighboring host proteins, whereas disordered proteins adapt their structures to form tight interactions with the host proteins. Our study provides insights into the key molecular principles of the localization and dynamics of guest proteins in liquid droplets.

Phase separation vs aggregation behavior for model disordered proteins

Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. Although the LLPS of proteins is known to occur in a sequence-dependent manner, it is unclear how sequence properties dictate the nature of the phase transition and thereby influence condensed phase morphology. In this work, we have utilized grand canonical Monte Carlo simulations for a simple coarse-grained model of disordered proteins to systematically investigate how sequence distribution, sticker fraction, and chain length impact the formation of finite-size aggregates, which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Additionally, we find that this order parameter is strongly correlated with the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase density. Results obtained from an analysis of the order parameter reveal that at sufficiently long chain lengths, the vast majority of sequences are likely to phase separate. Our results suggest that classical LLPS should be the primary phase transition for disordered proteins when short-ranged attractive interactions dominate and suggest a possible reason behind recent findings of widespread phase separation throughout living cells.

Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions

Multivalent proteins and nucleic acids can self-assemble into biomolecular condensates that contribute to compartmentalize the cell interior. Computer simulations offer a unique view to elucidate the mechanisms and key intermolecular interactions behind the dynamic formation and dissolution of these condensates. In this work, we present a novel approach to include explicit water and salt in sequence-dependent coarse-grained (CG) models for proteins and RNA, enabling the study of biomolecular condensate formation in a salt-dependent manner. Our framework combines a reparameterized version of the HPS protein force field with the monoatomic mW water model and the mW-ion potential for NaCl. We show how our CG model qualitatively captures the experimental radius of the gyration trend of a subset of intrinsically disordered proteins and reproduces the experimental protein concentration and water percentage of the human fused in sarcoma (FUS) low-complexity-domain droplets at physiological salt concentration. Moreover, we perform seeding simulations as a function of salt concentration for two antagonist systems: the engineered peptide PR₂₅ and poly-uridine/poly-arginine mixtures, finding good agreement with their reported in vitro phase behavior with salt concentration in both cases. Taken together, our work represents a step forward towards extending sequence-dependent CG models to include water and salt, and to consider their key role in biomolecular condensate self-assembly.

The diversity of molecular interactions involving intrinsically disordered proteins: A molecular modeling perspective

Intrinsically Disordered Proteins and Regions (IDPs/IDRs) are key components of a multitude of biological processes. Conformational malleability enables IDPs/IDRs to perform very specialized functions that cannot be accomplished by globular proteins. The functional role for most of these proteins is related to the recognition of other biomolecules to regulate biological processes or as a part of signaling pathways. Depending on the extent of disorder, the number of interacting sites and the type of partner, very different architectures for the resulting assemblies are possible. More recently, molecular condensates with liquid-like properties composed of multiple copies of IDPs and nucleic acids have been proven to regulate key processes in eukaryotic cells. The structural and kinetic details of disordered biomolecular complexes are difficult to unveil experimentally due to their inherent conformational heterogeneity. Computational approaches, alone or in combination with experimental data, have emerged as unavoidable tools to understand the functional mechanisms of this elusive type of assemblies. The level of description used, all-atom or coarse-grained, strongly depends on the size of the molecular systems and on the timescale of the investigated mechanism. In this mini-review, we describe the most relevant architectures found for molecular interactions involving IDPs/IDRs and the computational strategies applied for their investigation.

Liquid-Liquid Phase Separation in the Presence of Macromolecular Crowding and State-dependent Kinetics

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) are increasingly being shown to play major roles in cellular self-organization dynamics in health and disease. It is well established that macromolecular crowding has a profound impact on protein interactions, particularly those that lead to LLPS. Although synthetic crowding agents are used during in vitro LLPS experiments, they are considerably different from the highly crowded nucleo-/cytoplasm and the effects of in vivo crowding remain poorly understood. In this work, we applied computational modeling to investigate the effects of macromolecular crowding on LLPS. To include biologically relevant LLPS dynamics, we extended the conventional Cahn-Hilliard model for phase separation by coupling it to experimentally derived macromolecular crowding dynamics and state-dependent reaction kinetics. Through extensive field-theoretic computer simulations, we show that the inclusion of macromolecular crowding results in late-stage coarsening and the stabilization of relatively smaller condensates. At a high crowding concentration, there is an accelerated growth and late-stage arrest of droplet formation, effectively resulting in anomalous labyrinthine morphologies akin to protein gelation observed in experiments. These results not only elucidate the crowder effects observed in experiments, but also highlight the importance of including state-dependent kinetics in LLPS models, and may help in designing further experiments to probe the intricate roles played by LLPS in self-organization dynamics of cells.

Finite-size shifts in simulated protein droplet phase diagrams

Computer simulation can provide valuable insight into the forces driving biomolecular liquid-liquid phase separation. However, the simulated systems have a limited size, which makes it important to minimize and control finite-size effects. Here, using a phenomenological free-energy ansatz, we investigate how the single-phase densities observed in a canonical system under coexistence conditions depend on the system size and the total density. We compare the theoretical expectations with results from Monte Carlo simulations based on a simple hydrophobic/polar protein model. We consider both cubic systems with spherical droplets and elongated systems with slab-like droplets. The results presented suggest that the slab simulation method greatly facilitates the estimation of the coexistence densities in the large-system limit.

Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.