A theoretical method to compute sequence dependent configurational properties in charged polymers and proteins

Molecular interactions underlying the phase separation of HP1α: role of phosphorylation, ligand and nucleic acid binding

Heterochromatin protein 1α (HP1α) is a crucial element of chromatin organization. It has been proposed that HP1α functions through liquid-liquid phase separation (LLPS), which allows it to compact chromatin into transcriptionally repressed heterochromatin regions. In vitro, HP1α can undergo phase separation upon phosphorylation of its N-terminus extension (NTE) and/or through interactions with DNA and chromatin. Here, we combine computational and experimental approaches to elucidate the molecular interactions that drive these processes. In phosphorylation-driven LLPS, HP1α can exchange intradimer hinge-NTE interactions with interdimer contacts, which also leads to a structural change from a compacted to an extended HP1α dimer conformation. This process can be enhanced by the presence of positively charged HP1α peptide ligands and disrupted by the addition of negatively charged or neutral peptides. In DNA-driven LLPS, both positively and negatively charged peptide ligands can perturb phase separation. Our findings demonstrate the importance of electrostatic interactions in HP1α LLPS where binding partners can modulate the overall charge of the droplets and screen or enhance hinge region interactions through specific and non-specific effects. Our study illuminates the complex molecular framework that can fine-tune the properties of HP1α and that can contribute to heterochromatin regulation and function.

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.

The biophysics of disordered proteins from the point of view of single-molecule fluorescence spectroscopy

Intrinsically disordered proteins (IDPs) and regions (IDRs) have emerged as key players across many biological functions and diseases. Differently from structured proteins, disordered proteins lack stable structure and are particularly sensitive to changes in the surrounding environment. Investigation of disordered ensembles requires new approaches and concepts for quantifying conformations, dynamics, and interactions. Here, we provide a short description of the fundamental biophysical properties of disordered proteins as understood through the lens of single-molecule fluorescence observations. Single-molecule Förster resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) provides an extensive and versatile toolbox for quantifying the characteristics of conformational distributions and the dynamics of disordered proteins across many different solution conditions, both in vitro and in living cells.

Molecular Determinants for the Layering and Coarsening of Biological Condensates

Many membraneless organelles, or biological condensates, form through phase separation, and play key roles in signal sensing and transcriptional regulation. While the functional importance of these condensates has inspired many studies to characterize their stability and spatial organization, the underlying principles that dictate these emergent properties are still being uncovered. In this review, we examine recent work on biological condensates, especially multicomponent systems. We focus on connecting molecular factors such as binding energy, valency, and stoichiometry with the interfacial tension, explaining the nontrivial interior organization in many condensates. We further discuss mechanisms that arrest condensate coalescence by lowering the surface tension or introducing kinetic barriers to stabilize the multidroplet state.

Incorporation of D2O-Induced Fluorine Chemical Shift Perturbations into Ensemble-Structure Characterization of the ERalpha Disordered Region

Structural characterization of intrinsically disordered proteins (IDPs) requires a concerted effort between experiments and computations by accounting for their conformational heterogeneity. Given the diversity of experimental tools providing local and global structural information, constructing an experimental restraint-satisfying structural ensemble remains challenging. Here, we use the disordered N-terminal domain (NTD) of the estrogen receptor alpha (ERalpha) as a model system to combine existing small-angle X-ray scattering (SAXS) and hydroxyl radical protein footprinting (HRPF) data and newly acquired solvent accessibility data via D2O-induced fluorine chemical shifting (DFCS) measurements. A new set of DFCS data for the solvent exposure of a set of 12 amino acid positions were added to complement previously acquired HRPF measurements for the solvent exposure of the other 16 nonoverlapping amino acids, thereby improving the NTD ensemble characterization considerably. We also found that while choosing an initial ensemble of structures generated from a different atomic-level force field or sampling/modeling method can lead to distinct contact maps even when the same sets of experimental measurements were used for ensemble-fitting, comparative analyses from these initial ensembles reveal commonly recurring structural features in their ensemble-averaged contact map. Specifically, nonlocal or long-range transient interactions were found consistently between the N-terminal segments and the central region, sufficient to mediate the conformational ensemble and regulate how the NTD interacts with its coactivator proteins.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

Effect of Charge Distribution on the Dynamics of Polyampholytic Disordered Proteins

The stability and physiological function of many biomolecular coacervates depend on the structure and dynamics of intrinsically disordered proteins (IDPs) that typically contain a significant fraction of charged residues. Although the effect of relative arrangement of charged residues on IDP conformation is a well-studied problem, the associated changes in dynamics are far less understood. In this work, we systematically interrogate the effects of charge distribution on the chain-level and segmental dynamics of polyampholytic IDPs in dilute solutions. We study a coarse-grained model polyampholyte consisting of an equal fraction of two oppositely charged residues (glutamic acid and lysine) that undergoes a transition from an ideal chain-like conformation for uniformly charge-patterned sequences to a semi-compact conformation for highly charge-segregated sequences. Changes in the chain-level dynamics with increasing charge segregation correlate with changes in conformation. The chain-level and segmental dynamics conform to simple homopolymer models for uniformly charge-patterned sequences but deviate with increasing charge segregation, both in the presence and absence of hydrodynamic interactions. We discuss the significance of these findings, obtained for a model polyampholyte, in the context of a charge-rich intrinsically disordered region of the naturally occurring protein LAF-1. Our findings have important implications for understanding the effects of charge patterning on the dynamics of polyampholytic IDPs in dilute conditions using polymer scaling theories.

pH Induced Switch in the Conformational Ensemble of Intrinsically Disordered Protein Prothymosin-α and Its Implications for Amyloid Fibril Formation

Aggregation of intrinsically disordered proteins (IDPs) can lead to neurodegenerative diseases. Although there is experimental evidence that acidic pH promotes IDP monomer compaction leading to aggregation, the general mechanism is unclear. We studied the pH effect on the conformational ensemble of prothymosin-α (proTα), which is involved in multiple essential functions, and probed its role in aggregation using computer simulations. We show that compaction in the proTα dimension at low pH is due to the protein's collapse in the intermediate region (E41-D80) rich in glutamic acid residues, enhancing its β-sheet content. We observed by performing dimer simulations that the conformations with high β-sheet content could act as aggregation-prone (N*) states and nucleate the aggregation process. The simulations initiated using N* states form dimers within a microsecond time scale, whereas the non-N* states do not form dimers within this time scale. This study contributes to understanding the general principles of pH-induced IDP aggregation.

Connecting sequence features within the disordered C-terminal linker of Bacillus subtilis FtsZ to functions and bacterial cell division

Intrinsically disordered regions (IDRs) can function as autoregulators of folded enzymes to which they are tethered. One example is the bacterial cell division protein FtsZ. This includes a folded core and a C-terminal tail (CTT) that encompasses a poorly conserved, disordered C-terminal linker (CTL) and a well-conserved 17-residue C-terminal peptide (CT17). Sites for GTPase activity of FtsZs are formed at the interface between GTP binding sites and T7 loops on cores of adjacent subunits within dimers. Here, we explore the basis of autoregulatory functions of the CTT in Bacillus subtilis FtsZ (Bs-FtsZ). Molecular simulations show that the CT17 of Bs-FtsZ makes statistically significant CTL-mediated contacts with the T7 loop. Statistical coupling analysis of more than 1,000 sequences from FtsZ orthologs reveals clear covariation of the T7 loop and the CT17 with most of the core domain, whereas the CTL is under independent selection. Despite this, we discover the conservation of nonrandom sequence patterns within CTLs across orthologs. To test how the nonrandom patterns of CTLs mediate CTT-core interactions and modulate FtsZ functionalities, we designed Bs-FtsZ variants by altering the patterning of oppositely charged residues within the CTL. Such alterations disrupt the core-CTT interactions, lead to anomalous assembly and inefficient GTP hydrolysis in vitro and protein degradation, aberrant assembly, and disruption of cell division in vivo. Our findings suggest that viable CTLs in FtsZs are likely to be IDRs that encompass nonrandom, functionally relevant sequence patterns that also preserve three-way covariation of the CT17, the T7 loop, and core domain.

Sequence-Controlled Secondary Structures and Stimuli Responsiveness of Bioinspired Polyampholytes

A comprehensive study focusing on the influence of the sequence charge pattern on the secondary structure preferences of annealed polyampholytes and their responsiveness to external stimuli is presented. Two sequences are designed composed entirely of ionizable amino acids (charge fraction, f = 1) and an equal number of positive and negative charges (f+ = f- = 0.5) with distinct charge patterns consisting of lysine and glutamic acid monomers. The study reveals that the sequence charge pattern has a significant influence on the secondary structure preferences of polyampholytes at physiological pH. Furthermore, it shows that external stimuli such as pH, ionic strength, and solvent dielectric constant can be used to modulate the secondary structure of the two studied sequences. The observed secondary structure transformations for the two sequences are also substantially different from those determined for uniformly charged homo-polypeptides under matching conditions.

Analytical Solution to the Flory-Huggins Model

A self-consistent analytical solution for binodal concentrations of the two-component Flory-Huggins phase separation model is derived. We show that this form extends the validity of the Ginzburg-Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of the interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid-liquid phase separation boundaries to determine the effective chain length and solute-solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid-liquid phase separation.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

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.

Investigating Intrinsically Disordered Proteins With Brownian Dynamics

Intrinsically disordered proteins (IDPs) have recently become systems of great interest due to their involvement in modulating many biological processes and their aggregation being implicated in many diseases. Since IDPs do not have a stable, folded structure, however, they cannot be easily studied with experimental techniques. Hence, conducting a computational study of these systems can be helpful and be complementary with experimental work to elucidate their mechanisms. Thus, we have implemented the coarse-grained force field for proteins (COFFDROP) in Browndye 2.0 to study IDPs using Brownian dynamics (BD) simulations, which are often used to study large-scale motions with longer time scales and diffusion-limited molecular associations. Specifically, we have checked our COFFDROP implementation with eight naturally occurring IDPs and have investigated five (Glu-Lys)25 IDP sequence variants. From measuring the hydrodynamic radii of eight naturally occurring IDPs, we found the ideal scaling factor of 0.786 for non-bonded interactions. We have also measured the entanglement indices (average C α distances to the other chain) between two (Glu-Lys)25 IDP sequence variants, a property related to molecular association. We found that entanglement indices decrease for all possible pairs at excess salt concentration, which is consistent with long-range interactions of these IDP sequence variants getting weaker at increasing salt concentration.

Discovering molecular features of intrinsically disordered regions by using evolution for contrastive learning

A major challenge to the characterization of intrinsically disordered regions (IDRs), which are widespread in the proteome, but relatively poorly understood, is the identification of molecular features that mediate functions of these regions, such as short motifs, amino acid repeats and physicochemical properties. Here, we introduce a proteome-scale feature discovery approach for IDRs. Our approach, which we call "reverse homology", exploits the principle that important functional features are conserved over evolution. We use this as a contrastive learning signal for deep learning: given a set of homologous IDRs, the neural network has to correctly choose a held-out homolog from another set of IDRs sampled randomly from the proteome. We pair reverse homology with a simple architecture and standard interpretation techniques, and show that the network learns conserved features of IDRs that can be interpreted as motifs, repeats, or bulk features like charge or amino acid propensities. We also show that our model can be used to produce visualizations of what residues and regions are most important to IDR function, generating hypotheses for uncharacterized IDRs. Our results suggest that feature discovery using unsupervised neural networks is a promising avenue to gain systematic insight into poorly understood protein sequences.

BIAPSS: A Comprehensive Physicochemical Analyzer of Proteins Undergoing Liquid-Liquid Phase Separation

The liquid-liquid phase separation (LLPS) of biomolecules is a phenomenon which is nowadays recognized as the driving force for the biogenesis of numerous functional membraneless organelles and cellular bodies. The interplay between the protein primary sequence and phase separation remains poorly understood, despite intensive research. To uncover the sequence-encoded signals of protein capable of undergoing LLPS, we developed a novel web platform named BIAPSS (Bioinformatics Analysis of LLPS Sequences). This web server provides on-the-fly analysis, visualization, and interpretation of the physicochemical and structural features for the superset of curated LLPS proteins.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

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.

Cell cycle-specific phase separation regulated by protein charge blockiness

Dynamic morphological changes of intracellular organelles are often regulated by protein phosphorylation or dephosphorylation^1–6. Phosphorylation modulates stereospecific interactions among structured proteins, but how it controls molecular interactions among unstructured proteins and regulates their macroscopic behaviours remains unknown. Here we determined the cell cycle-specific behaviour of Ki-67, which localizes to the nucleoli during interphase and relocates to the chromosome periphery during mitosis. Mitotic hyperphosphorylation of disordered repeat domains of Ki-67 generates alternating charge blocks in these domains and increases their propensity for liquid–liquid phase separation (LLPS). A phosphomimetic sequence and the sequences with enhanced charge blockiness underwent strong LLPS in vitro and induced chromosome periphery formation in vivo. Conversely, mitotic hyperphosphorylation of NPM1 diminished a charge block and suppressed LLPS, resulting in nucleolar dissolution. Cell cycle-specific phase separation can be modulated via phosphorylation by enhancing or reducing the charge blockiness of disordered regions, rather than by attaching phosphate groups to specific sites.

Yamazaki et al. show that cell cycle-regulated changes in hyperphosphorylation of Ki-67 and NPM1 modulate alternating charge blocks in these proteins, which defines their propensity for liquid–liquid phase separation at chromatin.

On the stability and layered organization of protein-DNA condensates

Multi-component phase separation is emerging as a key mechanism for the formation of biological condensates that play essential roles in signal sensing and transcriptional regulation. The molecular factors that dictate these condensates' stability and spatial organization are not fully understood, and it remains challenging to predict their microstructures. Using a near-atomistic, chemically accurate force field, we studied the phase behavior of chromatin regulators that are crucial for heterochromatin organization and their interactions with DNA. Our computed phase diagrams recapitulated previous experimental findings on different proteins. They revealed a strong dependence of condensate stability on the protein-DNA mixing ratio as a result of balancing protein-protein interactions and charge neutralization. Notably, a layered organization was observed in condensates formed by mixing HP1, histone H1, and DNA. This layered organization may be of biological relevance, as it enables cooperative DNA packaging between the two chromatin regulators: histone H1 softens the DNA to facilitate the compaction induced by HP1 droplets. Our study supports near-atomistic models as a valuable tool for characterizing the structure and stability of biological condensates.

Field theory description of ion association in re-entrant phase separation of polyampholytes

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion-pairs through an association reaction. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion-association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.

Distribution of Charged Residues Affects the Average Size and Shape of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are ensembles of interconverting conformers whose conformational properties are governed by several physico-chemical factors, including their amino acid composition and the arrangement of oppositely charged residues within the primary structure. In this work, we investigate the effects of charge patterning on the average compactness and shape of three model IDPs with different proline content. We model IDP ensemble conformations as ellipsoids, whose size and shape are calculated by combining data from size-exclusion chromatography and native mass spectrometry. For each model IDP, we analyzed the wild-type protein and two synthetic variants with permuted positions of charged residues, where positive and negative amino acids are either evenly distributed or segregated. We found that charge clustering induces remodeling of the conformational ensemble, promoting compaction and/or increasing spherical shape. Our data illustrate that the average shape and volume of the ensembles depend on the charge distribution. The potential effect of other factors, such as chain length, number of proline residues, and secondary structure content, is also discussed. This methodological approach is a straightforward way to model IDP average conformation and decipher the salient sequence attributes influencing IDP structural properties.

Uncovering the Quantitative Relationships Among Chromosome Fluctuations, Epigenetics, and Gene Expressions of Transdifferentiation on Waddington Landscape

The 3D spatial organization of the chromosomes appears to be linked to the gene function, which is cell type-specific. The chromosome structural ensemble switching model (CSESM) is developed by employing a heteropolymer model on different cell types and the important quantitative relationships among the chromosome ensemble, the epigenetic marks, and the gene expressions are uncovered, that both chromosome fluctuation and epigenetic marks have strong linear correlations with the gene expressions. The results support that the two compartments have different behaviors, corresponding to the relatively sparse and fluctuating phase (compartment A) and the relatively dense and stable phase (compartment B). Importantly, through the investigation of the transdifferentiation processes between the peripheral blood mononuclear cell (PBMC) and the bipolar neuron (BN), a quantitative description for the transdifferentiation is provided, which can be linked to the Waddington landscape. In addition, compared to the direct transdifferentiation between PBMC and BN, the transdifferentiation via the intermediate state neural progenitor cell (NPC) follows a different path (an "uphill" followed by a "downhill"). These theoretical studies bridge the gap among the chromosome fluctuations/ensembles, the epigenetics, and gene expressions in determining the cell fate.

Tuning Formation of Protein-DNA Coacervates by Sequence and Environment

The high concentration of nucleic acids and positively charged proteins in the cell nucleus provides many possibilities for complex coacervation. We consider a prototypical mixture of nucleic acids together with the polycationic C-terminus of histone H1 (CH1). Using a minimal coarse-grained model that captures the shape, flexibility, and charge distributions of the molecules, we find that coacervates are readily formed at physiological ionic strengths, in agreement with experiment, with a progressive increase in local ordering at low ionic strength. Variation of the positions of charged residues in the protein tunes phase separation: for well-mixed or only moderately blocky distributions of charge, there is a modest increase of local ordering with increasing blockiness that is also associated with an increased propensity to phase separate. This ordering is also associated with a slowdown of rotational and translational diffusion in the dense phase. However, for more extreme blockiness (and consequently higher local charge density), we see a qualitative change in the condensed phase to become a segregated structure with a dramatically increased ordering of the DNA. Naturally occurring proteins with these sequence properties, such as protamines in sperm cells, are found to be associated with very dense packing of nucleic acids.

Uncovering Non-random Binary Patterns Within Sequences of Intrinsically Disordered Proteins

Sequence-ensemble relationships of intrinsically disordered proteins (IDPs) are governed by binary patterns such as the linear clustering or mixing of specific residues or residue types with respect to one another. To enable the discovery of potentially important, shared patterns across sequence families, we describe a computational method referred to as NARDINI for Non-random Arrangement of Residues in Disordered Regions Inferred using Numerical Intermixing. This work was partially motivated by the observation that parameters that are currently in use for describing different binary patterns are not interoperable across IDPs of different amino acid compositions and lengths. In NARDINI, we generate an ensemble of scrambled sequences to set up a composition-specific null model for the patterning parameters of interest. We then compute a series of pattern-specific z-scores to quantify how each pattern deviates from a null model for the IDP of interest. The z-scores help in identifying putative non-random linear sequence patterns within an IDP. We demonstrate the use of NARDINI derived z-scores by identifying sequence patterns in three well-studied IDP systems. We also demonstrate how NARDINI can be deployed to study archetypal IDPs across homologs and orthologs. Overall, NARDINI is likely to aid in designing novel IDPs with a view toward engineering new sequence-function relationships or uncovering cryptic ones. We further propose that the z-scores introduced here are likely to be useful for theoretical and computational descriptions of sequence-ensemble relationships across IDPs of different compositions and lengths.

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding

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

Motif-pattern dependence of biomolecular phase separation driven by specific interactions

Eukaryotic cells partition a wide variety of important materials and processes into biomolecular condensates—phase-separated droplets that lack a membrane. In addition to nonspecific electrostatic or hydrophobic interactions, phase separation also depends on specific binding motifs that link together constituent molecules. Nevertheless, few rules have been established for how these ubiquitous specific, saturating, motif-motif interactions drive phase separation. By integrating Monte Carlo simulations of lattice-polymers with mean-field theory, we show that the sequence of heterotypic binding motifs strongly affects a polymer’s ability to phase separate, influencing both phase boundaries and condensate properties (e.g. viscosity and polymer diffusion). We find that sequences with large blocks of single motifs typically form more inter-polymer bonds, which promotes phase separation. Notably, the sequence of binding motifs influences phase separation primarily by determining the conformational entropy of self-bonding by single polymers. This contrasts with systems where the molecular architecture primarily affects the energy of the dense phase, providing a new entropy-based mechanism for the biological control of phase separation.

Cells need to concentrate biomolecules in the right place at the right time in order to function. Many important intracellular compartments are liquid droplets formed by phase separation, the same process that separates oil from vinegar. The properties of such “biomolecular condensates” depend on the component molecules, such as proteins and RNAs. These molecules are polymers made of many interacting monomers, often organized into “motifs,” and the sequence of motifs shapes the properties of the condensates. Recent work has revealed important principles governing phase separation when the motifs are charged and interact across long distances, but many phase-separating molecules form specific interactions that are short-range and one-to-one. How does the sequence of specifically-interacting motifs affect phase separation? Using a combination of simulations and theoretical calculations, we show that the sequence has profound effects on both the formation and properties of condensates. Sequences with large blocks of identical motifs are better at phase separating but more viscous and solid-like. Importantly, we find that sequence controls phase separation via the proclivity to form self-bonds instead of forming bonds with other polymers. Thus the sequence of specifically-interacting motifs provides a control point for the formation and properties of phase-separated intracellular compartments.

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples-random charge densities and periodic charge densities-with different scaling properties. Under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

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.

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Intramolecular interactions play key role in stabilization of pHLIP at acidic conditions

The pH-Low Insertion Peptide (pHLIP) is a membrane-active peptide that spontaneously folds into a transmembrane α-helix upon acidification. This activity enables pHLIP to potentially act as a vector for drugs related to diseases characterized by acidosis such as cancer or heart ischemia. Presently, due to aggregation-based effects, formulations of pHLIP are only viable at near-μM concentrations. In addition, since most of pHLIP's measurable qualities involve a membrane, probing the details of pHLIP in the interstitial region is difficult. In attempts to shed light on these issues, we performed constant pH molecular dynamics simulations on pHLIP as well as P20G, a variant with increased helicity, in solution at 0 and 150 mM NaCl over a broad range of pHs. In general, the addition of ions reduced the effective pK_a of the acidic residues in pHLIP. P20G exhibits a higher helicity than pHLIP in general and is more compact than pHLIP at pH values under 4. In terms of charge effects, sodium cations localized predominantly to the C-terminus of the peptide with a high density of acidic residues. Additionally, the salt bridge between R11 and D14 is by far the most favored and particularly so with pHLIP at 150 mM NaCl. We expect that this approach will be a valuable tool to screen variants of pHLIP for favorable properties in solution, an aspect of pHLIP design that to this point has largely been neglected.

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.

Folded domain charge properties influence the conformational behavior of disordered tails

Intrinsically disordered proteins and protein regions (IDRs) make up around 30% of the human proteome where they play essential roles in dictating and regulating many core biological processes. While IDRs are often studied as isolated domains, in naturally occurring proteins most IDRs are found adjacent to folded domains, where they exist as either N- or C-terminal tails or as linkers connecting two folded domains. Prior work has shown that charge properties of IDRs can influence their conformational behavior, both in isolation and in the context of folded domains. In contrast, the converse scenario is less well-explored: how do the charge properties of folded domains influence IDR conformational behavior? To answer this question, we combined a large-scale structural bioinformatics analysis with all-atom implicit solvent simulations of both rationally designed and naturally occurring proteins. Our results reveal three key takeaways. Firstly, the relative position and accessibility of charged residues across the surface of a folded domain can dictate IDR conformational behavior, overriding expectations based on net surface charge properties. Secondly, naturally occurring proteins possess multiple charge patches that are physically accessible to local IDRs. Finally, even modest changes in the local electrostatic environment of a folded domain can substantially modulate IDR-folded domain interactions. Taken together, our results suggest that folded domain surfaces can act as local determinants of IDR conformational behavior.

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Intrinsically disordered regions (IDRs) are mostly found adjacent to folded domains.

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Here we propose that the folded domain surface properties influence IDR behavior.

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We combine all-atom simulations and sequence design of IDRs and folded domains.

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IDR conformational behavior is determined by a complex combination of factors.

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Folded domains can substantially alter IDR conformational biases.

Diffusion of a disordered protein on its folded ligand

Flexibility in complexes between intrinsically disordered proteins and folded ligands is widespread in nature. However, timescales and spatial amplitudes of such dynamics remained unexplored for most systems. Our results show that the disordered cytoplasmic tail of the cell adhesion protein E-cadherin diffuses across the entire surface of its folded binding partner β-catenin at fast submillisecond timescales. The nanometer amplitude of these motions could allow kinases to access their recognition motifs without requiring a dissociation of the complex. We expect that the rugged energy landscape found in the E-cadherin/β-catenin complex is a defining feature of dynamic and partially disordered protein complexes.

Intrinsically disordered proteins often form dynamic complexes with their ligands. Yet, the speed and amplitude of these motions are hidden in classical binding kinetics. Here, we directly measure the dynamics in an exceptionally mobile, high-affinity complex. We show that the disordered tail of the cell adhesion protein E-cadherin dynamically samples a large surface area of the protooncogene β-catenin. Single-molecule experiments and molecular simulations resolve these motions with high resolution in space and time. Contacts break and form within hundreds of microseconds without a dissociation of the complex. The energy landscape of this complex is rugged with many small barriers (3 to 4 k_BT) and reconciles specificity, high affinity, and extreme disorder. A few persistent contacts provide specificity, whereas unspecific interactions boost affinity.

Integrating single-molecule spectroscopy and simulations for the study of intrinsically disordered proteins

Over the last two decades, intrinsically disordered proteins and protein regions (IDRs) have emerged from a niche corner of biophysics to be recognized as essential drivers of cellular function. Various techniques have provided fundamental insight into the function and dysfunction of IDRs. Among these techniques, single-molecule fluorescence spectroscopy and molecular simulations have played a major role in shaping our modern understanding of the sequence-encoded conformational behavior of disordered proteins. While both techniques are frequently used in isolation, when combined they offer synergistic and complementary information that can help uncover complex molecular details. Here we offer an overview of single-molecule fluorescence spectroscopy and molecular simulations in the context of studying disordered proteins. We discuss the various means in which simulations and single-molecule spectroscopy can be integrated, and consider a number of studies in which this integration has uncovered biological and biophysical mechanisms.

Intrinsically disordered protein regions and phase separation: sequence determinants of assembly or lack thereof

Intrinsically disordered protein regions (IDRs) - regions that do not fold into a fixed three-dimensional structure but instead exist in a heterogeneous ensemble of conformations - have recently entered mainstream cell biology in the context of liquid-liquid phase separation (LLPS). IDRs are frequently found to be enriched in phase-separated compartments. Due to this observation, the presence of an IDR in a protein is frequently assumed to be diagnostic of its ability to phase separate. In this review, we clarify the role of IDRs in biological assembly and explore the physical principles through which amino acids can confer the attractive molecular interactions that underlie phase separation. While some disordered regions will robustly drive phase separation, many others will not. We emphasize that rather than 'disorder' driving phase separation, multivalency drives phase separation. As such, whether or not a disordered region is capable of driving phase separation will depend on the physical chemistry encoded within its amino acid sequence. Consequently, an in-depth understanding of that physical chemistry is a prerequisite to make informed inferences on how and why an IDR may be involved in phase separation or, more generally, in protein-mediated intermolecular interactions.

FG nucleoporins feature unique patterns that distinguish them from other IDPs

FG nucleoporins (FG Nups) are intrinsically disordered proteins and are the putative regulators of nucleocytoplasmic transport. They allow fast, yet selective, transport of molecules through the nuclear pore complex, but the underlying mechanism of nucleocytoplasmic transport is not yet fully discovered. As a result, FG Nups have been the subject of extensive research in the past two decades. Although most studies have been focused on analyzing the conformation and function of FG Nups from a biophysical standpoint, some recent studies have investigated the sequence-function relationship of FG Nups, with a few investigating amino acid sequences of a large number of FG Nups to understand common characteristics that might enable their function. Previously, we identified an evolutionarily conserved feature in FG Nup sequences, which are extended subsequences with low charge density, containing only positive charges, and located toward the N-terminus of FG Nups. We named these patterns longest positive like charge regions (lpLCRs). These patterns are specific to positively charged residues, and negatively charged residues do not demonstrate such a pattern. In this study, we compare FG Nups with other disordered proteins obtained from the DisProt and UniProt database in terms of presence of lpLCRs. Our results show that the lpLCRs are virtually exclusive to FG Nups and are not observed in other disordered proteins. Also, lpLCRs are what differentiate FG Nups from DisProt proteins in terms of charge distribution, meaning that excluding lpLCRs from the sequences of FG Nups make them similar to DisProt proteins in terms of charge distribution. We also previously showed the biophysical effect of lpLCRs in conformation of FG Nups. The results of this study are in line with our previous findings and imply that lpLCRs are virtually exclusive and functionally significant characteristics of FG Nups and nucleocytoplasmic transport.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

Targeted modulation of protein liquid-liquid phase separation by evolution of amino-acid sequence

Rationally and efficiently modifying the amino-acid sequence of proteins to control their ability to undergo liquid-liquid phase separation (LLPS) on demand is not only highly desirable, but can also help to elucidate which protein features are important for LLPS. Here, we propose a computational method that couples a genetic algorithm to a sequence-dependent coarse-grained protein model to evolve the amino-acid sequences of phase-separating intrinsically disordered protein regions (IDRs), and purposely enhance or inhibit their capacity to phase-separate. We validate the predicted critical solution temperatures of the mutated sequences with ABSINTH, a more accurate all-atom model. We apply the algorithm to the phase-separating IDRs of three naturally occurring proteins, namely FUS, hnRNPA1 and LAF1, as prototypes of regions that exist in cells and undergo homotypic LLPS driven by different types of intermolecular interaction, and we find that the evolution of amino-acid sequences towards enhanced LLPS is driven in these three cases, among other factors, by an increase in the average size of the amino acids. However, the direction of change in the molecular driving forces that enhance LLPS (such as hydrophobicity, aromaticity and charge) depends on the initial amino-acid sequence. Finally, we show that the evolution of amino-acid sequences to modulate LLPS is strongly coupled to the make-up of the medium (e.g. the presence or absence of RNA), which may have significant implications for our understanding of phase separation within the many-component mixtures of biological systems.

Salt-Dependent Conformational Changes of Intrinsically Disordered Proteins

The flexible structure of an intrinsically disordered protein (IDP) is known to be perturbed by salt concentrations, which can be understood by electrostatic screening on charged amino acids. However, an IDP usually contains more uncharged residues that are influenced by the salting-out effect. Here we have parametrized the salting-out effect into a coarse-grained model using a set of Förster resonance energy transfer data and verified with experimental salt-dependent liquid-liquid phase separation (LLPS) of 17 proteins. The new model can correctly capture the behavior of 6 more sequences, resulting in a total of 13 when varying salt concentrations. Together with a survey of more than 500 IDP sequences, we conclude that the salting-out effect, which was considered to be secondary to electrostatic screening, is important for IDP sequences with moderately charged residues at physiological salt concentrations. The presented scheme is generally applicable to other computational models for capturing salt-dependent IDP conformations.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

PhosIDP: a web tool to visualize the location of phosphorylation sites in disordered regions

Charge is a key determinant of intrinsically disordered protein (IDP) and intrinsically disordered region (IDR) properties. IDPs and IDRs are enriched in sites of phosphorylation, which alters charge. Visualizing the degree to which phosphorylation modulates the charge profile of a sequence would assist in the functional interpretation of IDPs and IDRs. PhosIDP is a web tool that shows variation of charge and fold propensity upon phosphorylation. In combination with the displayed location of protein domains, the information provided by the web tool can lead to functional inferences for the consequences of phosphorylation. IDRs are components of many proteins that form biological condensates. It is shown that IDR charge, and its modulation by phosphorylation, is more tightly controlled for proteins that are essential for condensate formation than for those present in condensates but inessential.

Physical modeling of multivalent interactions in the nuclear pore complex

In the nuclear pore complex, intrinsically disordered proteins (FG Nups), along with their interactions with more globular proteins called nuclear transport receptors (NTRs), are vital to the selectivity of transport into and out of the cell nucleus. Although such interactions can be modeled at different levels of coarse graining, in vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, in which the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and noncohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion and compare them with experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

Intrachain interaction topology can identify functionally similar intrinsically disordered proteins

Functionally similar IDPs (intrinsically disordered proteins) often have little sequence similarity. This is in stark contrast to folded proteins and poses a challenge for the inverse problem, functional classification of IDPs using sequence alignment. The problem is further compounded because of the lack of structure in IDPs, preventing structural alignment as an alternate tool for classification. Recent advances in heteropolymer theory unveiled a powerful set of sequence-patterning metrics bridging molecular interaction with chain conformation. Focusing only on charge patterning, these set of metrics yield a sequence charge decoration matrix (SCDM). SCDMs can potentially identify functionally similar IDPs not apparent from sequence alignment alone. Here, we illustrate how these information-rich "molecular blueprints" encoded in SCDMs can be used for functional classification of IDPs with specific application in three protein families-Ste50, PSC, and RAM-in which electrostatics is known to be important. For both the Ste50 and PSC protein family, the set of metrics appropriately classifies proteins in functional and nonfunctional groups in agreement with experiment. Furthermore, our algorithm groups synthetic variants of the disordered RAM region of the Notch receptor protein-important in gene expression-in reasonable accordance with classification based on experimentally measured binding constants of RAM and transcription factor. Taken together, the novel classification scheme reveals the critical role of a high-dimensional set of metrics-manifest in self-interaction maps and topology-in functional annotation of IDPs even when there is low sequence homology, providing the much-needed alternate to a traditional sequence alignment tool.

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

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.