Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins

Effects of Charge Sequence Pattern and Lysine-to-Arginine Substitution on the Structural Stability of Bioinspired Polyampholytes

A comprehensive study focusing on the combined influence of the charge sequence pattern and the type of positively charged amino acids on the formation of secondary structures in sequence-specific polyampholytes is presented. The sequences of interest consisting exclusively of ionizable amino acids (lysine, K; arginine, R; and glutamic acid, E) are (EKEK)5, (EKKE)5, (ERER)5, (ERRE)5, and (EKER)5. The stability of the secondary structure was examined at three pH values in the presence of urea and NaCl. The results presented here underscore the combined prominent effects of the charge sequence pattern and the type of positively charged monomers on secondary structure formation. Additionally, (ERRE)5 readily aggregated across a wide range of pH. In contrast, sequences with the same charge pattern, (EKKE)5, as well as the sequences with the equivalent amino acid content, (ERER)5, exhibited no aggregate formation under equivalent pH and concentration conditions.

HYPK: A marginally disordered protein sensitive to charge decoration

Intrinsically disordered proteins (IDPs) that lie close to the empirical boundary separating IDPs and folded proteins in Uversky's charge-hydropathy plot may behave as "marginal IDPs" and sensitively switch conformation upon changes in environment (temperature, crowding, and charge screening), sequence, or both. In our search for such a marginal IDP, we selected Huntingtin-interacting protein K (HYPK) near that boundary as a candidate; PKIα, also near that boundary, has lower secondary structure propensity; and Crk1, just across the boundary on the folded side, has higher secondary structure propensity. We used a qualitative Förster resonance energy transfer-based assay together with circular dichroism to simultaneously probe global and local conformation. HYPK shows several unique features indicating marginality: a cooperative transition in end-to-end distance with temperature, like Crk1 and folded proteins, but unlike PKIα; enhanced secondary structure upon crowding, in contrast to Crk1 and PKIα; and a cross-over from salt-induced expansion to compaction at high temperature, likely due to a structure-to-disorder transition not seen in Crk1 and PKIα. We then tested HYPK's sensitivity to charge patterning by designing charge-flipped variants including two specific sequences with identical amino acid composition that markedly differ in their predicted size and response to salt. The experimentally observed trends, also including mutants of PKIα, verify the predictions from sequence charge decoration metrics. Marginal proteins like HYPK show features of both folded and disordered proteins that make them sensitive to physicochemical perturbations and structural control by charge patterning.

Interplay between posttranslational modifications and liquid‒liquid phase separation in tumors

Liquid‒liquid phase separation (LLPS) is a general phenomenon recently recognized to be critically involved in the regulation of a variety of cellular biological processes, such as transcriptional regulation, heterochromatin formation and signal transduction, through the compartmentalization of proteins or nucleic acids into droplet-like condensates. These processes are directly or indirectly related to tumor initiation and treatment. Posttranslational modifications (PTMs), which represent a rapid and reversible mechanism involved in the functional regulation of proteins, have emerged as key events in modulating LLPS under physiological or pathophysiological conditions, including tumorigenesis and antitumor therapy. In this review, we introduce the biological functions participated in cancer-associated LLPS, discuss the potential roles of LLPS during tumor onset or therapy, and emphasize the mechanistic characteristics of LLPS regulated by PTMs and its effects on tumor progression. We then provide a perspective on further studies on LLPS and its regulation by PTMs in cancer research. This review aims to broaden the understanding of the functions of LLPS and its regulation by PTMs under normal or aberrant cellular conditions.

Sequence-Dependent Conformational Transitions of Disordered Proteins During Condensation

Intrinsically disordered proteins (IDPs) can form biomolecular condensates through phase separation. It is recognized that the conformation of IDPs in the dense and dilute phases as well as at the interfaces of condensates can critically impact the resulting properties associated with their functionality. However, a comprehensive understanding of the conformational transitions of IDPs during condensation remains elusive. In this study, we employ a coarse-grained polyampholyte model, comprising an equal number of oppositely charged residues-glutamic acid and lysine-whereby conformations and phase behavior can be readily tuned by altering the protein sequence. By manipulating the sequence patterns from perfectly alternating to block-like, we obtain chains with ideal-like conformations to semi-compact structures in the dilute phase, while in the dense phase, the chain conformation is approximately that of an ideal chain, irrespective of the protein sequence. By performing simulations at different concentrations, we find that the chains assemble from the dilute phase through small oligomeric clusters to the dense phase, accompanied by a gradual swelling of the individual chains. We further demonstrate that these findings are applicable to several naturally occurring proteins involved in the formation of biological condensates. Concurrently, we delve deeper into the chain conformations within the condensate, revealing that chains at the interface show a strong sequence dependence, but remain more collapsed than those in the bulk-like dense phase. This study addresses critical gaps in our knowledge of IDP conformations within condensates as a function of protein sequence.

Data-Driven Models for Predicting Intrinsically Disordered Protein Polymer Physics Directly from Composition or Sequence

The molecular-level understanding of intrinsically disordered proteins is challenging due to experimental characterization difficulties. Computational understanding of IDPs also requires fundamental advances, as the leading tools for predicting protein folding (e.g., AlphaFold), typically fail to describe the structural ensembles of IDPs. The focus of this paper is to 1) develop new representations for intrinsically disordered proteins and 2) pair these representations with classical machine learning and deep learning models to predict the radius of gyration and derived scaling exponent of IDPs. Here, we build a new physically-motivated feature called the bag of amino acid interactions representation, which encodes pairwise interactions explicitly into the representation. This feature essentially counts and weights all possible non-bonded interactions in a sequence and thus is, in principle, compatible with arbitrary sequence lengths. To see how well this new feature performs, both categorical and physically-motivated featurization techniques are tested on a computational dataset containing 10,000 sequences simulated at the coarse-grained level. The results indicate that this new feature outperforms the other purely categorical and physically-motivated features and possesses solid extrapolation capabilities. For future use, this feature can potentially provide physical insights into amino acid interactions, including their temperature dependence, and be applied to other protein spaces.

Theory and Simulation of Multiphase Coexistence in Biomolecular Mixtures

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase behavior of heterogeneous biomolecular mixtures are only beginning to be explored. Theory and simulation provide invaluable tools for probing the relationship between molecular determinants, such as protein and RNA sequences, and the emergence of phase-separated condensates in such complex environments. This review covers recent advances in the prediction and computational design of biomolecular mixtures that phase-separate into many coexisting phases. First, we review efforts to understand the phase behavior of mixtures with hundreds or thousands of species using theoretical models and statistical approaches. We then describe progress in developing analytical theories and coarse-grained simulation models to predict multiphase condensates with the molecular detail required to make contact with biophysical experiments. We conclude by summarizing the challenges ahead for modeling the inhomogeneous spatial organization of biomolecular mixtures in living cells.

The Analytical Flory Random Coil Is a Simple-to-Use Reference Model for Unfolded and Disordered Proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory random coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google Colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Structural Preferences Shape the Entropic Force of Disordered Protein Ensembles

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and exist in a dynamic conformational ensemble instead of a native, well-folded structure. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in these ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function. But how the magnitude of this force depends on IDR sequence remains unexplored. Here, we use all-atom simulations to analyze how structural preferences in IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force: compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate the IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

Role of Strong Localized vs Weak Distributed Interactions in Disordered Protein Phase Separation

Interaction strength and localization are critical parameters controlling the single-chain and condensed-state properties of intrinsically disordered proteins (IDPs). Here, we decipher these relationships using coarse-grained heteropolymers comprised of hydrophobic (H) and polar (P) monomers as model IDPs. We systematically vary the fraction of P monomers XP and employ two distinct particle-based models that include either strong localized attractions between only H-H pairs (HP model) or weak distributed attractions between both H-H and H-P pairs (HP+ model). To compare different sequences and models, we first carefully tune the attraction strength for all sequences to match the single-chain radius of gyration. Interestingly, we find that this procedure produces similar conformational ensembles, nonbonded potential energies, and chain-level dynamics for single chains of almost all sequences in both models, with some deviations for the HP model at large XP. However, we observe a surprisingly rich phase behavior for the sequences in both models that deviates from the expectation that similarity at the single-chain level will translate to a similar phase-separation propensity. Coexistence between dilute and dense phases is only observed up to a model-dependent XP, despite the presence of favorable interchain interactions, which we quantify using the second virial coefficient. Instead, the limited number of attractive sites (H monomers) leads to the self-assembly of finite-sized clusters of different sizes depending on XP. Our findings strongly suggest that models with distributed interactions favor the formation of liquid-like condensates over a much larger range of sequence compositions compared to models with localized interactions.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 μs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 μs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

The analytical Flory random coil is a simple-to-use reference model for unfolded and disordered proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory Random Coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

An intrinsically disordered protein region encoded by the human disease gene CLEC16A regulates mitophagy

CLEC16A regulates mitochondrial health through mitophagy and is associated with over 20 human diseases. However, the key structural and functional regions of CLEC16A, and their relevance for human disease, remain unknown. Here, we report that a disease-associated CLEC16A variant lacks a C-terminal intrinsically disordered protein region (IDPR) that is critical for mitochondrial quality control. IDPRs comprise nearly half of the human proteome, yet their mechanistic roles in human disease are poorly understood. Using carbon detect NMR, we find that the CLEC16A C terminus lacks secondary structure, validating the presence of an IDPR. Loss of the CLEC16A C-terminal IDPR in vivo impairs mitophagy, mitochondrial function, and glucose-stimulated insulin secretion, ultimately causing glucose intolerance. Deletion of the CLEC16A C-terminal IDPR increases CLEC16A ubiquitination and degradation, thus impairing assembly of the mitophagy regulatory machinery. Importantly, CLEC16A stability is dependent on proline bias within the C-terminal IDPR, but not amino acid sequence order or charge. Together, we elucidate how an IDPR in CLEC16A regulates mitophagy and implicate pathogenic human gene variants that disrupt IDPRs as novel contributors to diabetes and other CLEC16A-associated diseases.Abbreviations : CAS: carbon-detect amino-acid specific; IDPR: intrinsically disordered protein region; MEFs: mouse embryonic fibroblasts; NMR: nuclear magnetic resonance.

Functional partitioning of transcriptional regulators by patterned charge blocks

Components of transcriptional machinery are selectively partitioned into specific condensates, often mediated by protein disorder, yet we know little about how this specificity is achieved. Here, we show that condensates composed of the intrinsically disordered region (IDR) of MED1 selectively partition RNA polymerase II together with its positive allosteric regulators while excluding negative regulators. This selective compartmentalization is sufficient to activate transcription and is required for gene activation during a cell-state transition. The IDRs of partitioned proteins are necessary and sufficient for selective compartmentalization and require alternating blocks of charged amino acids. Disrupting this charge pattern prevents partitioning, whereas adding the pattern to proteins promotes partitioning with functional consequences for gene activation. IDRs with similar patterned charge blocks show similar partitioning and function. These findings demonstrate that disorder-mediated interactions can selectively compartmentalize specific functionally related proteins from a complex mixture of biomolecules, leading to regulation of a biochemical pathway.

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.

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.

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.

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.

An Interpretable Machine-Learning Algorithm to Predict Disordered Protein Phase Separation Based on Biophysical Interactions

Protein phase separation is increasingly understood to be an important mechanism of biological organization and biomaterial formation. Intrinsically disordered protein regions (IDRs) are often significant drivers of protein phase separation. A number of protein phase-separation-prediction algorithms are available, with many being specific for particular classes of proteins and others providing results that are not amenable to the interpretation of the contributing biophysical interactions. Here, we describe LLPhyScore, a new predictor of IDR-driven phase separation, based on a broad set of physical interactions or features. LLPhyScore uses sequence-based statistics from the RCSB PDB database of folded structures for these interactions, and is trained on a manually curated set of phase-separation-driving proteins with different negative training sets including the PDB and human proteome. Competitive training for a variety of physical chemical interactions shows the greatest contribution of solvent contacts, disorder, hydrogen bonds, pi–pi contacts, and kinked beta-structures to the score, with electrostatics, cation–pi contacts, and the absence of a helical secondary structure also contributing. LLPhyScore has strong phase-separation-prediction recall statistics and enables a breakdown of the contribution from each physical feature to a sequence’s phase-separation propensity, while recognizing the interdependence of many of these features. The tool should be a valuable resource for guiding experiments and providing hypotheses for protein function in normal and pathological states, as well as for understanding how specificity emerges in defining individual biomolecular condensates.

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.

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.

Conformational and Solvation Dynamics of an Amyloidogenic Intrinsically Disordered Domain of a Melanosomal Protein

The conformational plasticity of intrinsically disordered proteins (IDPs) allows them to adopt a range of conformational states that can be important for their biological functions. The driving force for the conformational preference of an IDP emanates from an intricate interplay between chain-chain and chain-solvent interactions. Using ultrafast femtosecond and picosecond time-resolved fluorescence measurements, we characterized the conformational and solvation dynamics around the N- and C-terminal segments of a disordered repeat domain of a melanosomal protein Pmel17 that forms functional amyloid responsible for melanin biosynthesis. Our time-resolved fluorescence anisotropy results revealed slight compaction and slower rotational dynamics around the amyloidogenic C-terminal segment when compared to the proline-rich N-terminal segment of the repeat domain. The compaction of the C-terminal region was also associated with the restrained mobility of hydration water as indicated by our solvation dynamics measurements. Our findings indicate that sequence-dependent chain-solvent interactions govern both the conformational and solvation dynamics that are crucial in directing the conversion of a highly dynamic IDP into an ordered amyloid assembly. Such an interplay of amino acid composition-dependent conformational and solvation dynamics might have important physicochemical consequences in specific water-protein, ion-protein, and protein-protein interactions involved in amyloid formation and phase transitions.

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.

The Effect of Multisite Phosphorylation on the Conformational Properties of Intrinsically Disordered Proteins

Intrinsically disordered proteins are involved in many biological processes such as signaling, regulation, and recognition. A common strategy to regulate their function is through phosphorylation, as it can induce changes in conformation, dynamics, and interactions with binding partners. Although phosphorylated intrinsically disordered proteins have received increased attention in recent years, a full understanding of the conformational and structural implications of phosphorylation has not yet been achieved. Here, we present all-atom molecular dynamics simulations of five disordered peptides originated from tau, statherin, and β-casein, in both phosphorylated and non-phosphorylated state, to compare changes in global dimensions and structural elements, in an attempt to gain more insight into the controlling factors. The changes are in qualitative agreement with experimental data, and we observe that the net charge is not enough to predict the impact of phosphorylation on the global dimensions. Instead, the distribution of phosphorylated and positively charged residues throughout the sequence has great impact due to the formation of salt bridges. In statherin, a preference for arginine-phosphoserine interaction over arginine-tyrosine accounts for a global expansion, despite a local contraction of the phosphorylated region, which implies that also non-charged residues can influence the effect of phosphorylation.

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.

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.

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.

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.

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.

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

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

An analytical theory to describe sequence-specific inter-residue distance profiles for polyampholytes and intrinsically disordered proteins

Intrinsically Disordered Proteins (IDPs), unlike folded proteins, lack a unique folded structure and rapidly interconvert among ensembles of disordered states. However, they have specific conformational properties when averaged over their ensembles of disordered states. It is critical to develop a theoretical formalism to predict these ensemble average conformational properties that are encoded in the IDP sequence (the specific order in which amino acids/residues are linked). We present a general heteropolymer theory that analytically computes the ensemble average distance profiles (⟨R_ij ²⟩) between any two (i, j) monomers (amino acids for IDPs) as a function of the sequence. Information rich distance profiles provide a detailed description of the IDP in contrast to typical metrics such as scaling exponents, radius of gyration, or end-to-end distance. This generalized formalism supersedes homopolymer-like models or models that are built only on the composition of amino acids but ignore sequence details. The prediction of these distance profiles for highly charged polyampholytes and naturally occurring IDPs unmasks salient features that are hidden in the sequence. Moreover, the model reveals strategies to modulate the entire distance map to achieve local or global swelling/compaction by subtle changes/modifications-such as phosphorylation, a biologically relevant process-in specific hotspots in the sequence. Sequence-specific distance profiles and their modulation have been benchmarked against all-atom simulations. Our new formalism also predicts residue-pair specific coil-globule transitions. The analytical nature of the theory will facilitate design of new sequences to achieve specific target distance profiles with broad applications in synthetic biology and polymer science.

Relevance of Electrostatic Charges in Compactness, Aggregation, and Phase Separation of Intrinsically Disordered Proteins

The abundance of intrinsic disorder in the protein realm and its role in a variety of physiological and pathological cellular events have strengthened the interest of the scientific community in understanding the structural and dynamical properties of intrinsically disordered proteins (IDPs) and regions (IDRs). Attempts at rationalizing the general principles underlying both conformational properties and transitions of IDPs/IDRs must consider the abundance of charged residues (Asp, Glu, Lys, and Arg) that typifies these proteins, rendering them assimilable to polyampholytes or polyelectrolytes. Their conformation strongly depends on both the charge density and distribution along the sequence (i.e., charge decoration) as highlighted by recent experimental and theoretical studies that have introduced novel descriptors. Published experimental data are revisited herein in the frame of this formalism, in a new and possibly unitary perspective. The physicochemical properties most directly affected by charge density and distribution are compaction and solubility, which can be described in a relatively simplified way by tools of polymer physics. Dissecting factors controlling such properties could contribute to better understanding complex biological phenomena, such as fibrillation and phase separation. Furthermore, this knowledge is expected to have enormous practical implications for the design, synthesis, and exploitation of bio-derived materials and the control of natural biological processes.

Information theoretic measures for quantifying sequence-ensemble relationships of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) contribute to a multitude of functions. De novo design of IDPs should open the door to modulating functions and phenotypes controlled by these systems. Recent design efforts have focused on compositional biases and specific sequence patterns as the design features. Analysis of the impact of these designs on sequence-function relationships indicates that individual sequence/compositional parameters are insufficient for describing sequence-function relationships in IDPs. To remedy this problem, we have developed information theoretic measures for sequence–ensemble relationships (SERs) of IDPs. These measures rely on prior availability of statistically robust conformational ensembles derived from all atom simulations. We show that the measures we have developed are useful for comparing sequence-ensemble relationships even when sequence is poorly conserved. Based on our results, we propose that de novo designs of IDPs, guided by knowledge of their SERs, should provide improved insights into their sequence–ensemble–function relationships.

Hydropathy Patterning Complements Charge Patterning to Describe Conformational Preferences of Disordered Proteins

Understanding the conformational ensemble of an intrinsically disordered protein (IDP) is of great interest due to its relevance to critical intracellular functions and diseases. It is now well established that the polymer scaling behavior can provide a great deal of information about the conformational properties as well as liquid-liquid phase separation of an IDP. It is, therefore, extremely desirable to be able to predict an IDP's scaling behavior from the protein sequence itself. The work in this direction so far has focused on highly charged proteins and how charge patterning can perturb their structural properties. As naturally occurring IDPs are composed of a significant fraction of uncharged amino acids, the rules based on charge content and patterning are only partially helpful in solving the problem. Here, we propose a new order parameter, sequence hydropathy decoration, which can provide a near-quantitative understanding of scaling and structural properties of IDPs devoid of charged residues. We combine this with a charge patterning parameter, sequence charge decoration, to obtain a general equation, parametrized from extensive coarse-grained simulation data, for predicting protein dimensions from the sequence. We finally test this equation against available experimental data and find a semiquantitative match in predicting the scaling behavior. We also provide guidance on how to extend this approach to experimental data, which should be feasible in the near future.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes

The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers is quite well described by theory, but it has been a challenge to develop general theories for the LLPS of heteropolymers involving charge-charge interactions. Here, we present a theory that combines a random-phase-approximation treatment of polymer density fluctuations and an account of intrachain conformational heterogeneity based on renormalized Kuhn lengths to provide predictions of LLPS properties as a function of pH, salt, and charge patterning along the chain sequence. Advancing beyond more limited analytical approaches, our LLPS theory is applicable to a wide variety of charged sequences ranging from highly charged polyelectrolytes to neutral or nearly neutral polyampholytes. This theory should be useful in high-throughput screening of protein and other sequences for their LLPS propensities and can serve as a basis for more comprehensive theories that incorporate nonelectrostatic interactions. Experimental ramifications of our theory are discussed.

Predicting Conformational Properties of Intrinsically Disordered Proteins from Sequence

Intrinsically disordered proteins (IDPs) can adopt a range of conformations from globules to swollen coils. This large range of conformational preferences for different IDPs raises the question of how conformational preferences are encoded by sequence. Global compositional features of a sequence such as the fraction of charged residues and the net charge per residue engender certain conformational biases. However, more specific sequence features such as the patterning of oppositely charged residues, expansion driving residues, or residues that can undergo posttranslational modifications can also influence the conformational ensembles of an IDP. Here, we outline how to calculate important global compositional features and patterning metrics that can be used to classify IDPs into different conformational classes and predict relative changes in conformation for sequences with the same amino acid composition. Although increased effort has been devoted to determining conformational properties of IDPs in recent years, quantitative predictions of conformation directly from sequence remain difficult and often inaccurate. Thus, if quantitative predictions of conformational properties are desired, then sequence-specific simulations must be performed.

Binding without folding - the biomolecular function of disordered polyelectrolyte complexes

Recent evidence shows that oppositely charged intrinsically disordered proteins (IDPs) can form high-affinity complexes that involve neither the formation of secondary or tertiary structure nor site-specific interactions between individual residues. Similar electrostatically dominated interactions have also been identified for positively charged IDPs binding to nucleic acids. These highly disordered polyelectrolyte complexes constitute an extreme case within the spectrum of biomolecular interactions involving disorder. Such interactions are likely to be widespread, since sequence analysis predicts proteins with highly charged disordered regions to be surprisingly numerous. Here, we summarize the insights that have emerged from the highly disordered polyelectrolyte complexes identified so far, and we highlight recent developments and future challenges in (i) establishing models for the underlying highly dynamic structural ensembles, (ii) understanding the novel binding mechanisms associated with them, and (iii) identifying the functional consequences.

Sequence specificity despite intrinsic disorder: How a disease-associated Val/Met polymorphism rearranges tertiary interactions in a long disordered protein

The role of electrostatic interactions and mutations that change charge states in intrinsically disordered proteins (IDPs) is well-established, but many disease-associated mutations in IDPs are charge-neutral. The Val66Met single nucleotide polymorphism (SNP) in precursor brain-derived neurotrophic factor (BDNF) is one of the earliest SNPs to be associated with neuropsychiatric disorders, and the underlying molecular mechanism is unknown. Here we report on over 250 μs of fully-atomistic, explicit solvent, temperature replica-exchange molecular dynamics (MD) simulations of the 91 residue BDNF prodomain, for both the V66 and M66 sequence. The simulations were able to correctly reproduce the location of both local and non-local secondary structure changes due to the Val66Met mutation, when compared with NMR spectroscopy. We find that the change in local structure is mediated via entropic and sequence specific effects. We developed a hierarchical sequence-based framework for analysis and conceptualization, which first identifies “blobs” of 4-15 residues representing local globular regions or linkers. We use this framework within a novel test for enrichment of higher-order (tertiary) structure in disordered proteins; the size and shape of each blob is extracted from MD simulation of the real protein (RP), and used to parameterize a self-avoiding heterogenous polymer (SAHP). The SAHP version of the BDNF prodomain suggested a protein segmented into three regions, with a central long, highly disordered polyampholyte linker separating two globular regions. This effective segmentation was also observed in full simulations of the RP, but the Val66Met substitution significantly increased interactions across the linker, as well as the number of participating residues. The Val66Met substitution replaces β-bridging between V66 and V94 (on either side of the linker) with specific side-chain interactions between M66 and M95. The protein backbone in the vicinity of M95 is then free to form β-bridges with residues 31-41 near the N-terminus, which condenses the protein. A significant role for Met/Met interactions is consistent with previously-observed non-local effects of the Val66Met SNP, as well as established interactions between the Met66 sequence and a Met-rich receptor that initiates neuronal growth cone retraction.

Intrinsically disordered proteins are proteins that have no well-defined structure in at least one functional form. Mutations in one amino acid may still affect their function significantly, especially in subtle ways with cumulative adverse effects on health. Here we report on molecular dynamics simulations of a protein that is critical for neuronal health throughout adulthood (brain-derived neurotrophic factor). We investigate the effects of a mutation carried by 30% of human population, which has been widely studied for its association with aging-related and stress-related disorders, reduced volume of the hippocampus, and variations in episodic memory. We identify a molecular mechanism in which the mutation may change the global conformations of the protein and its ability to bind to receptors.

Disordered domains in chromatin-binding proteins

Chromatin comprises proteins, DNA and RNA, and its function is to condense and package the genome in a way that allows the necessary transactions such as transcription, replication and repair to occur in a highly organised and regulated manner. The packaging of chromatin is often thought of in a hierarchical fashion starting from the most basic unit of DNA packaging, the nucleosome, to the condensation of nucleosomal 'beads on a string' by linker histones to form the 30-nm fibre and eventually large chromatin domains. However, a picture of a more heterogeneous, dynamic and liquid-like assembly is emerging, in which intrinsically disordered proteins (IDPs) and proteins containing intrinsically disordered regions (IDRs) play a central role. Disorder features at all levels of chromatin organisation, from the histone tails, which are sites of extensive post-translational modification (PTM) that change the fate of the underlying genomic information, right through to transcription hubs, and the recently elucidated roles of IDPs and IDRs in the condensation of large regions of the genome through liquid-liquid phase separation.

Complete Phase Diagram for Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

A number of intrinsically disordered proteins have been shown to self-assemble via liquid-liquid phase separation into protein-rich and dilute phases. The resulting coacervates can have important biological functions, and the ability to form these assemblies is dictated by the protein's primary amino acid sequence as well as by the solution conditions. We present a complete phase diagram for the simple coacervation of a polyampholyte intrinsically disordered protein using a field-theoretic simulation approach. We show that differences in the primary amino acid sequence and in the distribution of charged amino acids along the sequence lead to differences in the phase window for coacervation, with block-charged sequences having a larger coacervation window than sequences with a random patterning of charges. The model also captures how changing solution conditions modifies the phase diagram and can serve to guide experimental studies.

The combined force field-sampling problem in simulations of disordered amyloid-β peptides

Molecular dynamics simulations of intrinsically disordered proteins (IDPs) can provide high resolution structural ensembles if the force field is accurate enough and if the simulation sufficiently samples the conformational space of the IDP with the correct weighting of sub-populations. Here, we investigate the combined force field-sampling problem by testing a standard force field as well as newer fixed charge force fields, the latter specifically motivated for better description of unfolded states and IDPs, and comparing them with a standard temperature replica exchange (TREx) protocol and a non-equilibrium Temperature Cool Walking (TCW) sampling algorithm. The force field and sampling combinations are used to characterize the structural ensembles of the amyloid-beta peptides Aβ42 and Aβ43, which both should be random coils as shown recently by experimental nuclear magnetic resonance (NMR) and 2D Förster resonance energy transfer (FRET) experiments. The results illustrate the key importance of the sampling algorithm: while the standard force field using TREx is in poor agreement with the NMR J-coupling and nuclear Overhauser effect and 2D FRET data, when using the TCW method, the standard and optimized protein-water force field combinations are in very good agreement with the same experimental data since the TCW sampling method produces qualitatively different ensembles than TREx. We also discuss the relative merit of the 2D FRET data when validating structural ensembles using the different force fields and sampling protocols investigated in this work for small IDPs such as the Aβ42 and Aβ43 peptides.

Thermodynamically driven assemblies and liquid-liquid phase separations in biology

The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical origin of such organization is not fully understood, and even though it is clear that cells and organisms cannot maintain their integrity without consuming energy, there is growing evidence that individual assembly processes can be thermodynamically driven and occur spontaneously due to changes in thermodynamic variables such as intermolecular interactions and concentration. Understanding the phase separation in vivo requires a multidisciplinary approach, integrating the theory and physics of phase separation with experimental and computational techniques. This paper aims at providing a brief overview of the physics of phase separation and its biological implications, with a particular focus on the assembly of membraneless organelles. We discuss the underlying physical principles of phase separation from its thermodynamics to its kinetics. We also overview the wide range of methods utilized for experimental verification and characterization of phase separation of membraneless organelles, as well as the utility of molecular simulations rooted in thermodynamics and statistical physics in understanding the governing principles of thermodynamically driven biological self-assembly processes.

Coarse-grained residue-based models of disordered protein condensates: utility and limitations of simple charge pattern parameters

Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the "blockiness" measure κ and the "sequence charge decoration" (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature Tcr* increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and -SCD. Relative to RPA, the simulated sequence-dependent variation in Tcr* is often-though not always-smaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between κ and -SCD, the simulated Tcr*'s are quite insensitive to either parameter. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.

Preface: Special Topic on Single-Molecule Biophysics

Single-molecule measurements are now almost routinely used to study biological systems and processes. The scope of this special topic emphasizes the physics side of single-molecule observations, with the goal of highlighting new developments in physical techniques as well as conceptual insights that single-molecule measurements bring to biophysics. This issue also comprises recent advances in theoretical physical models of single-molecule phenomena, interpretation of single-molecule signals, and fundamental areas of statistical mechanics that are related to single-molecule observations. A particular goal is to illustrate the increasing synergy between theory, simulation, and experiment in single-molecule biophysics.