Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins

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 their functionality. However, a residue-level 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 tuned by altering the protein sequence. By manipulating sequence patterns from perfectly alternating to block-like, we obtain chains with ideal-like conformations to semi-compact structures in the dilute phase. In the dense phase, however, the chain conformation approaches that of an ideal chain, regardless of the sequence. Simulations across different concentrations reveal that chains transition from small oligomeric clusters in the dilute phase to the dense phase, with a gradual swelling of individual chains. These findings are further validated with naturally occurring protein sequences involved in biological condensate formation. Additionally, we show that chain conformations at the interface display a strong sequence dependence, remaining more collapsed than those in the bulk-like dense phase. This study provides detailed insights into how the conformations of a specific subclass of IDPs (lacking secondary structures) change within condensates and in solution, as governed by their sequences.

Physics-Based Machine Learning Trains Hamiltonians and Decodes the Sequence-Conformation Relation in the Disordered Proteome

Intrinsically disordered proteins and regions (IDPs) are involved in vital biological processes. To understand the IDP function, often controlled by conformation, we need to find the link between sequence and conformation. We decode this link by integrating theory, simulation, and machine learning (ML) where sequence-dependent electrostatics is modeled analytically while nonelectrostatic interaction is extracted from simulations for many sequences and subsequently trained using ML. The resulting Hamiltonian, combining physics-based electrostatics and machine-learned nonelectrostatics, accurately predicts sequence-specific global and local measures of conformations beyond the original observable used from the simulation. This is in contrast to traditional ML approaches that train and predict a specific observable, not a Hamiltonian. Our formalism reproduces experimental measurements, predicts multiple conformational features directly from sequence with high throughput that will give insights into IDP design and evolution, and illustrates the broad utility of using physics-based ML to train unknown parts of a Hamiltonian, rather than a specific observable, in combination with known physics.

Structural and Functional Relevance of Charge Based Transient Interactions inside Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) perform a wide range of biological functions without adopting stable, well-defined, three-dimensional structures. Instead, IDPs exist as dynamic ensembles of flexible conformations, traditionally thought to be governed by weak, nonspecific interactions, which are well described by homopolymer theory. However, recent research highlights the presence of transient, specific interactions in several IDPs, suggesting that factors beyond overall size influence their conformational behavior. In this study, we investigate how the spatial arrangement of charged amino acids within IDP sequences shapes the prevalence of transient, specific interactions. Through a series of model peptides, we establish a quantitative empirical relationship between the fraction of transient interactions and a novel sequence metric, termed effective charged patch length, which characterizes the ability of charged patches to drive these interactions. By examining IDP ensembles with varying levels of transient interactions, we further explore their heteropolymeric structural behavior in phase-separated condensates, where we observe the formation of a condensate-spanning network structure. Additionally, we perform a proteome-wide scan for charge-based transient interactions within disordered regions of the human proteome, revealing that approximately 10% of these regions exhibit such charge-driven transient interactions, leading to heteropolymeric behaviors in their conformational ensembles. Finally, we examine how these charge-based transient interactions correlate with molecular functions, identifying specific biological roles in which these interactions are enriched.

MEDOC: A fast, scalable and mathematically exact algorithm for the site-specific prediction of the protonation degree in large disordered proteins

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched in positively and negatively charged residues. While it is often convenient to assume these residues follow their model-compound pKa values, recent work has shown that local charge effects (charge regulation) can upshift or downshift sidechain pKa values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N , scales as~ 2 N . This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed MEDOC (Multisite Extent of Deprotonation Originating from Context) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytic, Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q-canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pKa values across the entire DisProt database. Our results show differences in the distribution of predicted pKa values for different amino acids, in agreement with NMR-measured distributions in proteins.

Structural transitions of a semi-flexible polyampholyte

Polyampholytes (PAs) are charged polymers composed of positively and negatively charged monomers along their backbone. The sequence of the charged monomers and the bending of the chain significantly influence the conformation and dynamical behavior of the PA. Using coarse-grained molecular dynamics simulations, we comprehensively study the structural and dynamical properties of flexible and semi-flexible PAs. The simulation results demonstrate a flexible PA chain, displaying a transition from a coil to a globule in the parameter space of the charge sequence. In addition, the behavior of the mean-square displacement (MSD), denoted as ⟨(Δr(t))2⟩, reveals distinct dynamics, specifically for the alternating and charge-segregated sequences. The MSD follows a power-law behavior, where ⟨(Δr(t))2⟩ ∼ tβ, with β ≈ 3/5 and β ≈ 1/2 for the alternating sequence and the charge-segregated sequence in the absence of hydrodynamic interactions, respectively. However, when hydrodynamic interactions are incorporated, the exponent β shifts to ∼3/5 for the charge-segregated sequence and 2/3 for the well-mixed alternating sequence. For a semi-flexible PA chain, varying the bending rigidity and electrostatic interaction strength (Γe) leads to distinct, fascinating conformational states, including globule, bundle, and torus-like conformations. We show that PAs acquire circular and hairpin-like conformations in the intermediate bending regime. The transition between various conformations is identified in terms of the shape factor estimated from the ratios of eigenvalues of the gyration tensor.

Beyond monopole electrostatics in regulating conformations of intrinsically disordered proteins

Conformations and dynamics of an intrinsically disordered protein (IDP) depend on its composition of charged and uncharged amino acids, and their specific placement in the protein sequence. In general, the charge (positive or negative) on an amino acid residue in the protein is not a fixed quantity. Each of the ionizable groups can exist in an equilibrated distribution of fully ionized state (monopole) and an ion-pair (dipole) state formed between the ionizing group and its counterion from the background electrolyte solution. The dipole formation (counterion condensation) depends on the protein conformation, which in turn depends on the distribution of charges and dipoles on the molecule. Consequently, effective charges of ionizable groups in the IDP backbone may differ from their chemical charges in isolation-a phenomenon termed charge-regulation. Accounting for the inevitable dipolar interactions, that have so far been ignored, and using a self-consistent procedure, we present a theory of charge-regulation as a function of sequence, temperature, and ionic strength. The theory quantitatively agrees with both charge reduction and salt-dependent conformation data of Prothymosin-alpha and makes several testable predictions. We predict charged groups are less ionized in sequences where opposite charges are well mixed compared to sequences where they are strongly segregated. Emergence of dipolar interactions from charge-regulation allows spontaneous coexistence of two phases having different conformations and charge states, sensitively depending on the charge patterning. These findings highlight sequence dependent charge-regulation and its potential exploitation by biological regulators such as phosphorylation and mutations in controlling protein conformation and function.

Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins

Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness" κ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration (Rgs) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to κ in predicting Rg because SCD accounts for effects of contact order, i.e., nonlocality, on dimensions of isolated chains. In contrast, κ and SCD are comparably good, though nonideal, predictors of UCST because frequencies of interchain contacts in the multiple-chain condensed phase are less sensitive to sequence positions than frequencies of intrachain contacts of an isolated chain, as reflected by κ correlating better with condensed-phase interaction energy than SCD.

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

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.

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.

Electrostatics and hydrophobicity in the dynamics of intrinsically disordered proteins

Internal friction is a major contribution to the dynamics of intrinsically disordered proteins (IDPs). Yet, the molecular origin of internal friction has so far been elusive. Here, we investigate whether attractive electrostatic interactions in IDPs modulate internal friction differently than the hydrophobic effect. To this end, we used nanosecond fluorescence correlation spectroscopy (nsFCS) and single-molecule Förster resonance energy transfer (FRET) to quantify the conformation and dynamics of the disordered DNA-binding domains Myc, Max and Mad at different salt concentrations. We find that internal friction effects are stronger when the chain is compacted by electrostatic attractions compared to the hydrophobic effect. Although the effect is moderate, the results show that the heteropolymeric nature of IDPs is reflected in their dynamics.

Intrinsically disordered regions are poised to act as sensors of cellular chemistry

Intrinsically disordered proteins and protein regions (IDRs) are abundant in eukaryotic proteomes and play a wide variety of essential roles. Instead of folding into a stable structure, IDRs exist in an ensemble of interconverting conformations whose structure is biased by sequence-dependent interactions. The absence of a stable 3D structure, combined with high solvent accessibility, means that IDR conformational biases are inherently sensitive to changes in their environment. Here, we argue that IDRs are ideally poised to act as sensors and actuators of cellular physicochemistry. We review the physical principles that underlie IDR sensitivity, the molecular mechanisms that translate this sensitivity to function, and recent studies where environmental sensing by IDRs may play a key role in their downstream function.

Flanking regions, amyloid cores, and polymorphism: the potential interplay underlying structural diversity

The β-sheet-rich amyloid core is the defining feature of protein aggregates associated with neurodegenerative disorders. Recent investigations have revealed that there exist multiple examples of the same protein, with the same sequence, forming a variety of amyloid cores with distinct structural characteristics. These structural variants, termed as polymorphs, are hypothesized to influence the pathological profile and the progression of different neurodegenerative diseases, giving rise to unique phenotypic differences. Thus, identifying the origin and properties of these structural variants remain a focus of studies, as a preliminary step in the development of therapeutic strategies. Here, we review the potential role of the flanking regions of amyloid cores in inducing polymorphism. These regions, adjacent to the amyloid cores, show a preponderance for being structurally disordered, imbuing them with functional promiscuity. The dynamic nature of the flanking regions can then manifest in the form of conformational polymorphism of the aggregates. We take a closer look at the sequences flanking the amyloid cores, followed by a review of the polymorphic aggregates of the well-characterized proteins amyloid-β, α-synuclein, Tau, and TDP-43. We also consider different factors that can potentially influence aggregate structure and how these regions can be viewed as novel targets for therapeutic strategies by utilizing their unique structural properties.

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.

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

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

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.

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.

Influence of ion specificity and concentration on the conformational transition of intrinsically disordered sheep prion peptide

The structural sensitivity of the IDPs with the ions has been observed experimentally; however, it is still unclear how the presence of different metal ions affects structural stability. We performed atomistic molecular dynamics simulation of sheep prion peptide (142-167) in presence of different monovalent, divalent ions at various concentrations to find out the effect of the size, charge, and ionic concentration on the structure of the peptide. It is found that Li + ions have a higher survival probability compared to Na + , K + and Mg2 + affecting the solvation structure of the protein leading to the alpha-helix structure. At high concentration, due to the increase in the ion-solvent and ion-counter interactions, the effect of the ions is screened on the surface of the protein and hence no ion specificity is observed. This study demonstrates how ions can be used to regulate the protein structure and function that can help in designing drugs.

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.

Regulation of Poly-E Motif Flexibility by pH, Ca2+ and the PPAK Motif

The disordered PEVK region of titin contains two main structural motifs: PPAK and poly-E. The distribution of these motifs in the PEVK region contributes to the elastic properties of this region, but the specific mechanism of how these motifs work together remains unclear. Previous work from our lab has demonstrated that 28-amino acid peptides of the poly-E motif are sensitive to shifts in pH, becoming more flexible as the pH decreases. We extend this work to longer poly-E constructs, including constructs containing PPAK motifs. Our results demonstrate that longer poly-E motifs have a much larger range of pH sensitivity and that the inclusion of the PPAK motif reduces this sensitivity. We also demonstrate that binding calcium can increase the conformational flexibility of the poly-E motif, though the PPAK motif can block this calcium-dependent change. The data presented here suggest a model where PPAK and calcium can alter the stiffness of the poly-E motif by modulating the degree of charge repulsion in the glutamate clusters.

Methodology of measurement of ionic strength based on field-flow fractionation

In this report, we put forward an experimental method to determine the ionic strength of an aqueous solution. To this end, we have developed a theory of ionic strength I expressed in terms of the retention ratios in field-flow fractionation (FFF) as I^1/2=κ(1-R)/(1-R_o)-ε^-1/2. Here R is a measured retention ratio using an FFF technique, for instance, sedimentation FFF (SdFFF), and R_o is the sterically-corrected standard retention ratio as given by the standard retention theory (SRT) for a latex particle system of diameter d. For a standard latex system with known d (or R_o) and I, we can construct a linear calibration of I^1/2 against (1-R)/(1-R_o). Therefore, if we measure the retention ratio R of a carrier liquid of which ionic strength is of interest, then we will be able to estimate the ionic strength from the calibration curve thus built. In this paper, we have demonstrated the relation of I^1/2with respect to (1-R)/(1-R_o) for the polystyrene latex systems of which information on R, R_o, and I is available from Ref. [1].

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.

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.

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.

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.

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.

Biomolecular Condensates: Sequence Determinants of Phase Separation, Microstructural Organization, Enzymatic Activity, and Material Properties

This perspective article highlights recent progress and emerging challenges in understanding the formation and function of membraneless organelles (MLOs). A long-term goal in the MLO field is to identify the sequence-encoded rules that dictate the formation of compositionally controlled biomolecular condensates, which cells utilize to perform a wide variety of functions. The molecular organization of the different components within a condensate can vary significantly, ranging from a homogeneous mixture to core-shell droplet structures. We provide many examples to highlight the richness of the observed behavior and potential research directions for improving our mechanistic understanding. The tunable environment within condensates can, in principle, alter enzymatic activity significantly. We examine recent examples where this was demonstrated, including applications in synthetic biology. An important question about MLOs is the role of liquid-like material properties in biological function. We discuss the need for improved quantitative characterization tools and the development of sequence-structure-dynamics relationships.

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.

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.

Enhancer Features that Drive Formation of Transcriptional Condensates

Enhancers are DNA elements that are bound by transcription factors (TFs), which recruit coactivators and the transcriptional machinery to genes. Phase-separated condensates of TFs and coactivators have been implicated in assembling the transcription machinery at particular enhancers, yet the role of DNA sequence in this process has not been explored. We show that DNA sequences encoding TF binding site number, density, and affinity above sharply defined thresholds drive condensation of TFs and coactivators. A combination of specific structured (TF-DNA) and weak multivalent (TF-coactivator) interactions allows for condensates to form at particular genomic loci determined by the DNA sequence and the complement of expressed TFs. DNA features found to drive condensation promote enhancer activity and transcription in cells. Our study provides a framework to understand how the genome can scaffold transcriptional condensates at specific loci and how the universal phenomenon of phase separation might regulate this process.

Networks of electrostatic and hydrophobic interactions modulate the complex folding free energy surface of a designed βα protein

The successful de novo design of proteins can provide insights into the physical chemical basis of stability, the role of evolution in constraining amino acid sequences, and the production of customizable platforms for engineering applications. Previous guanidine hydrochloride (GdnHCl; an ionic denaturant) experiments of a designed, naturally occurring βα fold, Di-III_14, revealed a cooperative, two-state unfolding transition and a modest stability. Continuous-flow mixing experiments in our laboratory revealed a simple two-state reaction in the microsecond to millisecond time range and consistent with the thermodynamic results. In striking contrast, the protein remains folded up to 9.25 M in urea, a neutral denaturant, and hydrogen exchange (HDX) NMR analysis in water revealed the presence of numerous high-energy states that interconvert on a time scale greater than seconds. The complex protection pattern for HDX corresponds closely with a pair of electrostatic networks on the surface and an extensive network of hydrophobic side chains in the interior of the protein. Mutational analysis showed that electrostatic and hydrophobic networks contribute to the resistance to urea denaturation for the WT protein; remarkably, single charge reversals on the protein surface restore the expected urea sensitivity. The roughness of the energy surface reflects the densely packed hydrophobic core; the removal of only two methyl groups eliminates the high-energy states and creates a smooth surface. The design of a very stable βα fold containing electrostatic and hydrophobic networks has created a complex energy surface rarely observed in natural proteins.