Temperature-dependent solvation modulates the dimensions of disordered proteins

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.

The disordered PCI-binding human proteins CSNAP and DSS1 have diverged in structure and function

Intrinsically disordered proteins (IDPs) regularly constitute components of larger protein assemblies contributing to architectural stability. Two small, highly acidic IDPs have been linked to the so-called PCI complexes carrying PCI-domain subunits, including the proteasome lid and the COP9 signalosome. These two IDPs, DSS1 and CSNAP, have been proposed to have similar structural propensities and functions, but they display differences in their interactions and interactome sizes. Here we characterized the structural properties of human DSS1 and CSNAP at the residue level using NMR spectroscopy and probed their propensities to bind ubiquitin. We find that distinct structural features present in DSS1 are completely absent in CSNAP, and vice versa, with lack of relevant ubiquitin binding to CSNAP, suggesting the two proteins to have diverged in both structure and function. Our work additionally highlights that different local features of seemingly similar IDPs, even subtle sequence variance, may endow them with different functional traits. Such traits may underlie their potential to engage in multiple interactions thereby impacting their interactome sizes.

Protein unfolded states populated at high and ambient pressure are similarly compact

The relationship between the dimensions of pressure-unfolded states of proteins compared with those at ambient pressure is controversial; resolving this issue is related directly to the mechanisms of pressure denaturation. Moreover, a significant pressure dependence of the compactness of unfolded states would complicate the interpretation of folding parameters from pressure perturbation and make comparison to those obtained using alternative perturbation approaches difficult. Here, we determined the compactness of the pressure-unfolded state of a small, cooperatively folding model protein, CTL9-I98A, as a function of temperature. This protein undergoes both thermal unfolding and cold denaturation, and the temperature dependence of the compactness at atmospheric pressure is known. High-pressure small angle x-ray scattering studies, yielding the radius of gyration and high-pressure diffusion ordered spectroscopy NMR experiments, yielding the hydrodynamic radius were carried out as a function of temperature at 250 MPa, a pressure at which the protein is unfolded. The radius of gyration values obtained at any given temperature at 250 MPa were similar to those reported previously at ambient pressure, and the trends with temperature are similar as well, although the pressure-unfolded state appears to undergo more pronounced expansion at high temperature than the unfolded state at atmospheric pressure. At 250 MPa, the compaction of the unfolded chain was maximal between 25 and 30°C, and the chain expanded upon both cooling and heating. These results reveal that the pressure-unfolded state of this protein is very similar to that observed at ambient pressure, demonstrating that pressure perturbation represents a powerful approach for observing the unfolded states of proteins under otherwise near-native conditions.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of KBFF20

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

SARS-CoV-2 NSP1 C-terminal (residues 131-180) is an intrinsically disordered region in isolation

The NSP1- C terminal structure in complex with ribosome using cryo-EM is available now, and the N-terminal region structure in isolation is also deciphered in literature. However, as a reductionist approach, the conformation of NSP1- C terminal region (NSP1-CTR; amino acids 131-180) has not been studied in isolation. We found that NSP1-CTR conformation is disordered in an aqueous solution. Further, we examined the conformational propensity towards alpha-helical structure using trifluoroethanol, we observed induction of helical structure conformation using CD spectroscopy. Additionally, in SDS, NSP1-CTR shows a conformational change from disordered to ordered, possibly gaining alpha-helix in part. But in the presence of neutral lipid DOPC, a slight change in conformation is observed, which implies the possible role of hydrophobic interaction and electrostatic interaction on the conformational changes of NSP1. Fluorescence-based studies have shown a blue shift and fluorescence quenching in the presence of SDS, TFE, and lipid vesicles. In agreement with these results, fluorescence lifetime and fluorescence anisotropy decay suggest a change in conformational dynamics. The zeta potential studies further validated that the conformational dynamics are primarily because of hydrophobic interaction. These experimental studies were complemented through Molecular Dynamics (MD) simulations, which have shown a good correlation and testifies our experiments. We believe that the intrinsically disordered nature of the NSP1-CTR will have implications for enhanced molecular recognition feature properties of this IDR, which may add disorder to order transition and disorder-based binding promiscuity with its interacting proteins.

Temperature Dependence of Internal Friction of Peptides

Internal friction is a valuable concept to describe the kinetics of proteins. As is well known, internal friction can be modulated by solvent features (such as viscosity). How can internal friction be affected by environmental temperature? The answer to this question is not evident. In the present work, we approach this problem with simulations on two model peptides. The thermodynamics and relaxation kinetics are characterized through long molecular dynamics simulations, with the viscosity modulated by varying the mass of solvent molecules. Based on the extrapolation to zero viscosity together with scaling of the relaxation time scales, we discover that internal friction is almost invariant at various temperatures. Controlled simulations further support the idea that internal friction is independent of environmental temperature. Comparisons between the two model peptides help us to understand the diverse phenomena in experiments.

Liquid-Liquid Phase Separation of Tau Protein Is Encoded at the Monomeric Level

Liquid-liquid phase separation (LLPS) is involved in both physiological and pathological processes. The intrinsically disordered protein Tau and its K18 construct can undergo LLPS in a distinct temperature-dependent manner, and the LLPS of Tau protein can initiate Tau aggregation. However, the underlying mechanism driving Tau LLPS remains largely elusive. To understand the temperature-dependent LLPS behavior of Tau at the monomeric level, we explored the conformational ensemble of Tau at different temperatures by performing all-atom replica-exchange molecular dynamic simulation on K18 monomer with an accumulated simulation time of 26.4 μs. Our simulation demonstrates that the compactness, β-structure propensity, and intramolecular interaction of K18 monomer exhibit nonlinear temperature-dependent behavior. ²⁹⁵DNIKHV³⁰⁰/³²⁶GNIHHK³³¹/³³⁷VEVKSE³⁴² make significant contributions to the temperature dependence of the β propensity of K18 monomer, while the two fibril-nucleating cores display relatively high β propensity at all temperatures. At a specific temperature, K18 monomer adopts the most collapsed state with exposed sites for both persistent and transient interactions. Given that more collapsed polypeptide chains were reported to be more prone to phase separate, our results suggest that K18 monomer inherently possesses conformational characteristics favoring LLPS. Our simulation predicts the importance of ²⁹⁵DNIKHV³⁰⁰/³²⁶GNIHHK³³¹/³³⁷VEVKSE³⁴² to the temperature-dependent conformational properties of K18, which is corroborated by CD spectra, turbidity assays, and DIC microscopy. Taken together, we offer a computational and experimental approach to comprehend the structural basis for LLPS by amyloidal building blocks.

Stretching of Bombyx mori Silk Protein in Flow

The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the ‘registration’ of aligned protein chains using intermolecularly interacting ‘sticky’ patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein–chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

The role of water in the primary nucleation of protein amyloid aggregation

The understanding of the complex conformational landscape of amyloid aggregation and its modulation by relevant physicochemical and cellular factors is a prerequisite for elucidating some of the molecular basis of pathology in amyloid related diseases, and for developing and evaluating effective disease-specific therapeutics to reduce or eliminate the underlying sources of toxicity in these diseases. Interactions of proteins with solvating water have been long considered to be fundamental in mediating their function and folding; however, the relevance of water in the process of protein amyloid aggregation has been largely overlooked. Here, we provide a perspective on the role water plays in triggering primary amyloid nucleation of intrinsically disordered proteins (IDPs) based on recent experimental evidences. The initiation of amyloid aggregation likely results from the synergistic effect between both protein intermolecular interactions and the properties of the water hydration layer of the protein surface. While the self-assembly of both hydrophobic and hydrophilic IDPs would be thermodynamically favoured due to large water entropy contributions, large desolvation energy barriers are expected, particularly for the nucleation of hydrophilic IDPs. Under highly hydrating conditions, primary nucleation is slow, being facilitated by the presence of nucleation-active surfaces (heterogeneous nucleation). Under conditions of poor water activity, such as those found in the interior of protein droplets generated by liquid-liquid phase separation, however, the desolvation energy barrier is significantly reduced, and nucleation can occur very rapidly in the bulk of the solution (homogeneous nucleation), giving rise to structurally distinct amyloid polymorphs. Water, therefore, plays a key role in modulating the transition free energy of amyloid nucleation, thus governing the initiation of the process, and dictating the type of preferred primary nucleation and the type of amyloid polymorph generated, which could vary depending on the particular microenvironment that the protein molecules encounter in the cell.

Structural and Energetic Characterization of the Denatured State from the Perspectives of Peptides, the Coil Library, and Intrinsically Disordered Proteins

The α and polyproline II (PPII) basins are the two most populated regions of the Ramachandran map when constructed from the protein coil library, a widely used denatured state model built from the segments of irregular structure found in the Protein Data Bank. This indicates the α and PPII conformations are dominant components of the ensembles of denatured structures that exist in solution for biological proteins, an observation supported in part by structural studies of short, and thus unfolded, peptides. Although intrinsic conformational propensities have been determined experimentally for the common amino acids in short peptides, and estimated from surveys of the protein coil library, the ability of these intrinsic conformational propensities to quantitatively reproduce structural behavior in intrinsically disordered proteins (IDPs), an increasingly important class of proteins in cell function, has thus far proven elusive to establish. Recently, we demonstrated that the sequence dependence of the mean hydrodynamic size of IDPs in water and the impact of heat on the coil dimensions, provide access to both the sequence dependence and thermodynamic energies that are associated with biases for the α and PPII backbone conformations. Here, we compare results from peptide-based studies of intrinsic conformational propensities and surveys of the protein coil library to those of the sequence-based analysis of heat effects on IDP hydrodynamic size, showing that a common structural and thermodynamic description of the protein denatured state is obtained.

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.

Conformational flexibility and oligomerization of BRCA2 regions induced by RAD51 interaction

BRCA2 is a key breast cancer associated protein that is predicted to have interspersed regions of intrinsic disorder. Intrinsic disorder coupled with large size likely allows BRCA2 to sample a broad range of conformational space. We expect that the resulting dynamic arrangements of BRCA2 domains are a functionally important aspect of its role in homologous recombination DNA repair. To determine the architectural organization and the associated conformational landscape of BRCA2, we used scanning force microscopy based single molecule analyses to map the flexible regions of the protein and characterize which regions influence oligomerization. We show that the N- and the C-terminal regions are the main flexible regions. Both of these regions also influence BRCA2 oligomerization and interaction with RAD51. In the central Brc repeat region, Brc 1–4 and Brc 5–8 contribute synergistically to BRCA2 interaction with RAD51. We also analysed several single amino acid changes that are potentially clinically relevant and found one, the variant of F1524V, which disrupts key interactions and alters the conformational landscape of the protein. We describe the overall conformation spectrum of BRCA2, which suggests that dynamic structural transitions are key features of its biological function, maintaining genomic stability.

Membrane Chemistry Tunes the Structure of a Peptide Transporter

Membrane proteins require lipid bilayers for function. While lipid compositions reach enormous complexities, high-resolution structures are usually obtained in artificial detergents. To understand whether and how lipids guide membrane protein function, we use single-molecule FRET to probe the dynamics of DtpA, a member of the proton-coupled oligopeptide transporter (POT) family, in various lipid environments. We show that detergents trap DtpA in a dynamic ensemble with cytoplasmic opening. Only reconstitutions in more native environments restore cooperativity, allowing an opening to the extracellular side and a sampling of all relevant states. Bilayer compositions tune the abundance of these states. A novel state with an extreme cytoplasmic opening is accessible in bilayers with anionic head groups. Hence, chemical diversity of membranes translates into structural diversity, with the current POT structures only sampling a portion of the full structural space.

Influence of electrostatic forces on the association kinetics and conformational ensemble of an intrinsically disordered protein

Recent work has revealed that the association of a disordered region of a protein with a folded binding partner can occur as rapidly as association between two folded proteins. This is the case for the phosphatase calcineurin (CaN) and its association with its activator calmodulin. Calmodulin binds to the intrinsically disordered regulatory domain of CaN. Previous studies have shown that electrostatic steering can accelerate the binding of folded proteins with disordered ligands. Given that electrostatic forces are strong determinants of disordered protein ensembles, the relationship between electrostatics, conformational ensembles, and quaternary interactions is unclear. Here, we employ experimental approaches to explore the impact of electrostatic interactions on the association of calmodulin with the disordered regulatory region of CaN. We find that estimated association rate constants of calmodulin with our chosen calmodulin-substrates are within the diffusion-limited regime. The association rates are dependent on the ionic strength, indicating that favorable electrostatic forces increase the rate of association. Further, we show that charged amino acids outside the calmodulin-binding site modulate the binding rate. Conformational ensembles obtained from computer simulations suggest that electrostatic interactions within the regulatory domain might bias the conformational ensemble such that the calmodulin binding region is readily accessible. Given the prevalence of charged residues in disordered protein chains, our findings are likely relevant to many protein-protein interactions.

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

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs, also known as stickers, is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter, such as temperature, that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single-chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low-complexity domains. We also leverage theories to compute sequence-specific percolation lines and thereby provide a thermodynamic framework for hardening transitions that have been observed for many biomolecular condensates.

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.

Silk Protein Solution: A Natural Example of Sticky Reptation

Silk is one of the most intriguing examples of biomolecular self-assembly, yet little is understood of molecular mechanisms behind the flow behavior generating these complex high-performance fibers. This work applies the polymer physics of entangled solution rheology to present a first microphysical understanding of silk in the linear viscoelastic regime. We show that silk solutions can be approximated as reptating polymers with "sticky" calcium bridges whose strength can be controlled through the potassium concentration. This approach provides a new window into critical microstructural parameters, in particular identifying the mechanism by which potassium and calcium ions are recruited as a powerful viscosity control in silk. Our model constitutes a viable starting point to understand not only the "flow-induced self-assembly" of silk fibers but also a broader range of phenomena in the emergent field of material-focused synthetic biology.

Emerging consensus on the collapse of unfolded and intrinsically disordered proteins in water

Establishing the degree of collapse of unfolded or disordered proteins is a fundamental problem in biophysics, because of its relation to protein folding and to the function of intrinsically disordered proteins. However, until recently, different experiments gave qualitatively different results on collapse and there were large discrepancies between experiments and all-atom simulations. New methodology introduced in the past three years has helped to resolve the differences between experiments, and improvements in simulations have closed the gap between experiment and simulation. These advances have led to an emerging consensus on the collapse of disordered proteins in water.

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.

Impact of Heat on Coil Hydrodynamic Size Yields the Energetics of Denatured State Conformational Bias

Conformational equilibria in the protein denatured state have key roles regulating folding, stability, and function. The extent of conformational bias in the protein denatured state under folding conditions, however, has thus far proven elusive to quantify, particularly with regard to its sequence dependence and energetic character. To better understand the structural preferences of the denatured state, we analyzed both the sequence dependence to the mean hydrodynamic size of disordered proteins in water and the impact of heat on the coil dimensions, showing that the sequence dependence and thermodynamic energies associated with intrinsic biases for the α and polyproline II (PPII) backbone conformations can be obtained. Experiments that evaluate how the hydrodynamic size changes with compositional changes in the protein reveal amino acid specific preferences for PPII that are in good quantitative agreement with calorimetry-measured values from unfolded peptides and those inferred by survey of the protein coil library. At temperatures above 25 °C, the denatured state follows the predictions of a PPII-dominant ensemble. Heat effects on coil hydrodynamic size indicate the α bias is comparable to the PPII bias at cold temperatures. Though historically thought to give poor resolution to structural details, the hydrodynamic size of the unfolded state is found to be an effective reporter on the extent of the biases for the α and PPII backbone conformations.

Controlling Structure and Dimensions of a Disordered Protein via Mutations

The dimensions of intrinsically disordered proteins (IDPs) are sensitive to small energetic-entropic differences between intramolecular and protein–solvent interactions. This is commonly observed on modulating solvent composition and temperature. However, the inherently heterogeneous conformational landscape of IDPs is also expected to be influenced by mutations that can (de)stabilize pockets of local and even global structure, native and non-native, and hence the average dimensions. Here, we show experimental evidence for the remarkably tunable landscape of IDPs by employing the DNA-binding domain of CytR, a high-sequence-complexity IDP, as a model system. CytR exhibits a range of structure and compactness upon introducing specific mutations that modulate microscopic terms, including main-chain entropy, hydrophobicity, and electrostatics. The degree of secondary structure, as monitored by far-UV circular dichroism (CD), is strongly correlated to average ensemble dimensions for 14 different mutants of CytR and is consistent with the Uversky–Fink relation. Our experiments highlight how average ensemble dimensions can be controlled via mutations even in the disordered regime, the prevalence of non-native interactions and provide testable controls for molecular simulations.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Protein plasticity driven by disorder and collapse governs the heterogeneous binding of CytR to DNA

The amplitude of thermodynamic fluctuations in biological macromolecules determines their conformational behavior, dimensions, nature of phase transitions and effectively their specificity and affinity, thus contributing to fine-tuned molecular recognition. Unique among large-scale conformational changes in proteins are temperature-induced collapse transitions in intrinsically disordered proteins (IDPs). Here, we show that CytR DNA-binding domain, an IDP that folds on binding DNA, undergoes a coil-to-globule transition with temperature in the absence of DNA while exhibiting energetically decoupled local and global structural rearrangements, and maximal thermodynamic fluctuations at the optimal bacterial growth temperature. The collapse is shown to be a continuous transition through a combination of statistical-mechanical modeling and all-atom implicit solvent simulations. Surprisingly, CytR binds single-site cognate DNA with negative cooperativity, described by Hill coefficients less than one, resulting in a graded binding response. We show that heterogeneity arising from varying binding-competent CytR conformations or orientations at the single-molecular level contributes to negative binding cooperativity at the level of bulk measurements due to the conflicting requirements of collapse transition, large fluctuations and folding-upon-binding. Our work reports strong evidence for functionally driven thermodynamic fluctuations in determining the extent of collapse and disorder with implications in protein search efficiency of target DNA sites and regulation.

Temperature-Controlled Liquid-Liquid Phase Separation of Disordered Proteins

The liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) is a commonly observed phenomenon within the cell, and such condensates are also highly attractive for applications in biomaterials and drug delivery. A better understanding of the sequence-dependent thermoresponsive behavior is of immense interest as it will aid in the design of protein sequences with desirable properties and in the understanding of cellular response to heat stress. In this work, we use a transferable coarse-grained model to directly probe the sequence-dependent thermoresponsive phase behavior of IDPs. To achieve this goal, we develop a unique knowledge-based amino acid potential that accounts for the temperature-dependent effects on solvent-mediated interactions for different types of amino acids. Remarkably, we are able to distinguish between more than 35 IDPs with upper or lower critical solution temperatures at experimental conditions, thus providing direct evidence that incorporating the temperature-dependent solvent-mediated interactions to IDP assemblies can capture the difference in the shape of the resulting phase diagrams. Given the success of the model in predicting experimental behavior, we use it as a high-throughput screening framework to scan through millions of disordered sequences to characterize the composition dependence of protein phase separation.

Extrinsic conditions influence the self-association and structure of IF1, the regulatory protein of mitochondrial ATP synthase

The endogenous inhibitor of ATP synthase in mitochondria, called IF1, conserves cellular energy when the proton-motive force collapses by inhibiting ATP hydrolysis. Around neutrality, the 84-amino-acid bovine IF1 is thought to self-assemble into active dimers and, under alkaline conditions, into inactive tetramers and higher oligomers. Dimerization is mediated by formation of an antiparallel α-helical coiled-coil involving residues 44-84. The inhibitory region of each monomer from residues 1-46 is largely α-helical in crystals, but disordered in solution. The formation of the inhibited enzyme complex requires the hydrolysis of two ATP molecules, and in the complex the disordered region from residues 8-13 is extended and is followed by an α-helix from residues 14-18 and a longer α-helix from residue 21, which continues unbroken into the coiled-coil region. From residues 21-46, the long α-helix binds to other α-helices in the C-terminal region of predominantly one of the β-subunits in the most closed of the three catalytic interfaces. The definition of the factors that influence the self-association of IF1 is a key to understanding the regulation of its inhibitory properties. Therefore, we investigated the influence of pH and salt-types on the self-association of bovine IF1 and the folding of its unfolded region. We identified the equilibrium between dimers and tetramers as a potential central factor in the in vivo modulation of the inhibitory activity and suggest that the intrinsically disordered region makes its inhibitory potency exquisitely sensitive and responsive to physiological changes that influence the capability of mitochondria to make ATP.

Engineering Order and Cooperativity in a Disordered Protein

Structural disorder in proteins arises from a complex interplay between weak hydrophobicity and unfavorable electrostatic interactions. The extent to which the hydrophobic effect contributes to the unique and compact native state of proteins is, however, confounded by large compensation between multiple entropic and energetic terms. Here we show that protein structural order and cooperativity arise as emergent properties upon hydrophobic substitutions in a disordered system with non-intuitive effects on folding and function. Aided by sequence-structure analysis, equilibrium, and kinetic spectroscopic studies, we engineer two hydrophobic mutations in the disordered DNA-binding domain of CytR that act synergistically, but not in isolation, to promote structure, compactness, and stability. The double mutant, with properties of a fully ordered domain, exhibits weak cooperativity with a complex and rugged conformational landscape. The mutant, however, binds cognate DNA with an affinity only marginally higher than that of the wild type, though nontrivial differences are observed in the binding to noncognate DNA. Our work provides direct experimental evidence of the dominant role of non-additive hydrophobic effects in shaping the molecular evolution of order in disordered proteins and vice versa, which could be generalized to even folded proteins with implications for protein design and functional manipulation.

Evolution of All-Atom Protein Force Fields to Improve Local and Global Properties

Experimental studies on intrinsically disordered and unfolded proteins have shown that in isolation they typically have low populations of secondary structure and exhibit distance scalings suggesting that they are at near-theta-solvent conditions. Until recently, however, all-atom force fields failed to reproduce these fundamental properties of intrinsically disordered proteins (IDPs). Recent improvements by refining against ensemble-averaged experimental observables for polypeptides in aqueous solution have addressed deficiencies including secondary structure bias, global conformational properties, and thermodynamic parameters of biophysical reactions such as folding and collapse. To date, studies utilizing these improved all-atom force fields have mostly been limited to a small set of unfolded or disordered proteins. Here, we present data generated for a diverse library of unfolded or disordered proteins using three progressively improved generations of Amber03 force fields, and we explore how global and local properties are affected by each successive change in the force field. We find that the most recent force field refinements significantly improve the agreement of the global properties such as radii of gyration and end-to-end distances with experimental estimates. However, these global properties are largely independent of the local secondary structure propensity. This result stresses the need to validate force fields with reference to a combination of experimental data providing information about both local and global structure formation.

A binding cooperativity switch driven by synergistic structural swelling of an osmo-regulatory protein pair

Uropathogenic E. coli experience a wide range of osmolarity conditions before and after successful infection. Stress-responsive regulatory proteins in bacteria, particularly proteins of the Hha family and H-NS, a transcription repressor, sense such osmolarity changes and regulate transcription through unknown mechanisms. Here we use an array of experimental probes complemented by molecular simulations to show that Cnu, a member of the Hha protein family, acts as an exquisite molecular sensor of solvent ionic strength. The osmosensory behavior of Cnu involves a fine-tuned modulation of disorder in the fourth helix and the three-dimensional structure in a graded manner. Order-disorder transitions in H-NS act synergistically with molecular swelling of Cnu contributing to a salt-driven switch in binding cooperativity. Thus, sensitivity to ambient conditions can be imprinted at the molecular level by tuning not just the degree of order in the protein conformational ensemble but also through population redistributions of higher-order molecular complexes.

The bacterial protein Cnu together with the transcription repressor H-NS regulate expression of virulence factors in an osmo-sensitive manner. Here authors show that the structure of Cnu swells with decreasing ionic strength driving the oligomerization of H-NS and regulating osmo-sensory response.

Designing Electrostatic Interactions via Polyelectrolyte Monomer Sequence

Charged polymers are ubiquitous in biological systems because electrostatic interactions can drive complicated structure formation and respond to environmental parameters such as ionic strength and pH. In these systems, function emerges from sophisticated molecular design; for example, intrinsically disordered proteins leverage specific sequences of monomeric charges to control the formation and function of intracellular compartments known as membraneless organelles. The role of a charged monomer sequence in dictating the strength of electrostatic interactions remains poorly understood despite extensive evidence that sequence is a powerful tool biology uses to tune soft materials. In this article, we use a combination of theory, experiment, and simulation to establish the physical principles governing sequence-driven control of electrostatic interactions. We predict how arbitrary sequences of charge give rise to drastic changes in electrostatic interactions and correspondingly phase behavior. We generalize a transfer matrix formalism that describes a phase separation phenomenon known as "complex coacervation" and provide a theoretical framework to predict the phase behavior of charge sequences. This work thus provides insights into both how charge sequence is used in biology and how it could be used to engineer properties of synthetic polymer systems.

Single Amino Acid Substitutions in Stickers, but Not Spacers, Substantially Alter UBQLN2 Phase Transitions and Dense Phase Material Properties

UBQLN2 450-624 oligomerizes and undergoes temperature-responsive liquid-liquid phase transitions following a closed-loop temperature-concentration phase diagram. We recently showed that disease-linked mutations to UBQLN2 450-624 impart highly varying effects to its phase behavior, ranging from little change to significant decrease of saturation concentration and formation of gels and aggregates. However, how single mutations lead to these properties is unknown. Here, we use UBQLN2 450-624 as a model system to study the sequence determinants of phase separation. We hypothesized that UBQLN2 450-624 regions previously identified to promote its oligomerization are the "stickers" that drive interchain interactions and phase separation. We systematically investigated how phase behavior is affected by all 19 possible single amino acid substitutions at three sticker and two "spacer" (sequences separating stickers) positions. Overall, substitutions to stickers, but not spacers, substantially altered the shape of the phase diagram. Within the sticker regions, increasing hydrophobicity decreased saturation concentrations at low temperatures and enhanced oligomerization propensity and viscoelasticity of the dense phase. Conversely, substitutions to acidic residues at all positions greatly increased saturation concentrations. Our data demonstrate that single amino acid substitutions follow a molecular code to tune phase transition behavior of biopolymers.

Recent Advances in Computational Protocols Addressing Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDP) are abundant in the human genome and have recently emerged as major therapeutic targets for various diseases. Unlike traditional proteins that adopt a definitive structure, IDPs in free solution are disordered and exist as an ensemble of conformations. This enables the IDPs to signal through multiple signaling pathways and serve as scaffolds for multi-protein complexes. The challenge in studying IDPs experimentally stems from their disordered nature. Nuclear magnetic resonance (NMR), circular dichroism, small angle X-ray scattering, and single molecule Förster resonance energy transfer (FRET) can give the local structural information and overall dimension of IDPs, but seldom provide a unified picture of the whole protein. To understand the conformational dynamics of IDPs and how their structural ensembles recognize multiple binding partners and small molecule inhibitors, knowledge-based and physics-based sampling techniques are utilized in-silico, guided by experimental structural data. However, efficient sampling of the IDP conformational ensemble requires traversing the numerous degrees of freedom in the IDP energy landscape, as well as force-fields that accurately model the protein and solvent interactions. In this review, we have provided an overview of the current state of computational methods for studying IDP structure and dynamics and discussed the major challenges faced in this field.

General Purpose Water Model Can Improve Atomistic Simulations of Intrinsically Disordered Proteins

Unconstrained atomistic simulations of intrinsically disordered proteins and peptides (IDP) remain a challenge: widely used, "general purpose" water models tend to favor overly compact structures relative to experiment. Here we have performed a total of 93 μs of unrestrained MD simulations to explore, in the context of IDPs, a recently developed "general-purpose" 4-point rigid water model OPC, which describes liquid state of water close to experiment. We demonstrate that OPC, together with a popular AMBER force field ff99SB, offers a noticeable improvement over TIP3P in producing more realistic structural ensembles of three common IDPs benchmarks: 55-residue apo N-terminal zinc-binding domain of HIV-1 integrase ("protein IN"), amyloid β-peptide (Aβ₄₂) (residues 1-42), and 26-reside H4 histone tail. As a negative control, computed folding profile of a regular globular miniprotein (CLN025) in OPC water is in appreciably better agreement with experiment than that obtained in TIP3P, which tends to overstabilize the compact native state relative to the extended conformations. We employed Aβ₄₂ peptide to investigate the possible influence of the solvent box size on simulation outcomes. We advocate a cautious approach for simulations of IDPs: we suggest that the solvent box size should be at least four times the radius of gyration of the random coil corresponding to the IDP. The computed free energy landscape of protein IN in OPC resembles a shallow "tub" - conformations with substantially different degrees of compactness that are within 2 k_B T of each other. Conformations with very different secondary structure content coexist within 1 k_B T of the global free energy minimum. States with higher free energy tend to have less secondary structure. Computed low helical content of the protein has virtually no correlation with its degree of compactness, which calls into question the possibility of using the helicity as a metric for assessing performance of water models for IDPs, when the helicity is low. Predicted radius of gyration ( R _g) of H4 histone tail in OPC water falls in-between that of a typical globular protein and a fully denatured protein of the same size; the predicted R _g is consistent with two independent predictions. In contrast, H4 tail in TIP3P water is as compact as the corresponding globular protein. The computed free energy landscape of H4 tail in OPC is relatively flat over a significant range of compactness, which, we argue, is consistent with its biological function as facilitator of internucleosome interactions.

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

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.

What Drives 15N Spin Relaxation in Disordered Proteins? Combined NMR/MD Study of the H4 Histone Tail

Backbone (¹⁵N) NMR relaxation is one of the main sources of information on dynamics of disordered proteins. Yet, we do not know very well what drives ¹⁵N relaxation in such systems, i.e., how different forms of motion contribute to the measurable relaxation rates. To address this problem, we have investigated, both experimentally and via molecular dynamics simulations, the dynamics of a 26-residue peptide imitating the N-terminal portion of the histone protein H4. One part of the peptide was found to be fully flexible, whereas the other part features some transient structure (a hairpin stabilized by hydrogen bonds). The following motional modes proved relevant for ¹⁵N relaxation. 1) Sub-picosecond librations attenuate relaxation rates according to S² ∼0.85-0.90. 2) Axial peptide-plane fluctuations along a stretch of the peptide chain contribute to relaxation-active dynamics on a fast timescale (from tens to hundreds of picoseconds). 3) φ/ψ backbone jumps contribute to relaxation-active dynamics on both fast (from tens to hundreds of picoseconds) and slow (from hundreds of picoseconds to a nanosecond) timescales. The major contribution is from polyproline II (PPII) ↔ β transitions in the Ramachandran space; in the case of glycine residues, the major contribution is from PPII ↔ (β) ↔ rPPII transitions, in which rPPII is the mirror-image (right-handed) version of the PPII geometry, whereas β geometry plays the role of an intermediate state. 4) Reorientational motion of certain (sufficiently long-lived) elements of transient structure, i.e., rotational tumbling, contributes to slow relaxation-active dynamics on ∼1-ns timescale (however, it is difficult to isolate this contribution). In conclusion, recent advances in the area of force-field development have made it possible to obtain viable Molecular Dynamics models of protein disorder. After careful validation against the experimental relaxation data, these models can provide a valuable insight into mechanistic origins of spin relaxation in disordered peptides and proteins.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.

Characterization of Dynamic IDP Complexes by NMR Spectroscopy

NMR spectroscopy has proven to be a key method for studying intrinsically disordered proteins (IDPs). Nonetheless, traditional NMR methods developed for solving structures of ordered protein complexes are insufficient for the full characterization of dynamic IDP complexes, where the energy landscape is broader and more rugged. Furthermore, due to their high sensitivity to environmental changes, NMR studies of IDP complexes must be conducted with extra care and the observed NMR parameters thoroughly evaluated to enable disentanglement of binding events from ensemble distribution changes. In this chapter, written for the non-NMR expert, we start out by outlining sample preparation for IDP complexes, guide through the recording and evaluation of diagnostic ¹H,¹⁵N-HSQC spectra, and delineate more sophisticated NMR strategies to follow for the particular type of complex. The most relevant experiments are then described in terms of aims, needs, pitfalls, analysis, and expected outcomes, with references to recent examples.

Helical Polyampholyte Sequences Have Unique Thermodynamic Properties

Helices are the most common structural pattern observed in structured proteins. Polypeptide sequences that form helices in isolation have been identified and extensively studied. These are generally rich in alanine, the amino acid with strongest helical propensity. Insertion of charged or polar amino acids has been shown to be necessary to make alanine-rich peptides soluble and sometimes even increase the helicity of the peptides. More recently sequences that contain mostly charged residues (E-R/K rich) have been found in naturally occurring proteins that are highly helical, soluble, and extended regardless their length. Artificial sequences composed mostly or exclusively of charged amino acids have been designed that are also highly helical, depending on the specific pattern of oppositely charged residues. Here we explore the thermodynamic properties of a number of 16-residue long peptides with varying helical propensity by performing equilibrium simulations over a broad range of temperatures. We observe quantitative differences in the peptides' helical propensities that can be related to qualitative differences in the free energy landscape, depending on the ampholytic patterns in the sequence. The results provide hints on how the specific physical properties of naturally occurring long sequences with similar patterns of charged residues may relate to their biological function.

Temperature-induced collapse of a disordered peptide observed by three sampling methods in molecular dynamics simulations

The conformational ensembles of a disordered peptide, polyglutamine Q15, over a wide temperature range were sampled using multiple replicates of conventional molecular dynamics (cMD) simulations as well as two enhanced sampling methods, temperature replica exchange (TREMD) and replica exchange with solute tempering (REST). The radius of gyration, asphericity, secondary structure, and hydrogen bonding patterns were used for the comparison of the sampling methods. Overall, the three sampling methods generated similar conformational ensembles, with progressive collapse at higher temperatures. Although accumulating the longest simulation time (90 μs), cMD at room temperature missed a small subspace that was sampled by both TREMD and REST. This subspace was high in α-helical content and separated from the main conformational space by an energy barrier. REST used less simulation time than TREMD (36 μs versus 42 μs), and this gap is expected to widen significantly for larger disordered proteins. We conclude that REST is the method of choice for conformational sampling of intrinsically disordered proteins.