Predictions from an Ising-like Statistical Mechanical Model on the Dynamic and Thermodynamic Effects of Protein Surface Electrostatics

Accurate prediction of protein folding mechanisms by simple structure-based statistical mechanical models

Recent breakthroughs in highly accurate protein structure prediction using deep neural networks have made considerable progress in solving the structure prediction component of the 'protein folding problem'. However, predicting detailed mechanisms of how proteins fold into specific native structures remains challenging, especially for multidomain proteins constituting most of the proteomes. Here, we develop a simple structure-based statistical mechanical model that introduces nonlocal interactions driving the folding of multidomain proteins. Our model successfully predicts protein folding processes consistent with experiments, without the limitations of protein size and shape. Furthermore, slight modifications of the model allow prediction of disulfide-oxidative and disulfide-intact protein folding. These predictions depict details of the folding processes beyond reproducing experimental results and provide a rationale for the folding mechanisms. Thus, our physics-based models enable accurate prediction of protein folding mechanisms with low computational complexity, paving the way for solving the folding process component of the 'protein folding problem'.

Thermodynamic architecture and conformational plasticity of GPCRs

G-protein-coupled receptors (GPCRs) are ubiquitous integral membrane proteins involved in diverse cellular signaling processes. Here, we carry out a large-scale ensemble thermodynamic study of 45 ligand-free GPCRs employing a structure-based statistical mechanical framework. We find that multiple partially structured states co-exist in the GPCR native ensemble, with the TM helices 1, 6 and 7 displaying varied folding status, and shaping the conformational landscape. Strongly coupled residues are anisotropically distributed, accounting for only 13% of the residues, illustrating that a large number of residues are inherently dynamic. Active-state GPCRs are characterized by reduced conformational heterogeneity with altered coupling-patterns distributed throughout the structural scaffold. In silico alanine-scanning mutagenesis reveals that extra- and intra-cellular faces of GPCRs are coupled thermodynamically, highlighting an exquisite structural specialization and the fluid nature of the intramolecular interaction network. The ensemble-based perturbation methodology presented here lays the foundation for understanding allosteric mechanisms and the effects of disease-causing mutations in GCPRs.

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.

Structure and activity of a thermally stable mutant of Acanthamoeba actophorin

Actophorin, which was recently tested for crystallization under microgravity on the International Space Station, was subjected to mutagenesis to identify a construct with improved biophysical properties that were expected to improve the extent of diffraction. First, 20 mutations, including one C-terminal deletion of three residues, were introduced individually into actophorin, resulting in modest increases in thermal stability of between +0.5°C and +2.2°C. All but two of the stabilizing mutants increased both the rates of severing F-actin filaments and of spontaneous polymerization of pyrenyl G-actin in vitro. When the individual mutations were combined into a single actophorin variant, Acto-2, the overall thermal stability was 22°C higher than that of wild-type actophorin. When an inactivating S2P mutation in Acto-2 was restored, Acto-2/P2S was more stable by 20°C but was notably more active than the wild-type protein. The inactivating S2P mutation reaffirms the importance that Ser2 plays in the F-actin-severing reaction. The crystal structure of Acto-2 was solved to 1.7 Å resolution in a monoclinic space group, a first for actophorin. Surprisingly, despite the increase in thermal stability, the extended β-turn region, which is intimately involved in interactions with F-actin, is disordered in one copy of Acto-2 in the asymmetric unit. These observations emphasize the complex interplay among protein thermal stability, function and dynamics.

Structural-Energetic Basis for Coupling between Equilibrium Fluctuations and Phosphorylation in a Protein Native Ensemble

The functioning of proteins is intimately tied to their fluctuations in the native ensemble. The structural-energetic features that determine fluctuation amplitudes and hence the shape of the underlying landscape, which in turn determine the magnitude of the functional output, are often confounded by multiple variables. Here, we employ the FF1 domain from human p190A RhoGAP protein as a model system to uncover the molecular basis for phosphorylation of a buried tyrosine, which is crucial to the transcriptional activity associated with transcription factor TFII-I. Combining spectroscopy, calorimetry, statistical-mechanical modeling, molecular simulations, and in vitro phosphorylation assays, we show that the FF1 domain samples a diverse array of conformations in its native ensemble, some of which are phosphorylation-competent. Upon eliminating unfavorable charge-charge interactions through a single charge-reversal (K53E) or charge-neutralizing (K53Q) mutation, we observe proportionately lower phosphorylation extents due to the altered structural coupling, damped equilibrium fluctuations, and a more compact native ensemble. We thus establish a conformational selection mechanism for phosphorylation in the FF1 domain with K53 acting as a "gatekeeper", modulating the solvent exposure of the buried tyrosine. Our work demonstrates the role of unfavorable charge-charge interactions in governing functional events through the modulation of native ensemble characteristics, a feature that could be prevalent in ordered protein domains.

Predicting and Simulating Mutational Effects on Protein Folding Kinetics

Mutational perturbations of protein structures, i.e., phi-value analysis, are commonly employed to probe the extent of involvement of a particular residue in the rate-determining step(s) of folding. This generally involves the measurement of folding thermodynamic parameters and kinetic rate constants for the wild-type and mutant proteins. While computational approaches have been reasonably successful in understanding and predicting the effect of mutations on folding thermodynamics, it has been challenging to explore the same on kinetics due to confounding structural, energetic, and dynamic factors. Accordingly, the frequent observation of fractional phi-values (mean of ~0.3) has resisted a precise and consistent interpretation. Here, we describe how to construct, parameterize, and employ a simple one-dimensional free energy surface model that is grounded in the basic tenets of the energy landscape theory to predict and simulate the effect of mutations on folding kinetics. As a proof of principle, we simulate one-dimensional free energy profiles of 806 mutations from 24 different proteins employing just the experimental destabilization as input, reproduce the relative unfolding activation free energies with a correlation of 0.91, and show that the mean phi-value of 0.3 essentially corresponds to the extent of stabilization energy gained at the barrier top while folding.

Combining Ancestral Reconstruction with Folding-Landscape Simulations to Engineer Heterologous Protein Expression

Obligate symbionts typically exhibit high evolutionary rates. Consequently, their proteins may differ considerably from their modern and ancestral homologs in terms of both sequence and properties, thus providing excellent models to study protein evolution. Also, obligate symbionts are challenging to culture in the lab and proteins from uncultured organisms must be produced in heterologous hosts using recombinant DNA technology. Obligate symbionts thus replicate a fundamental scenario of metagenomics studies aimed at the functional characterization and biotechnological exploitation of proteins from the bacteria in soil. Here, we use the thioredoxin from Candidatus Photodesmus katoptron, an uncultured symbiont of flashlight fish, to explore evolutionary and engineering aspects of protein folding in heterologous hosts. The symbiont protein is a standard thioredoxin in terms of 3D-structure, stability and redox activity. However, its folding outside the original host is severely impaired, as shown by a very slow refolding in vitro and an inefficient expression in E. coli that leads mostly to insoluble protein. By contrast, resurrected Precambrian thioredoxins express efficiently in E. coli, plausibly reflecting an ancient adaptation to unassisted folding. We have used a statistical-mechanical model of the folding landscape to guide back-to-ancestor engineering of the symbiont protein. Remarkably, we find that the efficiency of heterologous expression correlates with the in vitro (i.e., unassisted) folding rate and that the ancestral expression efficiency can be achieved with only 1-2 back-to-ancestor replacements. These results demonstrate a minimal-perturbation, sequence-engineering approach to rescue inefficient heterologous expression which may potentially be useful in metagenomics efforts targeting recent adaptations.

A hierarchy of coupling free energies underlie the thermodynamic and functional architecture of protein structures

Protein sequences and structures evolve by satisfying varied physical and biochemical constraints. This multi-level selection is enabled not just by the patterning of amino acids on the sequence, but also via coupling between residues in the native structure. Here, we employ an energetically detailed statistical mechanical model with millions of microstates to extract such long-range structural correlations, i.e. thermodynamic coupling free energies, from a diverse family of protein structures. We find that despite the intricate and anisotropic distribution of coupling patterns, the majority of residues (>70%) are only marginally coupled contributing to functional motions and catalysis. Physical origins of ‘sectors’, determinants of native ensemble heterogeneity in extant, ancient and designed proteins, and the basis for allostery emerge naturally from coupling free energies. The statistical framework highlights how evolutionary selection and optimization occur at the level of global interaction network for a given protein fold impacting folding, function, and allosteric outputs.

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Evolution of protein structures occurs at the level of global interaction network.

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More than 70% of the protein residues are weakly or marginally coupled.

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Functional ‘sector’ regions are a manifestation of marginal coupling.

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Coupling indices vary across the entire proteins in extant-ancient and natural-designed pairs.

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The proposed methodology can be used to understand allostery and epistasis.

Structural basis of the pleiotropic and specific phenotypic consequences of missense mutations in the multifunctional NAD(P)H:quinone oxidoreductase 1 and their pharmacological rescue

The multifunctional nature of human flavoproteins is critically linked to their ability to populate multiple conformational states. Ligand binding, post-translational modifications and disease-associated mutations can reshape this functional landscape, although the structure-function relationships of these effects are not well understood. Herein, we characterized the structural and functional consequences of two mutations (the cancer-associated P187S and the phosphomimetic S82D) on different ligation states which are relevant to flavin binding, intracellular stability and catalysis of the disease-associated NQO1 flavoprotein. We found that these mutations affected the stability locally and their effects propagated differently through the protein structure depending both on the nature of the mutation and the ligand bound, showing directional preference from the mutated site and leading to specific phenotypic manifestations in different functional traits (FAD binding, catalysis and inhibition, intracellular stability and pharmacological response to ligands). Our study thus supports that pleitropic effects of disease-causing mutations and phosphorylation events on human flavoproteins may be caused by long-range structural propagation of stability effects to different functional sites that depend on the ligation-state and site-specific perturbations. Our approach can be of general application to investigate these pleiotropic effects at the flavoproteome scale in the absence of high-resolution structural models.

The metal cofactor zinc and interacting membranes modulate SOD1 conformation-aggregation landscape in an in vitro ALS model

Aggregation of Cu-Zn superoxide dismutase (SOD1) is implicated in the motor neuron disease, amyotrophic lateral sclerosis (ALS). Although more than 140 disease mutations of SOD1 are available, their stability or aggregation behaviors in membrane environment are not correlated with disease pathophysiology. Here, we use multiple mutational variants of SOD1 to show that the absence of Zn, and not Cu, significantly impacts membrane attachment of SOD1 through two loop regions facilitating aggregation driven by lipid-induced conformational changes. These loop regions influence both the primary (through Cu intake) and the gain of function (through aggregation) of SOD1 presumably through a shared conformational landscape. Combining experimental and theoretical frameworks using representative ALS disease mutants, we develop a 'co-factor derived membrane association model' wherein mutational stress closer to the Zn (but not to the Cu) pocket is responsible for membrane association-mediated toxic aggregation and survival time scale after ALS diagnosis.

Diverse Native Ensembles Dictate the Differential Functional Responses of Nuclear Receptor Ligand-Binding Domains

Native states of folded proteins are characterized by a large ensemble of conformations whose relative populations and interconversion dynamics determine the functional output. This is more apparent in transcription factors that have evolved to be inherently sensitive to small perturbations, thus fine-tuning gene expression. To explore the extent to which such functional features are imprinted on the folding landscape of transcription factor ligand-binding domains (LBDs), we characterize paralogous LBDs of the nuclear receptor (NR) family employing an energetically detailed and ensemble-based Ising-like statistical mechanical model. We find that the native ensembles of the LBDs from glucocorticoid receptor, PPAγ, and thyroid hormone receptor display a remarkable diversity in the width of the native wells, the number and nature of partially structured states, and hence the degree of conformational order. Monte Carlo simulations employing the full state representation of the ensemble highlight that many of the functional conformations coexist in equilibrium, whose relative populations are sensitive to both temperature and the strength of ligand binding. Allosteric modulation of the degree of structure at a coregulator binding site on ligand binding is shown to arise via a redistribution of populations in the native ensembles of glucocorticoid and PPAγ LBDs. Our results illustrate how functional requirements can drive the evolution of conformationally diverse native ensembles in paralogs.

Weakening of interaction networks with aging in tip-link protein induces hearing loss

Age-related hearing loss (ARHL) is a common condition in humans marking the gradual decrease in hearing with age. Perturbations in the tip-link protein cadherin-23 that absorbs the mechanical tension from sound and maintains the integrity of hearing is associated with ARHL. Here, in search of molecular origins for ARHL, we dissect the conformational behavior of cadherin-23 along with the mutant S47P that progresses the hearing loss drastically. Using an array of experimental and computational approaches, we highlight a lower thermodynamic stability, significant weakening in the hydrogen-bond network and inter-residue correlations among β-strands, due to the S47P mutation. The loss in correlated motions translates to not only a remarkable two orders of magnitude slower folding in the mutant but also to a proportionately complex unfolding mechanism. We thus propose that loss in correlated motions within cadherin-23 with aging may trigger ARHL, a molecular feature that likely holds true for other disease-mutations in β-strand-rich proteins.

Slow Folding of a Helical Protein: Large Barriers, Strong Internal Friction, or a Shallow, Bumpy Landscape?

The rate at which a protein molecule folds is determined by opposing energetic and entropic contributions to the free energy that shape the folding landscape. Delineating the extent to which they impact the diffusional barrier-crossing events, including the magnitude of internal friction and barrier height, has largely been a challenging task. In this work, we extract the underlying thermodynamic and dynamic contributions to the folding rate of an unusually slow-folding helical DNA-binding domain, PurR, which shares the characteristics of ultrafast downhill-folding proteins but nonetheless appears to exhibit an apparent two-state equilibrium. We combine equilibrium spectroscopy, temperature-viscosity-dependent kinetics, statistical mechanical modeling, and coarse-grained simulations to show that the conformational behavior of PurR is highly heterogeneous characterized by a large spread in melting temperatures, marginal thermodynamic barriers, and populated partially structured states. PurR appears to be at the threshold of disorder arising from frustrated electrostatics and weak packing that in turn slows down folding due to a shallow, bumpy landscape and not due to large thermodynamic barriers or strong internal friction. Our work highlights how a strong temperature dependence on the pre-exponential could signal a shallow landscape and not necessarily a slow-folding diffusion coefficient, thus determining the folding timescales of even millisecond folding proteins and hints at possible structural origins for the shallow landscape.

A Disordered Loop Mediates Heterogeneous Unfolding of an Ordered Protein by Altering the Native Ensemble

The high flexibility of long disordered or partially structured loops in folded proteins allows for entropic stabilization of native ensembles. Destabilization of such loops could alter the native ensemble or promote alternate conformations within the native ensemble if the ordered regions themselves are held together weakly. This is particularly true of downhill folding systems that exhibit weak unfolding cooperativity. Here, we combine experimental and computational methods to probe the response of the native ensemble of a helical, downhill folding domain PDD, which harbors an 11-residue partially structured loop, to perturbations. Statistical mechanical modeling points to continuous structural changes on both temperature and mutational perturbations driven by entropic stabilization of partially structured conformations within the native ensemble. Long time-scale simulations of the wild-type protein and two mutants showcase a remarkable conformational switching behavior wherein the parallel helices in the wild-type protein sample an antiparallel orientation in the mutants, with the C-terminal helix and the loop connecting the helices displaying high flexibility, disorder, and non-native interactions. We validate these computational predictions via the anomalous fluorescence of a native tyrosine located at the interface of the helices. Our observations highlight the role of long loops in determining the unfolding mechanisms, sensitivity of the native ensembles to mutational perturbations and provide experimentally testable predictions that can be explored in even two-state folding systems.

Non-specific DNA-driven quinary interactions promote structural transitions in proteins

The nature and distribution of charged residues on the surface of proteins play a vital role in determining the binding affinity, selectivity and kinetics of association to ligands. When it comes to DNA-binding domains (DBDs), these functional features manifest as anisotropic distribution of positively charged residues on the protein surface driven by the requirement to bind DNA, a highly negatively charged polymer. In this work, we compare the thermodynamic behavior of nine different proteins belonging to three families - LacR, engrailed and Brk - some of which are disordered in solution in the absence of DNA. Combining detailed electrostatic calculations and statistical mechanical modeling of folding landscapes at different distances and relative orientations with respect to DNA, we show that non-specific electrostatic interactions between the protein and DNA can promote structural transitions in DBDs. Such quinary interactions that are strictly agnostic to the DNA sequence induce varied behaviors including folding of disordered domains, partial unfolding of ordered proteins and (de-)population of intermediate states. Our work highlights that the folding landscape of proteins can be tuned as a function of distance from DNA and hints at possible reasons for DBDs exhibiting complex kinetic-thermodynamic behaviors in the absence of DNA.

Molecular origins of folding rate differences in the thioredoxin family

Thioredoxins are a family of conserved oxidoreductases responsible for maintaining redox balance within cells. They have also served as excellent model systems for protein design and engineering studies particularly through ancestral sequence reconstruction methods. The recent work by Gamiz-Arco et al. [Biochem J (2019) 476, 3631–3647] answers fundamental questions on how specific sequence differences can contribute to differences in folding rates between modern and ancient thioredoxins but also among a selected subset of modern thioredoxins. They surprisingly find that rapid unassisted folding, a feature of ancient thioredoxins, is not conserved in the modern descendants suggestive of co-evolution of better folding machinery that likely enabled the accumulation of mutations that slow-down folding. The work thus provides an interesting take on the expected folding-stability-function constraint while arguing for additional factors that contribute to sequence evolution and hence impact folding efficiency.

pPerturb: A Server for Predicting Long-Distance Energetic Couplings and Mutation-Induced Stability Changes in Proteins via Perturbations

The strength of intraprotein interactions or contact network is one of the dominant factors determining the thermodynamic stabilities of proteins. The nature and the extent of connectivity of this network also play a role in allosteric signal propagation characteristics upon ligand binding to a protein domain. Here, we develop a server for rapid quantification of the strength of an interaction network by employing an experimentally consistent perturbation approach previously validated against a large data set of 375 mutations in 19 different proteins. The web server can be employed to predict the extent of destabilization of proteins arising from mutations in the protein interior in experimentally relevant units. Moreover, coupling distances-a measure of the extent of percolation on perturbation-and overall perturbation magnitudes are predicted in a residue-specific manner, enabling a first look at the distribution of energetic couplings in a protein or its changes upon ligand binding. We show specific examples of how the server can be employed to probe for the distribution of local stabilities in a protein, to examine changes in side chain orientations or packing before and after ligand binding, and to predict changes in stabilities of proteins upon mutations of buried residues. The web server is freely available at http://pbl.biotech.iitm.ac.in/pPerturb and supports recent versions of all major browsers.

Thermodynamics and folding landscapes of large proteins from a statistical mechanical model

Statistical mechanical models that afford an intermediate resolution between macroscopic chemical models and all-atom simulations have been successful in capturing folding behaviors of many small single-domain proteins. However, the applicability of one such successful approach, the Wako-Saitô-Muñoz-Eaton (WSME) model, is limited by the size of the protein as the number of conformations grows exponentially with protein length. In this work, we surmount this size limitation by introducing a novel approximation that treats stretches of 3 or 4 residues as blocks, thus reducing the phase space by nearly three orders of magnitude. The performance of the 'bWSME' model is validated by comparing the predictions for a globular enzyme (RNase H) and a repeat protein (IκBα), against experimental observables and the model without block approximation. Finally, as a proof of concept, we predict the free-energy surface of the 370-residue, multi-domain maltose binding protein and identify an intermediate in good agreement with single-molecule force-spectroscopy measurements. The bWSME model can thus be employed as a quantitative predictive tool to explore the conformational landscapes of large proteins, extract the structural features of putative intermediates, identify parallel folding paths, and thus aid in the interpretation of both ensemble and single-molecule experiments.

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.

Tunable order-disorder continuum in protein-DNA interactions

DNA-binding protein domains (DBDs) sample diverse conformations in equilibrium facilitating the search and recognition of specific sites on DNA over millions of energetically degenerate competing sites. We hypothesize that DBDs have co-evolved to sense and exploit the strong electric potential from the array of negatively charged phosphate groups on DNA. We test our hypothesis by employing the intrinsically disordered DBD of cytidine repressor (CytR) as a model system. CytR displays a graded increase in structure, stability and folding rate on increasing the osmolarity of the solution that mimics the non-specific screening by DNA phosphates. Electrostatic calculations and an Ising-like statistical mechanical model predict that CytR exhibits features of an electric potential sensor modulating its dimensions and landscape in a unique distance-dependent manner, while DNA plays the role of a non-specific macromolecular chaperone. Accordingly, CytR binds its natural half-site faster than the diffusion-controlled limit and even random DNA conforming to an electrostatic-steering binding mechanism. Our work unravels for the first time the synergistic features of a natural electrostatic potential sensor, a novel binding mechanism driven by electrostatic frustration and disorder, and the role of DNA in promoting distance-dependent protein structural transitions critical for switching between specific and non-specific DNA-binding modes.

pStab: prediction of stable mutants, unfolding curves, stability maps and protein electrostatic frustration

Summary

We present a web-server for rapid prediction of changes in protein stabilities over a range of temperatures and experimental conditions upon single- or multiple-point substitutions of charged residues. Potential mutants are identified by a charge-shuffling procedure while the stability changes (i.e. an unfolding curve) are predicted employing an ensemble-based statistical-mechanical model. We expect this server to be a simple yet detailed tool for engineering stabilities, identifying electrostatically frustrated residues, generating local stability maps and in constructing fitness landscapes.

Availability and implementation

The web-server is freely available at http://pbl.biotech.iitm.ac.in/pStab and supports recent versions of all major browsers.

Contact

athi@iitm.ac.in.

Supplementary information

Supplementary data are available at Bioinformatics online.

Modulation of allosteric coupling by mutations: from protein dynamics and packing to altered native ensembles and function

A large body of work has gone into understanding the effect of mutations on protein structure and function. Conventional treatments have involved quantifying the change in stability, activity and relaxation rates of the mutants with respect to the wild-type protein. However, it is now becoming increasingly apparent that mutational perturbations consistently modulate the packing and dynamics of a significant fraction of protein residues, even those that are located >10–15 Å from the mutated site. Such long-range modulation of protein features can distinctly tune protein stability and the native conformational ensemble contributing to allosteric modulation of function. In this review, I summarize a series of experimental and computational observations that highlight the incredibly pliable nature of proteins and their response to mutational perturbations manifested via the intra-protein interaction network. I highlight how an intimate understanding of mutational effects could pave the way for integrating stability, folding, cooperativity and even allostery within a single physical framework.

Switching Protein Conformational Substates by Protonation and Mutation

Protein modules that regulate the availability and conformational status of transcription factors determine the rapidity, duration, and magnitude of cellular response to changing conditions. One such system is the single-gene product Cnu, a four-helix bundle transcription co-repressor, which acts as a molecular thermosensor regulating the expression of virulence genes in enterobacteriaceae through modulation of its native conformational ensemble. Cnu and related genes have also been implicated in pH-dependent expression of virulence genes. We hypothesize that protonation of a conserved buried histidine (H45) in Cnu promotes large electrostatic frustration, thus disturbing the H-NS, a transcription factor, binding face. Spectroscopic and calorimetric methods reveal that H45 exhibits a suppressed p K_a of ∼5.1, the protonation of which switches the conformation to an alternate native ensemble in which the fourth helix is disordered. The population redistribution can also be achieved through a mutation H45V, which does not display any switching behavior at pH values greater than 4. The Wako-Saitô-Muñoz-Eaton (WSME) statistical mechanical model predicts specific differences in the conformations and fluctuations of the fourth and first helices of Cnu determining the observed pH response. We validate these predictions through fluorescence lifetime measurements of a sole tryptophan, highlighting the presence of both native and non-native interactions in the regions adjoining the binding face of Cnu. Our combined experimental-computational study thus shows that Cnu acts both as a thermo- and pH-sensor orchestrated via a subtle but quantifiable balance between the weak packing of a structural element and protonation of a buried histidine that promotes electrostatic frustration.

Entropic Control of an Excited Folded-Like Conformation in a Disordered Protein Ensemble

Many intrinsically disordered proteins switch between unfolded and folded-like forms in the presence of their binding partner. The possibility of a pre-equilibrium between the two macrostates is challenging to discern given the complex conformational landscape. Here, we show that CytR, a disordered DNA-binding domain, samples a folded-like excited state in its native ensemble through equilibrium multi-probe spectroscopy, kinetics and an Ising-like statistical mechanical model. The population of the excited state increases upon stabilization of the native ensemble with an osmolyte, while decreasing with increasing temperatures. A conserved proline residue, the mutation of which weakens the binding affinity to the target promoter, is found to uniquely control the population of the minor excited state. Semi-quantitative statistical mechanical modeling reveals that the conformational diffusion coefficient of disordered CytR is an order of magnitude slower than the estimates from folded domains. The osmolyte and proline mutation smoothen and roughen up the landscape, respectively, apart from modulation of populations. Our work uncovers general strategies to probe for excited structured states in disordered ensembles, and to measure and modulate the roughness of the disordered landscapes, inter-conversion rates of species and their populations.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

A self-consistent structural perturbation approach for determining the magnitude and extent of allosteric coupling in proteins

Elucidating the extent of energetic coupling between residues in single-domain proteins, which is a fundamental determinant of allostery, information transfer and folding cooperativity, has remained a grand challenge. While several sequence- and structure-based approaches have been proposed, a self-consistent description that is simultaneously compatible with unfolding thermodynamics is lacking. We recently developed a simple structural perturbation protocol that captures the changes in thermodynamic stabilities induced by point mutations within the protein interior. Here, we show that a fundamental residue-specific component of this perturbation approach, the coupling distance, is uniquely sensitive to the environment of a residue in the protein to a distance of ∼15 Å. With just the protein contact map as an input, we reproduce the extent of percolation of perturbations within the structure as observed in network analysis of intra-protein interactions, molecular dynamics simulations and NMR-observed changes in chemical shifts. Using this rapid protocol that relies on a single structure, we explain the results of statistical coupling analysis (SCA) that requires hundreds of sequences to identify functionally critical sectors, the propagation and dissipation of perturbations within proteins and the higher-order couplings deduced from detailed NMR experiments. Our results thus shed light on the possible mechanistic origins of signaling through the interaction network within proteins, the likely distance dependence of perturbations induced by ligands and post-translational modifications and the origins of folding cooperativity through many-body interactions.

Tuning the Continuum of Structural States in the Native Ensemble of a Regulatory Protein

The mesoscale nature of proteins allows for an efficient coupling between environmental cues and conformational changes, enabling their function as molecular transducers. Delineating the precise structural origins of such a connection and the expected spectroscopic response has, however, been challenging. In this work, we perform a combination of urea-temperature double perturbation experiments and theoretical modeling to probe the conformational landscape of Cnu, a natural thermosensor protein. We observe unique ensemble signatures that point to a continuum of conformational substates in the native ensemble and that respond intricately to perturbations upon monitoring secondary and tertiary structures, distances between an intrinsic FRET pair, and hydrodynamic volumes. Binding assays further reveal a weakening of the Cnu functional complex with temperature, highlighting the molecular origins of signal transduction critical for pathogenic response in enterobacteriaceae.

Toward a quantitative description of microscopic pathway heterogeneity in protein folding

Experimentally consistent statistical modeling of protein folding thermodynamics reveals unprecedented complexity with numerous parallel folding routes in five different proteins.

Energetic and topological determinants of a phosphorylation-induced disorder-to-order protein conformational switch

We show that the phosphorylation of 4E-BP2 acts as a triggering event to shape its folding-function landscape that is delicately balanced between conflicting favorable energetics and intrinsically unfavorable topological connectivity. We further provide first evidence that the fitness landscapes of proteins at the threshold of disorder can differ considerably from ordered domains.

A simple two-state protein unfolds mechanically via multiple heterogeneous pathways at single-molecule resolution

A major drive in protein folding has been to develop experimental technologies to resolve the myriads of microscopic pathways and complex mechanisms that purportedly underlie simple two-state folding behaviour. This is key for cross-validating predictions from theory and modern computer simulations. Detecting such complexity experimentally has remained elusive even using methods with improved time, structural or single-molecule resolution. Here, we investigate the mechanical unfolding of cold shock protein B (Csp), a showcase two-state folder, using single-molecule force-spectroscopy. Under controlled-moderate pulling forces, the unfolding of Csp emerges as highly heterogeneous with trajectories ranging from single sweeps to different combinations of multiple long-lived mechanical intermediates that also vary in order of appearance. Steered molecular dynamics simulations closely reproduce the experimental observations, thus matching unfolding patterns with structural events. Our results provide a direct glimpse at the nanoscale complexity underlying two-state folding, and postulate these combined methods as unique tools for dissecting the mechanical unfolding mechanisms of such proteins.

Previous investigations have indicated that the model protein CspB folds in a simple two-state fashion. Here, the authors provide direct experimental evidence for that the energy landscape of two-state folding proteins is highly heterogeneous and that unfolding can occur via multiple pathways.

Quantifying Protein Disorder through Measures of Excess Conformational Entropy

Intrinsically disordered proteins (IDPs) and proteins with a large degree of disorder are abundant in the proteomes of eukaryotes and viruses, and play a vital role in cellular homeostasis and disease. One fundamental question that has been raised on IDPs is the process by which they offset the entropic penalty involved in transitioning from a heterogeneous ensemble of conformations to a much smaller collection of binding-competent states. However, this has been a difficult problem to address, as the effective entropic cost of fixing residues in a folded-like conformation from disordered amino acid neighborhoods is itself not known. Moreover, there are several examples where the sequence complexity of disordered regions is as high as well-folded regions. Disorder in such cases therefore arises from excess conformational entropy determined entirely by correlated sequence effects, an entropic code that is yet to be identified. Here, we explore these issues by exploiting the order-disorder transitions of a helix in Pbx-Homeodomain together with a dual entropy statistical mechanical model to estimate the magnitude and sign of the excess conformational entropy of residues in disordered regions. We find that a mere 2.1-fold increase in the number of allowed conformations per residue (∼0.7kBT favoring the unfolded state) relative to a well-folded sequence, or ∼2(N) additional conformations for a N-residue sequence, is sufficient to promote disorder under physiological conditions. We show that this estimate is quite robust and helps in rationalizing the thermodynamic signatures of disordered regions in important regulatory proteins, modeling the conformational folding-binding landscapes of IDPs, quantifying the stability effects characteristic of disordered protein loops and their subtle roles in determining the partitioning of folding flux in ordered domains. In effect, the dual entropy model we propose provides a statistical thermodynamic basis for the relative conformational propensities of amino acids in folded and disordered environments in proteins. Our work thus lays the foundation for understanding and quantifying protein disorder through measures of excess conformational entropy.

Imprints of function on the folding landscape: functional role for an intermediate in a conserved eukaryotic binding protein

In the computational characterization of single domain protein folding, the effective free energies of numerous microstates are projected onto few collective degrees of freedom that in turn serve as well-defined reaction coordinates. In this regard, one-dimensional (1D) free energy profiles are widely used mainly for their simplicity. Since folding and functional landscapes are interlinked, how well can these reduced representations capture the structural and dynamic features of functional states while being simultaneously consistent with experimental observables? We investigate this issue by characterizing the folding of the four-helix bundle bovine acyl-CoA binding protein (bACBP), which exhibits complex equilibrium and kinetic behaviours, employing an Ising-like statistical mechanical model and molecular simulations. We show that the features of the 1D free energy profile are sufficient to quantitatively reproduce multiple experimental observations including millisecond chevron-like kinetics and temperature dependence, a microsecond fast phase, barrier heights, unfolded state movements, the intermediate structure and average ϕ-values. Importantly, we find that the structural features of the native-like intermediate (partial disorder in helix 1) are intricately linked to a unique interplay between packing and electrostatics in this domain. By comparison with available experimental data, we propose that this intermediate determines the promiscuous functional behaviour of bACBP that exhibits broad substrate specificity. Our results present evidence to the possibility of employing the statistical mechanical model and the resulting 1D free energy profile to not just understand folding mechanisms but to even extract features of functionally relevant states and their energetic origins.

Mapping the Topography of a Protein Energy Landscape

Protein energy landscapes are highly complex, yet the vast majority of states within them tend to be invisible to experimentalists. Here, using site-directed mutagenesis and exploiting the simplicity of tandem-repeat protein structures, we delineate a network of these states and the routes between them. We show that our target, gankyrin, a 226-residue 7-ankyrin-repeat protein, can access two alternative (un)folding pathways. We resolve intermediates as well as transition states, constituting a comprehensive series of snapshots that map early and late stages of the two pathways and show both to be polarized such that the repeat array progressively unravels from one end of the molecule or the other. Strikingly, we find that the protein folds via one pathway but unfolds via a different one. The origins of this behavior can be rationalized using the numerical results of a simple statistical mechanics model that allows us to visualize the equilibrium behavior as well as single-molecule folding/unfolding trajectories, thereby filling in the gaps that are not accessible to direct experimental observation. Our study highlights the complexity of repeat-protein folding arising from their symmetrical structures; at the same time, however, this structural simplicity enables us to dissect the complexity and thereby map the precise topography of the energy landscape in full breadth and remarkable detail. That we can recapitulate the key features of the folding mechanism by computational analysis of the native structure alone will help toward the ultimate goal of designed amino-acid sequences with made-to-measure folding mechanisms-the Holy Grail of protein folding.

A microscopic insight from conformational thermodynamics to functional ligand binding in proteins

We show that the thermodynamics of metal ion-induced conformational changes aid to understand the functions of protein complexes. This is illustrated in the case of a metalloprotein, alpha-lactalbumin (aLA), a divalent metal ion binding protein. We use the histograms of dihedral angles of the protein, generated from all-atom molecular dynamics simulations, to calculate conformational thermodynamics. The thermodynamically destabilized and disordered residues in different conformational states of a protein are proposed to serve as binding sites for ligands. This is tested for β-1,4-galactosyltransferase (β4GalT) binding to the Ca(2+)-aLA complex, in which the binding residues are known. Among the binding residues, the C-terminal residues like aspartate (D) 116, glutamine (Q) 117, tryptophan (W) 118 and leucine (L) 119 are destabilized and disordered and can dock β4GalT onto Ca(2+)-aLA. No such thermodynamically favourable binding residues can be identified in the case of the Mg(2+)-aLA complex. We apply similar analysis to oleic acid binding and predict that the Ca(2+)-aLA complex can bind to oleic acid through the basic histidine (H) 32 of the A2 helix and the hydrophobic residues, namely, isoleucine (I) 59, W60 and I95, of the interfacial cleft. However, the number of destabilized and disordered residues in Mg(2+)-aLA are few, and hence, the oleic acid binding to Mg(2+)-bound aLA is less stable than that to the Ca(2+)-aLA complex. Our analysis can be generalized to understand the functionality of other ligand bound proteins.

Evidence for the sequential folding mechanism in RNase H from an ensemble-based model

The number of distinct protein folding pathways starting from an unfolded ensemble, and hence, the folding mechanism is an intricate function of protein size, sequence complexity, and stability conditions. This has traditionally been a contentious issue particularly because of the ensemble nature of conventional experiments that can mask the complexity of the underlying folding landscape. Recent hydrogen-exchange experiments combined with mass spectrometry (HX-MS) reveal that the folding of RNase H proceeds in a hierarchical fashion with distinct intermediates and following a single discrete path. In our current work, we provide computational evidence for this unique folding mechanism by employing a structure-based statistical mechanical model. Upon calibrating the energetic terms of the model with equilibrium measurements, we predict multiple intermediate states in the folding of RNase H that closely resemble experimental observations. Remarkably, a simplified landscape representation adequately captures the folding complexity and predicts the possibility of a well-defined sequence of folding events. We supplement the statistical model study with both explicit solvent molecular simulations of the helical units and electrostatic calculations to provide structural and energetic insights into the early and late stages of RNase H folding that hint at the frustrated nature of its folding landscape.

A disorder-induced domino-like destabilization mechanism governs the folding and functional dynamics of the repeat protein IκBα

The stability of the repeat protein IκBα, a transcriptional inhibitor in mammalian cells, is critical in the functioning of the NF-κB signaling module implicated in an array of cellular processes, including cell growth, disease, immunity and apoptosis. Structurally, IκBα is complex, with both ordered and disordered regions, thus posing a challenge to the available computational protocols to model its conformational behavior. Here, we introduce a simple procedure to model disorder in systems that undergo binding-induced folding that involves modulation of the contact map guided by equilibrium experimental observables in combination with an Ising-like Wako-Saitô-Muñoz-Eaton model. This one-step procedure alone is able to reproduce a variety of experimental observables, including ensemble thermodynamics (scanning calorimetry, pre-transitions, m-values) and kinetics (roll-over in chevron plot, intermediates and their identity), and is consistent with hydrogen-deuterium exchange measurements. We further capture the intricate distance-dynamics between the domains as measured by single-molecule FRET by combining the model predictions with simple polymer physics arguments. Our results reveal a unique mechanism at work in IκBα folding, wherein disorder in one domain initiates a domino-like effect partially destabilizing neighboring domains, thus highlighting the effect of symmetry-breaking at the level of primary sequences. The offshoot is a multi-state and a dynamic conformational landscape that is populated by increasingly partially folded ensembles upon destabilization. Our results provide, in a straightforward fashion, a rationale to the promiscuous binding and short intracellular half-life of IκBα evolutionarily engineered into it through repeats with variable stabilities and expand the functional repertoire of disordered regions in proteins.

How well does a funneled energy landscape capture the folding mechanism of spectrin domains?

Three structurally similar domains from α-spectrin have been shown to fold very differently. First, there is a contrast in the folding mechanism, as probed by Φ-value analysis, between the R15 domain and the R16 and R17 domains. Second, there are very different contributions from internal friction to folding: the folding rate of the R15 domain was found to be inversely proportional to solvent viscosity, showing no apparent frictional contribution from the protein, but in the other two domains, a large internal friction component was evident. Non-native misdocking of helices has been suggested to be responsible for this phenomenon. Here, I study the folding of these three proteins with minimalist coarse-grained models based on a funneled energy landscape. Remarkably, I find that, despite the absence of non-native interactions, the differences in folding mechanism of the domains are well captured by the model, and the agreement of the Φ-values with experiment is fairly good. On the other hand, within the context of this model, there are no significant differences in diffusion coefficient along the chosen folding coordinate, and the model cannot explain the large differences in folding rates between the proteins found experimentally. These results are nonetheless consistent with the expectations from the energy landscape perspective of protein folding, namely, that the folding mechanism is primarily determined by the native-like interactions present in the Gō-like model, with missing non-native interactions being required to explain the differences in "internal friction" seen in experiment.