Statistical mechanics of protein allostery: roles of backbone and side-chain structural fluctuations

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'.

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.

Role of water-bridged interactions in metal ion coupled protein allostery

Allosteric communication between distant parts of proteins controls many cellular functions, in which metal ions are widely utilized as effectors to trigger the allosteric cascade. Due to the involvement of strong coordination interactions, the energy landscape dictating the metal ion binding is intrinsically rugged. How metal ions achieve fast binding by overcoming the landscape ruggedness and thereby efficiently mediate protein allostery is elusive. By performing molecular dynamics simulations for the Ca²⁺ binding mediated allostery of the calmodulin (CaM) domains, each containing two Ca²⁺ binding helix-loop-helix motifs (EF-hands), we revealed the key role of water-bridged interactions in Ca²⁺ binding and protein allostery. The bridging water molecules between Ca²⁺ and binding residue reduces the ruggedness of ligand exchange landscape by acting as a lubricant, facilitating the Ca²⁺ coupled protein allostery. Calcium-induced rotation of the helices in the EF-hands, with the hydrophobic core serving as the pivot, leads to exposure of hydrophobic sites for target binding. Intriguingly, despite being structurally similar, the response of the two symmetrically arranged EF-hands upon Ca²⁺ binding is asymmetric. Breakage of symmetry is needed for efficient allosteric communication between the EF-hands. The key roles that water molecules play in driving allosteric transitions are likely to be general in other metal ion mediated protein allostery.

Natural proteins often utilize allostery in executing a variety of functions. Metal ions are typical cofactors to trigger the allosteric cascade. In this work, using the Ca²⁺ sensor protein calmodulin as the model system, we revealed crucial roles of water-bridged interactions in the metal ion coupled protein allostery. The coordination of the Ca²⁺ to the binding site involves an intermediate in which the water molecule bridges the Ca²⁺ and the liganding residue. The bridging water reduces the free energy barrier height of ligand exchange, therefore facilitating the ligand exchange and allosteric coupling by acting as a lubricant. We also showed that the response of the two symmetrically arranged EF-hand motifs of CaM domains upon Ca²⁺ binding is asymmetric, which is directly attributed to the differing dehydration process of the Ca²⁺ ions and is needed for efficient allosteric communication.

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.

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.

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.

Unified understanding of folding and binding mechanisms of globular and intrinsically disordered proteins

Extensive experimental and theoretical studies have advanced our understanding of the mechanisms of folding and binding of globular proteins, and coupled folding and binding of intrinsically disordered proteins (IDPs). The forces responsible for conformational changes and binding are common in both proteins; however, these mechanisms have been separately discussed. Here, we attempt to integrate the mechanisms of coupled folding and binding of IDPs, folding of small and multi-subdomain proteins, folding of multimeric proteins, and ligand binding of globular proteins in terms of conformational selection and induced-fit mechanisms as well as the nucleation–condensation mechanism that is intermediate between them. Accumulating evidence has shown that both the rate of conformational change and apparent rate of binding between interacting elements can determine reaction mechanisms. Coupled folding and binding of IDPs occurs mainly by induced-fit because of the slow folding in the free form, while ligand binding of globular proteins occurs mainly by conformational selection because of rapid conformational change. Protein folding can be regarded as the binding of intramolecular segments accompanied by secondary structure formation. Multi-subdomain proteins fold mainly by the induced-fit (hydrophobic collapse) mechanism, as the connection of interacting segments enhances the binding (compaction) rate. Fewer hydrophobic residues in small proteins reduce the intramolecular binding rate, resulting in the nucleation–condensation mechanism. Thus, the folding and binding of globular proteins and IDPs obey the same general principle, suggesting that the coarse-grained, statistical mechanical model of protein folding is promising for a unified theoretical description of all mechanisms.

Detection of Correlated Protein Backbone and Side-Chain Angle Fluctuations

NMR methods for the characterization of local protein motions have attained a high level of sophistication. Measurement of the synchronization between those motions, however, poses a serious challenge. Such correlated motions are one of the underlying mechanisms for the propagation of local changes to remote sites and as such for information transfer. Here, we demonstrate the experimental detection of the synchronization of motion over an intermediate range. To that purpose, we designed pulse sequences for the measurement of cross-correlated relaxation between the backbone H^N -N and side-chain H^β -C^β dipoles in Ile, Thr, and Val in the protein GB3. These bonds are related through two and three intervening dihedral angles. We show that the correlated motions inherent in a structural ensemble obtained from a large and diverse array of NMR probes are in excellent agreement with our measurements.

Mutations in Antibody Fragments Modulate Allosteric Response Via Hydrogen-Bond Network Fluctuations

A mechanical perturbation method that locally restricts conformational entropy along the protein backbone is used to identify putative allosteric sites in a series of antibody fragments. The method is based on a distance constraint model that integrates mechanical and thermodynamic viewpoints of protein structure wherein mechanical clamps that mimic substrate or cosolute binding are introduced. Across a set of six single chain-Fv fragments of the anti-lymphotoxin-β receptor antibody, statistically significant responses are obtained by averaging over 10 representative structures sampled from a molecular dynamics simulation. As expected, the introduced clamps locally rigidify the protein, but long-ranged increases in both rigidity and flexibility are also frequently observed. Expanding our analysis to every molecular dynamics frame demonstrates that the allosteric responses are modulated by fluctuations within the hydrogen-bond network where the native ensemble is comprised of conformations that both are, and are not, affected by the perturbation in question. Population shifts induced by the mutations alter the allosteric response by adjusting which hydrogen-bond networks are the most probable. These effects are compared using response maps that track changes across each single chain-Fv fragment, thus providing valuable insight into how sensitive allosteric mechanisms are to mutations.

Comparing allosteric transitions in the domains of calmodulin through coarse-grained simulations

Calmodulin (CaM) is a ubiquitous Ca(2+)-binding protein consisting of two structurally similar domains with distinct stabilities, binding affinities, and flexibilities. We present coarse grained simulations that suggest that the mechanism for the domain's allosteric transitions between the open and closed conformations depends on subtle differences in the folded state topology of the two domains. Throughout a wide temperature range, the simulated transition mechanism of the N-terminal domain (nCaM) follows a two-state transition mechanism while domain opening in the C-terminal domain (cCaM) involves unfolding and refolding of the tertiary structure. The appearance of the unfolded intermediate occurs at a higher temperature in nCaM than it does in cCaM consistent with nCaM's higher thermal stability. Under approximate physiological conditions, the simulated unfolded state population of cCaM accounts for 10% of the population with nearly all of the sampled transitions (approximately 95%) unfolding and refolding during the conformational change. Transient unfolding significantly slows the domain opening and closing rates of cCaM, which can potentially influence its Ca(2+)-binding mechanism.

Cooperativity and modularity in protein folding

A simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The Φ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

SCMHBP: prediction and analysis of heme binding proteins using propensity scores of dipeptides

Background

Heme binding proteins (HBPs) are metalloproteins that contain a heme ligand (an iron-porphyrin complex) as the prosthetic group. Several computational methods have been proposed to predict heme binding residues and thereby to understand the interactions between heme and its host proteins. However, few in silico methods for identifying HBPs have been proposed.

Results

This work proposes a scoring card method (SCM) based method (named SCMHBP) for predicting and analyzing HBPs from sequences. A balanced dataset of 747 HBPs (selected using a Gene Ontology term GO:0020037) and 747 non-HBPs (selected from 91,414 putative non-HBPs) with an identity of 25% was firstly established. Consequently, a set of scores that quantified the propensity of amino acids and dipeptides to be HBPs is estimated using SCM to maximize the predictive accuracy of SCMHBP. Finally, the informative physicochemical properties of 20 amino acids are identified by utilizing the estimated propensity scores to be used to categorize HBPs. The training and mean test accuracies of SCMHBP applied to three independent test datasets are 85.90% and 71.57%, respectively. SCMHBP performs well relative to comparison with such methods as support vector machine (SVM), decision tree J48, and Bayes classifiers. The putative non-HBPs with high sequence propensity scores are potential HBPs, which can be further validated by experimental confirmation. The propensity scores of individual amino acids and dipeptides are examined to elucidate the interactions between heme and its host proteins. The following characteristics of HBPs are derived from the propensity scores: 1) aromatic side chains are important to the effectiveness of specific HBP functions; 2) a hydrophobic environment is important in the interaction between heme and binding sites; and 3) the whole HBP has low flexibility whereas the heme binding residues are relatively flexible.

Conclusions

SCMHBP yields knowledge that improves our understanding of HBPs rather than merely improves the prediction accuracy in predicting HBPs.

A unified view of "how allostery works"

The question of how allostery works was posed almost 50 years ago. Since then it has been the focus of much effort. This is for two reasons: first, the intellectual curiosity of basic science and the desire to understand fundamental phenomena, and second, its vast practical importance. Allostery is at play in all processes in the living cell, and increasingly in drug discovery. Many models have been successfully formulated, and are able to describe allostery even in the absence of a detailed structural mechanism. However, conceptual schemes designed to qualitatively explain allosteric mechanisms usually lack a quantitative mathematical model, and are unable to link its thermodynamic and structural foundations. This hampers insight into oncogenic mutations in cancer progression and biased agonists' actions. Here, we describe how allostery works from three different standpoints: thermodynamics, free energy landscape of population shift, and structure; all with exactly the same allosteric descriptors. This results in a unified view which not only clarifies the elusive allosteric mechanism but also provides structural grasp of agonist-mediated signaling pathways, and guides allosteric drug discovery. Of note, the unified view reasons that allosteric coupling (or communication) does not determine the allosteric efficacy; however, a communication channel is what makes potential binding sites allosteric.

Evidence against the "Y-T coupling" mechanism of activation in the response regulator NtrC

The dominant theory on the mechanism of response regulators activation in two-component bacterial signaling systems is the "Y-T coupling" mechanism, wherein the χ1 rotameric state of a highly conserved aromatic residue correlates with the activation of the protein via structural rearrangements coupled to a conserved tyrosine. In this paper, we present evidence that, in the receiver domain of the response regulator nitrogen regulatory protein C (NtrC(R)), the interconversion of this tyrosine (Y101) between its rotameric states is actually faster than the rate of inactive/active conversion and is not correlated to the activation process. Data gathered from NMR relaxation dispersion experiments show that a subset of residues surrounding the conserved tyrosine sense a process that is occurring at a faster rate than the inactive/active conformational transition. We show that this process is related to χ1 rotamer exchange of Y101 and that mutation of this aromatic residue to a leucine eliminated this second faster process without affecting activation. Computational simulations of NtrC(R) in its active conformation further demonstrate that the rotameric state of Y101 is uncorrelated with the global conformational transition during activation. Moreover, the tyrosine does not appear to be involved in the stabilization of the active form upon phosphorylation and is not essential in propagating the signal downstream for ATPase activity of the central domain. Our data provide experimental evidence against the generally accepted "Y-T coupling" mechanism of activation in NtrC(R).

Entropic mechanism of allosteric communication in conformational transitions of dihydrofolate reductase

The mechanism of allosteric conformational transitions of Escherichia coli dihydrofolate reductase (DHFR) is investigated theoretically by applying a newly developed coarse-grained model. Functional forms of interaction potentials in the model depend on the local structural environments around those interactions to represent the many-residue effects due to atomic packing in each local region, and hence, this model is called "the chameleon model". The chameleon model consistently describes the free-energy landscape of two conformational transitions in the catalytic cycle of DHFR, which we call conformational transition 1 (CT1) and conformational transition 2 (CT2); CT1 is accompanied by the hydride transfer reaction, and CT2 is accompanied by the product ligand release. The transition state of CT1 is entropically stabilized by the disordering of loops at the peripheral regions of the protein, which enhances the positively correlated fluctuations at the center part of the protein, showing that the allosteric communication between distant regions through the central region is intrinsically associated with the entropic stabilization of the transition state. The transition state of CT2 is entropically stabilized through the mechanism that enhances the breathing motion of two domains, showing that the difference in the distribution of interactions brings about the difference in the transition mechanism between CT1 and CT2. The chameleon model opens a way to consistently describe the dynamical energy landscape of enzymatic reactions.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Conformational flexibility and the mechanisms of allosteric transitions in topologically similar proteins

Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.