The Dominant Folding Route Minimizes Backbone Distortion in SH3

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.     

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C_α structure‐based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well‐separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non‐native contact interactions in different folding scenarios. These findings strongly correlate with the protein free‐energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.Proteins 2013; 81:1727–1737. © 2013 Wiley Periodicals, Inc.     

Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins

Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small, fast-folding proteins. To investigate the extent of the topological control of the folding process, we studied the folding of simplified models of five small globular proteins constructed using a Go-like potential to retain the information about the native structures but drastically reduce the energetic frustration and energetic heterogeneity among residue-residue native interactions. By comparing the structure of the transition state ensemble (experimentally determined by Phi-values) and of the intermediates with those obtained using our models, we show that these energetically unfrustrated models can reproduce the global experimentally known features of the transition state ensembles and "en-route" intermediates, at least for the analyzed proteins. This result clearly indicates that, as long as the protein sequence is sufficiently minimally frustrated, topology plays a central role in determining the folding mechanism.     

The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein

Models of protein energetics that neglect interactions between amino acids that are not adjacent in the native state, such as the Gō model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by nonnative contacts, typically argued to be a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences that fold to the same native structure. Contrary to previous conjectures, we find a multiplicity of folding mechanisms, suggesting that Gō-like models cannot be justified by considerations of topology alone. Instead, we find that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies: The order in which native contacts accumulate is profoundly insensitive to omission of nonnative interactions, provided that native contact heterogeneity is retained. This robustness holds over a surprisingly wide range of folding rates for our designed sequences. Mirroring predictions based on the principle of minimum frustration, fast-folding sequences match their Gō-like counterparts in both topological mechanism and transit times. Less optimized sequences dwell much longer in the unfolded state and/or off-pathway intermediates than do Gō-like models. For dynamics that bridge unfolded and unfolded states, however, even slow folders exhibit topological mechanisms and transit times nearly identical with those of their Gō-like counterparts. Our results do not imply a direct correspondence between folding trajectories of Gō-like models and those of real proteins, but they do help to clarify key topological and energetic assumptions that are commonly used to justify such caricatures.     

Molecular Determinants Underlying Binding Specificities of the ABL Kinase Inhibitors: Combining Alanine Scanning of Binding Hot Spots with Network Analysis of Residue Interactions and Coevolution

Quantifying binding specificity and drug resistance of protein kinase inhibitors is of fundamental importance and remains highly challenging due to complex interplay of structural and thermodynamic factors. In this work, molecular simulations and computational alanine scanning are combined with the network-based approaches to characterize molecular determinants underlying binding specificities of the ABL kinase inhibitors. The proposed theoretical framework unveiled a relationship between ligand binding and inhibitor-mediated changes in the residue interaction networks. By using topological parameters, we have described the organization of the residue interaction networks and networks of coevolving residues in the ABL kinase structures. This analysis has shown that functionally critical regulatory residues can simultaneously embody strong coevolutionary signal and high network centrality with a propensity to be energetic hot spots for drug binding. We have found that selective (Nilotinib) and promiscuous (Bosutinib, Dasatinib) kinase inhibitors can use their energetic hot spots to differentially modulate stability of the residue interaction networks, thus inhibiting or promoting conformational equilibrium between inactive and active states. According to our results, Nilotinib binding may induce a significant network-bridging effect and enhance centrality of the hot spot residues that stabilize structural environment favored by the specific kinase form. In contrast, Bosutinib and Dasatinib can incur modest changes in the residue interaction network in which ligand binding is primarily coupled only with the identity of the gate-keeper residue. These factors may promote structural adaptability of the active kinase states in binding with these promiscuous inhibitors. Our results have related ligand-induced changes in the residue interaction networks with drug resistance effects, showing that network robustness may be compromised by targeted mutations of key mediating residues. This study has outlined mechanisms by which inhibitor binding could modulate resilience and efficiency of allosteric interactions in the kinase structures, while preserving structural topology required for catalytic activity and regulation.     

Repeat-protein folding: new insights into origins of cooperativity, stability, and topology

Although our understanding of globular protein folding continues to advance, the irregular tertiary structures and high cooperativity of globular proteins complicates energetic dissection. Recently, proteins with regular, repetitive tertiary structures have been identified that sidestep limitations imposed by globular protein architecture. Here we review recent studies of repeat-protein folding. These studies uniquely advance our understanding of both the energetics and kinetics of protein folding. Equilibrium studies provide detailed maps of local stabilities, access to energy landscapes, insights into cooperativity, determination of nearest-neighbor interaction parameters using statistical thermodynamics, relationships between consensus sequences and repeat-protein stability. Kinetic studies provide insight into the influence of short-range topology on folding rates, the degree to which folding proceeds by parallel (versus localized) pathways, and the factors that select among multiple potential pathways. The recent application of force spectroscopy to repeat-protein unfolding is providing a unique route to test and extend many of these findings.     

Prediction of folding mechanism for circular-permuted proteins

Recent theoretical and experimental studies have suggested that real proteins have sequences with sufficiently small energetic frustration that topological effects are central in determining the folding mechanism. A particularly interesting and challenging framework for exploring and testing the viability of these energetically unfrustrated models is the study of circular-permuted proteins. Here we present the results of the application of a topology-based model to the study of circular permuted SH3 and CI2, in comparison with the available experimental results. The folding mechanism of the permuted proteins emerging from our simulations is in very good agreement with the experimental observations. The differences between the folding mechanisms of the permuted and wild-type proteins seem then to be strongly related to the change in the native state topology.     

Computational design of proteins stereochemically optimized in size, stability, and folding speed

Artificial proteins potentially barrier-free in the folding kinetics are approached computationally under the guidance of protein-folding theories. The smallest and fastest folding globular protein triple-helix-bundle (THB) is so modified as to minimize or eliminate its presumed barriers in folding speed. As the barriers may reside in the ordering of either secondary or tertiary structure, the elements of both secondary and tertiary structure in the protein are targeted for prenucleation with suitable stereochemically constrained amino acid residues. The required elements of topology and sequence for the THB are optimized independently; first the topology is optimized with simulated annealing in polypeptides of highly simplified alphabet; next, the sequence in side chains is optimized using the standard inverse design methods. The resultant three best-adapted THBs, variable in topology and distinctive in sequences, are assessed by comparing them with a few benchmark proteins. The results of mainly molecular dynamics (MD) comparisons, undertaken in explicit water at different temperatures, show that the designed sequences are favorably placed against the chosen benchmarks as THB proteins potentially thermostable in the native folds. Folding simulation experiments with MD establish that the designed sequences are rapid in the folding of individual helices, but not in the evolution of tertiary structure; energetic cum topological frustrations remain but could be the artifacts of the starting conformations that were chosen in the THBs in the folding simulations. Overall, a practical high-throughput approach for de novo protein design has been developed that may have fruitful application for any type of tertiary structure.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

Critical role of beta-hairpin formation in protein G folding

Comparison of the folding mechanisms of proteins with similar structures but very different sequences can provide fundamental insights into the determinants of protein folding mechanisms. Despite very little sequence similarity, the approximately 60 residue IgG binding domains of protein G and protein L both consist of a single helix packed against a four-stranded sheet formed by two symmetrically disposed beta-hairpins. We demonstrate that, as in the case of protein L, one of the two beta-turns of protein G is formed and the other disrupted in the folding transition state. Unlike protein L, however, in protein G it is the second beta-turn that is formed in the folding transition state ensemble. Substitution of an Asp residue by Ala in protein G that eliminates an i,i+2 side chain-main chain hydrogen bond in the second beta-turn slows the folding rate approximately 20-fold but has virtually no effect on the unfolding rate. Taken together with previous results, these findings suggest that the presence of an intact beta-turn in the folding transition state is a consequence of the overall topology of protein L and protein G, but the particular hairpin that is formed is determined by the detailed interatomic interactions that determine the free energies of formation of the isolated beta-hairpins.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Probing the Effects of Local Frustration in the Folding of a Multidomain Protein

Our current knowledge of protein folding is primarily based on experimental data obtained from isolated domains. In fact, because of their complexity, multidomain proteins have been elusive to the experimental characterization. Thus, the folding of a domain in isolation is generally assumed to resemble what should be observed for more complex structural architectures. Here we compared the folding mechanism of a protein domain in isolation and in the context of its supramodular multidomain structure. By carrying out an extensive mutational analysis we illustrate that while the early events of folding are malleable and influenced by the absence/presence of the neighboring structures, the late events appear to be more robust. These effects may be explained by analyzing the local frustration patterns of the domain, providing critical support for the funneled energy landscape theory of protein folding, and highlighting the role of protein frustration in sculpting the early events of the reaction.     

Single-molecule dynamics reveals cooperative binding-folding in protein recognition

The study of associations between two biomolecules is the key to understanding molecular function and recognition. Molecular function is often thought to be determined by underlying structures. Here, combining a single-molecule study of protein binding with an energy-landscape–inspired microscopic model, we found strong evidence that biomolecular recognition is determined by flexibilities in addition to structures. Our model is based on coarse-grained molecular dynamics on the residue level with the energy function biased toward the native binding structure (the Go model). With our model, the underlying free-energy landscape of the binding can be explored. There are two distinct conformational states at the free-energy minimum, one with partial folding of CBD itself and significant interface binding of CBD to Cdc42, and the other with native folding of CBD itself and native interface binding of CBD to Cdc42. This shows that the binding process proceeds with a significant interface binding of CBD with Cdc42 first, without a complete folding of CBD itself, and that binding and folding are then coupled to reach the native binding state. The single-molecule experimental finding of dynamic fluctuations among the loosely and closely bound conformational states can be identified with the theoretical, calculated free-energy minimum and explained quantitatively in the model as a result of binding associated with large conformational changes. The theoretical predictions identified certain key residues for binding that were consistent with mutational experiments. The combined study identified fundamental mechanisms and provided insights about designing and further exploring biomolecular recognition with large conformational changes.     

Coevolution of function and the folding landscape: correlation with density of native contacts

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gomacr;-like coarse-grained models in reproducing protein dynamics.     

The Role of High-Dimensional Diffusive Search,Stabilization, and Frustration in Protein Folding

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold.     

Electrostatically Accelerated Encounter and Folding for Facile Recognition of Intrinsically Disordered Proteins

Achieving facile specific recognition is essential for intrinsically disordered proteins (IDPs) that are involved in cellular signaling and regulation. Consideration of the physical time scales of protein folding and diffusion-limited protein-protein encounter has suggested that the frequent requirement of protein folding for specific IDP recognition could lead to kinetic bottlenecks. How IDPs overcome such potential kinetic bottlenecks to viably function in signaling and regulation in general is poorly understood. Our recent computational and experimental study of cell-cycle regulator p27 (Ganguly et al., J. Mol. Biol. (2012)) demonstrated that long-range electrostatic forces exerted on enriched charges of IDPs could accelerate protein-protein encounter via “electrostatic steering” and at the same time promote “folding-competent” encounter topologies to enhance the efficiency of IDP folding upon encounter. Here, we further investigated the coupled binding and folding mechanisms and the roles of electrostatic forces in the formation of three IDP complexes with more complex folded topologies. The surface electrostatic potentials of these complexes lack prominent features like those observed for the p27/Cdk2/cyclin A complex to directly suggest the ability of electrostatic forces to facilitate folding upon encounter. Nonetheless, similar electrostatically accelerated encounter and folding mechanisms were consistently predicted for all three complexes using topology-based coarse-grained simulations. Together with our previous analysis of charge distributions in known IDP complexes, our results support a prevalent role of electrostatic interactions in promoting efficient coupled binding and folding for facile specific recognition. These results also suggest that there is likely a co-evolution of IDP folded topology, charge characteristics, and coupled binding and folding mechanisms, driven at least partially by the need to achieve fast association kinetics for cellular signaling and regulation.     

The denatured state dictates the topology of two proteins with almost identical sequence but different native structure and function

The protein folding problem is often studied by comparing the mechanisms of proteins sharing the same structure but different sequence. The recent design of the two proteins G_A88 and G_B88, displaying different structures and functions while sharing 88% sequence identity (49 out of 56 amino acids), allows the unique opportunity for a complementary approach. At which stage of its folding pathway does a protein commit to a given topology? Which residues are crucial in directing folding mechanisms to a given structure? By using a combination of biophysical and computational techniques, we have characterized the folding of both G_A88 and G_B88. We show that, contrary to expectation, G_B88, characterized by a native α+β fold, displays in the denatured state a content of native-like helical structure greater than G_A88, which is all-α in its native state. Both experiments and simulations indicate that such residual structure may be tuned by changing pH. Thus, despite the high sequence identity, the folding pathways for these two proteins appear to diverge as early as in the denatured state. Our results suggest a mechanism whereby protein topology is committed very early along the folding pathway, being imprinted in the residual structure of the denatured state.     

Ligand binding and circular permutation modify residue interaction network in DHFR

Residue interaction networks and loop motions are important for catalysis in dihydrofolate reductase (DHFR). Here, we investigate the effects of ligand binding and chain connectivity on network communication in DHFR. We carry out systematic network analysis and molecular dynamics simulations of the native DHFR and 19 of its circularly permuted variants by breaking the chain connections in ten folding element regions and in nine nonfolding element regions as observed by experiment. Our studies suggest that chain cleavage in folding element areas may deactivate DHFR due to large perturbations in the network properties near the active site. The protein active site is near or coincides with residues through which the shortest paths in the residue interaction network tend to go. Further, our network analysis reveals that ligand binding has “network-bridging effects” on the DHFR structure. Our results suggest that ligand binding leads to a modification, with most of the interaction networks now passing through the cofactor, shortening the average shortest path. Ligand binding at the active site has profound effects on the network centrality, especially the closeness.