The effects of nonnative interactions on protein folding rates: theory and simulation

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate-enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse-grained protein model, by using an off-lattice C(alpha)model of the src-SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.     

Learning about protein folding via potential functions

Over the last few years we have developed an empirical potential function that solves the protein structure recognition problem: given the sequence for an n-residue globular protein and a collection of plausible protein conformations, including the native conformation for that sequence, identify the correct, native conformation. Having determined this potential on the basis of only some 6500 native/nonnative pairs of structures for 58 proteins, we find it recognizes the native conformation for essentially all compact, soluble, globular proteins having known native conformations in comparisons with 10⁴ to 10⁶ reasonable alternative conformations apiece. In this sense, the potential encodes nearly all the essential features of globular protein conformational preference. In addition it “knows” about many additional factors in protein folding, such as the stabilization of multimeric proteins, quaternary structure, the role of disulfide bridges and ligands, proproteins vs. processed proteins, and minimal strand lengths in globular proteins. Comparisons are made with other sorts of protein folding problems, and applications in protein conformational determination and prediction are discussed. © 1994 Wiley-Liss, Inc.     

Interaction of SecB with intermediates along the folding pathway of maltose-binding protein.

SecB, a molecular chaperone involved in protein export in Escherichia coli, displays the remarkable ability to selectively bind many different polypeptide ligands whose only common feature is that of being nonnative. The selectivity is explained in part by a kinetic partitioning between the folding of a polypeptide and its association with SecB. SecB has no affinity for native, stably folded polypeptides but interacts tightly with polypeptides that are nonnative. In order to better understand the nature of the binding, we have examined the interaction of SecB with intermediates along the folding pathway of maltose-binding protein. Taking advantage of forms of maltose-binding protein that are altered in their folding properties, we show that the first intermediate in folding, represented by the collapsed state, binds to SecB, and that the polypeptide remains active as a ligand until it crosses the final energy barrier to attain the native state.     

Failures of inverse folding and threading with gapped alignment

To calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has some of the features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we show that even the given contact potential, which by definition is used to identify the folding sequences and their unique native conformations, cannot always correctly select which sequences will fold to a given structure. Second, we demonstrate that the given contact potential is not always able to favor the native alignment of a native sequence on its own native conformation over other gapped alignments of different folding sequences onto that same conformation. Because of these shortcomings, even in this simple model system in which all conformations and all native sequences are known and determined directly by the given potential, we must reexamine our expectations for empirical potentials used for inverse folding and gapped alignment on more realistic representations of proteins. © 1996 Wiley-Liss, Inc.     

Reconstruction of the src-SH3 protein domain transition state ensemble using multiscale molecular dynamics simulations

We use an integrated computational approach to reconstruct accurately the transition state ensemble (TSE) for folding of the src-SH3 protein domain. We first identify putative TSE conformations from free energy surfaces generated by importance sampling molecular dynamics for a fully atomic, solvated model of the src-SH3 protein domain. These putative TSE conformations are then subjected to a folding analysis using a coarse-grained representation of the protein and rapid discrete molecular dynamics simulations. Those conformations that fold to the native conformation with a probability (P(fold)) of approximately 0.5, constitute the true transition state. Approximately 20% of the putative TSE structures were found to have a P(fold) near 0.5, indicating that, although correct TSE conformations are populated at the free energy barrier, there is a critical need to refine this ensemble. Our simulations indicate that the true TSE conformations are compact, with a well-defined central beta sheet, in good agreement with previous experimental and theoretical studies. A structured central beta sheet was found to be present in a number of pre-TSE conformations, however, indicating that this element, although required in the transition state, does not define it uniquely. An additional tight cluster of contacts between highly conserved residues belonging to the diverging turn and second beta-sheet of the protein emerged as being critical elements of the folding nucleus. A number of commonly used order parameters to identify the transition state for folding were investigated, with the number of native Cbeta contacts displaying the most satisfactory correlation with P(fold) values.     

Theory of kinetic partitioning in protein folding with possible applications to prions

This study focuses on the phenomenon of kinetic partitioning when a polypeptide chain has two ground-state conformations, one of which is kinetically more reachable than the other. We designed sequences for lattice model proteins with two different conformations of equal energy corresponding to the global energy minimum. Folding simulations revealed that one of these conformations was indeed much more kinetically accessible than the other. We found that the number and strength of local contacts in the ground-state conformation are the major factors that determine which conformation is reached faster; the greater the number of local contacts, the more kinetically reachable a conformation is. We present simple statistical–mechanical arguments to explain these findings. Our results may be relevant in explaining the phenomenology of such proteins as human plasminogen activator inhibitor-1 (PAI-1), photosystem II, and prions. Proteins 31:335–344, 1998. © 1998 Wiley-Liss, Inc.     

Understanding the Role of Three-Dimensional Topology in Determining the?Folding Intermediates of Group I Introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg²⁺-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (⋅OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ⋅OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Analysis on folding of misgurin using two-dimensional HP model

Misgurin is an antimicrobial peptide from the loach, while the hydrophobic-polar (HP) model is a way to study the folding conformations and native states in peptide and protein although several amino acids cannot be classified either hydrophobic or polar. Practically, the HP model requires extremely intensive computations, thus it has yet to be used widely. In this study, we use the two-dimensional HP model to analyze all possible folding conformations and native states of misgurin with conversion of natural amino acids according to the normalized amino acid hydrophobicity index as well as the shortest benchmark HP sequence. The results show that the conversion of misgurin into HP sequence with glycine as hydrophobic amino acid at pH 2 has 1212 folding conformations with the same native state of minimal energy -6; the conversion of glycine as polar amino acid at pH 2 has 13,386 folding conformations with three native states of minimal energy -5; the conversion of glycine as hydrophobic amino acid at pH 7 has 2538 folding conformations with three native states of minimal energy -5; and the conversion of glycine as polar amino acid at pH 7 has 12,852 folding conformations with three native states of minimal energy -4. Those native states can be ranked according to the normalized amino acid hydrophobicity index. The detailed discussions suggest two ways to modify misgurin.     

Identification and Characterization of a Misfolded Monomeric Serpin Formed at Physiological Temperature

The native serpin state is kinetically trapped. However, under mildly destabilizing conditions, the conformational landscape changes, and a number of nonnative conformations with increased stability can be readily formed. The ability to undergo structural change is due to intrinsic strain within the serpin's tertiary fold, which is utilized for proteinase inhibition but renders the protein susceptible to aberrant folding and self-association. The relationship between these various conformations is poorly understood. Antichymotrypsin (ACT) is an inhibitory serpin that readily forms a number of inactive conformations, induced via either environmental stress or interaction with proteinases. Here we have used a variety of biophysical and structural techniques to characterize the relationship between some of these conformations. Incubation of ACT at physiological temperature results in the formation of a range of conformations, including both polymer and misfolded monomer. The ability to populate these nonnative states and the native conformation reflects an energy landscape that is very sensitive to the solution conditions. X-ray crystallography reveals that the misfolded monomeric conformation is in the delta conformation. Further polymerization and seeding experiments show that the delta conformation is an end point in the misfolding pathway of ACT and not an on-pathway intermediate formed during polymerization. The observation that ACT readily forms this inactive conformation at physiological temperature and pH suggests that it may have a role in both health and disease.     

Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have “chevron plot” dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponental behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process. Proteins 30:2–33, 1998. © 1998 Wiley-Liss, Inc.     

Circular dichroic investigation of the native and non-native conformational states of the growth factor receptor-binding protein 2 N-terminal src homology domain 3: effect of binding to a proline-rich peptide from guanine nucleotide exchange factor

SH3 (src homology domain 3) domains are small protein modules that interact with proline-rich peptides. The structure of the N-terminal SH3 domain from growth factor receptor-binding protein 2 (Grb2), an adapter protein in the intracellular signaling pathway to Ras, was investigated by circular dichroic (CD) spectroscopy. The compact native beta-barrel conformation, previously elucidated by NMR spectroscopy, was largely predominant at pH = 4.8, in the absence of salt. From the structural changes induced by varying pH, ionic strength, temperature, or hydrophobicity of the environment, evidence for the existence of distinct nonnative conformations was obtained in the far- and near-UV domains. Along the free energy scale, these appear to distribute into two conformational ensembles, depending on the extent of structural and thermodynamic differences compared to the native conformation. The first ensemble consists of non-native conformations with a nativelike secondary structure, and the second is composed of partially unfolded conformations having short alpha-helical fragments or turnlike motifs in their nonnative secondary structure. Most of the observed nonnative conformations exist in mild or nondenaturing conditions. They probably have distinct compactness of their inner structure, depending on the strength of nonlocal interactions, but only the native all-beta conformation possesses a condensed protein exterior, appropriate for the binding to the VPPPVPPRRR decapeptide from Sos. Upon binding, the native conformation undergoes a local tertiary structure change in a hydrophobic pocket at the binding site. This is accompanied by the PP-II helix folding of the proline-rich peptide. Interestingly, in the near-UV domain, a significant change in the spectral contribution of an aromatic exciton was observed, thus allowing quantitative tracking of the binding process.     

Loop propensity of the sequence YKGQP from staphylococcal nuclease: implications for the folding of nuclease.

Recently we performed molecular dynamics (MD) simulations on the folding of the hairpin peptide DTVKLMYKGQPMTFR from staphylococcal nuclease in explicit water. We found that the peptide folds into a hairpin conformation with native and nonnative hydrogen-bonding patterns. In all the folding events observed in the folding of the hairpin peptide, loop formation involving the region YKGQP was an important event. In order to trace the origins of the loop propensity of the sequence YKGQP, we performed MD simulations on the sequence starting from extended, polyproline II and native type I' turn conformations for a total simulation length of 300 ns, using the GROMOS96 force field under constant volume and temperature (NVT) conditions. The free-energy landscape of the peptide YKGQP shows minima corresponding to loop conformation with Tyr and Pro side-chain association, turn and extended conformational forms, with modest free-energy barriers separating the minima. To elucidate the role of Gly in facilitating loop formation, we also performed MD simulations of the mutated peptide YKAQP (Gly --> Ala mutation) under similar conditions starting from polyproline II conformation for 100 ns. Two minima corresponding to bend/turn and extended conformations were observed in the free-energy landscape for the peptide YKAQP. The free-energy barrier between the minima in the free-energy landscape of the peptide YKAQP was also modest. Loop conformation is largely sampled by the YKGQP peptide, while extended conformation is largely sampled by the YKAQP peptide. We also explain why the YKGQP sequence samples type II turn conformation in these simulations, whereas the sequence as part of the hairpin peptide DTVKLMYKGQPMTFR samples type I' turn conformation both in the X-ray crystal structure and in our earlier simulations on the folding of the hairpin peptide. We discuss the implications of our results to the folding of the staphylococcal nuclease.     

Modeling the role of disulfide bonds in protein folding: Entropic barriers and pathways

The role of disulfide bonds in directing protein folding is studied using lattice models. We find that the stability and the specificity of the disulfide bond interactions play quite different roles in the folding process: Under some conditions, the stability decreases the overall rate of folding; the specificity, however, by yielding a simpler connectivity of intermediates, always increases the rate of folding. This conclusion is intimately related to the selection mechanism entailed by entropic driving forces, such as the loop formation probability, and entropic barriers separating the native and the many native-like metastable states. The folding time is found to be a minimum for a certain range of the effective disulfide bond interaction. Examination of a model, which allows for the formation of disulfide bonded intermediates, suggests that folding proceeds via a threestage multiple pathways kinetics. We show that there are pathways to the native state involving only native-like intermediates, as well as those that are mediated by nonnative intermediates. These findings are interpreted in terms of the appropriate energy landscape describing the barriers connecting low energy conformations. The consistency of our conclusions with several experimental studies is also discussed. © 1995 Wiley-Liss, Inc.     

Conformation of P22 tailspike folding and aggregation intermediates probed by monoclonal antibodies.

The partitioning of partially folded polypeptide chains between correctly folded native states and off-pathway inclusion bodies is a critical reaction in biotechnology. Multimeric partially folded intermediates, representing early stages of the aggregation pathway for the P22 tailspike protein, have been trapped in the cold and isolated by nondenaturing polyacrylamide gel electrophoresis (PAGE) (speed MA, Wang DIC, King J. 1995. Protein Sci 4:900-908). Monoclonal antibodies against tailspike chains discriminate between folding intermediates and native states (Friguet B, Djavadi-Ohaniance L, King J, Goldberg ME. 1994. J Biol Chem 269:15945-15949). Here we describe a nondenaturing Western blot procedure to probe the conformation of productive folding intermediates and off-pathway aggregation intermediates. The aggregation intermediates displayed epitopes in common with productive folding intermediates but were not recognized by antibodies against native epitopes. The nonnative epitope on the folding and aggregation intermediates was located on the partially folded N-terminus, indicating that the N-terminus remained accessible and nonnative in the aggregated state. Antibodies against native epitopes blocked folding, but the monoclonal directed against the N-terminal epitope did not, indicating that the conformation of the N-terminus is not a key determinant of the productive folding and chain association pathway.     

Visualization of Protein Folding Funnels in Lattice Models

Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed.