Scoring a diverse set of high-quality docked conformations: a metascore based on electrostatic and desolvation interactions

Predicting protein-protein interactions involves sampling and scoring docked conformations. Barring some large structural rearrangement, rapidly sampling the space of docked conformations is now a real possibility, and the limiting step for the successful prediction of protein interactions is the scoring function used to reduce the space of conformations from billions to a few, and eventually one high affinity complex. An atomic level free-energy scoring function that estimates in units of kcal/mol both electrostatic and desolvation interactions (plus van der Waals if appropriate) of protein-protein docked conformations is used to rerank the blind predictions (860 in total) submitted for six targets to the community-wide Critical Assessment of PRediction of Interactions (CAPRI; http://capri.ebi.ac.uk). We found that native-like models often have varying intermolecular contacts and atom clashes, making unlikely that one can construct a universal function that would rank all these models as native-like. Nevertheless, our scoring function is able to consistently identify the native-like complexes as those with the lowest free energy for the individual models of 16 (out of 17) human predictors for five of the targets, while at the same time the modelers failed to do so in more than half of the cases. The scoring of high-quality models developed by a wide variety of methods and force fields confirms that electrostatic and desolvation forces are the dominant interactions determining the bound structure. The CAPRI experiment has shown that modelers can predict valuable models of protein-protein complexes, and improvements in scoring functions should soon solve the docking problem for complexes whose backbones do not change much upon binding. A scoring server and programs are available at http://structure.pitt.edu.     

Sampling realistic protein conformations using local structural bias

The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

Dependence of protein stability on the structure of the denatured state: free energy calculations of I56V mutation in human lysozyme.

Free energy calculations were carried out to understand the effect of the I56V mutation of human lysozyme on its thermal stability. In the simulation of the denatured state, a short peptide including the mutation site in the middle is employed. To study the dependence of the stability on the denatured-state structure, five different initial conformations, native-like, extended, and three random-coil-like conformations, were examined. We found that the calculated free energy difference, DeltaDeltaGcal, depends significantly on the structure of the denatured state. When native-like structure is employed, DeltaDeltaGcal is in good agreement with the experimental free energy difference, DeltaDeltaGexp, whereas in the other four models, DeltaDeltaGcal differs sharply from DeltaDeltaGexp. It is therefore strongly suggested that the structure around the mutation site takes a native-like conformation rather than an extended or random-coil conformation. From the free energy component analysis, it has been shown that free energy components originating from Lennard-Jones and covalent interactions dominantly determine DeltaDeltaGcal. The contribution of protein-protein interactions to the nonbonded component of DeltaDeltaGcal is about the same as that from protein-water interactions. The residues that are located in a hydrophobic core (F3, L8, Y38, N39, T40, and I89) contribute significantly to the nonbonded free energy component of DeltaDeltaGcal. We also propose a general computational strategy for the study of protein stability that is equally conscious of the denatured and native states.     

Enhanced sampling near the native conformation using statistical potentials for local side-chain and backbone interactions

In the preceding article in this issue of Proteins, an empirical energy function consisting of 4 statistical potentials that quantify local side-chain-backbone and side-chain-side-chain interactions has been demonstrated to successfully identify the native conformations of short sequence fragments and the native structure within large sets of high-quality decoys. Because this energy function consists entirely of interactions between residues separated by fewer than 5 positions, it can be used at the earliest stage of ab initio structure prediction to enhance the efficiency of conformational search. In this article, protein fragments are generated de novo by recombining very short segments of protein structures (2, 4, or 6 residues), either selected at random or optimized with respect this local energy function. When local energy is optimized in selected fragments, more efficient sampling of conformational space near the native conformation is consistently observed for 450 randomly selected single turn fragments, with turn lengths varying from 3 to 12 residues and all 4 combinations of flanking secondary structure. These results further demonstrate the energetic significance of local interactions in protein conformations. When used in combination with longer range energy functions, application of these potentials should lead to more accurate prediction of protein structure.     

Decoys 'R' Us: a database of incorrect conformations to improve protein structure prediction

The development of an energy or scoring function for protein structure prediction is greatly enhanced by testing the function on a set of computer-generated conformations (decoys) to determine whether it can readily distinguish native-like conformations from nonnative ones. We have created "Decoys 'R' Us," a database containing many such sets of conformations, to provide a resource that allows scoring functions to be improved.     

Beta-sheet folding of fragment (16-36) of bovine pancreatic trypsin inhibitor as predicted by Monte Carlo simulated annealing.

A tertiary structure prediction is described using Monte Carlo simulated annealing for the peptide fragment corresponding to residues 16-36 of bovine pancreatic trypsin inhibitor (BPTI). The simulation starts with randomly chosen initial conformations and is performed without imposing experimental constraints using energy functions given for generic interatomic interactions. Out of 20 simulation trials, seven conformations show a sheet-like structure--two strands connected by a turn--although this sheet-like structure is not as rigid as that observed in native BPTI. It is also shown that these conformations are mostly looped and exhibit a native-like right-handed twist. Unlike the case with the C-peptide of RNase A, no conspicuous alpha-helical structure is found in any of the final conformations obtained in the simulation. However, the lowest-energy conformation does not resemble exactly the native structure. This indicates that the rigid beta-sheet conformation of native BPTI merely corresponds to a local minimum of the energy function if the fragment with residues 16-36 is isolated from the native protein. A statistical analysis of all 20 final conformations suggests that the tendency for the peptide segments to form extended beta-strands is strong for those with residues 18-24, and moderate for those with residues 30-35. The segment of residues 25-29 does not tend to form any definite structure. In native BPTI, the former segments are involved in the beta-sheet and the latter in the turn. A folding scenario is also speculated from this analysis.     

Denatured collapsed states in protein folding: example of apomyoglobin.

Experimental approaches, including circular dichroism, small angle X-ray scattering, steady-state fluorescence, and fluorescence energy transfer, were applied to study the 3D-structure of apomyolgobin in different conformational states. These included the native and molten globules, along with either less ordered conformations induced by the addition of anions or completely unfolded states. The results show that the partially folded forms of apomyoglobin stabilized by KCl and/or Na(2)SO(4) under unfolding conditions (pH 2) exhibit a significant amount of secondary structure (circular dichroism), low packing density of protein molecules (SAXS), and native-like dimensions of the AGH core (fluorescence energy transfer). This finding indicates that a native-like tertiary fold of the polypeptide chain, i.e., the spatial organization of secondary structure elements, most likely emerges prior to the formation of the molten globule state.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

Distance geometry generates native-like folds for small helical proteins using the consensus distances of predicted protein structures.

For successful ab initio protein structure prediction, a method is needed to identify native-like structures from a set containing both native and non-native protein-like conformations. In this regard, the use of distance geometry has shown promise when accurate inter-residue distances are available. We describe a method by which distance geometry restraints are culled from sets of 500 protein-like conformations for four small helical proteins generated by the method of Simons et al. (1997). A consensus-based approach was applied in which every inter-Calpha distance was measured, and the most frequently occurring distances were used as input restraints for distance geometry. For each protein, a structure with lower coordinate root-mean-square (RMS) error than the mean of the original set was constructed; in three cases the topology of the fold resembled that of the native protein. When the fold sets were filtered for the best scoring conformations with respect to an all-atom knowledge-based scoring function, the remaining subset of 50 structures yielded restraints of higher accuracy. A second round of distance geometry using these restraints resulted in an average coordinate RMS error of 4.38 A.     

Folding of thermolysin fragments. Correlation between conformational stability and antigenicity of carboxyl-terminal fragments

Circular dichroism (CD) and immunochemical measurements have been used to examine conformational properties of COOH-terminal fragments 121-316, 206-316 and 225(226)-316 of thermolysin, and to compare these properties to those of native thermolysin and thermolysin S, the stable partially active two-fragment complex composed of fragments 5-224(225) and 225(226)-316. In aqueous solution at neutral pH, all the COOH-terminal fragments attain a native-like conformation, as judged both by the content of secondary structure deduced from far-ultraviolet CD spectra and by the recognition of rabbit polyclonal antibodies specific for the COOH-terminal region in native thermolysin. The three fragments showed reversible cooperative unfolding transitions mediated by both heat and guanidine hydrochloride (Gdn X HCl). The phase transition curves were analyzed for Tm (temperature of half-denaturation) and Gibbs free energies (delta GD) of unfolding from native to denatured state. The observed order of thermal stability is 225(226)-316 less than or equal to 206-316 less than 121-316 less than thermolysin S less than thermolysin. The ranking of delta GD values for the three fragments correlates with the size of each fragment. Competitive binding studies by radioimmunoassay using 14C-labeled thermolysin and affinity purified antibodies specific for native antigenic determinants in segment 206-316 of native thermolysin indicate that the COOH-terminal fragments adopt native-like conformations which are in equilibrium with non-native conformations. These equilibria are shifted towards the native state as the fragment size increases from 225(226)-316, to 206-316, to 121-316. Fragment 225(226)-316, when combined with fragment 5-224(225) in the thermolysin S complex, adopts a more stable native-like conformation and becomes much more antigenic. It has been shown that the degree of antigenicity of COOH-terminal fragments towards thermolysin antibodies correlates directly with their conformational stability. The results of this study are discussed in relation to the recently proposed correlation between antigenicity and segmental mobility of globular proteins.     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

A polar, solvent-exposed residue can be essential for native protein structure

BACKGROUND: A large energy gap between the native state and the non-native folded states is required for folding into a unique three-dimensional structure. The features that define this energy gap are not well understood, but can be addressed using de novo protein design. Previously, alpha(2)D, a dimeric four-helix bundle, was designed and shown to adopt a native-like conformation. The high-resolution solution structure revealed that this protein adopted a bisecting U motif. Glu7, a solvent-exposed residue that adopts many conformations in solution, might be involved in defining the unique three-dimensional structure of alpha(2)D. RESULTS: A variety of hydrophobic and polar residues were substituted for Glu7 and the dynamic and thermodynamic properties of the resulting proteins were characterized by analytical ultracentrifugation, circular dichroism spectroscopy, and nuclear magnetic resonance spectroscopy. The majority of substitutions at this solvent-exposed position had little affect on the ability to fold into a dimeric four-helix bundle. The ability to adopt a unique conformation, however, was profoundly modulated by the residue at this position despite the similar free energies of folding of each variant. CONCLUSIONS: Although Glu7 is not involved directly in stabilizing the native state of alpha(2)D, it is involved indirectly in specifying the observed fold by modulating the energy gap between the native state and the non-native folded states. These results provide experimental support for hypothetical models arising from lattice simulations of protein folding, and underscore the importance of polar interfacial residues in defining the native conformations of proteins.     

Monte carlo simulations of protein folding. II. Application to protein A,ROP, and crambin

The hierarchy of lattice Monte Carlo models described in the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 18:338–352, 1994) is applied to the simulation of protein folding and the prediction of 3-dimensional structure. Using sequence information alone, three proteins have been successfully folded: the B domain of staphylococcal protein A, a 120 residue, monomeric version of ROP dimer, and crambin. Starting from a random expanded conformation, the model proteins fold along relatively well-defined folding pathways. These involve a collection of early intermediates, which are followed by the final (and rate-determining) transition from compact intermediates closely resembling the molten globule state to the native-like state. The predicted structures are rather unique, with native-like packing of the side chains. The accuracy of the predicted native conformations is better than those obtained in previous folding simulations. The best (but by no means atypical) folds of protein A have a coordinate rms of 2.25 Å from the native Cα trace, and the best coordinate rms from crambin is 3.18 Å. For ROP monomer, the lowest coordinate rms from equivalent Cαs of ROP dimer is 3.65 Å. Thus, for two simple helical proteins and a small α/β protein, the ability to predict protein structure from sequence has been demonstrated. © 1994 John Wiley & Sons, Inc.     

Iterative assembly of helical proteins by optimal hydrophobic packing

We present a method for the computer-based iterative assembly of native-like tertiary structures of helical proteins from alpha-helical fragments. For any pair of helices, our method, called MATCHSTIX, first generates an ensemble of possible relative orientations of the helices with various ways to form hydrophobic contacts between them. Those conformations having steric clashes, or a large radius of gyration of hydrophobic residues, or with helices too far separated to be connected by the intervening linking region, are discarded. Then, we attempt to connect the two helical fragments by using a robotics-based loop-closure algorithm. When loop closure is feasible, the algorithm generates an ensemble of viable interconnecting loops. After energy minimization and clustering, we use a representative set of conformations for further assembly with the remaining helices, adding one helix at a time. To efficiently sample the conformational space, the order of assembly generally proceeds from the pair of helices connected by the shortest loop, followed by joining one of its adjacent helices, always proceeding with the shorter connecting loop. We tested MATCHSTIX on 28 helical proteins each containing up to 5 helices and found it to heavily sample native-like conformations. The average rmsd of the best conformations for the 17 helix-bundle proteins that have 2 or 3 helices is less than 2 A; errors increase somewhat for proteins containing more helices. Native-like states are even more densely sampled when disulfide bonds are known and imposed as restraints. We conclude that, at least for helical proteins, if the secondary structures are known, this rapid rigid-body maximization of hydrophobic interactions can lead to small ensembles of highly native-like structures. It may be useful for protein structure prediction.     

Specific non-native hydrophobic interactions in a hidden folding intermediate: implications for protein folding

Structures of intermediates and transition states in protein folding are usually characterized by amide hydrogen exchange and protein engineering methods and interpreted on the basis of the assumption that they have native-like conformations. We were able to stabilize and determine the high-resolution structure of a partially unfolded intermediate that exists after the rate-limiting step of a four-helix bundle protein, Rd-apocyt b(562), by multidimensional NMR methods. The intermediate has partial native-like secondary structure and backbone topology, consistent with our earlier native state hydrogen exchange results. However, non-native hydrophobic interactions exist throughout the structure. These and other results in the literature suggest that non-native hydrophobic interactions may occur generally in partially folded states. This can alter the interpretation of mutational protein engineering results in terms of native-like side chain interactions. In addition, since the intermediate exists after the rate-limiting step and Rd-apocyt b(562) folds very rapidly (k(f) approximately 10(4) s(-1)), these results suggest that non-native hydrophobic interactions, in the absence of topological misfolding, are repaired too rapidly to slow folding and cause the accumulation of folding intermediates. More generally, these results illustrate an approach for determining the high-resolution structure of folding intermediates.     

Unfolding of the cold shock protein studied with biased molecular dynamics

The cold shock protein from Bacillus caldolyticus is a small beta-barrel protein that folds in a two-state mechanism. For the native protein and for several mutants, a wealth of experimental data are available on stability and folding, so that it is an optimal system to study this process. We compare data from unfolding simulations (trajectories of 5 and up to 12 ns) obtained with a bias potential at room temperature and from unbiased thermal unfolding simulations with experimental data. The unfolding patterns derived from the trajectories starting from different native-like conformations and subject to different unfolding conditions agree. The transition state found in the simulations of unfolding is close to the native structure in agreement with experiment. Moreover, a lower value of the free energy barrier of unfolding was found for the mutant R3E than for the mutant E46A and the native protein, as indicated by experimental data. The first unfolding event involves the three-stranded beta-sheet whose decomposition corresponds to the transition state. In contrast to conclusions drawn from experiments, we found that the two-stranded beta-strand forms the most stable substructure, which decomposes very late in the unfolding process. However, assuming that this structure forms very early in the folding process, our findings would not contradict the experiments but require a different interpretation of them.     

Synthesis and Biological Activity of Scyllatoxin-Based BH3 Domain Mimetics Containing Two Disulfide Linkages

The B cell lymphoma 2 (BCL2) proteins are a family of evolutionarily related proteins that act as positive or negative regulators of the intrinsic apoptosis pathway. Overexpression of anti-apoptotic BCL2 proteins in cells is associated with apoptotic resistance, which can result in cancerous phenotypes and pathogenic cell survival. Consequently, anti-apoptotic BCL2 proteins have attracted considerable interest as therapeutic targets. We recently reported the development of a novel class of synthetic protein based on scyllatoxin (ScTx) designed to mimic the helical BH3 interaction domain of the pro-apoptotic BCL2 protein Bax. These studies showed that the number and position of native disulfide linkages contained within the ScTx-Bax structure significantly influences the ability for these constructs to target anti-apoptotic BCL2 proteins in vitro. The goal of the present study is to investigate the contribution of two disulfide linkages in the folding and biological activity of ScTx-Bax proteins. Here, we report the full chemical synthesis of three ScTx-Bax sequence variants, each presenting two native disulfide linkages at different positions within the folded structure. It was observed that two disulfide linkages were sufficient to fold ScTx-Bax proteins into native-like architectures reminiscent of wild-type ScTx. Furthermore, we show that select (bis)disulfide ScTx-Bax variants can target Bcl-2 (proper) in vitro and that the position of the disulfide bonds significantly influences binding affinity. Despite exhibiting only modest binding to Bcl-2, the successful synthesis of ScTx-Bax proteins containing two disulfide linkages represents a viable route to ScTx-based BH3 domain mimetics that preserve native-like conformations. Finally, structural models of ScTx-Bax proteins in complex with Bcl-2 indicate that these helical mimetics bind in similar configurations as wild-type Bax BH3 domains. Taken together, these results suggest that ScTx-Bax proteins may serve as potent lead compounds that expand the repertoire of “druggable” protein–protein interactions.     

Molecular dynamics simulations of hydrophobic collapse of ubiquitin.

Nine nonnative conformations of ubiquitin, generated during two different thermal denaturation trajectories, were simulated under nearly native conditions (62 degrees C). The simulations included all protein and solvent atoms explicitly, and simulation times ranged from 1-2.4 ns. The starting structures had alpha-carbon root-mean-square deviations (RMSDs) from the crystal structure of 4-12 A and radii of gyration as high as 1.3 times that of the native state. In all but one case, the protein collapsed when the temperature was lowered and sampled conformations as compact as those reached in a control simulation beginning from the crystal structure. In contrast, the protein did not collapse when simulated in a 60% methanol:water mixture. The behavior of the protein depended on the starting structure: during simulation of the most native-like starting structures (<5 A RMSD to the crystal structure) the RMSD decreased, the number of native hydrogen bonds increased, and the secondary and tertiary structure increased. Intermediate starting structures (5-10 A RMSD) collapsed to the radius of gyration of the control simulation, hydrophobic residues were preferentially buried, and the protein acquired some native contacts. However, the protein did not refold. The least native starting structures (10-12 A RMSD) did not collapse as completely as the more native-like structures; instead, they experienced large fluctuations in radius of gyration and went through cycles of expansion and collapse, with improved burial of hydrophobic residues in successive collapsed states.