A novel parameterization scheme for energy equations and its use to calculate the structure of protein molecules

A novel scheme for the parameterization of a type of “potential energy” function for protein molecules is introduced. The function is parameterized based on the known conformations of previously determined protein structures and their sequence similarity to a molecule whose conformation is to be calculated. Once parameterized, minima of the potential energy function can be located using a version of simulated annealing which has been previously shown to locate global and near-global minima with the given functional form. As a test problem, the potential was parameterized based on the known structures of the rubredoxins from Desulfovibrio vulgaris, Desulfovibrio desulfuricans, and Clostridium pasteurianum, which vary from 45 to 54 amino acids in length, and the sequence alignments of these molecules with the rubredoxin sequence from Desulfovibrio gigas. Since the Desulfovibrio gigas rubredeoxin conformation has also been determined, it is possible to check the accuracy of the results. Ten simulated-annealing runs from random starting conformations were performed. Seven of the 10 resultant conformations have an all-C_α rms deviation from the crystallographically determined conformation of less than 1.7 Å. For five of the structures, the rms deviation is less than 0.8 Å. Four of the structures have conformations which are virtually identical to each other except for the position of the carboxy-terminal residue. This is also the conformation which is achieved if the determined crystal structure is minimized with the same potential. The all-C_α rms difference between the crystal and minimized crystal structures is 0.6 Å. It is further observed that the “energies” of the structures according to the potential function exhibit a strong correlation with rms deviation from the native structure. The conformations of the individual model structures and the computational aspects of the modeling procedure are discussed. © 1993 Wiley-Liss, Inc.     

Structures of ubiquitin insertion mutants support site-specific reflex response to insertions hypothesis

We previously concluded that, judging from NMR chemical shifts, the effects of insertions into ubiquitin on its conformation appear to depend primarily on the site of insertion rather than the sequence of the insertion. To obtain a more complete and atomic-resolution understanding of how these insertions modulate the conformation of ubiquitin, we have solved the crystal structures of four insertional mutants of ubiquitin. Insertions between residues 9 and 10 of ubiquitin are minimally perturbing to the remainder of the protein, while larger alterations occur when the insertion is between residues 35 and 36. Further, the alterations in response to insertions are very similar for each mutant at a given site. Two insertions, one at each site, were designed from structurally homologous proteins. Interestingly, the secondary structure within these five to seven amino acid residue insertions is conserved in the new protein. Overall, the crystal structures support the previous conclusion that the conformational effects of these insertions are determined largely by the site of insertion and only secondarily by the sequence of the insert.     

Assessment of the ability to model proteins with leucine-rich repeats in light of the latest structural information

The three-dimensional structures of leucine-rich repeat (LRR)-containing proteins from five different families were previously predicted based on the crystal structure of the ribonuclease inhibitor, using an approach that combined homology-based modeling, structure-based sequence alignment of LRRs, and several rational assumptions. The structural models have been produced based on very limited sequence similarity, which, in general, cannot yield trustworthy predictions. Recently, the protein structures from three of these five families have been determined. In this report we estimate the quality of the modeling approach by comparing the models with the experimentally determined structures. The comparison suggests that the general architecture, curvature, "interior/exterior" orientations of side chains, and backbone conformation of the LRR structures can be predicted correctly. On the other hand, the analysis revealed that, in some cases, it is difficult to predict correctly the twist of the overall super-helical structure. Taking into consideration the conclusions from these comparisons, we identified a new family of bacterial LRR proteins and present its structural model. The reliability of the LRR protein modeling suggests that it would be informative to apply similar modeling approaches to other classes of solenoid proteins.     

Homology modeling of histidine-containing phosphocarrier protein and eosinophil-derived neurotoxin: Construction of models and comparison with experiment

Homology modeling methods have been used to construct models of two proteins—the histidine-containing phosphocarrier protein (HPr) from Mycoplasma capricolum and human eosinophil-derived neurotoxin (EDN). Comparison of the models with the subsequently determined X-ray crystal structures indicates that the core regions of both proteins are reasonably well reproduced, although the template structures are closer to the X-ray structures in these regions—possible enhancements are discussed. The conformations of most of the side chains in the core of HPr are well reproduced in the modeled structure. As expected, the conformations of surface side chains in this protein differ significantly from the X-ray structure. The loop regions of EDN were incorrectly modeled—reasons for this and possible enhancements are discussed. © 1995 Wiley-Liss, Inc.     

Structural templates for modeling homodimers

Oligomeric proteins are more abundant in nature than monomeric proteins, and involved in all biological processes. In the absence of an experimental structure, their subunits can be modeled from their sequence like monomeric proteins, but reliable procedures to build the oligomeric assembly are scarce. Template‐based methods, which start from known protein structures, are commonly applied to model subunits. We present a method to model homodimers that relies on a structural alignment of the subunits, and test it on a set of 511 target structures recently released by the Protein Data Bank, taking as templates the earlier released structures of 3108 homodimeric proteins (H‐set), and 2691 monomeric proteins that form dimer‐like assemblies in crystals (M‐set). The structural alignment identifies a H‐set template for 97% of the targets, and in half of the cases, it yields a correct model of the dimer geometry and residue–residue contacts in the target. It also identifies a M‐set template for most of the targets, and some of the crystal dimers are very similar to the target homodimers. The procedure efficiently detects homology at low levels of sequence identities, and points to erroneous quaternary structures in the Protein Data Bank. The high coverage of the target set suggests that the content of the Protein Data Bank already approaches the structural diversity of protein assemblies in nature, and that template‐based methods should become the choice method for modeling oligomeric as well as monomeric proteins.     

Evaluation of comparative protein modeling by MODELLER

We evaluate 3D models of human nucleoside diphosphate kinase, mouse cellular retinoic acid binding protein I, and human eosinophil neurotoxin that were calculated by MODELLER , a program for comparative protein modeling by satisfaction of spatial restraints. The models have good stereochemistry and are at least as similar to the crystallographic structures as the closest template structures. The largest errors occur in the regions that were not aligned correctly or where the template structures are not similar to the correct structure. These regions correspond predominantly to exposed loops, insertions of any length, and non-conserved side chains. When a template structure with more than 40% sequence identity to the target protein is available, the model is likely to have about 90% of the mainchain atoms modeled with an rms deviation from the X-ray structure of ≈ 1 Å, in large part because the templates are likely to be that similar to the X-ray structure of the target. This rms deviation is comparable to the overall differences between refined NMR and X-ray crystallography structures of the same protein. © 1995 Wiley-Liss, Inc.     

Protein structure prediction by threading methods: Evaluation of current techniques

This paper evaluates the results of a protein structure prediction contest. The predictions were made using threading procedures, which employ techniques for aligning sequences with 3D structures to select the correct fold of a given sequence from a set of alternatives. Nine different teams submitted 86 predictions, on a total of 21 target proteins with little or no sequence homology to proteins of known structure. The 3D structures of these proteins were newly determined by experimental methods, but not yet published or otherwise available to the predictors. The predictions, made from the amino acid sequence alone, thus represent a genuine test of the current performance of threading methods. Only a subset of all the predictions is evaluated here. It corresponds to the 44 predictions submitted for the 11 target proteins seen to adopt known folds. The predictions for the remaining 10 proteins were not analyzed, although weak similarities with known folds may also exist in these proteins. We find that threading methods are capable of identifying the correct fold in many cases, but not reliably enough as yet. Every team predicts correctly a different set of targets, with virtually all targets predicted correctly by at least one team. Also, common folds such as TIM barrels are recognized more readily than folds with only a few known examples. However, quite surprisingly, the quality of the sequence-structure alignments, corresponding to correctly recognized folds, is generally very poor, as judged by comparison with the corresponding 3D structure alignments. Thus, threading can presently not be relied upon to derive a detailed 3D model from the amino acid sequence. This raises a very intriguing question: how is fold recognition achieved? Our analysis suggests that it may be achieved because threading procedures maximize hydrophobic interactions in the protein core, and are reasonably good at recognizing local secondary structure. © 1995 Wiley-Liss, Inc.     

Statistical potentials for fold assessment

A protein structure model generally needs to be evaluated to assess whether or not it has the correct fold. To improve fold assessment, four types of a residue-level statistical potential were optimized, including distance-dependent, contact, Phi/Psi dihedral angle, and accessible surface statistical potentials. Approximately 10,000 test models with the correct and incorrect folds were built by automated comparative modeling of protein sequences of known structure. The criterion used to discriminate between the correct and incorrect models was the Z-score of the model energy. The performance of a Z-score was determined as a function of many variables in the derivation and use of the corresponding statistical potential. The performance was measured by the fractions of the correctly and incorrectly assessed test models. The most discriminating combination of any one of the four tested potentials is the sum of the normalized distance-dependent and accessible surface potentials. The distance-dependent potential that is optimal for assessing models of all sizes uses both C(alpha) and C(beta) atoms as interaction centers, distinguishes between all 20 standard residue types, has the distance range of 30 A, and is derived and used by taking into account the sequence separation of the interacting atom pairs. The terms for the sequentially local interactions are significantly less informative than those for the sequentially nonlocal interactions. The accessible surface potential that is optimal for assessing models of all sizes uses C(beta) atoms as interaction centers and distinguishes between all 20 standard residue types. The performance of the tested statistical potentials is not likely to improve significantly with an increase in the number of known protein structures used in their derivation. The parameters of fold assessment whose optimal values vary significantly with model size include the size of the known protein structures used to derive the potential and the distance range of the accessible surface potential. Fold assessment by statistical potentials is most difficult for the very small models. This difficulty presents a challenge to fold assessment in large-scale comparative modeling, which produces many small and incomplete models. The results described in this study provide a basis for an optimal use of statistical potentials in fold assessment.     

Crystal structure of a recombinant form of the maltodextrin-binding protein carrying an inserted sequence of a B-cell epitope from the preS2 region of hepatitis B virus

We report the crystal structure of MalE-B133, a recombinant form of the maltodextrin-binding protein (MBP) of Escherichia coli carrying an inserted amino-acid sequence of a B-cell epitope from the preS2 region of the hepatitis B virus (HBV). The structure was determined by molecular replacement methods and refined to 2.7 Å resolution. MalE-B133 is an insertion/deletion mutant of MBP in which residues from positions 134 to 142, an external α helix in the wild-type structure, are replaced by a foreign peptide segment of 19 amino acids. The inserted residues correspond to the preS2 sequence from positions 132 to 145 and five flanking residues that arise from the creation of restriction sites. The conformation of the recombinant protein, excluding the inserted segment, closely resembles that of wild-type MBP in the closed maltose-bound form. MalE-B133 was shown by previous studies to display certain immunogenic and antigenic properties of the hepatitis B surface antigen (HBsAg), which contains the preS2 region. The crystal structure reveals the conformation of the first nine epitope residues (preS2 positions 132 to 140) exposed on the surface of the molecule. The remaining five epitope residues (preS2 positions 141 to 145) are not visible in electron density maps. The path of the polypeptide chain in the visible portion of the insert differs from that of the deleted segment in the structure of wild-type MBP, displaying a helical conformation at positions 134 to 140 (preS2 sequence numbering). A tripeptide (Asp-Pro-Arg) at the N terminus of the helix forms a stable structural motif that may be implicated in the cross-reactivity of anti-HBsAg antibodies with the hybrid protein. Proteins 27:1–8 © 1997 Wiley-Liss, Inc.     

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

Comparing short protein substructures by a method based on backbone torsion angles

An efficient algorithm was characterized that determines the similarity in main chain conformation between short protein substructures. The algorithm computes Δt, the root mean square difference in ? and ψ torsion angles over a small number of amino acids (typically 3–5). Using this algorithm, large number of protein substrates comparisons were feasible. The parameter Δt was sensitive to variations in local protein conformation, and it correlates with Δr, the root mean square deviation in atomic coordinates. Values for Δt were obtained that define similarity thresholds, which determine whether two substructure are considered structurally similar. To set a lower bound on the similarity threshold, we estimated the component of Δt due to measurement noise fromcomparisons of independently refined coordinates of the same protein. A sample distribution of Δt from nonhomologous protein comparisons identified an upper bound on the similarity threshold, one that refrains from incorporating large numbers of nonmatching comparisons large numbers of nonmatching comparisons. Unlike methods based on Cα atoms alone, Δt was sensitive to rotations in the peptide plane, shown to occur in several proteins. Comparisons of homologus proteins by Δt showed that the active site torsion angles are highly conserved. The Δt method was applied to the α-chain of human hemoglobin, where it readily demonstrated the local differences in the structures of different ligation states.     

Progress in fold recognition

The prediction experiment reveals that fold recognition has become a powerful tool in structural biology. We applied our fold recognition technique to 13 target sequences. In two cases, replication terminating protein and prosequence of subtilisin, the predicted structures are very similar to the experimentally determined folds. For the first time, in a public blind test, the unknown structures of proteins have been predicted ahead of experiment to an accuracy approaching molecular detail. In two other cases the approximate folds have been predicted correctly. According to the assessors there were 12 recognizable folds among the target proteins. In our postprediction analysis we find that in 7 cases our fold recognition technique is successful. In several of the remaining cases the predicted folds have interesting features in common with the experimental results. We present our procedure, discuss the results, and comment on several fundamental and technical problems encountered in fold recognition. © 1995 Wiley-Liss, Inc.     

Solution structure of alpha-conotoxin SI

The nuclear magnetic resonance solution structure of alpha-conotoxin SI has been determined at pH 4.2. The 36 lowest energy structures show that alpha-conotoxin SI exists in a single major solution conformation and is stabilized by six hydrogen bonds. Comparisons are made between the SI solution structure and the solution and crystal structures of alpha-conotoxin GI. Surprisingly, a high degree of similarity between the backbone conformations of the GI crystal and the SI solution structures is seen in the region of lowest sequence homology, namely residues Gly-8 to Ser-12. This similarity is more surprising when considering that in SI a proline replaces the Arg-9 found in GI. The correspondence in conformation in this region provides the definitive evidence that it is the loss of the arginine basic charge at residue 9 which determines the differences in toxicity between GI and SI, rather than any changes in conformation induced by the cyclic proline residue.     

Modeling structurally variable regions in homologous proteins with rosetta

A major limitation of current comparative modeling methods is the accuracy with which regions that are structurally divergent from homologues of known structure can be modeled. Because structural differences between homologous proteins are responsible for variations in protein function and specificity, the ability to model these differences has important functional consequences. Although existing methods can provide reasonably accurate models of short loop regions, modeling longer structurally divergent regions is an unsolved problem. Here we describe a method based on the de novo structure prediction algorithm, Rosetta, for predicting conformations of structurally divergent regions in comparative models. Initial conformations for short segments are selected from the protein structure database, whereas longer segments are built up by using three- and nine-residue fragments drawn from the database and combined by using the Rosetta algorithm. A gap closure term in the potential in combination with modified Newton's method for gradient descent minimization is used to ensure continuity of the peptide backbone. Conformations of variable regions are refined in the context of a fixed template structure using Monte Carlo minimization together with rapid repacking of side-chains to iteratively optimize backbone torsion angles and side-chain rotamers. For short loops, mean accuracies of 0.69, 1.45, and 3.62 A are obtained for 4, 8, and 12 residue loops, respectively. In addition, the method can provide reasonable models of conformations of longer protein segments: predicted conformations of 3A root-mean-square deviation or better were obtained for 5 of 10 examples of segments ranging from 13 to 34 residues. In combination with a sequence alignment algorithm, this method generates complete, ungapped models of protein structures, including regions both similar to and divergent from a homologous structure. This combined method was used to make predictions for 28 protein domains in the Critical Assessment of Protein Structure 4 (CASP 4) and 59 domains in CASP 5, where the method ranked highly among comparative modeling and fold recognition methods. Model accuracy in these blind predictions is dominated by alignment quality, but in the context of accurate alignments, long protein segments can be accurately modeled. Notably, the method correctly predicted the local structure of a 39-residue insertion into a TIM barrel in CASP 5 target T0186.     

Recognition of distantly related proteins through energy calculations

A new method to detect remote relationships between protein sequences and known three-dimensional structures based on direct energy calculations and without reliance on statistics has been developed. The likelihood of a residue to occupy a given position on the structural template was represented by an estimate of the stabilization free energy made after explicit prediction of the substituted side chain conformation. The profile matrix derived from these energy values and modified by increasing the residue self-exchange values successfully predicted compatibility of heatshock protein and globin sequences with the three-dimensional structures of actin and phycocyanin, respectively, from a full protein sequence databank search. The high sensitivity of the method makes it a unique tool for predicting the three-dimensional fold for the rapidly growing number of protein sequences. © 1994 Wiley-Liss, Inc.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

SPINFAST: using structure alignment profiles to enhance the accuracy and assess the reliability of protein side-chain modeling

We present a novel, knowledge-based method for the side-chain addition step in protein structure modeling. The foundation of the method is a conditional probability equation, which specifies the probability that a side-chain will occupy a specific rotamer state, given a set of evidence about the rotamer states adopted by the side-chains at aligned positions in structurally homologous crystal structures. We demonstrate that our method increases the accuracy of homology model side-chain addition when compared with the widely employed practice of preserving the side-chain conformation from the homology template to the target at conserved residue positions. Furthermore, we demonstrate that our method accurately estimates the probability that the correct rotamer state has been selected. This interesting result implies that our method can be used to understand the reliability of each and every side-chain in a protein homology model.     

Alanine-scanning mutagenesis of the beta-sheet region of phage T4 lysozyme suggests that tertiary context has a dominant effect on beta-sheet formation

In general, alpha-helical conformations in proteins depend in large part on the amino acid residues within the helix and their proximal interactions. For example, an alanine residue has a high propensity to adopt an alpha-helical conformation, whereas that of a glycine residue is low. The sequence preferences for beta-sheet formation are less obvious. To identify the factors that influence beta-sheet conformation, a series of scanning polyalanine mutations were made within the strands and associated turns of the beta-sheet region in T4 lysozyme. For each construct the stability of the folded protein was reduced substantially, consistent with removal of native packing interactions. However, the crystal structures showed that each of the mutants retained the beta-sheet conformation. These results suggest that the structure of the beta-sheet region of T4 lysozyme is maintained to a substantial extent by tertiary interactions with the surrounding parts of the protein. Such tertiary interactions may be important in determining the structures of beta-sheets in general.