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.     

A composite score for predicting errors in protein structure models

Reliable prediction of model accuracy is an important unsolved problem in protein structure modeling. To address this problem, we studied 24 individual assessment scores, including physics-based energy functions, statistical potentials, and machine learning-based scoring functions. Individual scores were also used to construct approximately 85,000 composite scoring functions using support vector machine (SVM) regression. The scores were tested for their abilities to identify the most native-like models from a set of 6000 comparative models of 20 representative protein structures. Each of the 20 targets was modeled using a template of <30% sequence identity, corresponding to challenging comparative modeling cases. The best SVM score outperformed all individual scores by decreasing the average RMSD difference between the model identified as the best of the set and the model with the lowest RMSD (DeltaRMSD) from 0.63 A to 0.45 A, while having a higher Pearson correlation coefficient to RMSD (r=0.87) than any other tested score. The most accurate score is based on a combination of the DOPE non-hydrogen atom statistical potential; surface, contact, and combined statistical potentials from MODPIPE; and two PSIPRED/DSSP scores. It was implemented in the SVMod program, which can now be applied to select the final model in various modeling problems, including fold assignment, target-template alignment, and loop modeling.     

Structural Characteristics of Novel Protein Folds

Folds are the basic building blocks of protein structures. Understanding the emergence of novel protein folds is an important step towards understanding the rules governing the evolution of protein structure and function and for developing tools for protein structure modeling and design. We explored the frequency of occurrences of an exhaustively classified library of supersecondary structural elements (Smotifs), in protein structures, in order to identify features that would define a fold as novel compared to previously known structures. We found that a surprisingly small set of Smotifs is sufficient to describe all known folds. Furthermore, novel folds do not require novel Smotifs, but rather are a new combination of existing ones. Novel folds can be typified by the inclusion of a relatively higher number of rarely occurring Smotifs in their structures and, to a lesser extent, by a novel topological combination of commonly occurring Smotifs. When investigating the structural features of Smotifs, we found that the top 10% of most frequent ones have a higher fraction of internal contacts, while some of the most rare motifs are larger, and contain a longer loop region.     

A simple Cα-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C_α-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.     

Increased detection of structural templates using alignments of designed sequences

Protein structure prediction by comparative modeling benefits greatly from the use of multiple sequence alignment information to improve the accuracy of structural template identification and the alignment of target sequences to structural templates. Unfortunately, this benefit is limited to those protein sequences for which at least several natural sequence homologues exist. We show here that the use of large diverse alignments of computationally designed protein sequences confers many of the same benefits as natural sequences in identifying structural templates for comparative modeling targets. A large-scale massively parallelized application of an all-atom protein design algorithm, including a simple model of peptide backbone flexibility, has allowed us to generate 500 diverse, non-native, high-quality sequences for each of 264 protein structures in our test set. PSI-BLAST searches using the sequence profiles generated from the designed sequences ("reverse" BLAST searches) give near-perfect accuracy in identifying true structural homologues of the parent structure, with 54% coverage. In 41 of 49 genomes scanned using reverse BLAST searches, at least one novel structural template (not found by the standard method of PSI-BLAST against PDB) is identified. Further improvements in coverage, through optimizing the scoring function used to design sequences and continued application to new protein structures beyond the test set, will allow this method to mature into a useful strategy for identifying distantly related structural templates.     

Multiple Model Approach: Exploring the Limits of Comparative Modeling

One of the biggest problems in modeling distantly related proteins is the quality of the target-template alignment. This problem often results in low quality models that do not utilize all the information available in the template structure. The divergence of alignments at a low sequence identity level, which is a hindrance in most modeling attempts, is used here as a basis for a new technique of Multiple Model Approach (MMA). Alternative alignments prepared here using different mutation matrices and gap penalties, combined with automated model building, are used to create a set of models that explore a range of possible conformations for the target protein. Models are evaluated using different techniques to identify the best model. In the set of examples studied here, the correct target structure is known, which allows the evaluation of various alignment and evaluation strategies. For a randomly selected group of distantly homologous protein pairs representing all structural classes and various fold types, it is shown that a threading score based on simplified statistical potentials of mean force can identify the best models and, consequently, the most reliable alignment. In cases where the difference between target and template structures is significant, the threading score shows clearly that all models are wrong, therefore disqualifying the template.     

Targeting novel folds for structural genomics

The ultimate goal of structural genomics is to obtain the structure of each protein coded by each gene within a genome to determine gene function. Because of cost and time limitations, it remains impractical to solve the structure for every gene product experimentally. Up to a point, reasonably accurate three‐dimensional structures can be deduced for proteins with homologous sequences by using comparative modeling. Beyond this, fold recognition or threading methods can be used for proteins showing little homology to any known fold, although this is relatively time‐consuming and limited by the library of template folds currently available. Therefore, it is appropriate to develop methods that can increase our knowledge base, expanding our fold libraries by earmarking potentially “novel” folds for experimental structure determination. How can we sift through proteomic data rapidly and yet reliably identify novel folds as targets for structural genomics? We have analyzed a number of simple methods that discriminate between “novel” and “known” folds. We propose that simple alignments of secondary structure elements using predicted secondary structure could potentially be a more selective method than both a simple fold recognition method (GenTHREADER) and standard sequence alignment at finding novel folds when sequences show no detectable homology to proteins with known structures. Proteins 2002;48:44–52. © 2002 Wiley‐Liss, Inc.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

How well can the accuracy of comparative protein structure models be predicted?

Comparative structure models are available for two orders of magnitude more protein sequences than are experimentally determined structures. These models, however, suffer from two limitations that experimentally determined structures do not: They frequently contain significant errors, and their accuracy cannot be readily assessed. We have addressed the latter limitation by developing a protocol optimized specifically for predicting the Calpha root-mean-squared deviation (RMSD) and native overlap (NO3.5A) errors of a model in the absence of its native structure. In contrast to most traditional assessment scores that merely predict one model is more accurate than others, this approach quantifies the error in an absolute sense, thus helping to determine whether or not the model is suitable for intended applications. The assessment relies on a model-specific scoring function constructed by a support vector machine. This regression optimizes the weights of up to nine features, including various sequence similarity measures and statistical potentials, extracted from a tailored training set of models unique to the model being assessed: If possible, we use similarly sized models with the same fold; otherwise, we use similarly sized models with the same secondary structure composition. This protocol predicts the RMSD and NO3.5A errors for a diverse set of 580,317 comparative models of 6174 sequences with correlation coefficients (r) of 0.84 and 0.86, respectively, to the actual errors. This scoring function achieves the best correlation compared to 13 other tested assessment criteria that achieved correlations ranging from 0.35 to 0.71.     

A global machine learning based scoring function for protein structure prediction

We present a knowledge‐based function to score protein decoys based on their similarity to native structure. A set of features is constructed to describe the structure and sequence of the entire protein chain. Furthermore, a qualitative relationship is established between the calculated features and the underlying electromagnetic interaction that dominates this scale. The features we use are associated with residue–residue distances, residue–solvent distances, pairwise knowledge‐based potentials and a four‐body potential. In addition, we introduce a new target to be predicted, the fitness score, which measures the similarity of a model to the native structure. This new approach enables us to obtain information both from decoys and from native structures. It is also devoid of previous problems associated with knowledge‐based potentials. These features were obtained for a large set of native and decoy structures and a back‐propagating neural network was trained to predict the fitness score. Overall this new scoring potential proved to be superior to the knowledge‐based scoring functions used as its inputs. In particular, in the latest CASP (CASP10) experiment our method was ranked third for all targets, and second for freely modeled hard targets among about 200 groups for top model prediction. Ours was the only method ranked in the top three for all targets and for hard targets. This shows that initial results from the novel approach are able to capture details that were missed by a broad spectrum of protein structure prediction approaches. Source codes and executable from this work are freely available at http://mathmed.org /#Software and http://mamiris.com/ . Proteins 2014; 82:752–759. © 2013 Wiley Periodicals, Inc.     

A critical assessment of comparative molecular modeling of tertiary structures of proteins*

In spite of the tremendous increase in the rate at which protein structures are being determined, there is still an enormous gap between the numbers of known DNA-derived sequences and the numbers of three-dimensional structures. In order to shed light on the biological functions of the molecules, researchers often resort to comparative molecular modeling. Earlier work has shown that when the sequence alignment is in error, then the comparative model is guaranteed to be wrong. In addition, loops, the sites of insertions and deletions in families of homologous proteins, are exceedingly difficult to model. Thus, many of the current problems in comparative molecular modeling are minor versions of the global protein folding problem. In order to assess objectively the current state of comparative molecular modeling, 13 groups submitted blind predictions of seven different proteins of undisclosed tertiary structure. This assessment shows that where sequence identity between the target and the template structure is high (> 70%), comparative molecular modeling is highly successful. On the other hand, automated modeling techniques and sophisticated energy minimization methods fail to improve upon the starting structures when the sequence identity is low (～30%). Based on these results it appears that insertions and deletions are still major problems. Successfully deducing the correct sequence alignment when the local similarity is low is still difficult. We suggest some minimal testing of submitted coordinates that should be required of authors before papers on comparative molecular modeling are accepted for publication in journals. © 1995 Wiley-Liss, Inc.     

Cell surface proteins in archaeal and bacterial genomes comprising "LVIVD", "RIVW" and "LGxL" tandem sequence repeats are predicted to fold as beta-propeller

Proteins that share even low sequence homologies are known to adopt similar folds. The beta-propeller structural motif is one such example. Identifying sequences that adopt a beta-propeller fold is useful to annotate protein structure and function. Often, tandem sequence repeats provide the necessary signal for identifying beta-propellers in proteins. In our recent analysis to identify cell surface proteins in archaeal and bacterial genomes, we identified some proteins that contain novel tandem repeats "LVIVD", "RIVW" and "LGxL". In this work, based on protein fold predictions and three-dimensional comparative modeling methods, we predicted that these repeat types fold as beta-propeller. Further, the evolutionary trace analysis of all proteins constituting amino acid sequence repeats in beta-propellers suggest that the novel repeats have diverged from a common ancestor.     

The use of soluble protein structures in modeling helical proteins in a layered membrane

Major advances have been made in the prediction of soluble protein structures, led by the knowledge-based modeling methods that extract useful structural trends from known protein structures and incorporate them into scoring functions. The same cannot be reported for the class of transmembrane proteins, primarily due to the lack of high-resolution structural data for transmembrane proteins, which render many of the knowledge-based method unreliable or invalid. We have developed a method that harnesses the vast structural knowledge available in soluble protein data for use in the modeling of transmembrane proteins. At the core of the method, a set of transmembrane protein decoy sets that allow us to filter and train features recognized from soluble proteins for transmembrane protein modeling into a set of scoring functions. We have demonstrated that structures of soluble proteins can provide significant insight into transmembrane protein structures. A complementary novel two-stage modeling/selection process that mimics the two-stage helical membrane protein folding was developed. Combined with the scoring function, the method was successfully applied to model 5 transmembrane proteins. The root mean square deviations of the predicted models ranged from 5.0 to 8.8?Å to the native structures.     

An Evolution-Based Approach to De Novo Protein Design and Case Study on Mycobacterium tuberculosis

Computational protein design is a reverse procedure of protein folding and structure prediction, where constructing structures from evolutionarily related proteins has been demonstrated to be the most reliable method for protein 3-dimensional structure prediction. Following this spirit, we developed a novel method to design new protein sequences based on evolutionarily related protein families. For a given target structure, a set of proteins having similar fold are identified from the PDB library by structural alignments. A structural profile is then constructed from the protein templates and used to guide the conformational search of amino acid sequence space, where physicochemical packing is accommodated by single-sequence based solvation, torsion angle, and secondary structure predictions. The method was tested on a computational folding experiment based on a large set of 87 protein structures covering different fold classes, which showed that the evolution-based design significantly enhances the foldability and biological functionality of the designed sequences compared to the traditional physics-based force field methods. Without using homologous proteins, the designed sequences can be folded with an average root-mean-square-deviation of 2.1 Å to the target. As a case study, the method is extended to redesign all 243 structurally resolved proteins in the pathogenic bacteria Mycobacterium tuberculosis, which is the second leading cause of death from infectious disease. On a smaller scale, five sequences were randomly selected from the design pool and subjected to experimental validation. The results showed that all the designed proteins are soluble with distinct secondary structure and three have well ordered tertiary structure, as demonstrated by circular dichroism and NMR spectroscopy. Together, these results demonstrate a new avenue in computational protein design that uses knowledge of evolutionary conservation from protein structural families to engineer new protein molecules of improved fold stability and biological functionality.     

The influence of stereospecific assignments on the determination of three-dimensional structures of proteins by nuclear magnetic resonance spectroscopy. Application to the sea anemone protein BDS-I

The influence of the stereospecific assignments of beta-methylene protons and the classification of chi 1 torsion angles on the definition of the three-dimensional structures of proteins determined from NMR data is investigated using the sea anemone protein BDS-I (43 residues) as a model system. Two sets of structures are computed. The first set comprises 42 converged structures (denoted STEREO structures) calculated on the basis of the complete list of restraints derived from the NMR data, consisting of 489 interproton and 24 hydrogen bonding distance restraints, supplemented by 23 phi backbone and 21 chi 1 side chain torsion angle restraints. The second set comprises 31 converged structures (denoted NOSTEREO structures) calculated from a reduced data set in which those restraints arising from stereospecific assignments, and the corresponding chi 1 torsion angle restraints, are explicitly omitted. The results show that the inclusion of the stereospecific restraints leads to a significant improvement in the definition of the structure of BDS-I, both with respect to the backbone and the detailed arrangement of the side chains. Average atomic rms differences between the individual structures and the mean structures for the backbone atoms are 0.67 +/- 0.12 A and 0.93 +/- 0.16 A for the STEREO and NOSTEREO structures, respectively; the corresponding values for all atoms are 0.90 +/- 0.17 A and 1.17 +/- 0.17 A, respectively. In addition, while the overall fold remains unchanged, there is a small but significant atomic displacement between the two sets of structures.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

ProVal: a protein-scoring function for the selection of native and near-native folds

A low-resolution scoring function for the selection of native and near-native structures from a set of predicted structures for a given protein sequence has been developed. The scoring function, ProVal (Protein Validate), used several variables that describe an aspect of protein structure for which the proximity to the native structure can be assessed quantitatively. Among the parameters included are a packing estimate, surface areas, and the contact order. A partial least squares for latent variables (PLS) model was built for each candidate set of the 28 decoy sets of structures generated for 22 different proteins using the described parameters as independent variables. The C(alpha) RMS of the candidate structures versus the experimental structure was used as the dependent variable. The final generalized scoring function was an average of all models derived, ensuring that the function was not optimized for specific fold classes or method of structure generation of the candidate folds. The results show that the crystal structure was scored best in 64% of the 28 test sets and was clearly separated from the decoys in many examples. In all the other cases in which the crystal structure did not rank first, it ranked within the top 10%. Thus, although ProVal could not distinguish between predicted structures that were similar overall in fold quality due to its inherently low resolution, it can clearly be used as a primary filter to eliminate approximately 90% of fold candidates generated by current prediction methods from all-atom modeling and further evaluation. The correlation between the predicted and actual C(alpha) RMS values varies considerably between the candidate fold sets.     

Modeling large regions in proteins: applications to loops, termini, and folding

Template-based methods for predicting protein structure provide models for a significant portion of the protein but often contain insertions or chain ends (InsEnds) of indeterminate conformation. The local structure prediction "problem" entails modeling the InsEnds onto the rest of the protein. A well-known limit involves predicting loops of ≤12 residues in crystal structures. However, InsEnds may contain as many as ~50 amino acids, and the template-based model of the protein itself may be imperfect. To address these challenges, we present a free modeling method for predicting the local structure of loops and large InsEnds in both crystal structures and template-based models. The approach uses single amino acid torsional angle "pivot" moves of the protein backbone with a C(β) level representation. Nevertheless, our accuracy for loops is comparable to existing methods. We also apply a more stringent test, the blind structure prediction and refinement categories of the CASP9 tournament, where we improve the quality of several homology based models by modeling InsEnds as long as 45 amino acids, sizes generally inaccessible to existing loop prediction methods. Our approach ranks as one of the best in the CASP9 refinement category that involves improving template-based models so that they can function as molecular replacement models to solve the phase problem for crystallographic structure determination.     

Assessment and Challenges of Ligand Docking into Comparative Models of G-Protein Coupled Receptors

The rapidly increasing number of high-resolution X-ray structures of G-protein coupled receptors (GPCRs) creates a unique opportunity to employ comparative modeling and docking to provide valuable insight into the function and ligand binding determinants of novel receptors, to assist in virtual screening and to design and optimize drug candidates. However, low sequence identity between receptors, conformational flexibility, and chemical diversity of ligands present an enormous challenge to molecular modeling approaches. It is our hypothesis that rapid Monte-Carlo sampling of protein backbone and side-chain conformational space with Rosetta can be leveraged to meet this challenge. This study performs unbiased comparative modeling and docking methodologies using 14 distinct high-resolution GPCRs and proposes knowledge-based filtering methods for improvement of sampling performance and identification of correct ligand-receptor interactions. On average, top ranked receptor models built on template structures over 50% sequence identity are within 2.9 Å of the experimental structure, with an average root mean square deviation (RMSD) of 2.2 Å for the transmembrane region and 5 Å for the second extracellular loop. Furthermore, these models are consistently correlated with low Rosetta energy score. To predict their binding modes, ligand conformers of the 14 ligands co-crystalized with the GPCRs were docked against the top ranked comparative models. In contrast to the comparative models themselves, however, it remains difficult to unambiguously identify correct binding modes by score alone. On average, sampling performance was improved by 10³ fold over random using knowledge-based and energy-based filters. In assessing the applicability of experimental constraints, we found that sampling performance is increased by one order of magnitude for every 10 residues known to contact the ligand. Additionally, in the case of DOR, knowledge of a single specific ligand-protein contact improved sampling efficiency 7 fold. These findings offer specific guidelines which may lead to increased success in determining receptor-ligand complexes.