Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.     

Smooth statistical torsion angle potential derived from a large conformational database via adaptive kernel density estimation improves the quality of NMR protein structures

Statistical potentials that embody torsion angle probability densities in databases of high‐quality X‐ray protein structures supplement the incomplete structural information of experimental nuclear magnetic resonance (NMR) datasets. By biasing the conformational search during the course of structure calculation toward highly populated regions in the database, the resulting protein structures display better validation criteria and accuracy. Here, a new statistical torsion angle potential is developed using adaptive kernel density estimation to extract probability densities from a large database of more than 10⁶ quality‐filtered amino acid residues. Incorporated into the Xplor‐NIH software package, the new implementation clearly outperforms an older potential, widely used in NMR structure elucidation, in that it exhibits simultaneously smoother and sharper energy surfaces, and results in protein structures with improved conformation, nonbonded atomic interactions, and accuracy.     

Structural analysis and prediction of protein mutant stability using distance and torsion potentials: role of secondary structure and solvent accessibility

Platelet-activating factor receptor (PAFR) is a member of G-protein coupled receptor (GPCR) superfamily. Understanding the regulation mechanisms of PAFR by its agonists and antagonists at the atomic level is essential for designing PAFR antagonists as drug candidates for treating PAF-mediated diseases. In this study, a 3D model of PAFR was constructed by a hierarchical approach integrating homology modeling, molecular docking and molecular dynamics (MD) simulations. Based on the 3D model, regulation mechanisms of PAFR by agonists and antagonists were investigated via three 8-ns MD simulations on the systems of apo-PAFR, PAFR-PAF and PAFR-GB. The simulations revealed that binding of PAF to PAFR triggers the straightening process of the kinked helix VI, leading to its activated state. In contrast, binding of GB to PAFR locks PAFR in its inactive state.     

An atomic environment potential for use in protein structure prediction

We describe the derivation and testing of a knowledge-based atomic environment potential for the modeling of protein structural energetics. An analysis of the probabilities of atomic interactions in a dataset of high-resolution protein structures shows that the probabilities of non-bonded inter-atomic contacts are not statistically independent events, and that the multi-body contact frequencies are poorly predicted from pairwise contact potentials. A pseudo-energy function is defined that measures the preferences for protein atoms to be in a given microenvironment defined by the number of contacting atoms in the environment and its atomic composition. This functional form is tested for its ability to recognize native protein structures amongst an ensemble of decoy structures and a detailed relative performance comparison is made with a number of common functions used in protein structure prediction.     

On statistical energy functions for biomolecular modeling and design

Statistical energy functions are general models about atomic or residue-level interactions in biomolecules, derived from existing experimental data. They provide quantitative foundations for structural modeling as well as for structure-based protein sequence design. Statistical energy functions can be derived computationally either based on statistical distributions or based on variational assumptions. We present overviews on the theoretical assumptions underlying the various types of approaches. Theoretical considerations underlying important pragmatic choices are discussed.     

Derivation of rules for comparative protein modeling from a database of protein structure alignments

We describe a database of protein structure alignments as well as methods and tools that use this database to improve comparative protein modeling. The current version of the database contains 105 alignments of similar proteins or protein segments. The database comprises 416 entries, 78,495 residues, 1,233 equivalent entry pairs, and 230,396 pairs of equivalent alignment positions. At present, the main application of the database is to improve comparative modeling by satisfaction of spatial restraints implemented in the program MODELLER (?ali A, Blundell TL, 1993, J Mol Biol 234:779–815). To illustrate the usefulness of the database, the restraints on the conformation of a disulfide bridge provided by an equivalent disulfide bridge in a related structure are derived from the alignments; the prediction success of the disulfide dihedral angle classes is increased to approximately 80%, compared to approximately 55% for modeling that relies on the stereochemistry of disulfide bridges alone. The second example of the use of the database is the derivation of the probability density function for comparative modeling of the cis/trans isomerism of the proline residues; the prediction success is increased from 0% to 82.9% for cis-proline and from 93.3% to 96.2% for trans-proline. The database is available via electronic mail.     

A beta‐complex statistical four body contact potential combined with a hydrogen bond statistical potential recognizes the correct native structure from protein decoy sets

We present a new four‐body knowledge‐based potential for recognizing the native state of proteins from their misfolded states. This potential was extracted from a large set of protein structures determined by X‐ray crystallography using BetaMol, a software based on the recent theory of the beta‐complex (β‐complex) and quasi‐triangulation of the Voronoi diagram of spheres. This geometric construct reflects the size difference among atoms in their full Euclidean metric; property not accounted for in a typical 3D Delaunay triangulation. The ability of this potential to identify the native conformation over a large set of decoys was evaluated. Experiments show that this potential outperforms a potential constructed with a classical Delaunay triangulation in decoy discrimination tests. The addition of a statistical hydrogen bond potential to our four‐body potential allows a significant improvement in the decoy discrimination, in such a way that we are able to predict successfully the native structure in 90% of cases. Proteins 2013; 81:1420–1433. © 2013 Wiley Periodicals, Inc.     

An improved protein decoy set for testing energy functions for protein structure prediction

We have improved the original Rosetta centroid/backbone decoy set by increasing the number of proteins and frequency of near native models and by building on sidechains and minimizing clashes. The new set consists of 1,400 model structures for 78 different and diverse protein targets and provides a challenging set for the testing and evaluation of scoring functions. We evaluated the extent to which a variety of all-atom energy functions could identify the native and close-to-native structures in the new decoy sets. Of various implicit solvent models, we found that a solvent-accessible surface area-based solvation provided the best enrichment and discrimination of close-to-native decoys. The combination of this solvation treatment with Lennard Jones terms and the original Rosetta energy provided better enrichment and discrimination than any of the individual terms. The results also highlight the differences in accuracy of NMR and X-ray crystal structures: a large energy gap was observed between native and non-native conformations for X-ray structures but not for NMR structures.     

A rapid protein structure alignment algorithm based on a text modeling technique

Structural alignment of proteins is widely used in various fields of structural biology. In order to further improve the quality of alignment, we describe an algorithm for structural alignment based on text modelling techniques. The technique firstly superimposes secondary structure elements of two proteins and then, models the 3D-structure of the protein in a sequence of alphabets. These sequences are utilized by a step-by-step sequence alignment procedure to align two protein structures. A benchmark test was organized on a set of 200 non-homologous proteins to evaluate the program and compare it to state of the art programs, e.g. CE, SAL, TM-align and 3D-BLAST. On average, the results of all-against-all structure comparison by the program have a competitive accuracy with CE and TM-align where the algorithm has a high running speed like 3D-BLAST.     

3Drefine: Consistent protein structure refinement by optimizing hydrogen bonding network and atomic‐level energy minimization

One of the major limitations of computational protein structure prediction is the deviation of predicted models from their experimentally derived true, native structures. The limitations often hinder the possibility of applying computational protein structure prediction methods in biochemical assignment and drug design that are very sensitive to structural details. Refinement of these low‐resolution predicted models to high‐resolution structures close to the native state, however, has proven to be extremely challenging. Thus, protein structure refinement remains a largely unsolved problem. Critical assessment of techniques for protein structure prediction (CASP) specifically indicated that most predictors participating in the refinement category still did not consistently improve model quality. Here, we propose a two‐step refinement protocol, called 3Drefine, to consistently bring the initial model closer to the native structure. The first step is based on optimization of hydrogen bonding (HB) network and the second step applies atomic‐level energy minimization on the optimized model using a composite physics and knowledge‐based force fields. The approach has been evaluated on the CASP benchmark data and it exhibits consistent improvement over the initial structure in both global and local structural quality measures. 3Drefine method is also computationally inexpensive, consuming only few minutes of CPU time to refine a protein of typical length (300 residues). 3Drefine web server is freely available at http://sysbio.rnet.missouri.edu/3Drefine/ . Proteins 2013. © 2012 Wiley Periodicals, Inc.     

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.     

Multiple mapping method: a novel approach to the sequence-to-structure alignment problem in comparative protein structure modeling

A major bottleneck in comparative protein structure modeling is the quality of input alignment between the target sequence and the template structure. A number of alignment methods are available, but none of these techniques produce consistently good solutions for all cases. Alignments produced by alternative methods may be superior in certain segments but inferior in others when compared to each other; therefore, an accurate solution often requires an optimal combination of them. To address this problem, we have developed a new approach, Multiple Mapping Method (MMM). The algorithm first identifies the alternatively aligned regions from a set of input alignments. These alternatively aligned segments are scored using a composite scoring function, which determines their fitness within the structural environment of the template. The best scoring regions from a set of alternative segments are combined with the core part of the alignments to produce the final MMM alignment. The algorithm was tested on a dataset of 1400 protein pairs using 11 combinations of two to four alignment methods. In all cases MMM showed statistically significant improvement by reducing alignment errors in the range of 3 to 17%. MMM also compared favorably over two alignment meta-servers. The algorithm is computationally efficient; therefore, it is a suitable tool for genome scale modeling studies.     

VoroMQA: Assessment of protein structure quality using interatomic contact areas

In the absence of experimentally determined protein structure many biological questions can be addressed using computational structural models. However, the utility of protein structural models depends on their quality. Therefore, the estimation of the quality of predicted structures is an important problem. One of the approaches to this problem is the use of knowledge‐based statistical potentials. Such methods typically rely on the statistics of distances and angles of residue‐residue or atom‐atom interactions collected from experimentally determined structures. Here, we present VoroMQA (Voronoi tessellation‐based Model Quality Assessment), a new method for the estimation of protein structure quality. Our method combines the idea of statistical potentials with the use of interatomic contact areas instead of distances. Contact areas, derived using Voronoi tessellation of protein structure, are used to describe and seamlessly integrate both explicit interactions between protein atoms and implicit interactions of protein atoms with solvent. VoroMQA produces scores at atomic, residue, and global levels, all in the fixed range from 0 to 1. The method was tested on the CASP data and compared to several other single‐model quality assessment methods. VoroMQA showed strong performance in the recognition of the native structure and in the structural model selection tests, thus demonstrating the efficacy of interatomic contact areas in estimating protein structure quality. The software implementation of VoroMQA is freely available as a standalone application and as a web server at http://bioinformatics.lt/software/voromqa . Proteins 2017; 85:1131–1145. © 2017 Wiley Periodicals, Inc.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.