Statistical torsion angle potential energy functions for protein structure modeling: A bicubic interpolation approach

A set of grid type knowledge‐based energy functions is introduced for ?–χ₁, ψ–χ₁, ?–ψ, and χ₁–χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X‐ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement. Proteins 2013. Proteins 2013; 81:1156–1165. © 2013 Wiley Periodicals, Inc.     

Change in backbone torsion angle distribution on protein folding

Understanding protein folding requires the determination of the configurational space accessible to the protein at different stages in folding. Here, computer simulation analysis of small angle neutron scattering results is used to probe the change in the distribution of configurations on strong denaturation of a globular protein, phosphoglycerate kinase, in 4 M guanidine hydrochloride solution. To do this atomic-detail ensembles of the unfolded protein chain are modeled and their scattering profiles compared with the experiment. The local conformational statistics are found to strongly influence the experimental intensity at scattering vectors between 0.05 and 0.3 A(-1). Denaturation leads to a reduction in the protein atom-pair distance distribution function over the approximately 3-15 A region that is associated with a quantifiable shift in the backbone torsional angle (phi, psi) distribution toward the beta region of the Ramachandran plot.     

ANGLOR: a composite machine-learning algorithm for protein backbone torsion angle prediction

We developed a composite machine-learning based algorithm, called ANGLOR, to predict real-value protein backbone torsion angles from amino acid sequences. The input features of ANGLOR include sequence profiles, predicted secondary structure and solvent accessibility. In a large-scale benchmarking test, the mean absolute error (MAE) of the phi/psi prediction is 28 degrees/46 degrees , which is approximately 10% lower than that generated by software in literature. The prediction is statistically different from a random predictor (or a purely secondary-structure-based predictor) with p-value <1.0 x 10(-300) (or <1.0 x 10(-148)) by Wilcoxon signed rank test. For some residues (ILE, LEU, PRO and VAL) and especially the residues in helix and buried regions, the MAE of phi angles is much smaller (10-20 degrees ) than that in other environments. Thus, although the average accuracy of the ANGLOR prediction is still low, the portion of the accurately predicted dihedral angles may be useful in assisting protein fold recognition and ab initio 3D structure modeling.     

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.     

TALI: local alignment of protein structures using backbone torsion angles

Torsion angle alignment (TALI) is a novel approach to local structural motif alignment, based on backbone torsion angles (phi, psi) rather than the more traditional atomic distance matrices. Representation of a protein structure in the form of a sequence of torsion angles enables easy integration of sequence and structural information, and adopts mature techniques in sequence alignment to improve performance and alignment quality. We show that TALI is able to match local structural motifs as well as identify global structural similarity. TALI is also compared to other structure alignment methods such as DALI, CE, and SSM, as well as sequence alignment based on PSI-BLAST; TALI is shown to be equally successful as, or more successful than, these other methods when applied to challenging structural alignments. The inference of the evolutionary tree of class II aminoacyl-tRNA synthetase shows the potential for TALI in estimating protein structural evolution and in identifying structural divergence among homologous structures. Availability: http://redcat.cse.sc.edu/index.php/Project:TALI/.     

Prediction of protein secondary structure with a reliability score estimated by local sequence clustering

Most algorithms for protein secondary structure prediction are based on machine learning techniques, e.g. neural networks. Good architectures and learning methods have improved the performance continuously. The introduction of profile methods, e.g. PSI-BLAST, has been a major breakthrough in increasing the prediction accuracy to close to 80%. In this paper, a brute-force algorithm is proposed and the reliability of each prediction is estimated by a z-score based on local sequence clustering. This algorithm is intended to perform well for those secondary structures in a protein whose formation is mainly dominated by the neighboring sequences and short-range interactions. A reliability z-score has been defined to estimate the goodness of a putative cluster found for a query sequence in a database. The database for prediction was constructed by experimentally determined, non-redundant protein structures with <25% sequence homology, a list maintained by PDBSELECT. Our test results have shown that this new algorithm, belonging to what is known as nearest neighbor methods, performed very well within the expectation of previous methods and that the reliability z-score as defined was correlated with the reliability of prediction. This led to the possibility of making very accurate predictions for a few selected residues in a protein with an accuracy measure of Q3 > 80%. The further development of this algorithm, and a nucleation mechanism for protein folding are suggested.     

HYPLOSP: a knowledge-based approach to protein local structure prediction

Local structure prediction can facilitate ab initio structure prediction, protein threading, and remote homology detection. However, the accuracy of existing methods is limited. In this paper, we propose a knowledge-based prediction method that assigns a measure called the local match rate to each position of an amino acid sequence to estimate the confidence of our method. Empirically, the accuracy of the method correlates positively with the local match rate; therefore, we employ it to predict the local structures of positions with a high local match rate. For positions with a low local match rate, we propose a neural network prediction method. To better utilize the knowledge-based and neural network methods, we design a hybrid prediction method, HYPLOSP (HYbrid method to Protein LOcal Structure Prediction) that combines both methods. To evaluate the performance of the proposed methods, we first perform cross-validation experiments by applying our knowledge-based method, a neural network method, and HYPLOSP to a large dataset of 3,925 protein chains. We test our methods extensively on three different structural alphabets and evaluate their performance by two widely used criteria, Maximum Deviation of backbone torsion Angle (MDA) and Q(N), which is similar to Q(3) in secondary structure prediction. We then compare HYPLOSP with three previous studies using a dataset of 56 new protein chains. HYPLOSP shows promising results in terms of MDA and Q(N) accuracy and demonstrates its alphabet-independent capability.     

Generalized propensity score approach to causal inference with spatial interference

Many spatial phenomena exhibit interference, where exposures at one location may affect the response at other locations. Because interference violates the stable unit treatment value assumption, standard methods for causal inference do not apply. We propose a new causal framework to recover direct and spill-over effects in the presence of spatial interference, taking into account that exposures at nearby locations are more influential than exposures at locations further apart. Under the no unmeasured confounding assumption, we show that a generalized propensity score is sufficient to remove all measured confounding. To reduce dimensionality issues, we propose a Bayesian spline-based regression model accounting for a sufficient set of variables for the generalized propensity score. A simulation study demonstrates the accuracy and coverage properties. We apply the method to estimate the causal effect of wildland fires on air pollution in the Western United States over 2005–2018.     

An alternative approach to normalization and evaluation for gait patterns: Procrustes analysis applied to the cyclograms of sprinters and middle-distance runners

In order to compare gait patterns, a common procedure is to normalize strides both in time and magnitude. The stride duration is usually normalized to a time percentage before averaging curves. As the timing of event occurrences may shift across strides, the shape of the averaged curves is distorted and therefore the standard deviation is overvalued. Stride magnitude normalization is performed by means of dimensionless numbers. However, there is little agreement on which body size correction methods should be used. The Procrustes method describes curve shape and shape change in a mathematical and statistical framework, independently of time and size factors. The present study aims to explore how this technique may be used for time- and magnitude-stride normalization to reflect individual and group mean responses. The Procrustes method, which combines quantitative and visual features, is applied to the shape of the ankle and knee cyclograms. Superimposition of 25 cyclograms (10 for sprinters (SP) and 15 for middle-distance runners (MDR)) was supplemented by statistical procedures (principal component analysis, discriminant function) to extract the main key events, which vary according to the athletic specialities. In comparison with the MDR (poulaine-shaped cyclogram), the ovoid cyclogram of SP reveals the following gait indicators: a short braking phase, a rapid initial lower limb swing in the forward direction, a fast upward movement of the knee and ankle, and an active foot contact. The Procrustes approach could be used to describe other quasi-periodic movements through relative motion plots (e.g., cyclograms, angle-angle diagrams, phase plane portraits).     

3dRNAscore: a distance and torsion angle dependent evaluation function of 3D RNA structures

Model evaluation is a necessary step for better prediction and design of 3D RNA structures. For proteins, this has been widely studied and the knowledge-based statistical potential has been proved to be one of effective ways to solve this problem. Currently, a few knowledge-based statistical potentials have also been proposed to evaluate predicted models of RNA tertiary structures. The benchmark tests showed that they can identify the native structures effectively but further improvements are needed to identify near-native structures and those with non-canonical base pairs. Here, we present a novel knowledge-based potential, 3dRNAscore, which combines distance-dependent and dihedral-dependent energies. The benchmarks on different testing datasets all show that 3dRNAscore are more efficient than existing evaluation methods in recognizing native state from a pool of near-native states of RNAs as well as in ranking near-native states of RNA models.     

PSEUDYANA for NMR structure calculation of paramagnetic metalloproteins using torsion angle molecular dynamics

The program DYANA, for calculation of solution structures of biomolecules with an algorithm based on simulated annealing by torsion angle dynamics, has been supplemented with a new routine, PSEUDYANA, that enables efficient use of pseudocontact shifts as additional constraints in structure calculations of paramagnetic metalloproteins. PSEUDYANA can determine the location of the metal ion inside the protein frame and allows to define a single tensor of magnetic susceptibility from a family of conformers. As an illustration, a PSEUDYANA structure calculation is provided for a metal-undecapeptide complex, where simulated pseudocontact shifts but no NOE restraints are used as conformational constraints.     

Decoy models for protein structure comparison score normalisation

A method is described to construct sets of decoy models that can be used to generate a background score distribution for protein structure comparison. The models are derived directly from the two proteins being compared and retain all the essential properties of the structures, including length, density, shape and secondary structure composition but have different folds. As each comparison involves a pair of proteins of the same length, no explicit normalisation is required to adjust for the length of the proteins being compared. This allows substructure (or domain) matches to score almost equally to the comparison of isolated domains. A normalised probability measure was derived that allows joint family/family comparison. The method was applied to some of the CASP6 models for targets with new folds.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

TANGLE: two-level support vector regression approach for protein backbone torsion angle prediction from primary sequences

Protein backbone torsion angles (Phi) and (Psi) involve two rotation angles rotating around the C(α)-N bond (Phi) and the C(α)-C bond (Psi). Due to the planarity of the linked rigid peptide bonds, these two angles can essentially determine the backbone geometry of proteins. Accordingly, the accurate prediction of protein backbone torsion angle from sequence information can assist the prediction of protein structures. In this study, we develop a new approach called TANGLE (Torsion ANGLE predictor) to predict the protein backbone torsion angles from amino acid sequences. TANGLE uses a two-level support vector regression approach to perform real-value torsion angle prediction using a variety of features derived from amino acid sequences, including the evolutionary profiles in the form of position-specific scoring matrices, predicted secondary structure, solvent accessibility and natively disordered region as well as other global sequence features. When evaluated based on a large benchmark dataset of 1,526 non-homologous proteins, the mean absolute errors (MAEs) of the Phi and Psi angle prediction are 27.8° and 44.6°, respectively, which are 1% and 3% respectively lower than that using one of the state-of-the-art prediction tools ANGLOR. Moreover, the prediction of TANGLE is significantly better than a random predictor that was built on the amino acid-specific basis, with the p-value<1.46e-147 and 7.97e-150, respectively by the Wilcoxon signed rank test. As a complementary approach to the current torsion angle prediction algorithms, TANGLE should prove useful in predicting protein structural properties and assisting protein fold recognition by applying the predicted torsion angles as useful restraints. TANGLE is freely accessible at http://sunflower.kuicr.kyoto-u.ac.jp/~sjn/TANGLE/.     

Interaction-based evaluation of the propensity for amyloid formation with cross-beta structure

In order to reveal the requirements for amino acid sequences prone to form amyloid fibrils, a novel prediction method based on the original structural model of amyloids was developed. As a working hypothesis, two fundamental conditions were introduced into the design of the present system for the evaluation of the propensity for amyloidogenicity. The first of these two conditions was to ensure that the hydrophobic and hydrogen-bonding interactions between residues on neighboring antiparallel beta-strands were formed along a fibril axis. The other condition was that the hydrophobic interacting residues appeared on both faces of the protofibril, which gave line-matching interactions. Most peptides with sequences exhibiting high scores, as evaluated by this method, were found to easily form amyloids with the aid of a turn-inducing structure designed as a connection of two beta-strands. On the other hand, peptides with low-scoring native sequences and those modified by an internal residue-residue exchange (the latter yielding a null score) did not lead to amyloid formation. These data demonstrated the validity of this method for the prediction of amyloid structures. Moreover, the present study provided support for the proposed model of the essential structure associated with the above working hypothesis. The predicted high-scoring regions were in good agreement with the putative amyloid core regions reported thus far.     

Matt: local flexibility aids protein multiple structure alignment

Even when there is agreement on what measure a protein multiple structure alignment should be optimizing, finding the optimal alignment is computationally prohibitive. One approach used by many previous methods is aligned fragment pair chaining, where short structural fragments from all the proteins are aligned against each other optimally, and the final alignment chains these together in geometrically consistent ways. Ye and Godzik have recently suggested that adding geometric flexibility may help better model protein structures in a variety of contexts. We introduce the program Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments: small translations and rotations are temporarily allowed to bring sets of aligned fragments closer, even if they are physically impossible under rigid body transformations. After a dynamic programming assembly guided by these “bent” alignments, geometric consistency is restored in the final step before the alignment is output. Matt is tested against other recent multiple protein structure alignment programs on the popular Homstrad and SABmark benchmark datasets. Matt's global performance is competitive with the other programs on Homstrad, but outperforms the other programs on SABmark, a benchmark of multiple structure alignments of proteins with more distant homology. On both datasets, Matt demonstrates an ability to better align the ends of α-helices and β-strands, an important characteristic of any structure alignment program intended to help construct a structural template library for threading approaches to the inverse protein-folding problem. The related question of whether Matt alignments can be used to distinguish distantly homologous structure pairs from pairs of proteins that are not homologous is also considered. For this purpose, a p-value score based on the length of the common core and average root mean squared deviation (RMSD) of Matt alignments is shown to largely separate decoys from homologous protein structures in the SABmark benchmark dataset. We postulate that Matt's strong performance comes from its ability to model proteins in different conformational states and, perhaps even more important, its ability to model backbone distortions in more distantly related proteins.     

LOMETS: a local meta-threading-server for protein structure prediction

We developed LOMETS, a local threading meta-server, for quick and automated predictions of protein tertiary structures and spatial constraints. Nine state-of-the-art threading programs are installed and run in a local computer cluster, which ensure the quick generation of initial threading alignments compared with traditional remote-server-based meta-servers. Consensus models are generated from the top predictions of the component-threading servers, which are at least 7% more accurate than the best individual servers based on TM-score at a t-test significance level of 0.1%. Moreover, side-chain and C-alpha (C(alpha)) contacts of 42 and 61% accuracy respectively, as well as long- and short-range distant maps, are automatically constructed from the threading alignments. These data can be easily used as constraints to guide the ab initio procedures such as TASSER for further protein tertiary structure modeling. The LOMETS server is freely available to the academic community at http://zhang.bioinformatics.ku.edu/LOMETS.     

Escher: A new docking procedure applied to the reconstruction of protein tertiary structure

Evaluation of Surface Complementarity, Hydrogen bonding, and Electrostatic interaction in molecular Recognition (ESCHER) is a new docking procedure consisting of three modules that work in series. The first module evaluates the geometric complementarity and produces a set of rough solutions for the docking problem. The second module identifies molecular collisions within those solutions, and the third evaluates their electrostatic complementarity. We describe the algorithm and its application to the docking of cocrystallized protein domains and unbound components of protein-protein complexes. Furthermore, ESCHER has been applied to the reassociation of secondary and supersecondary structure elements. The possibility of applying a docking method to the problem of protein structure prediction is discussed. Proteins 28:556–567, 1997. © 1997 Wiley-Liss, Inc.     

Measuring the chi 1 torsion angle in protein by CH-CH cross-correlated relaxation: a new resolution-optimised experiment

Here we introduce an experiment with high sensitivity and resolution for the measurement of CH-CH dipolar-dipolar cross-correlated relaxation rates (CCRR) in protein side-chains. The new methodology aims to the determination of structural and dynamical parameters around the torsion angle ₁ by measuring CH-CH cross-correlated relaxation rates. The method is validated on the protein ubiquitin: the ₁ angles determined from the CCRR data are compared with the ₁ angles of a previously determined NMR structure. The agreement between the two data sets is excellent for most residues. The few discrepancies that were found between the CCR-derived ₁ angles and the angles of the previously determined NMR structure could be explained by taking internal motion into account. The new methodology represents a very powerful tool to determine both structure and dynamics of protein side-chains in only one experiment.