Improving the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins by guided-learning through a two-layer neural network

This article attempts to increase the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins through improved learning. Most methods developed for improving the backpropagation algorithm of artificial neural networks are limited to small neural networks. Here, we introduce a guided-learning method suitable for networks of any size. The method employs a part of the weights for guiding and the other part for training and optimization. We demonstrate this technique by predicting residue solvent accessibility and real-value backbone torsion angles of proteins. In this application, the guiding factor is designed to satisfy the intuitive condition that for most residues, the contribution of a residue to the structural properties of another residue is smaller for greater separation in the protein-sequence distance between the two residues. We show that the guided-learning method makes a 2-4% reduction in 10-fold cross-validated mean absolute errors (MAE) for predicting residue solvent accessibility and backbone torsion angles, regardless of the size of database, the number of hidden layers and the size of input windows. This together with introduction of two-layer neural network with a bipolar activation function leads to a new method that has a MAE of 0.11 for residue solvent accessibility, 36 degrees for psi, and 22 degrees for phi. The method is available as a Real-SPINE 3.0 server in http://sparks.informatics.iupui.edu.     

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.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Controlling the secondary-structure-forming tendencies of proteins by a backbone torsion-energy term

We examined a new backbone torsion-energy term proposed by us in the force field for protein systems. This torsion-energy term is represented by a double Fourier series in two variables, namely the backbone dihedral angles φ and ψ. It gives a natural representation of the torsion energy in the Ramachandran space in the sense that any two-dimensional energy surface periodic in both φ and ψ can be expanded by the double Fourier series. We can then easily control secondary-structure-forming tendencies by modifying the torsion-energy surface. For instance, we can increase or decrease the α-helix-forming-tendencies by lowering or raising the torsion-energy surface in the α-helix region and likewise increase or decrease the β-sheet-forming tendencies by lowering or raising the surface in the β-sheet region in the Ramachandran space. We applied this torsion-energy modification method to six force fields, AMBER parm94, AMBER parm96, AMBER parm99, CHARMM27, OPLS-AA and OPLS-AA/L, and demonstrated that our modifications of the torsion-energy terms resulted in the expected changes of secondary-structure-forming tendencies by performing folding simulations of α-helical and β-hairpin peptides.     

Protein secondary structure prediction with dihedral angles

We present DESTRUCT, a new method of protein secondary structure prediction, which achieves a three-state accuracy (Q3) of 79.4% in a cross-validated trial on a nonredundant set of 513 proteins. An iterative set of cascade-correlation neural networks is used to predict both secondary structure and psi dihedral angles, with predicted values enhancing the subsequent iteration. Predictive accuracies of 80.7% and 81.7% are achieved on the CASP4 and CASP5 targets, respectively. Our approach is significantly more accurate than other contemporary methods, due to feedback and a novel combination of structural representations.     

神经网络在蛋白质二级结构预测中的应用

介绍了蛋白质二级结构预测的研究意义,讨论了用在蛋白质二级结构预测方面的神经网络设计问题,并且较详尽地评述了近些年来用神经网络方法在蛋白质二级结构预测中的主要工作进展情况,展望了蛋白质结构预测的前景。     

Automated NMR determination of protein backbone dihedral angles from cross-correlated spin relaxation

The simultaneous interpretation of a suite of dipole-dipole and dipole-CSA cross-correlation rates involving the backbone nuclei ¹³C, ¹H,¹³CO, ¹⁵N and ¹H^N can be used to resolve the ambiguities associated with each individual cross-correlation rate. The method is based on the transformation of experimental cross-correlation rates via calculated values based on standard peptide plane geometry and solid-state ¹³CO CSA parameters into a dihedral angle probability surface. Triple resonance NMR experiments with improved sensitivity have been devised for the quantification of relaxation interference between ¹H(i)-¹³C(i)/¹⁵N(i)-¹H^N(i) and ¹H(i–1)-¹³C(i–1)/¹⁵N(i)-¹H^N(i) dipole-dipole mechanisms in ¹⁵N,¹³C-labeled proteins. The approach is illustrated with an application to ¹³C,¹⁵N-labeled ubiquitin.     

Presence of distinct virtual backbone torsion angles in dipeptide conformers

Zwitterionic dipeptides have recently been shown to exist in water mainly as nine conformational forms with specific combinations of backbone Psi, omega and Phi torsions, which allows conformer-specific molecular recognition of peptide ligands by proteins. Here, we show that pairs of virtual backbone torsions can also define these nine conformational forms, and that comparing these virtual torsions in dipeptides with those of backbone-modified pseudopeptides offers an improved procedure for evaluating peptidomimetics for therapeutic applications.     

Progress of 1D protein structure prediction at last

Accuracy of predicting protein secondary structure and solvent accessibility from sequence information has been improved significantly by using information contained in multiple sequence alignments as input to a neural 'network system. For the Asilomar meeting, predictions for 13 proteins were generated automatically using the publicly available prediction method PHD. The results confirm the estimate of 72% three-state prediction accuracy. The fairly accurate predictions of secondary structure segments made the tool useful as a starting point for modeling of higher dimensional aspects of protein structure. © 1995 Wiley-Liss, Inc.     

Correlation between omega and psi dihedral angles in protein structures

The planarity of the peptide group is one of the fundamental features of protein structure that is described in every chemistry and biochemistry textbook. By surveying a dataset of 163 atomic resolution protein structures we here identify the stereochemical conditions that favor significant deformations of peptide bond planarity. In particular, we demonstrate that the values of the omega dihedral angle are strictly correlated to the values of the adjacent psi angle. This trend is also observed in highly strained states such as those occurring in vicinal disulfide bridges. These findings provide direct evidence for the mutual influence of the geometrical parameters that describe the protein structure.     

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the α and β regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.     

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/.     

TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts

NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between ¹³C, ¹⁵N and ¹H chemical shifts and backbone torsion angles ϕ and ψ (Cornilescu et al. J Biomol NMR 13 289–302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted ϕ and ψ angles, equals ±13°. Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Combining prediction of secondary structure and solvent accessibility in proteins

Owing to the use of evolutionary information and advanced machine learning protocols, secondary structures of amino acid residues in proteins can be predicted from the primary sequence with more than 75% per-residue accuracy for the 3-state (i.e., helix, beta-strand, and coil) classification problem. In this work we investigate whether further progress may be achieved by incorporating the relative solvent accessibility (RSA) of an amino acid residue as a fingerprint of the overall topology of the protein. Toward that goal, we developed a novel method for secondary structure prediction that uses predicted RSA in addition to attributes derived from evolutionary profiles. Our general approach follows the 2-stage protocol of Rost and Sander, with a number of Elman-type recurrent neural networks (NNs) combined into a consensus predictor. The RSA is predicted using our recently developed regression-based method that provides real-valued RSA, with the overall correlation coefficients between the actual and predicted RSA of about 0.66 in rigorous tests on independent control sets. Using the predicted RSA, we were able to improve the performance of our secondary structure prediction by up to 1.4% and achieved the overall per-residue accuracy between 77.0% and 78.4% for the 3-state classification problem on different control sets comprising, together, 603 proteins without homology to proteins included in the training. The effects of including solvent accessibility depend on the quality of RSA prediction. In the limit of perfect prediction (i.e., when using the actual RSA values derived from known protein structures), the accuracy of secondary structure prediction increases by up to 4%. We also observed that projecting real-valued RSA into 2 discrete classes with the commonly used threshold of 25% RSA decreases the classification accuracy for secondary structure prediction. While the level of improvement of secondary structure prediction may be different for prediction protocols that implicitly account for RSA in other ways, we conclude that an increase in the 3-state classification accuracy may be achieved when combining RSA with a state-of-the-art protocol utilizing evolutionary profiles. The new method is available through a Web server at http://sable.cchmc.org.     

MUFOLD‐SS: New deep inception‐inside‐inception networks for protein secondary structure prediction

Protein secondary structure prediction can provide important information for protein 3D structure prediction and protein functions. Deep learning offers a new opportunity to significantly improve prediction accuracy. In this article, a new deep neural network architecture, named the Deep inception‐inside‐inception (Deep3I) network, is proposed for protein secondary structure prediction and implemented as a software tool MUFOLD‐SS. The input to MUFOLD‐SS is a carefully designed feature matrix corresponding to the primary amino acid sequence of a protein, which consists of a rich set of information derived from individual amino acid, as well as the context of the protein sequence. Specifically, the feature matrix is a composition of physio‐chemical properties of amino acids, PSI‐BLAST profile, and HHBlits profile. MUFOLD‐SS is composed of a sequence of nested inception modules and maps the input matrix to either eight states or three states of secondary structures. The architecture of MUFOLD‐SS enables effective processing of local and global interactions between amino acids in making accurate prediction. In extensive experiments on multiple datasets, MUFOLD‐SS outperformed the best existing methods and other deep neural networks significantly. MUFold‐SS can be downloaded from http://dslsrv8.cs.missouri.edu/~cf797/MUFoldSS/download.html .     

Locally oscillatory motion of RNA helix derived from linear relationships of backbone torsion angles

A linear relationship in each of the torsion angle pairs, α-β, β-?, ?-ζ, and α-γ, has been found by applying a statistical method based on the concept of circular variates to backbone torsion angle data of helical in yeast tTNA^Phe. A series of helical dimer models generated with these relationships have been found to be stereochemically acceptable, and the models also indicate that the backbone unit in the RNA helix is geometrically capable of an oscillatory motion with the distance of about 3.4 Å between adjacent bases. The motion of the backbone unit is analogous to that of a helical spring. The adjacent bases, because of being attached to the backbone, oscillate in a manner similar to the oscillatory dimer model proposed by Davis and Tinoco [Davis, R. C. & Tinoco, I., Jr. (1968) Biopolymers 6 , 223–242]. Here, the oscillation of the backbone unit in the RNA helix is discussed in terms of two geometrical quantities: the torsion (τ) and curvature (κ) of the helix. On these lines, a stereochemical model of RNA strand separation is proposed.     

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.     

Analysis of the steric strain in the polypeptide backbone of protein molecules.

The extent to which local strain is present in the polypeptide backbone of folded protein molecules has been examined. The occurrence of steric strain associated with nonproline cis peptide bonds and energetically unfavorable main chain dihedral angles can be identified reliably from the well ordered parts of high resolution, refined crystal structures. The analysis reveals that there are relatively few sterically strained features. Those that do occur are located overwhelmingly in regions concerned with function. We attribute this to the greater precision necessary for ligand binding and catalysis, compared with the requirements of satisfactory folding.