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.     

Real-value prediction of backbone torsion angles

The backbone structure of a protein is largely determined by the phi and psi torsion angles. Thus, knowing these angles, even if approximately, will be very useful for protein-structure prediction. However, in a previous work, a sequence-based, real-value prediction of psi angle could only achieve a mean absolute error of 54 degrees (83 degrees, 35 degrees, 33 degrees for coil, strand, and helix residues, respectively) between predicted and actual angles. Moreover, a real-value prediction of phi angle is not yet available. This article employs a neural-network based approach to improve psi prediction by taking advantage of angle periodicity and apply the new method to the prediction to phi angles. The 10-fold-cross-validated mean absolute error for the new method is 38 degrees (58 degrees, 33 degrees, 22 degrees for coil, strand, and helix, respectively) for psi and 25 degrees (35 degrees, 22 degrees, 16 degrees for coil, strand, and helix, respectively) for phi. The accuracy of real-value prediction is comparable to or more accurate than the predictions based on multistate classification of the phi-psi map. More accurate prediction of real-value angles will likely be useful for improving the accuracy of fold recognition and ab initio protein-structure prediction. The Real-SPINE 2.0 server is available on the website http://sparks.informatics.iupui.edu.     

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/.     

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.     

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.     

A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions

Rotamer libraries are used in protein structure determination, prediction, and design. The backbone-dependent rotamer library consists of rotamer frequencies, mean dihedral angles, and variances as?a function of the backbone dihedral angles. Structure prediction and design methods that employ backbone flexibility would strongly benefit from smoothly varying probabilities and angles. A new version of the?backbone-dependent rotamer library has been developed using adaptive kernel density estimates for the rotamer frequencies and adaptive kernel regression for the mean dihedral angles and variances. This formulation allows for evaluation of the rotamer probabilities, mean angles, and variances as?a smooth and continuous function of phi and psi. Continuous probability density estimates for the nonrotameric degrees of freedom of amides, carboxylates, and aromatic side chains have been modeled as a function of the backbone dihedrals and rotamers of the remaining degrees of freedom. New backbone-dependent rotamer libraries at varying levels of smoothing are available from http://dunbrack.fccc.edu.     

NetSurfP-2.0: Improved prediction of protein structural features by integrated deep learning

The ability to predict local structural features of a protein from the primary sequence is of paramount importance for unraveling its function in absence of experimental structural information. Two main factors affect the utility of potential prediction tools: their accuracy must enable extraction of reliable structural information on the proteins of interest, and their runtime must be low to keep pace with sequencing data being generated at a constantly increasing speed. Here, we present NetSurfP-2.0, a novel tool that can predict the most important local structural features with unprecedented accuracy and runtime. NetSurfP-2.0 is sequence-based and uses an architecture composed of convolutional and long short-term memory neural networks trained on solved protein structures. Using a single integrated model, NetSurfP-2.0 predicts solvent accessibility, secondary structure, structural disorder, and backbone dihedral angles for each residue of the input sequences. We assessed the accuracy of NetSurfP-2.0 on several independent test datasets and found it to consistently produce state-of-the-art predictions for each of its output features. We observe a correlation of 80% between predictions and experimental data for solvent accessibility, and a precision of 85% on secondary structure 3-class predictions. In addition to improved accuracy, the processing time has been optimized to allow predicting more than 1000 proteins in less than 2 hours, and complete proteomes in less than 1 day.     

Polypeptide motions are dominated by peptide group oscillations resulting from dihedral angle correlations between nearest neighbors

To identify basic local backbone motions in unfolded chains, simulations are performed for a variety of peptide systems using three popular force fields and for implicit and explicit solvent models. A dominant "crankshaft-like" motion is found that involves only a localized oscillation of the plane of the peptide group. This motion results in a strong anticorrelated motion of the phi angle of the ith residue (phi(i)) and the psi angle of the residue i - 1 (psi(i-1)) on the 0.1 ps time scale. Only a slight correlation is found between the motions of the two backbone dihedral angles of the same residue. Aside from the special cases of glycine and proline, no correlations are found between backbone dihedral angles that are separated by more than one torsion angle. These short time, correlated motions are found both in equilibrium fluctuations and during the transit process between Ramachandran basins, e.g., from the beta to the alpha region. A residue's complete transit from one Ramachandran basin to another, however, occurs in a manner independent of its neighbors' conformational transitions. These properties appear to be intrinsic because they are robust across different force fields, solvent models, nonbonded interaction routines, and most amino acids.     

Beta-breakers: an aperiodic secondary structure

We have studied the architecture of parallel beta-sheets in proteins and focused on the residues that initiate and terminate the beta-strands. These beta-breaker residues are at the origin of the kink between the beta-strand and the turn that precedes or follows it. beta-Breakers can be located automatically using a consensus approach based on algorithmic secondary structure assignment, solvent accessibility and backbone dihedral angles. These beta-breakers are conformationally homogeneous with respect to side-chain solvent accessibility and backbone dihedral angle profile. A sequence-structure correlation is noted: a restricted subset of amino acids is observed at these positions. Analysis of homologous protein sequences shows that these residues are more highly conserved than other residues in the loop. We conclude that beta-breakers are the structural analogs of the N and C-terminal caps of alpha-helices. The identification of this aperiodic substructure suggests a strategy for improving secondary structure prediction and may guide site-directed mutagenesis experiments.     

Theoretical conformational analysis of methylamide of N-acetyl-L-lysine]

The spatial structure of the methylamide of N-acetyl-L-lysine has been analysed taking into account non-bonded and electrostatic interactions, torsional energy, bond angles distortion and hydrogen bonding. Conformational capacities of the backbone and mutual dependence of spatial structures of the backbone and the side chain was described by conformational maps obtained by energy minimisation, the dihedral angles and the bond angles of the side chain being varied for every phi, psi point. Every possible combination for phi, psi, x1-x5-angles was used corresponding to the stable form of the backbone and to torsion potential minima of the initial approximations in the calculation of preferred conformations of the molecule. Comparisons are made between stable forms of the methylamide of N-acetyl-L-lysine and Lys residues in proteins with known structure.     

SVM-Cabins: prediction of solvent accessibility using accumulation cutoff set and support vector machine

A number of methods for predicting levels of solvent accessibility or accessible surface area (ASA) of amino acid residues in proteins have been developed. These methods either predict regularly spaced states of relative solvent accessibility or an analogue real value indicating relative solvent accessibility. While discrete states of exposure can be easily obtained by post prediction assignment of thresholds to the predicted or computed real values of ASA, the reverse, that is, obtaining a real value from quantized states of predicted ASA, is not straightforward as a two-state prediction in such cases would give a large real valued errors. However, prediction of ASA into larger number of ASA states and then finding a corresponding scheme for real value prediction may be helpful in integrating the two approaches of ASA prediction. We report a novel method of obtaining numerical real values of solvent accessibility, using accumulation cutoff set and support vector machine. This so-called SVM-Cabins method first predicts discrete states of ASA of amino acid residues from their evolutionary profile and then maps the predicted states onto a real valued linear space by simple algebraic methods. Resulting performance of such a rigorous approach using 13-state ASA prediction is at least comparable with the best methods of ASA prediction reported so far. The mean absolute error in this method reaches the best performance of 15.1% on the tested data set of 502 proteins with a coefficient of correlation equal to 0.66. Since, the method starts with the prediction of discrete states of ASA and leads to real value predictions, performance of prediction in binary states and real values are simultaneously optimized.     

Achieving 80% ten-fold cross-validated accuracy for secondary structure prediction by large-scale training

An integrated system of neural networks, called SPINE, is established and optimized for predicting structural properties of proteins. SPINE is applied to three-state secondary-structure and residue-solvent-accessibility (RSA) prediction in this paper. The integrated neural networks are carefully trained with a large dataset of 2640 chains, sequence profiles generated from multiple sequence alignment, representative amino acid properties, a slow learning rate, overfitting protection, and an optimized sliding-widow size. More than 200,000 weights in SPINE are optimized by maximizing the accuracy measured by Q(3) (the percentage of correctly classified residues). SPINE yields a 10-fold cross-validated accuracy of 79.5% (80.0% for chains of length between 50 and 300) in secondary-structure prediction after one-month (CPU time) training on 22 processors. An accuracy of 87.5% is achieved for exposed residues (RSA >95%). The latter approaches the theoretical upper limit of 88-90% accuracy in assigning secondary structures. An accuracy of 73% for three-state solvent-accessibility prediction (25%/75% cutoff) and 79.3% for two-state prediction (25% cutoff) is also obtained.     

PredRSA: a gradient boosted regression trees approach for predicting protein solvent accessibility

Protein solvent accessibility prediction is a pivotal intermediate step towards modeling protein tertiary structures directly from one-dimensional sequences. It also plays an important part in identifying protein folds and domains. Although some methods have been presented to the protein solvent accessibility prediction in recent years, the performance is far from satisfactory. In this work, we propose PredRSA, a computational method that can accurately predict relative solvent accessible surface area (RSA) of residues by exploring various local and global sequence features which have been observed to be associated with solvent accessibility. Based on these features, a novel and efficient approach, Gradient Boosted Regression Trees (GBRT), is first adopted to predict RSA. Experimental results obtained from 5-fold cross-validation based on the Manesh-215 dataset show that the mean absolute error (MAE) and the Pearson correlation coefficient (PCC) of PredRSA are 9.0 % and 0.75, respectively, which are better than that of the existing methods. Moreover, we evaluate the performance of PredRSA using an independent test set of 68 proteins. Compared with the state-of-the-art approaches (SPINE-X and ASAquick), PredRSA achieves a significant improvement on the prediction quality. Our experimental results show that the Gradient Boosted Regression Trees algorithm and the novel feature combination are quite effective in relative solvent accessibility prediction. The proposed PredRSA method could be useful in assisting the prediction of protein structures by applying the predicted RSA as useful restraints.     

Modeling protein loops using a phi i + 1, psi i dimer database.

We present an automated method for modeling backbones of protein loops. The method samples a database of phi i + 1 and psi i angles constructed from a nonredundant version of the Protein Data Bank (PDB). The dihedral angles phi i + 1 and psi i completely define the backbone conformation of a dimer when standard bond lengths, bond angles, and a trans planar peptide configuration are used. For the 400 possible dimers resulting from 20 natural amino acids, a list of allowed phi i + 1, psi i pairs for each dimer is created by pooling all such pairs from the loop segments of each protein in the nonredundant version of the PDB. Starting from the N-terminus of the loop sequence, conformations are generated by assigning randomly selected pairs of phi i + 1, psi i for each dimer from the respective pool using standard bond lengths, bond angles, and a trans peptide configuration. We use this database to simulate protein loops of lengths varying from 5 to 11 amino acids in five proteins of known three-dimensional structures. Typically, 10,000-50,000 models are simulated for each protein loop and are evaluated for stereochemical consistency. Depending on the length and sequence of a given loop, 50-80% of the models generated have no stereochemical strain in the backbone atoms. We demonstrate that, when simulated loops are extended to include flanking residues from homologous segments, only very few loops from an ensemble of sterically allowed conformations orient the flanking segments consistent with the protein topology. The presence of near-native backbone conformations for loops from five different proteins suggests the completeness of the dimeric database for use in modeling loops of homologous proteins. Here, we take advantage of this observation to design a method that filters near-native loop conformations from an ensemble of sterically allowed conformations. We demonstrate that our method eliminates the need for a loop-closure algorithm and hence allows for the use of topological constraints of the homologous proteins or disulfide constraints to filter near-native loop conformations.     

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.     

Predicting residue solvent accessibility from protein sequence by considering the sequence environment

The solvent accessibility of each residue is predicted on the basis of the protein sequence. A set of 338 monomeric, non-homologous and high-resolution protein crystal structures is used as a learning set and a jackknife procedure is applied to each entry. The prediction is based on the comparison of the observed and the average values of the solvent-accessible area. It appears that the prediction accuracy is significantly improved by considering the residue types preceding and/or following the residue whose accessibility must be predicted. In contrast, the separate treatment of different secondary structural types does not improve the quality of the prediction. It is furthermore shown that the residue accessibility is much better predicted in small than in larger proteins. Such a discrepancy must be carefully considered in any algorithm for predicting residue accessibility.     

Local backbone structure prediction of proteins

A statistical analysis of the PDB structures has led us to define a new set of small 3D structural prototypes called Protein Blocks (PBs). This structural alphabet includes 16 PBs, each one is defined by the (phi, psi) dihedral angles of 5 consecutive residues. The amino acid distributions observed in sequence windows encompassing these PBs are used to predict by a Bayesian approach the local 3D structure of proteins from the sole knowledge of their sequences. LocPred is a software which allows the users to submit a protein sequence and performs a prediction in terms of PBs. The prediction results are given both textually and graphically.     

QBES: predicting real values of solvent accessibility from sequences by efficient, constrained energy optimization

Solvent accessibility, one of the key properties of amino acid residues in proteins, can be used to assist protein structure prediction. Various approaches such as neural network, support vector machines, probability profiles, information theory, Bayesian theory, logistic function, and multiple linear regression have been developed for solvent accessibility prediction. In this article, a much simpler quadratic programming method based on the buriability parameter set of amino acid residues is developed. The new method, called QBES (Quadratic programming and Buriability Energy function for Solvent accessibility prediction), is reasonably accurate for predicting the real value of solvent accessibility. By using a dataset of 30 proteins to optimize three parameters, the average correlation coefficients between the predicted and actual solvent accessibility are about 0.5 for all four independent test sets ranging from 126 to 513 proteins. The method is efficient. It takes only 20 min for a regular PC to obtain results of 30 proteins with an average length of 263 amino acids. Although the proposed method is less accurate than a few more sophisticated methods based on neural network or support vector machines, this is the first attempt to predict solvent accessibility by energy optimization with constraints. Possible improvements and other applications of the method are discussed.     

Predicting the solvent accessibility of transmembrane residues from protein sequence

In this study, we propose a novel method to predict the solvent accessible surface areas of transmembrane residues. For both transmembrane alpha-helix and beta-barrel residues, the correlation coefficients between the predicted and observed accessible surface areas are around 0.65. On the basis of predicted accessible surface areas, residues exposed to the lipid environment or buried inside a protein can be identified by using certain cutoff thresholds. We have extensively examined our approach based on different definitions of accessible surface areas and a variety of sets of control parameters. Given that experimentally determining the structures of membrane proteins is very difficult and membrane proteins are actually abundant in nature, our approach is useful for theoretically modeling membrane protein tertiary structures, particularly for modeling the assembly of transmembrane domains. This approach can be used to annotate the membrane proteins in proteomes to provide extra structural and functional information.     

On the properties and sequence context of structurally ambivalent fragments in proteins

The goal of this work is to characterize structurally ambivalent fragments in proteins. We have searched the Protein Data Bank and identified all structurally ambivalent peptides (SAPs) of length five or greater that exist in two different backbone conformations. The SAPs were classified in five distinct categories based on their structure. We propose a novel index that provides a quantitative measure of conformational variability of a sequence fragment. It measures the context-dependent width of the distribution of (phi,xi) dihedral angles associated with each amino acid type. This index was used to analyze the local structural propensity of both SAPs and the sequence fragments contiguous to them. We also analyzed type-specific amino acid composition, solvent accessibility, and overall structural properties of SAPs and their sequence context. We show that each type of SAP has an unusual, type-specific amino acid composition and, as a result, simultaneous intrinsic preferences for two distinct types of backbone conformation. All types of SAPs have lower sequence complexity than average. Fragments that adopt helical conformation in one protein and sheet conformation in another have the lowest sequence complexity and are sampled from a relatively limited repertoire of possible residue combinations. A statistically significant difference between two distinct conformations of the same SAP is observed not only in the overall structural properties of proteins harboring the SAP but also in the properties of its flanking regions and in the pattern of solvent accessibility. These results have implications for protein design and structure prediction.