fRMSDPred: predicting local RMSD between structural fragments using sequence information

The effectiveness of comparative modeling approaches for protein structure prediction can be substantially improved by incorporating predicted structural information in the initial sequence-structure alignment. Motivated by the approaches used to align protein structures, this article focuses on developing machine learning approaches for estimating the RMSD value of a pair of protein fragments. These estimated fragment-level RMSD values can be used to construct the alignment, assess the quality of an alignment, and identify high-quality alignment segments. We present algorithms to solve this fragment-level RMSD prediction problem using a supervised learning framework based on support vector regression and classification that incorporates protein profiles, predicted secondary structure, effective information encoding schemes, and novel second-order pairwise exponential kernel functions. Our comprehensive empirical study shows superior results compared with the profile-to-profile scoring schemes. We also show that for protein pairs with low sequence similarity (less than 12% sequence identity) these new local structural features alone or in conjunction with profile-based information lead to alignments that are considerably accurate than those obtained by schemes that use only profile and/or predicted secondary structure information.     

Comprehensive evaluation of protein structure alignment methods: scoring by geometric measures

We report the largest and most comprehensive comparison of protein structural alignment methods. Specifically, we evaluate six publicly available structure alignment programs: SSAP, STRUCTAL, DALI, LSQMAN, CE and SSM by aligning all 8,581,970 protein structure pairs in a test set of 2930 protein domains specially selected from CATH v.2.4 to ensure sequence diversity. We consider an alignment good if it matches many residues, and the two substructures are geometrically similar. Even with this definition, evaluating structural alignment methods is not straightforward. At first, we compared the rates of true and false positives using receiver operating characteristic (ROC) curves with the CATH classification taken as a gold standard. This proved unsatisfactory in that the quality of the alignments is not taken into account: sometimes a method that finds less good alignments scores better than a method that finds better alignments. We correct this intrinsic limitation by using four different geometric match measures (SI, MI, SAS, and GSAS) to evaluate the quality of each structural alignment. With this improved analysis we show that there is a wide variation in the performance of different methods; the main reason for this is that it can be difficult to find a good structural alignment between two proteins even when such an alignment exists. We find that STRUCTAL and SSM perform best, followed by LSQMAN and CE. Our focus on the intrinsic quality of each alignment allows us to propose a new method, called "Best-of-All" that combines the best results of all methods. Many commonly used methods miss 10-50% of the good Best-of-All alignments. By putting existing structural alignments into proper perspective, our study allows better comparison of protein structures. By highlighting limitations of existing methods, it will spur the further development of better structural alignment methods. This will have significant biological implications now that structural comparison has come to play a central role in the analysis of experimental work on protein structure, protein function and protein evolution.     

MatAlign: precise protein structure comparison by matrix alignment

We propose a detailed protein structure alignment method named "MatAlign". It is a two-step algorithm. Firstly, we represent 3D protein structures as 2D distance matrices, and align these matrices by means of dynamic programming in order to find the initially aligned residue pairs. Secondly, we refine the initial alignment iteratively into the optimal one according to an objective scoring function. We compare our method against DALI and CE, which are among the most accurate and the most widely used of the existing structural comparison tools. On the benchmark set of 68 protein structure pairs by Fischer et al., MatAlign provides better alignment results, according to four different criteria, than both DALI and CE in a majority of cases. MatAlign also performs as well in structural database search as DALI does, and much better than CE does. MatAlign is about two to three times faster than DALI, and has about the same speed as CE. The software and the supplementary information for this paper are available at http://xena1.ddns.comp.nus.edu.sg/~genesis/MatAlign/.     

Structure-dependent sequence alignment for remotely related proteins

MOTIVATION: The quality of a model structure derived from a comparative modeling procedure is dictated by the accuracy of the predicted sequence-template alignment. As the sequence-template pairs are increasingly remote in sequence relationship, the prediction of the sequence-template alignments becomes increasingly problematic with sequence alignment methods. Structural information of the template, used in connection with the sequence relationship of the sequence-template pair, could significantly improve the accuracy of the sequence-template alignment. In this paper, we describe a sequence-template alignment method that integrates sequence and structural information to enhance the accuracy of sequence-template alignments for distantly related protein pairs. RESULTS: The structure-dependent sequence alignment (SDSA) procedure was optimized for coverage and accuracy on a training set of 412 protein pairs; the structures for each of the training pairs are similar (RMSD< approximately 4A) but the sequence relationship is undetectable (average pair-wise sequence identity = 8%). The optimized SDSA procedure was then applied to extend PSI-BLAST local alignments by calculating the global alignments under the constraint of the residue pairs in the local alignments. This composite alignment procedure was assessed with a testing set of 1421 protein pairs, of which the pair-wise structures are similar (RMSD< approximately 4A) but the sequences are marginally related at best in each pair (average pair-wise sequence identity = 13%). The assessment showed that the composite alignment procedure predicted more aligned residues pairs with an average of 27% increase in correctly aligned residues over the standard PSI-BLAST alignments for the protein pairs in the testing set.     

SimShift: identifying structural similarities from NMR chemical shifts

MOTIVATION: An important quantity that arises in NMR spectroscopy experiments is the chemical shift. The interpretation of these data is mostly done by human experts; to our knowledge there are no algorithms that predict protein structure from chemical shift sequences alone. One approach to facilitate this process could be to compare two such sequences, where the structure of one protein has already been resolved. Our claim is that similarity of chemical shifts thereby found implies structural similarity of the respective proteins. RESULTS: We present an algorithm to identify structural similarities of proteins by aligning their associated chemical shift sequences. To evaluate the correctness of our predictions, we propose a benchmark set of protein pairs that have high structural similarity, but low sequence similarity (because with high sequence similarity the structural similarities could easily be detected by a sequence alignment algorithm). We compare our results with those of HHsearch and SSEA and show that our method outperforms both in >50% of all cases.     

A machine learning information retrieval approach to protein fold recognition

MOTIVATION: Recognizing proteins that have similar tertiary structure is the key step of template-based protein structure prediction methods. Traditionally, a variety of alignment methods are used to identify similar folds, based on sequence similarity and sequence-structure compatibility. Although these methods are complementary, their integration has not been thoroughly exploited. Statistical machine learning methods provide tools for integrating multiple features, but so far these methods have been used primarily for protein and fold classification, rather than addressing the retrieval problem of fold recognition-finding a proper template for a given query protein. RESULTS: Here we present a two-stage machine learning, information retrieval, approach to fold recognition. First, we use alignment methods to derive pairwise similarity features for query-template protein pairs. We also use global profile-profile alignments in combination with predicted secondary structure, relative solvent accessibility, contact map and beta-strand pairing to extract pairwise structural compatibility features. Second, we apply support vector machines to these features to predict the structural relevance (i.e. in the same fold or not) of the query-template pairs. For each query, the continuous relevance scores are used to rank the templates. The FOLDpro approach is modular, scalable and effective. Compared with 11 other fold recognition methods, FOLDpro yields the best results in almost all standard categories on a comprehensive benchmark dataset. Using predictions of the top-ranked template, the sensitivity is approximately 85, 56, and 27% at the family, superfamily and fold levels respectively. Using the 5 top-ranked templates, the sensitivity increases to 90, 70, and 48%.     

Vorolign--fast structural alignment using Voronoi contacts

Vorolign, a fast and flexible structural alignment method for two or more protein structures is introduced. The method aligns protein structures using double dynamic programming and measures the similarity of two residues based on the evolutionary conservation of their corresponding Voronoi-contacts in the protein structure. This similarity function allows aligning protein structures even in cases where structural flexibilities exist. Multiple structural alignments are generated from a set of pairwise alignments using a consistency-based, progressive multiple alignment strategy. RESULTS: The performance of Vorolign is evaluated for different applications of protein structure comparison, including automatic family detection as well as pairwise and multiple structure alignment. Vorolign accurately detects the correct family, superfamily or fold of a protein with respect to the SCOP classification on a set of difficult target structures. A scan against a database of >4000 proteins takes on average 1 min per target. The performance of Vorolign in calculating pairwise and multiple alignments is found to be comparable with other pairwise and multiple protein structure alignment methods. AVAILABILITY: Vorolign is freely available for academic users as a web server at http://www.bio.ifi.lmu.de/Vorolign     

Topological classification of RNA structures

We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non-planar diagrams correspond to pseudoknotted structures and have higher genus. The topological genus allows for the definition of topological folding motifs, similar in spirit to those introduced and commonly used in protein folding. We analyze real RNA structures from the databases Worldwide Protein Data Bank and Pseudobase and classify them according to their topological genus. For simplicity, we limit our analysis by considering only Watson-Crick complementary base pairs and G-U wobble base pairs. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.     

Consensus alignment for reliable framework prediction in homology modeling

MOTIVATION: Even the best sequence alignment methods frequently fail to correctly identify the framework regions for which backbones can be copied from the template into the target structure. Since the underprediction and, more significantly, the overprediction of these regions reduces the quality of the final model, it is of prime importance to attain as much as possible of the true structural alignment between target and template. RESULTS: We have developed an algorithm called Consensus that consistently provides a high quality alignment for comparative modeling. The method follows from a benchmark analysis of the 3D models generated by ten alignment techniques for a set of 79 homologous protein structure pairs. For 20-to-40% of the targets, these methods yield models with at least 6 A root mean square deviation (RMSD) from the native structure. We have selected the top five performing methods, and developed a consensus algorithm to generate an improved alignment. By building on the individual strength of each method, a set of criteria was implemented to remove the alignment segments that are likely to correspond to structurally dissimilar regions. The automated algorithm was validated on a different set of 48 protein pairs, resulting in 2.2 A average RMSD for the predicted models, and only four cases in which the RMSD exceeded 3 A. The average length of the alignments was about 75% of that found by standard structural superposition methods. The performance of Consensus was consistent from 2 to 32% target-template sequence identity, and hence it can be used for accurate prediction of framework regions in homology modeling.     

An optimized FM-index library for nucleotide and amino acid search

In computational structural biology, structure comparison is fundamental for our understanding of proteins. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. Based on the data we conclude that our program ProteinAlignmentObstruction provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs.     

Assessing annotation transfer for genomics: quantifying the relations between protein sequence, structure and function through traditional and probabilistic scores

Measuring in a quantitative, statistical sense the degree to which structural and functional information can be "transferred" between pairs of related protein sequences at various levels of similarity is an essential prerequisite for robust genome annotation. To this end, we performed pairwise sequence, structure and function comparisons on approximately 30,000 pairs of protein domains with known structure and function. Our domain pairs, which are constructed according to the SCOP fold classification, range in similarity from just sharing a fold, to being nearly identical. Our results show that traditional scores for sequence and structure similarity have the same basic exponential relationship as observed previously, with structural divergence, measured in RMS, being exponentially related to sequence divergence, measured in percent identity. However, as the scale of our survey is much larger than any previous investigations, our results have greater statistical weight and precision. We have been able to express the relationship of sequence and structure similarity using more "modern scores," such as Smith-Waterman alignment scores and probabilistic P-values for both sequence and structure comparison. These modern scores address some of the problems with traditional scores, such as determining a conserved core and correcting for length dependency; they enable us to phrase the sequence-structure relationship in more precise and accurate terms. We found that the basic exponential sequence-structure relationship is very general: the same essential relationship is found in the different secondary-structure classes and is evident in all the scoring schemes. To relate function to sequence and structure we assigned various levels of functional similarity to the domain pairs, based on a simple functional classification scheme. This scheme was constructed by combining and augmenting annotations in the enzyme and fly functional classifications and comparing subsets of these to the Escherichia coli and yeast classifications. We found sigmoidal relationships between similarity in function and sequence, with clear thresholds for different levels of functional conservation. For pairs of domains that share the same fold, precise function appears to be conserved down to approximately 40 % sequence identity, whereas broad functional class is conserved to approximately 25 %. Interestingly, percent identity is more effective at quantifying functional conservation than the more modern scores (e.g. P-values). Results of all the pairwise comparisons and our combined functional classification scheme for protein structures can be accessed from a web database at http://bioinfo.mbb.yale.edu/alignCopyright 2000 Academic Press.     

Structure alignment of membrane proteins: Accuracy of available tools and a consensus strategy

Protein structure alignment methods are used for the detection of evolutionary and functionally related positions in proteins. A wide array of different methods are available, but the choice of the best method is often not apparent to the user. Several studies have assessed the alignment accuracy and consistency of structure alignment methods, but none of these explicitly considered membrane proteins, which are important targets for drug development and have distinct structural features. Here, we compared 13 widely used pairwise structural alignment methods on a test set of homologous membrane protein structures (called HOMEP3). Each pair of structures was aligned and the corresponding sequence alignment was used to construct homology models. The model accuracy compared to the known structures was assessed using scoring functions not incorporated in the tested structural alignment methods. The analysis shows that fragment‐based approaches such as FR‐TM‐align are the most useful for aligning structures of membrane proteins. Moreover, fragment‐based approaches are more suitable for comparison of protein structures that have undergone large conformational changes. Nevertheless, no method was clearly superior to all other methods. Additionally, all methods lack a measure to rate the reliability of a position within a structure alignment. To solve both of these problems, we propose a consensus‐type approach, combining alignments from four different methods, namely FR‐TM‐align, DaliLite, MATT, and FATCAT. Agreement between the methods is used to assign confidence values to each position of the alignment. Overall, we conclude that there remains scope for the improvement of structural alignment methods for membrane proteins. Proteins 2015; 83:1720–1732. © 2015 Wiley Periodicals, Inc.     

Structural Alphabets for Protein Structure Classification: A Comparison Study

Finding structural similarities between proteins often helps reveal shared functionality, which otherwise might not be detected by native sequence information alone. Such similarity is usually detected and quantified by protein structure alignment. Determining the optimal alignment between two protein structures, however, remains a hard problem. An alternative approach is to approximate each three-dimensional protein structure using a sequence of motifs derived from a structural alphabet. Using this approach, structure comparison is performed by comparing the corresponding motif sequences or structural sequences. In this article, we measure the performance of such alphabets in the context of the protein structure classification problem. We consider both local and global structural sequences. Each letter of a local structural sequence corresponds to the best matching fragment to the corresponding local segment of the protein structure. The global structural sequence is designed to generate the best possible complete chain that matches the full protein structure. We use an alphabet of 20 letters, corresponding to a library of 20 motifs or protein fragments having four residues. We show that the global structural sequences approximate well the native structures of proteins, with an average coordinate root mean square of 0.69 Å over 2225 test proteins. The approximation is best for all α-proteins, while relatively poorer for all β-proteins. We then test the performance of four different sequence representations of proteins (their native sequence, the sequence of their secondary-structure elements, and the local and global structural sequences based on our fragment library) with different classifiers in their ability to classify proteins that belong to five distinct folds of CATH. Without surprise, the primary sequence alone performs poorly as a structure classifier. We show that addition of either secondary-structure information or local information from the structural sequence considerably improves the classification accuracy. The two fragment-based sequences perform better than the secondary-structure sequence but not well enough at this stage to be a viable alternative to more computationally intensive methods based on protein structure alignment.     

FlexProt: alignment of flexible protein structures without a predefinition of hinge regions.

FlexProt is a novel technique for the alignment of flexible proteins. Unlike all previous algorithms designed to solve the problem of structural comparisons allowing hinge-bending motions, FlexProt does not require an a priori knowledge of the location of the hinge(s). FlexProt carries out the flexible alignment, superimposing the matching rigid subpart pairs, and detects the flexible hinge regions simultaneously. A large number of methods are available to handle rigid structural alignment. However, proteins are flexible molecules, which may appear in different conformations. Hence, protein structural analysis requires algorithms that can deal with molecular flexibility. Here, we present a method addressing specifically a flexible protein alignment task. First, the method efficiently detects maximal congruent rigid fragments in both molecules. Transforming the task into a graph theoretic problem, our method proceeds to calculate the optimal arrangement of previously detected maximal congruent rigid fragments. The fragment arrangement does not violate the protein sequence order. A clustering procedure is performed on fragment-pairs which have the same 3-D rigid transformation regardless of insertions and deletions (such as loops and turns) which separate them. Although the theoretical worst case complexity of the algorithm is O(n(6)), in practice FlexProt is highly efficient. It performs a structural comparison of a pair of proteins 300 amino acids long in about seven seconds on a standard desktop PC (400 MHz Pentium II processor with 256MB internal memory). We have performed extensive experiments with the algorithm. An assortment of these results is presented here. FlexProt can be accessed via WWW at bioinfo3d.cs.tau.ac.il/FlexProt/.     

Alternative alignments from comparison of protein structures

Comparison of two protein structures often results in not only a global alignment but also a number of distinct local alignments; the latter, referred to as alternative alignments, are however usually ignored in existing protein structure comparison analyses. Here, we used a novel method of protein structure comparison to extensively identify and characterize the alternative alignments obtained for structure pairs of a fold classification database. We showed that all alternative alignments can be classified into one of just a few types, and with which illustrated the potential of using alternative alignments to identify recurring protein substructures, including the internal structural repeats of a protein. Furthermore, we showed that among the alternative alignments obtained, permuted alignments, which included both circular and scrambled permutations, are as prevalent as topological alignments. These results demonstrated that the so far largely unattended alternative alignments of protein structures have implications and applications for research of protein classification and evolution.     

Disentangling Direct from Indirect Co-Evolution of Residues in Protein Alignments

Predicting protein structure from primary sequence is one of the ultimate challenges in computational biology. Given the large amount of available sequence data, the analysis of co-evolution, i.e., statistical dependency, between columns in multiple alignments of protein domain sequences remains one of the most promising avenues for predicting residues that are contacting in the structure. A key impediment to this approach is that strong statistical dependencies are also observed for many residue pairs that are distal in the structure. Using a comprehensive analysis of protein domains with available three-dimensional structures we show that co-evolving contacts very commonly form chains that percolate through the protein structure, inducing indirect statistical dependencies between many distal pairs of residues. We characterize the distributions of length and spatial distance traveled by these co-evolving contact chains and show that they explain a large fraction of observed statistical dependencies between structurally distal pairs. We adapt a recently developed Bayesian network model into a rigorous procedure for disentangling direct from indirect statistical dependencies, and we demonstrate that this method not only successfully accomplishes this task, but also allows contacts with weak statistical dependency to be detected. To illustrate how additional information can be incorporated into our method, we incorporate a phylogenetic correction, and we develop an informative prior that takes into account that the probability for a pair of residues to contact depends strongly on their primary-sequence distance and the amount of conservation that the corresponding columns in the multiple alignment exhibit. We show that our model including these extensions dramatically improves the accuracy of contact prediction from multiple sequence alignments.     

Genome analysis: Assigning protein coding regions to three-dimensional structures

We describe the results of a procedure for maximizing the number of sequences that can be reliably linked to a protein of known three-dimensional structure. Unlike other methods, which try to increase sensitivity through the use of fold recognition software, we only use conventional sequence alignment tools, but apply them in a manner that significantly increases the number of relationships detected. We analyzed 11 genomes and found that, depending on the genome, between 23 and 32% of the ORFs had significant matches to proteins of known structure. In all cases, the aligned region consisted of either >100 residues or >50% of the smaller sequence. Slightly higher percentages could be attained if smaller motifs were also included. This is significantly higher than most previously reported methods, even those that have a fold-recognition component. We survey the biochemical and structural characteristics of the most frequently occurring proteins, and discuss the extent to which alignment methods can realistically assign function to gene products.     

Support Vector Machine-based classification of protein folds using the structural properties of amino acid residues and amino acid residue pairs

MOTIVATION: Fold recognition is a key step in the protein structure discovery process, especially when traditional sequence comparison methods fail to yield convincing structural homologies. Although many methods have been developed for protein fold recognition, their accuracies remain low. This can be attributed to insufficient exploitation of fold discriminatory features. RESULTS: We have developed a new method for protein fold recognition using structural information of amino acid residues and amino acid residue pairs. Since protein fold recognition can be treated as a protein fold classification problem, we have developed a Support Vector Machine (SVM) based classifier approach that uses secondary structural state and solvent accessibility state frequencies of amino acids and amino acid pairs as feature vectors. Among the individual properties examined secondary structural state frequencies of amino acids gave an overall accuracy of 65.2% for fold discrimination, which is better than the accuracy by any method reported so far in the literature. Combination of secondary structural state frequencies with solvent accessibility state frequencies of amino acids and amino acid pairs further improved the fold discrimination accuracy to more than 70%, which is approximately 8% higher than the best available method. In this study we have also tested, for the first time, an all-together multi-class method known as Crammer and Singer method for protein fold classification. Our studies reveal that the three multi-class classification methods, namely one versus all, one versus one and Crammer and Singer method, yield similar predictions. AVAILABILITY: Dataset and stand-alone program are available upon request.     

Protein structure mining using a structural alphabet

We present a comprehensive evaluation of a new structure mining method called PB-ALIGN. It is based on the encoding of protein structure as 1D sequence of a combination of 16 short structural motifs or protein blocks (PBs). PBs are short motifs capable of representing most of the local structural features of a protein backbone. Using derived PB substitution matrix and simple dynamic programming algorithm, PB sequences are aligned the same way amino acid sequences to yield structure alignment. PBs are short motifs capable of representing most of the local structural features of a protein backbone. Alignment of these local features as sequence of symbols enables fast detection of structural similarities between two proteins. Ability of the method to characterize and align regions beyond regular secondary structures, for example, N and C caps of helix and loops connecting regular structures, puts it a step ahead of existing methods, which strongly rely on secondary structure elements. PB-ALIGN achieved efficiency of 85% in extracting true fold from a large database of 7259 SCOP domains and was successful in 82% cases to identify true super-family members. On comparison to 13 existing structure comparison/mining methods, PB-ALIGN emerged as the best on general ability test dataset and was at par with methods like YAKUSA and CE on nontrivial test dataset. Furthermore, the proposed method performed well when compared to flexible structure alignment method like FATCAT and outperforms in processing speed (less than 45 s per database scan). This work also establishes a reliable cut-off value for the demarcation of similar folds. It finally shows that global alignment scores of unrelated structures using PBs follow an extreme value distribution. PB-ALIGN is freely available on web server called Protein Block Expert (PBE) at http://bioinformatics.univ-reunion.fr/PBE/.