Evaluation performance of substitution matrices,based on contacts between residue terminal groups

Sequence alignment is a standard method for the estimation of the evolutionary, structural, and functional relationships among amino acid sequences. The quality of alignments depends on the used similarity matrix. Statistical contact potentials (CPs) contain information on contact propensities among residues in native protein structures. Substitution matrices (SMs) based on CPs are applicable for the comparison of distantly related sequences. Here, contact between amino acids was estimated on the basis of the evaluation of the distances between side-chain terminal groups (SCTGs), which are defined as the group of the side-chain heavy atoms with fixed distances between them. In this paper, two new types of CPs and similarity matrices have been constructed: one based on fixed cutoff distance obtained from geometric characteristics of the SCTGs (TGC1), while the other is distance-dependent potential (TGC2). These matrices are compared with other popular SMs. The performance of the matrices was evaluated by comparing sequence with structural alignments. The obtained results show that TGC2 has the best performance among contact-based matrices, but on the whole, contact-based matrices have slightly lower performance than other SMs except fold-level similarity.     

Evaluation performance of substitution matrices, based on contacts between residue terminal groups

Sequence alignment is a standard method for the estimation of the evolutionary, structural, and functional relationships among amino acid sequences. The quality of alignments depends on the used similarity matrix. Statistical contact potentials (CPs) contain information on contact propensities among residues in native protein structures. Substitution matrices (SMs) based on CPs are applicable for the comparison of distantly related sequences. Here, contact between amino acids was estimated on the basis of the evaluation of the distances between side-chain terminal groups (SCTGs), which are defined as the group of the side-chain heavy atoms with fixed distances between them. In this paper, two new types of CPs and similarity matrices have been constructed: one based on fixed cutoff distance obtained from geometric characteristics of the SCTGs (TGC1), while the other is distance-dependent potential (TGC2). These matrices are compared with other popular SMs. The performance of the matrices was evaluated by comparing sequence with structural alignments. The obtained results show that TGC2 has the best performance among contact-based matrices, but on the whole, contact-based matrices have slightly lower performance than other SMs except fold-level similarity.     

The structural alignment between two proteins: is there a unique answer?

Structurally similar but sequentially unrelated proteins have been discovered and rediscovered by many researchers, using a variety of structure comparison tools. For several pairs of such proteins, existing structural alignments obtained from the literature, as well as alignments prepared using several different similarity criteria, are compared with each other. It is shown that, in general, they differ from each other, with differences increasing with diminishing sequence similarity. Differences are particularly strong between alignments optimizing global similarity measures, such as RMS deviation between C alpha atoms, and alignments focusing on more local features, such as packing or interaction pattern similarity. Simply speaking, by putting emphasis on different aspects of structure, different structural alignments show the unquestionable similarity in a different way. With differences between various alignments extending to a point where they can differ at all positions, analysis of structural similarities leads to contradictory results reported by groups using different alignment techniques. The problem of uniqueness and stability of structural alignments is further studied with the help of visualization of the suboptimal alignments. It is shown that alignments are often degenerate and whole families of alignments can be generated with almost the same score as the "optimal alignment." However, for some similarity criteria, specially those based on side-chain positions, rather than C alpha positions, alignments in some areas of the protein are unique. This opens the question of how and if the structural alignments can be used as "standards of truth" for protein comparison.     

A comparison of position-specific score matrices based on sequence and structure alignments

Sequence comparison methods based on position-specific score matrices (PSSMs) have proven a useful tool for recognition of the divergent members of a protein family and for annotation of functional sites. Here we investigate one of the factors that affects overall performance of PSSMs in a PSI-BLAST search, the algorithm used to construct the seed alignment upon which the PSSM is based. We compare PSSMs based on alignments constructed by global sequence similarity (ClustalW and ClustalW-pairwise), local sequence similarity (BLAST), and local structure similarity (VAST). To assess performance with respect to identification of conserved functional or structural sites, we examine the accuracy of the three-dimensional molecular models predicted by PSSM-sequence alignments. Using the known structures of those sequences as the standard of truth, we find that model accuracy varies with the algorithm used for seed alignment construction in the pattern local-structure (VAST) > local-sequence (BLAST) > global-sequence (ClustalW). Using structural similarity of query and database proteins as the standard of truth, we find that PSSM recognition sensitivity depends primarily on the diversity of the sequences included in the alignment, with an optimum around 30-50% average pairwise identity. We discuss these observations, and suggest a strategy for constructing seed alignments that optimize PSSM-sequence alignment accuracy and recognition sensitivity.     

Adaptive GDDA-BLAST: fast and efficient algorithm for protein sequence embedding

A major computational challenge in the genomic era is annotating structure/function to the vast quantities of sequence information that is now available. This problem is illustrated by the fact that most proteins lack comprehensive annotations, even when experimental evidence exists. We previously theorized that embedded-alignment profiles (simply "alignment profiles" hereafter) provide a quantitative method that is capable of relating the structural and functional properties of proteins, as well as their evolutionary relationships. A key feature of alignment profiles lies in the interoperability of data format (e.g., alignment information, physio-chemical information, genomic information, etc.). Indeed, we have demonstrated that the Position Specific Scoring Matrices (PSSMs) are an informative M-dimension that is scored by quantitatively measuring the embedded or unmodified sequence alignments. Moreover, the information obtained from these alignments is informative, and remains so even in the "twilight zone" of sequence similarity (<25% identity). Although our previous embedding strategy was powerful, it suffered from contaminating alignments (embedded AND unmodified) and high computational costs. Herein, we describe the logic and algorithmic process for a heuristic embedding strategy named "Adaptive GDDA-BLAST." Adaptive GDDA-BLAST is, on average, up to 19 times faster than, but has similar sensitivity to our previous method. Further, data are provided to demonstrate the benefits of embedded-alignment measurements in terms of detecting structural homology in highly divergent protein sequences and isolating secondary structural elements of transmembrane and ankyrin-repeat domains. Together, these advances allow further exploration of the embedded alignment data space within sufficiently large data sets to eventually induce relevant statistical inferences. We show that sequence embedding could serve as one of the vehicles for measurement of low-identity alignments and for incorporation thereof into high-performance PSSM-based alignment profiles.     

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     

A new progressive-iterative algorithm for multiple structure alignment

MOTIVATION: Multiple structure alignments are becoming important tools in many aspects of structural bioinformatics. The current explosion in the number of available protein structures demands multiple structural alignment algorithms with an adequate balance of accuracy and speed, for large scale applications in structural genomics, protein structure prediction and protein classification. RESULTS: A new multiple structural alignment program, MAMMOTH-mult, is described. It is demonstrated that the alignments obtained with the new method are an improvement over previous manual or automatic alignments available in several widely used databases at all structural levels. Detailed analysis of the structural alignments for a few representative cases indicates that MAMMOTH-mult delivers biologically meaningful trees and conservation at the sequence and structural levels of functional motifs in the alignments. An important improvement over previous methods is the reduction in computational cost. Typical alignments take only a median time of 5 CPU seconds in a single R12000 processor. MAMMOTH-mult is particularly useful for large scale applications. AVAILABILITY: http://ub.cbm.uam.es/mammoth/mult.     

Pair hidden Markov models on tree structures

MOTIVATION: Computationally identifying non-coding RNA regions on the genome has much scope for investigation and is essentially harder than gene-finding problems for protein-coding regions. Since comparative sequence analysis is effective for non-coding RNA detection, efficient computational methods are expected for structural alignments of RNA sequences. On the other hand, Hidden Markov Models (HMMs) have played important roles for modeling and analysing biological sequences. Especially, the concept of Pair HMMs (PHMMs) have been examined extensively as mathematical models for alignments and gene finding. RESULTS: We propose the pair HMMs on tree structures (PHMMTSs), which is an extension of PHMMs defined on alignments of trees and provides a unifying framework and an automata-theoretic model for alignments of trees, structural alignments and pair stochastic context-free grammars. By structural alignment, we mean a pairwise alignment to align an unfolded RNA sequence into an RNA sequence of known secondary structure. First, we extend the notion of PHMMs defined on alignments of 'linear' sequences to pair stochastic tree automata, called PHMMTSs, defined on alignments of 'trees'. The PHMMTSs provide various types of alignments of trees such as affine-gap alignments of trees and an automata-theoretic model for alignment of trees. Second, based on the observation that a secondary structure of RNA can be represented by a tree, we apply PHMMTSs to the problem of structural alignments of RNAs. We modify PHMMTSs so that it takes as input a pair of a 'linear' sequence and a 'tree' representing a secondary structure of RNA to produce a structural alignment. Further, the PHMMTSs with input of a pair of two linear sequences is mathematically equal to the pair stochastic context-free grammars. We demonstrate some computational experiments to show the effectiveness of our method for structural alignments, and discuss a complexity issue of PHMMTSs.     

Multiple protein sequence alignment

Multiple sequence alignments are essential in computational analysis of protein sequences and structures, with applications in structure modeling, functional site prediction, phylogenetic analysis and sequence database searching. Constructing accurate multiple alignments for divergent protein sequences remains a difficult computational task, and alignment speed becomes an issue for large sequence datasets. Here, I review methodologies and recent advances in the multiple protein sequence alignment field, with emphasis on the use of additional sequence and structural information to improve alignment quality.     

Alignment algorithm for homology modeling and threading.

A DNA/protein sequence comparison is a popular computational tool for molecular biologists. Finding a good alignment implies an evolutionary and/or functional relationship between proteins or genomic loci. Sequential similarity between two proteins indicates their structural resemblance, providing a practical approach for structural modeling, when structure of one of these proteins is known. The first step in the homology modeling is a construction of an accurate sequence alignment. The commonly used alignment algorithms do not provide an adequate treatment of the structurally mismatched residues in locally dissimilar regions. We propose a simple modification of the existing alignment algorithm which treats these regions properly and demonstrate how this modification improves sequence alignments in real proteins.     

Structure-derived substitution matrices for alignment of distantly related sequences

Sequence alignment is a standard method to infer evolutionary, structural, and functional relationships among sequences. The quality of alignments depends on the substitution matrix used. Here we derive matrices based on superimpositions from protein pairs of similar structure, but of low or no sequence similarity. In a performance test the matrices are compared with 12 other previously published matrices. It is found that the structure-derived matrices are applicable for comparisons of distantly related sequences. We investigate the influence of evolutionary relationships of protein pairs on the alignment accuracy.     

MALIDUP: a database of manually constructed structure alignments for duplicated domain pairs

We describe MALIDUP (manual alignments of duplicated domains), a database of 241 pairwise structure alignments for homologous domains originated by internal duplication within the same polypeptide chain. Since duplicated domains within a protein frequently diverge in function and thus in sequence, this would be the first database of structurally similar homologs that is not strongly biased by sequence or functional similarity. Our manual alignments in most cases agree with the automatic structural alignments generated by several commonly used programs. This carefully constructed database could be used in studies on protein evolution and as a reference for testing structure alignment programs. The database is available at http://prodata.swmed.edu/malidup.     

Statistical potential-based amino acid similarity matrices for aligning distantly related protein sequences

Aligning distantly related protein sequences is a long-standing problem in bioinformatics, and a key for successful protein structure prediction. Its importance is increasing recently in the context of structural genomics projects because more and more experimentally solved structures are available as templates for protein structure modeling. Toward this end, recent structure prediction methods employ profile-profile alignments, and various ways of aligning two profiles have been developed. More fundamentally, a better amino acid similarity matrix can improve a profile itself; thereby resulting in more accurate profile-profile alignments. Here we have developed novel amino acid similarity matrices from knowledge-based amino acid contact potentials. Contact potentials are used because the contact propensity to the other amino acids would be one of the most conserved features of each position of a protein structure. The derived amino acid similarity matrices are tested on benchmark alignments at three different levels, namely, the family, the superfamily, and the fold level. Compared to BLOSUM45 and the other existing matrices, the contact potential-based matrices perform comparably in the family level alignments, but clearly outperform in the fold level alignments. The contact potential-based matrices perform even better when suboptimal alignments are considered. Comparing the matrices themselves with each other revealed that the contact potential-based matrices are very different from BLOSUM45 and the other matrices, indicating that they are located in a different basin in the amino acid similarity matrix space.     

Structure alignment via Delaunay tetrahedralization

A novel protein structure alignment technique has been developed reducing much of the secondary and tertiary structure to a sequential representation greatly accelerating many structural computations, including alignment. Constructed from incidence relations in the Delaunay tetrahedralization, alignments of the sequential representation describe structural similarities that cannot be expressed with rigid-body superposition and complement existing techniques minimizing root-mean-squared distance through superposition. Restricting to the largest substructure superimposable by a single rigid-body transformation determines an alignment suitable for root-mean-squared distance comparisons and visualization. Restricted alignments of a test set of histones and histone-like proteins determined superpositions nearly identical to those produced by the established structure alignment routines of DaliLite and ProSup. Alignment of three, increasingly complex proteins: ferredoxin, cytidine deaminase, and carbamoyl phosphate synthetase, to themselves, demonstrated previously identified regions of self-similarity. All-against-all similarity index comparisons performed on a test set of 45 class I and class II aminoacyl-tRNA synthetases closely reproduced the results of established distance matrix methods while requiring 1/16 the time. Principal component analysis of pairwise tetrahedral decomposition similarity of 2300 molecular dynamics snapshots of tryptophanyl-tRNA synthetase revealed discrete microstates within the trajectory consistent with experimental results. The method produces results with sufficient efficiency for large-scale multiple structure alignment and is well suited to genomic and evolutionary investigations where no geometric model of similarity is known a priori.     

Database searching by flexible protein structure alignment

We have recently developed a flexible protein structure alignment program (FATCAT) that identifies structural similarity, at the same time accounting for flexibility of protein structures. One of the most important applications of a structure alignment method is to aid in functional annotations by identifying similar structures in large structural databases. However, none of the flexible structure alignment methods were applied in this task because of a lack of significance estimation of flexible alignments. In this paper, we developed an estimate of the statistical significance of FATCAT alignment score, allowing us to use it as a database-searching tool. The results reported here show that (1) the distribution of the similarity score of FATCAT alignment between two unrelated protein structures follows the extreme value distribution (EVD), adding one more example to the current collection of EVDs of sequence and structure similarities; (2) introducing flexibility into structure comparison only slightly influences the sensitivity and specificity of identifying similar structures; and (3) the overall performance of FATCAT as a database searching tool is comparable to that of the widely used rigid-body structure comparison programs DALI and CE. Two examples illustrating the advantages of using flexible structure alignments in database searching are also presented. The conformational flexibilities that were detected in the first example may be involved with substrate specificity, and the conformational flexibilities detected in the second example may reflect the evolution of structures by block building.     

SANA: an algorithm for sequential and non-sequential protein structure alignment

Protein structure alignment algorithms play an important role in the studies of protein structure and function. In this paper, a novel approach for structure alignment is presented. Specifically, core regions in two protein structures are first aligned by identifying connected components in a network of neighboring geometrically compatible aligned fragment pairs. The initial alignments then are refined through a multi-objective optimization method. The algorithm can produce both sequential and non-sequential alignments. We show the superior performance of the proposed algorithm by the computational experiments on several benchmark datasets and the comparisons with the well-known structure alignment algorithms such as DALI, CE and MATT. The proposed method can obtain accurate and biologically significant alignment results for the case with occurrence of internal repeats or indels, identify the circular permutations, and reveal conserved functional sites. A ranking criterion of our algorithm for fold similarity is presented and found to be comparable or superior to the Z-score of CE in most cases from the numerical experiments. The software and supplementary data of computational results are available at .     

A comparative study of available software for high-accuracy homology modeling: from sequence alignments to structural models

An open question in protein homology modeling is, how well do current modeling packages satisfy the dual criteria of quality of results and practical ease of use? To address this question objectively, we examined homology‐built models of a variety of therapeutically relevant proteins. The sequence identities across these proteins range from 19% to 76%. A novel metric, the difference alignment index (DAI), is developed to aid in quantifying the quality of local sequence alignments. The DAI is also used to construct the relative sequence alignment (RSA), a new representation of global sequence alignment that facilitates comparison of sequence alignments from different methods. Comparisons of the sequence alignments in terms of the RSA and alignment methodologies are made to better understand the advantages and caveats of each method. All sequence alignments and corresponding 3D models are compared to their respective structure‐based alignments and crystal structures. A variety of protein modeling software was used. We find that at sequence identities >40%, all packages give similar (and satisfactory) results; at lower sequence identities (<25%), the sequence alignments generated by Profit and Prime, which incorporate structural information in their sequence alignment, stand out from the rest. Moreover, the model generated by Prime in this low sequence identity region is noted to be superior to the rest. Additionally, we note that DSModeler and MOE, which generate reasonable models for sequence identities >25%, are significantly more functional and easier to use when compared with the other structure‐building software.     

Adaptive Smith–Waterman residue match seeding for protein structural alignment

The POLYFIT rigid‐body algorithm for automated global pairwise and multiple protein structural alignment is presented. Smith–Waterman local alignment is used to establish a set of seed equivalences that are extended using Needleman–Wunsch dynamic programming techniques. Structural and functional interaction constraints provided by evolution are encoded as one‐dimensional residue physical environment strings for alignment of highly structurally overlapped protein pairs. Local structure alignment of more distantly related pairs is carried out using rigid‐body conformational matching of 15‐residue fragments, with allowance made for less stringent conformational matching of metal‐ion and small molecule ligand‐contact, disulphide bridge, and cis‐peptide correspondences. Protein structural plasticity is accommodated through the stepped adjustment of a single empirical distance parameter value in the calculation of the Smith–Waterman dynamic programming matrix. Structural overlap is used both as a measure of similarity and to assess alignment quality. Pairwise alignment accuracy has been benchmarked against that of 10 widely used aligners on the Sippl and Wiederstein set of difficult pairwise structure alignment problems, and more extensively against that of Matt, SALIGN, and MUSTANG in pairwise and multiple structural alignments of protein domains with low shared sequence identity in the SCOP‐ASTRAL 40% compendium. The results demonstrate the advantages of POLYFIT over other aligners in the efficient and robust identification of matching seed residue positions in distantly related protein targets and in the generation of longer structurally overlapped alignment lengths. Superposition‐based application areas include comparative modeling and protein and ligand design. POLYFIT is available on the Web server at http://polyfit.insa‐toulouse.fr . Proteins 2013; 81:1823–1839. © 2013 Wiley Periodicals, Inc.     

GASH: An improved algorithm for maximizing the number of equivalent residues between two protein structures

Background  

We introduce GASH, a new, publicly accessible program for structural alignment and superposition. Alignments are scored by the Number of Equivalent Residues (NER), a quantitative measure of structural similarity that can be applied to any structural alignment method. Multiple alignments are optimized by conjugate gradient maximization of the NER score within the genetic algorithm framework. Initial alignments are generated by the program Local ASH, and can be supplemented by alignments from any other program.