Sequence alignment with an appropriate substitution matrix.

A widely used algorithm for computing an optimal local alignment between two sequences requires a parameter set with a substitution matrix and gap penalties. It is recognized that a proper parameter set should be selected to suit the level of conservation between sequences. We describe an algorithm for selecting an appropriate substitution matrix at given gap penalties for computing an optimal local alignment between two sequences. In the algorithm, a substitution matrix that leads to the maximum alignment similarity score is selected among substitution matrices at various evolutionary distances. The evolutionary distance of the selected substitution matrix is defined as the distance of the computed alignment. To show the effects of gap penalties on alignments and their distances and help select appropriate gap penalties, alignments and their distances are computed at various gap penalties. The algorithm has been implemented as a computer program named SimDist. The SimDist program was compared with an existing local alignment program named SIM for finding reciprocally best-matching pairs (RBPs) of sequences in each of 100 protein families, where RBPs are commonly used as an operational definition of orthologous sequences. SimDist produced more accurate results than SIM on 50 of the 100 families, whereas both programs produced the same results on the other 50 families. SimDist was also used to compare three types of substitution matrices in scoring 444,461 pairs of homologous sequences from the 100 families.     

Structure-based evaluation of sequence comparison and fold recognition alignment accuracy

The biological role, biochemical function, and structure of uncharacterized protein sequences is often inferred from their similarity to known proteins. A constant goal is to increase the reliability, sensitivity, and accuracy of alignment techniques to enable the detection of increasingly distant relationships. Development, tuning, and testing of these methods benefit from appropriate benchmarks for the assessment of alignment accuracy.Here, we describe a benchmark protocol to estimate sequence-to-sequence and sequence-to-structure alignment accuracy. The protocol consists of structurally related pairs of proteins and procedures to evaluate alignment accuracy over the whole set. The set of protein pairs covers all the currently known fold types. The benchmark is challenging in the sense that it consists of proteins lacking clear sequence similarity.Correct target alignments are derived from the three-dimensional structures of these pairs by rigid body superposition. An evaluation engine computes the accuracy of alignments obtained from a particular algorithm in terms of alignment shifts with respect to the structure derived alignments. Using this benchmark we estimate that the best results can be obtained from a combination of amino acid residue substitution matrices and knowledge-based potentials.     

A transition probability model for amino acid substitutions from blocks.

Substitution matrices have been useful for sequence alignment and protein sequence comparisons. The BLOSUM series of matrices, which had been derived from a database of alignments of protein blocks, improved the accuracy of alignments previously obtained from the PAM-type matrices estimated from only closely related sequences. Although BLOSUM matrices are scoring matrices now widely used for protein sequence alignments, they do not describe an evolutionary model. BLOSUM matrices do not permit the estimation of the actual number of amino acid substitutions between sequences by correcting for multiple hits. The method presented here uses the Blocks database of protein alignments, along with the additivity of evolutionary distances, to approximate the amino acid substitution probabilities as a function of actual evolutionary distance. The PMB (Probability Matrix from Blocks) defines a new evolutionary model for protein evolution that can be used for evolutionary analyses of protein sequences. Our model is directly derived from, and thus compatible with, the BLOSUM matrices. The model has the additional advantage of being easily implemented.     

STRUCLA: a WWW meta-server for protein structure comparison and evolutionary classification

MOTIVATION: Evolutionary relationships of proteins have long been derived from the alignment of protein sequences. But from the view of function, most restraints of evolutionary divergence operate at the level of tertiary structure. It has been demonstrated that quantitative measures of dissimilarity in families of structurally similar proteins can be applied to the construction of trees from a comparison of their three-dimensional structures. However, no convenient tool is publicly available to carry out such analyses. RESULTS: We developed STRUCLA (STRUcture CLAssification), a WWW tool for generation of trees based on evolutionary distances inferred from protein structures according to various methods. The server takes as an input a list of PDB files or the initial alignment of protein coordinates provided by the user (for instance exported from SWISS PDB VIEWER). The user specifies the distance cutoff and selects the distance measures. The server returns series of unrooted trees in the NEXUS format and corresponding distance matrices, as well as a consensus tree. The results can be used as an alternative and a complement to a fixed hierarchy of current protein structure databases. It can complement sequence-based phylogenetic analysis in the 'twilight zone of homology', where amino acid sequences are too diverged to provide reliable relationships.     

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.     

Evaluation of PSI-BLAST alignment accuracy in comparison to structural alignments

The PSI-BLAST algorithm has been acknowledged as one of the most powerful tools for detecting remote evolutionary relationships by sequence considerations only. This has been demonstrated by its ability to recognize remote structural homologues and by the greatest coverage it enables in annotation of a complete genome. Although recognizing the correct fold of a sequence is of major importance, the accuracy of the alignment is crucial for the success of modeling one sequence by the structure of its remote homologue. Here we assess the accuracy of PSI-BLAST alignments on a stringent database of 123 structurally similar, sequence-dissimilar pairs of proteins, by comparing them to the alignments defined on a structural basis. Each protein sequence is compared to a nonredundant database of the protein sequences by PSI-BLAST. Whenever a pair member detects its pair-mate, the positions that are aligned both in the sequential and structural alignments are determined, and the alignment sensitivity is expressed as the percentage of these positions out of the structural alignment. Fifty-two sequences detected their pair-mates (for 16 pairs the success was bi-directional when either pair member was used as a query). The average percentage of correctly aligned residues per structural alignment was 43.5+/-2.2%. Other properties of the alignments were also examined, such as the sensitivity vs. specificity and the change in these parameters over consecutive iterations. Notably, there is an improvement in alignment sensitivity over consecutive iterations, reaching an average of 50.9+/-2.5% within the five iterations tested in the current study.     

Definition of general topological equivalence in protein structures. A procedure involving comparison of properties and relationships through simulated annealing and dynamic programming

A protein is defined as an indexed string of elements at each level in the hierarchy of protein structure: sequence, secondary structure, super-secondary structure, etc. The elements, for example, residues or secondary structure segments such as helices or beta-strands, are associated with a series of properties and can be involved in a number of relationships with other elements. Element-by-element dissimilarity matrices are then computed and used in the alignment procedure based on the sequence alignment algorithm of Needleman & Wunsch, expanded by the simulated annealing technique to take into account relationships as well as properties. The utility of this method for exploring the variability of various aspects of protein structure and for comparing distantly related proteins is demonstrated by multiple alignment of serine proteinases, aspartic proteinase lobes and globins.     

Amino acid similarity matrices based on force fields

MOTIVATION: We propose a general method for deriving amino acid substitution matrices from low resolution force fields. Unlike current popular methods, the approach does not rely on evolutionary arguments or alignment of sequences or structures. Instead, residues are computationally mutated and their contribution to the total energy/score is collected. The average of these values over each position within a set of proteins results in a substitution matrix. RESULTS: Example substitution matrices have been calculated from force fields based on different philosophies and their performance compared with conventional substitution matrices. Although this can produce useful substitution matrices, the methodology highlights the virtues, deficiencies and biases of the source force fields. It also allows a rather direct comparison of sequence alignment methods with the score functions underlying protein sequence to structure threading. AVAILABILITY: Example substitution matrices are available from http://www.rsc.anu.edu.au/~zsuzsa/suppl/matrices.html. SUPPLEMENTARY INFORMATION: The list of proteins used for data collection and the optimized parameters for the alignment are given as supplementary material at http://www.rsc.anu.edu.au/~zsuzsa/suppl/matrices.html.     

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/.     

Exploiting the co-evolution of interacting proteins to discover interaction specificity

Protein interactions are fundamental to the functioning of cells, and high throughput experimental and computational strategies are sought to map interactions. Predicting interaction specificity, such as matching members of a ligand family to specific members of a receptor family, is largely an unsolved problem. Here we show that by using evolutionary relationships within such families, it is possible to predict their physical interaction specificities. We introduce the computational method of matrix alignment for finding the optimal alignment between protein family similarity matrices. A second method, 3D embedding, allows visualization of interacting partners via spatial representation of the protein families. These methods essentially align phylogenetic trees of interacting protein families to define specific interaction partners. Prediction accuracy depends strongly on phylogenetic tree complexity, as measured with information theoretic methods. These results, along with simulations of protein evolution, suggest a model for the evolution of interacting protein families in which interaction partners are duplicated in coupled processes. Using these methods, it is possible to successfully find protein interaction specificities, as demonstrated for >18 protein families.     

A protein alignment scoring system sensitive at all evolutionary distances

Summary Protein sequence alignments generally are constructed with the aid of a substitution matrix that specifies a score for aligning each pair of amino acids. Assuming a simple random protein model, it can be shown that any such matrix, when used for evaluating variable-length local alignments, is implicitly a log-odds matrix, with a specific probability distribution for amino acid pairs to which it is uniquely tailored. Given a model of protein evolution from which such distributions may be derived, a substitution matrix adapted to detecting relationships at any chosen evolutionary distance can be constructed. Because in a database search it generally is not known a priori what evolutionary distances will characterize the similarities found, it is necessary to employ an appropriate range of matrices in order not to overlook potential homologies. This paper formalizes this concept by defining a scoring system that is sensitive at all detectable evolutionary distances. The statistical behavior of this scoring system is analyzed, and it is shown that for a typical protein database search, estimating the originally unknown evolutionary distance appropriate to each alignment costs slightly over two bits of information, or somewhat less than a factor of five in statistical significance. A much greater cost may be incurred, however, if only a single substitution matrix, corresponding to the wrong evolutionary distance, is employed.     

CAB-Align: A Flexible Protein Structure Alignment Method Based on the Residue-Residue Contact Area

Proteins are flexible, and this flexibility has an essential functional role. Flexibility can be observed in loop regions, rearrangements between secondary structure elements, and conformational changes between entire domains. However, most protein structure alignment methods treat protein structures as rigid bodies. Thus, these methods fail to identify the equivalences of residue pairs in regions with flexibility. In this study, we considered that the evolutionary relationship between proteins corresponds directly to the residue–residue physical contacts rather than the three-dimensional (3D) coordinates of proteins. Thus, we developed a new protein structure alignment method, contact area-based alignment (CAB-align), which uses the residue–residue contact area to identify regions of similarity. The main purpose of CAB-align is to identify homologous relationships at the residue level between related protein structures. The CAB-align procedure comprises two main steps: First, a rigid-body alignment method based on local and global 3D structure superposition is employed to generate a sufficient number of initial alignments. Then, iterative dynamic programming is executed to find the optimal alignment. We evaluated the performance and advantages of CAB-align based on four main points: (1) agreement with the gold standard alignment, (2) alignment quality based on an evolutionary relationship without 3D coordinate superposition, (3) consistency of the multiple alignments, and (4) classification agreement with the gold standard classification. Comparisons of CAB-align with other state-of-the-art protein structure alignment methods (TM-align, FATCAT, and DaliLite) using our benchmark dataset showed that CAB-align performed robustly in obtaining high-quality alignments and generating consistent multiple alignments with high coverage and accuracy rates, and it performed extremely well when discriminating between homologous and nonhomologous pairs of proteins in both single and multi-domain comparisons. The CAB-align software is freely available to academic users as stand-alone software at http://www.pharm.kitasato-u.ac.jp/bmd/bmd/Publications.html.     

Phyletic relationships of protein structures based on spatial preference of residues

Summary A structure-based scoring matrix MDPRE was derived from amino acid spatial preferences in protein structures. Sequence alignment and evolutionary studies by using MDPRE matrix gave similar results as those from ordinary sequence and structure alignments. It is interesting that a matrix derived from structure data solely could give comparable alignment results, strongly indicating the intimate connection between protein sequences and structures. The branch order and length from this approach were close to those obtained by a structure comparison method. Thus, by applying this structure-based matrix, the trees obtained should reflect evolutionary characteristics of protein structure. This approach takes advantage over a direct structure comparison in that (1) only a sequence and MDPRE matrix are needed, making it simple and widely applicable (especially in the absence of 3-dimensional protein structure data); (2) an established algorithm for sequence alignment and tree building could be employed, providing opportunities for direct comparison between matrices from different methodologies. One of the most striking features of this method is its capability to detect protein structure homologies when the sequence identities are low. This was well reflected in the given examples of the alignment of dinucleotidebinding domains.     

Circular permuted proteins in the universe of protein folds

Finding and identifying circular permuted protein pairs (CPP) is one of the harder tasks for structure alignment programs, because of the different location of the break in the polypeptide chain connectivity. The protein structure alignment tool GANGSTA+ was used to search for CPPs in a database of nearly 10,000 protein structures. It also allows determination of the statistical significance of the occurrence of circular permutations in the protein universe. The number of detected CPPs was found to be higher than expected, raising questions about the evolutionary processes leading to CPPs. The GANGSTA+ protein structure alignment tool is available online via the web server at http://gangsta.chemie.fu‐berlin.de . On the same webpage the complete data base of similar protein structure pairs based on the ASTRAL40 set of protein domains is provided and one can select CPPs specifically. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Tree-based maximal likelihood substitution matrices and hidden Markov models

There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.     

Improving the alignment quality of consistency based aligners with an evaluation function using synonymous protein words

Most sequence alignment tools can successfully align protein sequences with higher levels of sequence identity. The accuracy of corresponding structure alignment, however, decreases rapidly when considering distantly related sequences (<20% identity). In this range of identity, alignments optimized so as to maximize sequence similarity are often inaccurate from a structural point of view. Over the last two decades, most multiple protein aligners have been optimized for their capacity to reproduce structure-based alignments while using sequence information. Methods currently available differ essentially in the similarity measurement between aligned residues using substitution matrices, Fourier transform, sophisticated profile-profile functions, or consistency-based approaches, more recently.In this paper, we present a flexible similarity measure for residue pairs to improve the quality of protein sequence alignment. Our approach, called SymAlign, relies on the identification of conserved words found across a sizeable fraction of the considered dataset, and supported by evolutionary analysis. These words are then used to define a position specific substitution matrix that better reflects the biological significance of local similarity. The experiment results show that the SymAlign scoring scheme can be incorporated within T-Coffee to improve sequence alignment accuracy. We also demonstrate that SymAlign is less sensitive to the presence of structurally non-similar proteins. In the analysis of the relationship between sequence identity and structure similarity, SymAlign can better differentiate structurally similar proteins from non- similar proteins. We show that protein sequence alignments can be significantly improved using a similarity estimation based on weighted n-grams. In our analysis of the alignments thus produced, sequence conservation becomes a better indicator of structural similarity. SymAlign also provides alignment visualization that can display sub-optimal alignments on dot-matrices. The visualization makes it easy to identify well-supported alternative alignments that may not have been identified by dynamic programming. SymAlign is available at http://bio-cluster.iis.sinica.edu.tw/SymAlign/.     

<Emphasis Type="Italic">Scoredist</Emphasis>: A simple and robust protein sequence distance estimator

Background  

Distance-based methods are popular for reconstructing evolutionary trees thanks to their speed and generality. A number of methods exist for estimating distances from sequence alignments, which often involves some sort of correction for multiple substitutions. The problem is to accurately estimate the number of true substitutions given an observed alignment. So far, the most accurate protein distance estimators have looked for the optimal matrix in a series of transition probability matrices, e.g. the Dayhoff series. The evolutionary distance between two aligned sequences is here estimated as the evolutionary distance of the optimal matrix. The optimal matrix can be found either by an iterative search for the Maximum Likelihood matrix, or by integration to find the Expected Distance. As a consequence, these methods are more complex to implement and computationally heavier than correction-based methods. Another problem is that the result may vary substantially depending on the evolutionary model used for the matrices. An ideal distance estimator should produce consistent and accurate distances independent of the evolutionary model used.     

HIV-specific probabilistic models of protein evolution

Comparative sequence analyses, including such fundamental bioinformatics techniques as similarity searching, sequence alignment and phylogenetic inference, have become a mainstay for researchers studying type 1 Human Immunodeficiency Virus (HIV-1) genome structure and evolution. Implicit in comparative analyses is an underlying model of evolution, and the chosen model can significantly affect the results. In general, evolutionary models describe the probabilities of replacing one amino acid character with another over a period of time. Most widely used evolutionary models for protein sequences have been derived from curated alignments of hundreds of proteins, usually based on mammalian genomes. It is unclear to what extent these empirical models are generalizable to a very different organism, such as HIV-1-the most extensively sequenced organism in existence. We developed a maximum likelihood model fitting procedure to a collection of HIV-1 alignments sampled from different viral genes, and inferred two empirical substitution models, suitable for describing between-and within-host evolution. Our procedure pools the information from multiple sequence alignments, and provided software implementation can be run efficiently in parallel on a computer cluster. We describe how the inferred substitution models can be used to generate scoring matrices suitable for alignment and similarity searches. Our models had a consistently superior fit relative to the best existing models and to parameter-rich data-driven models when benchmarked on independent HIV-1 alignments, demonstrating evolutionary biases in amino-acid substitution that are unique to HIV, and that are not captured by the existing models. The scoring matrices derived from the models showed a marked difference from common amino-acid scoring matrices. The use of an appropriate evolutionary model recovered a known viral transmission history, whereas a poorly chosen model introduced phylogenetic error. We argue that our model derivation procedure is immediately applicable to other organisms with extensive sequence data available, such as Hepatitis C and Influenza A viruses.