A non-local gap-penalty for profile alignment

The length of an alignment of biological sequences is typically longer than the mean length of its component sequences. (This arises from the insertion of gaps in the alignment.) When such an alignment is used as a profile for the alignment of further sequences (or profiles), it will have a bias toward additional sequences that match the length of the profile, rather than the mean length of sequences in the profile, as the alignment of these well entail fewer (or smaller) insertions) so avoiding gap-penalties). An algorithm is described to correct this bias that entails monitoring the correspondence, for every pair of positions, of the mean separations in both profiles as they are aligned. The correction was incorporated into a standard dynamic programming algorithm through a modification of the gap-penalty, but, unlike other approaches, this modification is not local and takes into consideration the overall alignment of the sequences. This implies that the algorithm cannot guarantee to find the optimal alignment, but tests suggest that close approximations are obtained. The method was tested on protein families by measuring the area in the parameter space of the phase containing the correct multiple alignment. No improvement (increase in phase area) was found with a family that required few gaps to be aligned correctly. However, for highly gapped alignments, a 50% increase in area was obtained with one family and the correct alignment was found for another that could not be aligned with the unbiased method.     

Murlet: a practical multiple alignment tool for structural RNA sequences

MOTIVATION: Structural RNA genes exhibit unique evolutionary patterns that are designed to conserve their secondary structures; these patterns should be taken into account while constructing accurate multiple alignments of RNA genes. The Sankoff algorithm is a natural alignment algorithm that includes the effect of base-pair covariation in the alignment model. However, the extremely high computational cost of the Sankoff algorithm precludes its application to most RNA sequences. RESULTS: We propose an efficient algorithm for the multiple alignment of structural RNA sequences. Our algorithm is a variant of the Sankoff algorithm, and it uses an efficient scoring system that reduces the time and space requirements considerably without compromising on the alignment quality. First, our algorithm computes the match probability matrix that measures the alignability of each position pair between sequences as well as the base pairing probability matrix for each sequence. These probabilities are then combined to score the alignment using the Sankoff algorithm. By itself, our algorithm does not predict the consensus secondary structure of the alignment but uses external programs for the prediction. We demonstrate that both the alignment quality and the accuracy of the consensus secondary structure prediction from our alignment are the highest among the other programs examined. We also demonstrate that our algorithm can align relatively long RNA sequences such as the eukaryotic-type signal recognition particle RNA that is approximately 300 nt in length; multiple alignment of such sequences has not been possible by using other Sankoff-based algorithms. The algorithm is implemented in the software named 'Murlet'. AVAILABILITY: The C++ source code of the Murlet software and the test dataset used in this study are available at http://www.ncrna.org/papers/Murlet/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Evaluation and improvements in the automatic alignment of protein sequences

The accuracy of protein sequence alignment obtained by applying a commonly used global sequence comparison algorithm is assessed. Alignments based on the superposition of the three-dimensional structures are used as a standard for testing the automatic, sequence-based methods. Alignments obtained from the global comparison of five pairs of homologous protein sequences studied gave 54% agreement overall for residues in secondary structures. The inclusion of information about the secondary structure of one of the proteins in order to limit the number of gaps inserted in regions of secondary structure, improved this figure to 68%. A similarity score of greater than six standard deviation units suggests that an alignment which is greater than 75% correct within secondary structural regions can be obtained automatically for the pair of sequences.     

Bayesian adaptive sequence alignment algorithms

The selection of a scoring matrix and gap penalty parameters continues to be an important problem in sequence alignment. We describe here an algorithm, the 'Bayes block aligner, which bypasses this requirement. Instead of requiring a fixed set of parameter settings, this algorithm returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest. Furthermore, instead of returning the single best alignment for the chosen parameter settings, this algorithm returns the posterior distribution of all alignments considering the full range of gapping and scoring matrices selected, weighing each in proportion to its probability based on the data. We compared the Bayes aligner with the popular Smith-Waterman algorithm with parameter settings from the literature which had been optimized for the identification of structural neighbors, and found that the Bayes aligner correctly identified more structural neighbors. In a detailed examination of the alignment of a pair of kinase and a pair of GTPase sequences, we illustrate the algorithm's potential to identify subsequences that are conserved to different degrees. In addition, this example shows that the Bayes aligner returns an alignment-free assessment of the distance between a pair of sequences.      

A new algorithm for detecting low-complexity regions in protein sequences

MOTIVATION: Pair-wise alignment of protein sequences and local similarity searches produce many false positives because of compositionally biased regions, also called low-complexity regions (LCRs), of amino acid residues. Masking and filtering such regions significantly improves the reliability of homology searches and, consequently, functional predictions. Most of the available algorithms are based on a statistical approach. We wished to investigate the structural properties of LCRs in biological sequences and develop an algorithm for filtering them. RESULTS: We present an algorithm for detecting and masking LCRs in protein sequences to improve the quality of database searches. We developed the algorithm based on the complexity analysis of subsequences delimited by a pair of identical, repeating subsequences. Given a protein sequence, the algorithm first computes the suffix tree of the sequence. It then collects repeating subsequences from the tree. Finally, the algorithm iteratively tests whether each subsequence delimited by a pair of repeating subsequences meets a given criteria. Test results with 1000 proteins from 20 families in Pfam show that the repeating subsequences are a good indicator for the low-complexity regions, and the algorithm based on such structural information strongly compete with others. AVAILABILITY: http://bioinfo.knu.ac.kr/research/CARD/ CONTACT: swshin@bioinfo.knu.ac.kr     

Predicting reliable regions in protein alignments from sequence profiles

For applications such as comparative modelling one major issue is the reliability of sequence alignments. Reliable regions in alignments can be predicted using sub-optimal alignments of the same pair of sequences. Here we show that reliable regions in alignments can also be predicted from multiple sequence profile information alone.Alignments were created for a set of remotely related pairs of proteins using five different test methods. Structural alignments were used to assess the quality of the alignments and the aligned positions were scored using information from the observed frequencies of amino acid residues in sequence profiles pre-generated for each template structure. High-scoring regions of these profile-derived alignment scores were a good predictor of reliably aligned regions.These profile-derived alignment scores are easy to obtain and are applicable to any alignment method. They can be used to detect those regions of alignments that are reliably aligned and to help predict the quality of an alignment. For those residues within secondary structure elements, the regions predicted as reliably aligned agreed with the structural alignments for between 92% and 97.4% of the residues. In loop regions just under 92% of the residues predicted to be reliable agreed with the structural alignments. The percentage of residues predicted as reliable ranged from 32.1% for helix residues to 52.8% for strand residues.This information could also be used to help predict conserved binding sites from sequence alignments. Residues in the template that were identified as binding sites, that aligned to an identical amino acid residue and where the sequence alignment agreed with the structural alignment were in highly conserved, high scoring regions over 80% of the time. This suggests that many binding sites that are present in both target and template sequences are in sequence-conserved regions and that there is the possibility of translating reliability to binding site prediction.     

The role played by environmental residues on sidechain torsional angles within homologous families of proteins: A new method of sidechain modeling

We investigated the conservation of sidechain conformation for each residue within a homologous family of proteins in the Protein Data Bank (PDB) and performed sidechain modeling using this information. The information was represented by the probability of conserved sidechain torsional angles obtained from many families of proteins, and these were calculated for a pair of residues at topologically equivalent positions as a result of structural alignment. Probabilities were obtained for a pair of same amino acids and for a pair of different amino acids. The correlation between environmental residues and the fluctuation of probability was examined for the pair of same amino acid residues, and the simple probability was calculated for the pair of different amino acids. From the results on the same amino acid pairs, 17 amino acids, except for Ala, Gly, and Pro, were divided into two types: those that were influenced and those that were not influenced by the environmental residues. From results on different amino acid pairs, a replacement between large residues, such as Trp, Phe, and Tyr, was performed assuming conservation of their torsional angles within a homologous family of proteins. We performed sidechain modeling for 11 known proteins from their native and modeled backbones, respectively. With the native backbones, the percentage of the χ₁ angle correct within 30° was found to be 67% and 80% for all and core residues, respectively. With the modeled backbones, the percentage of the correct χ₁ angle was found to be 60% and 72% for all and core residues, respectively. To estimate an upper limit on the accuracy for predicting sidechain conformations, we investigated the probability of conserved sidechain torsional angles for highly similar proteins having > 90% sequence identity and <2.5-Å X-ray resolution. In those proteins, 83% of the sidechain conformations were conserved for the χ₁ angle. Proteins 31:355–369, 1998. © 1998 Wiley-Liss, Inc.     

Optimal pairwise alignment of fixed protein structures in subquadratic time

The problem of finding an optimal structural alignment for a pair of superimposed proteins is often amenable to the Smith-Waterman dynamic programming algorithm, which runs in time proportional to the product of lengths of the sequences being aligned. While the quadratic running time is acceptable for computing a single alignment of two fixed protein structures, the time complexity becomes a bottleneck when running the Smith-Waterman routine multiple times in order to find a globally optimal superposition and alignment of the input proteins. We present a subquadratic running time algorithm capable of computing an alignment that optimizes one of the most widely used measures of protein structure similarity, defined as the number of pairs of residues in two proteins that can be superimposed under a predefined distance cutoff. The algorithm presented in this article can be used to significantly improve the speed-accuracy tradeoff in a number of popular protein structure alignment methods.     

A hidden Markov model for progressive multiple alignment

MOTIVATION: Progressive algorithms are widely used heuristics for the production of alignments among multiple nucleic-acid or protein sequences. Probabilistic approaches providing measures of global and/or local reliability of individual solutions would constitute valuable developments. RESULTS: We present here a new method for multiple sequence alignment that combines an HMM approach, a progressive alignment algorithm, and a probabilistic evolution model describing the character substitution process. Our method works by iterating pairwise alignments according to a guide tree and defining each ancestral sequence from the pairwise alignment of its child nodes, thus, progressively constructing a multiple alignment. Our method allows for the computation of each column minimum posterior probability and we show that this value correlates with the correctness of the result, hence, providing an efficient mean by which unreliably aligned columns can be filtered out from a multiple alignment.     

Towards an automatic method of predicting protein structure by homology: an evaluation of suboptimal sequence alignments.

A major problem in predicting protein structure by homology modelling is that the sequence alignment from which the model is built may not be the best one in terms of the correct equivalencing of residues assessed by structural or functional criteria. A useful strategy is to generate and examine a number of suboptimal alignments as better alignments can often be found away from the optimal. A procedure to filter rapidly suboptimal alignments based on measurement of core volumes and packing pair potentials is investigated. The approach is benchmarked on three pairs of sequences which are non-trivial to align correctly, namely two immunoglobulin domains, plastocyanin with azurin and two distant globin sequences. It is shown to be useful to reduce a large ensemble of possible alignments down to a few which correspond more closely to the correct (structure based) alignment.     

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.     

Optimal contact map alignment of protein-protein interfaces

The long-standing problem of constructing protein structure alignments is of central importance in computational biology. The main goal is to provide an alignment of residue correspondences, in order to identify homologous residues across chains. A critical next step of this is the alignment of protein complexes and their interfaces. Here, we introduce the program CMAPi, a two-dimensional dynamic programming algorithm that, given a pair of protein complexes, optimally aligns the contact maps of their interfaces: it produces polynomial-time near-optimal alignments in the case of multiple complexes. We demonstrate the efficacy of our algorithm on complexes from PPI families listed in the SCOPPI database and from highly divergent cytokine families. In comparison to existing techniques, CMAPi generates more accurate alignments of interacting residues within families of interacting proteins, especially for sequences with low similarity. While previous methods that use an all-atom based representation of the interface have been successful, CMAPi's use of a contact map representation allows it to be more tolerant to conformational changes and thus to align more of the interaction surface. These improved interface alignments should enhance homology modeling and threading methods for predicting PPIs by providing a basis for generating template profiles for sequence-structure alignment.     

Multiple alignment by sequence annealing

MOTIVATION: We introduce a novel approach to multiple alignment that is based on an algorithm for rapidly checking whether single matches are consistent with a partial multiple alignment. This leads to a sequence annealing algorithm, which is an incremental method for building multiple sequence alignments one match at a time. Our approach improves significantly on the standard progressive alignment approach to multiple alignment. RESULTS: The sequence annealing algorithm performs well on benchmark test sets of protein sequences. It is not only sensitive, but also specific, drastically reducing the number of incorrectly aligned residues in comparison to other programs. The method allows for adjustment of the sensitivity/specificity tradeoff and can be used to reliably identify homologous regions among protein sequences. AVAILABILITY: An implementation of the sequence annealing algorithm is available at http://bio.math.berkeley.edu/amap/     

Suboptimal sequence alignment in molecular biology. Alignment with error analysis

A molecular sequence alignment algorithm based on dynamic programming has been extended to allow the computation of all pairs of residues that can be part of optimal and suboptimal sequence alignments. The uncertainties inherent in sequence alignment can be displayed using a new form of dot plot. The method allows the qualitative assessment of whether or not two sequences are related, and can reveal what parts of the alignment are better determined than others. It also permits the computation of representative optimal and suboptimal alignments. The relation between alignment reliability and alignment parameters is discussed. Other applications are to cyclical permutations of sequences and the detection of self-similarity. An application to multiple sequence alignment is noted.     

Statistical evaluation and comparison of a pairwise alignment algorithm that a priori assigns the number of gaps rather than employing gap penalties

MOTIVATION: Although pairwise sequence alignment is essential in comparative genomic sequence analysis, it has proven difficult to precisely determine the gap penalties for a given pair of sequences. A common practice is to employ default penalty values. However, there are a number of problems associated with using gap penalties. First, alignment results can vary depending on the gap penalties, making it difficult to explore appropriate parameters. Second, the statistical significance of an alignment score is typically based on a theoretical model of non-gapped alignments, which may be misleading. Finally, there is no way to control the number of gaps for a given pair of sequences, even if the number of gaps is known in advance. RESULTS: In this paper, we develop and evaluate the performance of an alignment technique that allows the researcher to assign a priori set of the number of allowable gaps, rather than using gap penalties. We compare this approach with the Smith-Waterman and Needleman-Wunsch techniques on a set of structurally aligned protein sequences. We demonstrate that this approach outperforms the other techniques, especially for short sequences (56-133 residues) with low similarity (<25%). Further, by employing a statistical measure, we show that it can be used to assess the quality of the alignment in relation to the true alignment with the associated optimal number of gaps. AVAILABILITY: The implementation of the described methods SANK_AL is available at http://cbbc.murdoch.edu.au/ CONTACT: matthew@cbbc.murdoch.edu.au.     

A simple genetic algorithm for multiple sequence alignment

Multiple sequence alignment plays an important role in molecular sequence analysis. An alignment is the arrangement of two (pairwise alignment) or more (multiple alignment) sequences of 'residues' (nucleotides or amino acids) that maximizes the similarities between them. Algorithmically, the problem consists of opening and extending gaps in the sequences to maximize an objective function (measurement of similarity). A simple genetic algorithm was developed and implemented in the software MSA-GA. Genetic algorithms, a class of evolutionary algorithms, are well suited for problems of this nature since residues and gaps are discrete units. An evolutionary algorithm cannot compete in terms of speed with progressive alignment methods but it has the advantage of being able to correct for initially misaligned sequences; which is not possible with the progressive method. This was shown using the BaliBase benchmark, where Clustal-W alignments were used to seed the initial population in MSA-GA, improving outcome. Alignment scoring functions still constitute an open field of research, and it is important to develop methods that simplify the testing of new functions. A general evolutionary framework for testing and implementing different scoring functions was developed. The results show that a simple genetic algorithm is capable of optimizing an alignment without the need of the excessively complex operators used in prior study. The clear distinction between objective function and genetic algorithms used in MSA-GA makes extending and/or replacing objective functions a trivial task.     

A memory-efficient algorithm for multiple sequence alignment with constraints

MOTIVATION: Recently, the concept of the constrained sequence alignment was proposed to incorporate the knowledge of biologists about structures/functionalities/consensuses of their datasets into sequence alignment such that the user-specified residues/nucleotides are aligned together in the computed alignment. The currently developed programs use the so-called progressive approach to efficiently obtain a constrained alignment of several sequences. However, the kernels of these programs, the dynamic programming algorithms for computing an optimal constrained alignment between two sequences, run in (gamman2) memory, where gamma is the number of the constraints and n is the maximum of the lengths of sequences. As a result, such a high memory requirement limits the overall programs to align short sequences only. RESULTS: We adopt the divide-and-conquer approach to design a memory-efficient algorithm for computing an optimal constrained alignment between two sequences, which greatly reduces the memory requirement of the dynamic programming approaches at the expense of a small constant factor in CPU time. This new algorithm consumes only O(alphan) space, where alpha is the sum of the lengths of constraints and usually alpha < n in practical applications. Based on this algorithm, we have developed a memory-efficient tool for multiple sequence alignment with constraints. AVAILABILITY: http://genome.life.nctu.edu.tw/MUSICME.     

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.     

Estimation of P-values for global alignments of protein sequences.

MOTIVATION: The global alignment of protein sequence pairs is often used in the classification and analysis of full-length sequences. The calculation of a Z-score for the comparison gives a length and composition corrected measure of the similarity between the sequences. However, the Z-score alone, does not indicate the likely biological significance of the similarity. In this paper, all pairs of domains from 250 sequences belonging to different SCOP folds were aligned and Z-scores calculated. The distribution of Z-scores was fitted with a peak distribution from which the probability of obtaining a given Z-score from the global alignment of two protein sequences of unrelated fold was calculated. A similar analysis was applied to subsequence pairs found by the Smith-Waterman algorithm. These analyses allow the probability that two protein sequences share the same fold to be estimated by global sequence alignment. RESULTS: The relationship between Z-score and probability varied little over the matrix/gap penalty combinations examined. However, an average shift of +4.7 was observed for Z-scores derived from global alignment of locally-aligned subsequences compared to global alignment of the full-length sequences. This shift was shown to be the result of pre-selection by local alignment, rather than any structural similarity in the subsequences. The search ability of both methods was benchmarked against the SCOP superfamily classification and showed that global alignment Z-scores generated from the entire sequence are as effective as SSEARCH at low error rates and more effective at higher error rates. However, global alignment Z-scores generated from the best locally-aligned subsequence were significantly less effective than SSEARCH. The method of estimating statistical significance described here was shown to give similar values to SSEARCH and BLAST, providing confidence in the significance estimation. AVAILABILITY: Software to apply the statistics to global alignments is available from http://barton.ebi.ac.uk. CONTACT: geoff@ebi.ac.uk     

SQUARE--determining reliable regions in sequence alignments

The Server for Quick Alignment Reliability Evaluation (SQUARE) is a Web-based version of the method we developed to predict regions of reliably aligned residues in sequence alignments. Given an alignment between a query sequence and a sequence of known structure, SQUARE is able to predict which residues are reliably aligned. The server accesses a database of profiles of sequences of known three-dimensional structures in order to calculate the scores for each residue in the alignment. SQUARE produces a graphical output of the residue profile-derived alignment scores along with an indication of the reliability of the alignment. In addition, the scores can be compared against template secondary structure, conserved residues and important sites.