DIALIGN 2: improvement of the segment-to-segment approach to multiple sequence alignment

MOTIVATION: The performance and time complexity of an improved version of the segment-to-segment approach to multiple sequence alignment is discussed. In this approach, alignments are composed from gap-free segment pairs, and the score of an alignment is defined as the sum of so-called weights of these segment pairs. RESULTS: A modification of the weight function used in the original version of the alignment program DIALIGN has two important advantages: it can be applied to both globally and locally related sequence sets, and the running time of the program is considerably improved. The time complexity of the algorithm is discussed theoretically, and the program running time is reported for various test examples. AVAILABILITY: The program is available on-line at the Bielefeld University Bioinformatics Server (BiBiServ) http://bibiserv.TechFak.Uni-Bielefeld.DE/dial ign/     

Tsukuba BB: a branch and bound algorithm for local multiple alignment of DNA and protein sequences.

In this paper we present a branch and bound algorithm for local gapless multiple sequence alignment (motif alignment) and its implementation. The algorithm uses both score-based bounding and a novel bounding technique based on the "consistency" of the alignment. A sequence order independent search tree is used in conjunction with a technique for avoiding redundant calculations inherent in the structure of the tree. This is the first program to exploit the fact that the motif alignment problem is easier for short motifs. Indeed, for a short fixed motif width, the running time of the algorithm is asymptotically linear in the size of the input. We tested the performance of the program on a dataset of 300 E. coli promoter sequences and a dataset of 85 lipocalin protein sequences. For a motif width of 4, the optimal alignment of the entire set of sequences can be found. For the more natural motif width of 6, the program can align 21 sequences of length 100, more than twice the number of sequences which can be aligned by the best previous exact algorithm. The algorithm can relax the constraint of requiring each sequence to be aligned, and align 105 of the 300 promoter sequences with a motif width of 6. For the lipocalin dataset, we introduce a technique for reducing the effective alphabet size with a minimal loss of useful information. With this technique, we show that the program can find meaningful motifs in a reasonable amount of time by optimizing the score over three motif positions.     

ParAlign: a parallel sequence alignment algorithm for rapid and sensitive database searches

There is a need for faster and more sensitive algorithms for sequence similarity searching in view of the rapidly increasing amounts of genomic sequence data available. Parallel processing capabilities in the form of the single instruction, multiple data (SIMD) technology are now available in common microprocessors and enable a single microprocessor to perform many operations in parallel. The ParAlign algorithm has been specifically designed to take advantage of this technology. The new algorithm initially exploits parallelism to perform a very rapid computation of the exact optimal ungapped alignment score for all diagonals in the alignment matrix. Then, a novel heuristic is employed to compute an approximate score of a gapped alignment by combining the scores of several diagonals. This approximate score is used to select the most interesting database sequences for a subsequent Smith-Waterman alignment, which is also parallelised. The resulting method represents a substantial improvement compared to existing heuristics. The sensitivity and specificity of ParAlign was found to be as good as Smith-Waterman implementations when the same method for computing the statistical significance of the matches was used. In terms of speed, only the significantly less sensitive NCBI BLAST 2 program was found to outperform the new approach. Online searches are available at http://dna.uio.no/search/     

Multiple sequence alignment with arbitrary gap costs: computing an optimal solution using polyhedral combinatorics

Multiple sequence alignment is one of the dominant problems in computational molecular biology. Numerous scoring functions and methods have been proposed, most of which result in NP-hard problems. In this paper we propose for the first time a general formulation for multiple alignment with arbitrary gap-costs based on an integer linear program (ILP). In addition we describe a branch-and-cut algorithm to effectively solve the ILP to optimality. We evaluate the performances of our approach in terms of running time and quality of the alignments using the BAliBase database of reference alignments. The results show that our implementation ranks amongst the best programs developed so far.     

The multiple common point set problem and its application to molecule binding pattern detection.

Recognition of binding patterns common to a set of protein structures is important for recognition of function, prediction of binding, and drug design. We consider protein binding sites represented by a set of 3D points with assigned physico-chemical and geometrical properties important for protein-ligand interactions. We formulate the multiple binding site alignment problem as detection of the largest common set of such 3D points. We discuss the computational problem of multiple common point set detection and, particularly, the matching problem in K-partite-epsilon graphs, where K partitions are associated with K structures and edges are defined between epsilon-close points. We show that the K-partite-epsilon matching problem is NP-hard in the Euclidean space with dimension larger than one. Consequently, we show that the largest common point set problem between three point sets is NP-hard. On the practical side, we present a novel computational method, MultiBind, for recognition of binding patterns common to a set of protein structures. It performs a multiple alignment between protein binding sites in the absence of overall sequence, fold, or binding partner similarity. Despite the NP-hardness results, in our applications, we practically overcome the exponential number of multiple alignment combinations by applying an efficient branchand- bound filtering procedure. We show applications of MultiBind to several biological targets. The method recognizes patterns which are responsible for binding small molecules, such as estradiol, ATP/ANP, and transition state analogues.     

MUSTANG: a multiple structural alignment algorithm

Multiple structural alignment is a fundamental problem in structural genomics. In this article, we define a reliable and robust algorithm, MUSTANG (MUltiple STructural AligNment AlGorithm), for the alignment of multiple protein structures. Given a set of protein structures, the program constructs a multiple alignment using the spatial information of the C(alpha) atoms in the set. Broadly based on the progressive pairwise heuristic, this algorithm gains accuracy through novel and effective refinement phases. MUSTANG reports the multiple sequence alignment and the corresponding superposition of structures. Alignments generated by MUSTANG are compared with several handcurated alignments in the literature as well as with the benchmark alignments of 1033 alignment families from the HOMSTRAD database. The performance of MUSTANG was compared with DALI at a pairwise level, and with other multiple structural alignment tools such as POSA, CE-MC, MALECON, and MultiProt. MUSTANG performs comparably to popular pairwise and multiple structural alignment tools for closely related proteins, and performs more reliably than other multiple structural alignment methods on hard data sets containing distantly related proteins or proteins that show conformational changes.     

Multiple sequence alignment in parallel on a workstation cluster

SUMMARY: Multiple sequence alignment is the NP-hard problem of aligning three or more DNA or amino acid sequences in an optimal way so as to match as many characters as possible from the set of sequences. The popular sequence alignment program ClustalW uses the classical method of approximating a sequence alignment, by first computing a distance matrix and then constructing a guide tree to show the evolutionary relationship of the sequences. We show that parallelizing the ClustalW algorithm can result in significant speedup. We used a cluster of workstations using C and message passing interface for our implementation. Experimental results show that speedup of over 5.5 on six processors is obtainable for most inputs. AVAILABILITY: The software is available upon request from the second author.     

MASTR: multiple alignment and structure prediction of non-coding RNAs using simulated annealing

MOTIVATION: As more non-coding RNAs are discovered, the importance of methods for RNA analysis increases. Since the structure of ncRNA is intimately tied to the function of the molecule, programs for RNA structure prediction are necessary tools in this growing field of research. Furthermore, it is known that RNA structure is often evolutionarily more conserved than sequence. However, few existing methods are capable of simultaneously considering multiple sequence alignment and structure prediction. RESULT: We present a novel solution to the problem of simultaneous structure prediction and multiple alignment of RNA sequences. Using Markov chain Monte Carlo in a simulated annealing framework, the algorithm MASTR (Multiple Alignment of STructural RNAs) iteratively improves both sequence alignment and structure prediction for a set of RNA sequences. This is done by minimizing a combined cost function that considers sequence conservation, covariation and basepairing probabilities. The results show that the method is very competitive to similar programs available today, both in terms of accuracy and computational efficiency. AVAILABILITY: Source code available from http://mastr.binf.ku.dk/     

3DCoffee: combining protein sequences and structures within multiple sequence alignments

Most bioinformatics analyses require the assembly of a multiple sequence alignment. It has long been suspected that structural information can help to improve the quality of these alignments, yet the effect of combining sequences and structures has not been evaluated systematically. We developed 3DCoffee, a novel method for combining protein sequences and structures in order to generate high-quality multiple sequence alignments. 3DCoffee is based on TCoffee version 2.00, and uses a mixture of pairwise sequence alignments and pairwise structure comparison methods to generate multiple sequence alignments. We benchmarked 3DCoffee using a subset of HOMSTRAD, the collection of reference structural alignments. We found that combining TCoffee with the threading program Fugue makes it possible to improve the accuracy of our HOMSTRAD dataset by four percentage points when using one structure only per dataset. Using two structures yields an improvement of ten percentage points. The measures carried out on HOM39, a HOMSTRAD subset composed of distantly related sequences, show a linear correlation between multiple sequence alignment accuracy and the ratio of number of provided structure to total number of sequences. Our results suggest that in the case of distantly related sequences, a single structure may not be enough for computing an accurate multiple sequence alignment.     

APDB: a novel measure for benchmarking sequence alignment methods without reference alignments

MOTIVATION: We describe APDB, a novel measure for evaluating the quality of a protein sequence alignment, given two or more PDB structures. This evaluation does not require a reference alignment or a structure superposition. APDB is designed to efficiently and objectively benchmark multiple sequence alignment methods. RESULTS: Using existing collections of reference multiple sequence alignments and existing alignment methods, we show that APDB gives results that are consistent with those obtained using conventional evaluations. We also show that APDB is suitable for evaluating sequence alignments that are structurally equivalent. We conclude that APDB provides an alternative to more conventional methods used for benchmarking sequence alignment packages.     

The correlation error and finite-size correction in an ungapped sequence alignment

MOTIVATION: The BLAST program for comparing two sequences assumes independent sequences in its random model. The resulting random alignment matrices have correlations across their diagonals. Analytic formulas for the BLAST p-value essentially neglect these correlations and are equivalent to a random model with independent diagonals. Progress on the independent diagonals model has been surprisingly rapid, but the practical magnitude of the correlations it neglects remains unknown. In addition, BLAST uses a finite-size correction that is particularly important when either of the sequences being compared is short. Several formulas for the finite-size correction have now been given, but the corresponding errors in the BLAST p-values have not been quantified. As the lengths of compared sequences tend to infinity, it is also theoretically unknown whether the neglected correlations vanish faster than the finite-size correction. RESULTS: Because we required certain analytic formulas, our study restricted its computer experiments to ungapped sequence alignment. We expect some of our conclusions to extend qualitatively to gapped sequence alignment, however. With this caveat, the finite-size correction appeared to vanish faster than the neglected correlations. Although the finite-size correction underestimated the BLAST p-value, it improved the approximation substantially for all but very short sequences. In practice, the Altschul-Gish finite-size correction was superior to Spouge's. The independent diagonals model was always within a factor of 2 of the true BLAST p-value, although fitting p-value parameters from it probably is unwise. CONTACT: spouge@ncbi.nlm.nih.gov     

On the inference of parsimonious indel evolutionary scenarios

Given a multiple alignment of orthologous DNA sequences and a phylogenetic tree for these sequences, we investigate the problem of reconstructing a most parsimonious scenario of insertions and deletions capable of explaining the gaps observed in the alignment. This problem, called the Indel Parsimony Problem, is a crucial component of the problem of ancestral genome reconstruction, and its solution provides valuable information to many genome functional annotation approaches. We first show that the problem is NP-complete. Second, we provide an algorithm, based on the fractional relaxation of an integer linear programming formulation. The algorithm is fast in practice, and the solutions it produces are, in most cases, provably optimal. We describe a divide-and-conquer approach that makes it possible to solve very large instances on a simple desktop machine, while retaining guaranteed optimality. Our algorithms are tested and shown efficient and accurate on a set of 1.8 Mb mammalian orthologous sequences in the CFTR region.     

Homology-extended sequence alignment

We present a profile–profile multiple alignment strategy that uses database searching to collect homologues for each sequence in a given set, in order to enrich their available evolutionary information for the alignment. For each of the alignment sequences, the putative homologous sequences that score above a pre-defined threshold are incorporated into a position-specific pre-alignment profile. The enriched position-specific profile is used for standard progressive alignment, thereby more accurately describing the characteristic features of the given sequence set. We show that owing to the incorporation of the pre-alignment information into a standard progressive multiple alignment routine, the alignment quality between distant sequences increases significantly and outperforms state-of-the-art methods, such as T-COFFEE and MUSCLE. We also show that although entirely sequence-based, our novel strategy is better at aligning distant sequences when compared with a recent contact-based alignment method. Therefore, our pre-alignment profile strategy should be advantageous for applications that rely on high alignment accuracy such as local structure prediction, comparative modelling and threading.     

A workbench for multiple alignment construction and analysis

Multiple sequence alignment can be a useful technique for studying molecular evolution, as well as for analyzing relationships between structure or function and primary sequence. We have developed for this purpose an interactive program, MACAW (Multiple Alignment Construction and Analysis Workbench), that allows the user to construct multiple alignments by locating, analyzing, editing, and combining "blocks" of aligned sequence segments. MACAW incorporates several novel features. (1) Regions of local similarity are located by a new search algorithm that avoids many of the limitations of previous techniques. (2) The statistical significance of blocks of similarity is evaluated using a recently developed mathematical theory. (3) Candidate blocks may be evaluated for potential inclusion in a multiple alignment using a variety of visualization tools. (4) A user interface permits each block to be edited by moving its boundaries or by eliminating particular segments, and blocks may be linked to form a composite multiple alignment. No completely automatic program is likely to deal effectively with all the complexities of the multiple alignment problem; by combining a powerful similarity search algorithm with flexible editing, analysis and display tools, MACAW allows the alignment strategy to be tailored to the problem at hand.     

AliGROOVE – visualization of heterogeneous sequence divergence within multiple sequence alignments and detection of inflated branch support

Background

Masking of multiple sequence alignment blocks has become a powerful method to enhance the tree-likeness of the underlying data. However, existing masking approaches are insensitive to heterogeneous sequence divergence which can mislead tree reconstructions. We present AliGROOVE, a new method based on a sliding window and a Monte Carlo resampling approach, that visualizes heterogeneous sequence divergence or alignment ambiguity related to single taxa or subsets of taxa within a multiple sequence alignment and tags suspicious branches on a given tree.

Results

We used simulated multiple sequence alignments to show that the extent of alignment ambiguity in pairwise sequence comparison is correlated with the frequency of misplaced taxa in tree reconstructions. The approach implemented in AliGROOVE allows to detect nodes within a tree that are supported despite the absence of phylogenetic signal in the underlying multiple sequence alignment. We show that AliGROOVE equally well detects heterogeneous sequence divergence in a case study based on an empirical data set of mitochondrial DNA sequences of chelicerates.

Conclusions

The AliGROOVE approach has the potential to identify single taxa or subsets of taxa which show predominantly randomized sequence similarity in comparison with other taxa in a multiple sequence alignment. It further allows to evaluate the reliability of node support in a novel way.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-294) contains supplementary material, which is available to authorized users.     

A polynomial time solvable formulation of multiple sequence alignment.

Since traditional multiple alignment formulations are NP-hard, heuristics are commonly employed to find acceptable alignments with no guaranteed performance bound. This causes a substantial difficulty in understanding what the resulting alignment means and in assessing the quality of these alignments. We propose an alternative formulation of multiple alignment based on the idea of finding a multiple alignment of k sequences which preserves k - 1 pairwise alignments as specified by edges of a given tree. Although it is well known that such a preserving alignment always exists, it did not become a mainstream method for multiple alignment since it seems that a lot of information is lost from ignoring pairwise similarities outside the tree. In contrast, by using pairwise alignments that incorporate consistency information from other sequences, we show that it is possible to obtain very good accuracy with the preserving alignment formulation. We show that a reasonable objective function to use is to find the shortest preserving alignment, and, by a reduction to a graph-theoretic problem, that the problem of finding the shortest preserving multiple alignment can be solved in polynomial time. We demonstrate the success of this approach on three sets of benchmark multiple alignments by using consistency-based pairwise alignments from the first stage of two of the best performing progressive alignment algorithms TCoffee and ProbCons and replace the second heuristic progressive step of these algorithms by the exact preserving alignment step. We apply this strategy to TCoffee and show that our approach outperforms TCoffee on two of the three test sets. We apply the strategy to a variant of ProbCons with no iterative refinements and show that our approach achieves similar or better accuracy except on one test set. We also compare our performance to ProbCons with iterative refinements and show that our approach achieves similar or better accuracy on many subcategories even without further refinements. The most important advantage of the preserving alignment formulation is that we are certain that we can solve the problem in polynomial time without using a heuristic. A software program implementing this approach (PSAlign) is available at http://faculty.cs.tamu.edu/shsze/psalign.     

STRAL: progressive alignment of non-coding RNA using base pairing probability vectors in quadratic time

MOTIVATION: Alignment of RNA has a wide range of applications, for example in phylogeny inference, consensus structure prediction and homology searches. Yet aligning structural or non-coding RNAs (ncRNAs) correctly is notoriously difficult as these RNA sequences may evolve by compensatory mutations, which maintain base pairing but destroy sequence homology. Ideally, alignment programs would take RNA structure into account. The Sankoff algorithm for the simultaneous solution of RNA structure prediction and RNA sequence alignment was proposed 20 years ago but suffers from its exponential complexity. A number of programs implement lightweight versions of the Sankoff algorithm by restricting its application to a limited type of structure and/or only pairwise alignment. Thus, despite recent advances, the proper alignment of multiple structural RNA sequences remains a problem. RESULTS: Here we present StrAl, a heuristic method for alignment of ncRNA that reduces sequence-structure alignment to a two-dimensional problem similar to standard multiple sequence alignment. The scoring function takes into account sequence similarity as well as up- and downstream pairing probability. To test the robustness of the algorithm and the performance of the program, we scored alignments produced by StrAl against a large set of published reference alignments. The quality of alignments predicted by StrAl is far better than that obtained by standard sequence alignment programs, especially when sequence homologies drop below approximately 65%; nevertheless StrAl's runtime is comparable to that of ClustalW.     

BCL::Align—Sequence alignment and fold recognition with a custom scoring function online

BCL::Align is a multiple sequence alignment tool that utilizes the dynamic programming method in combination with a customizable scoring function for sequence alignment and fold recognition. The scoring function is a weighted sum of the traditional PAM and BLOSUM scoring matrices, position-specific scoring matrices output by PSI-BLAST, secondary structure predicted by a variety of methods, chemical properties, and gap penalties. By adjusting the weights, the method can be tailored for fold recognition or sequence alignment tasks at different levels of sequence identity. A Monte Carlo algorithm was used to determine optimized weight sets for sequence alignment and fold recognition that most accurately reproduced the SABmark reference alignment test set. In an evaluation of sequence alignment performance, BCL::Align ranked best in alignment accuracy (Cline score of 22.90 for sequences in the Twilight Zone) when compared with Align-m, ClustalW, T-Coffee, and MUSCLE. ROC curve analysis indicates BCL::Align's ability to correctly recognize protein folds with over 80% accuracy. The flexibility of the program allows it to be optimized for specific classes of proteins (e.g. membrane proteins) or fold families (e.g. TIM-barrel proteins). BCL::Align is free for academic use and available online at http://www.meilerlab.org/.