A fast algorithm for the constrained multiple sequence alignment problem

Given n strings S1, S2, ..., Sn, and a pattern string P, the constrained multiple sequence alignment (CMSA) problem is to find an optimal multiple alignment of S1, S2, ..., Sn such that the alignment contains P, i.e. in the alignment matrix there exists a sequence of columns each entirely composed of symbol P[k] for every k, where P[k] is the kth symbol in P, 1 ≤ k ≤ |P|, and in the sequence, a column containing P[i] appears before the column containing P[j] for all i,j, i < j. The problem is motivated from the problem of comparing multiple sequences that share a common structure, or sequence pattern. There are O(2ns1s2...snr)-time dynamic programming algorithms for the problem, where s1,s2, ...,sn and r are, respectively, the lengths of the input strings and the pattern string. Feasibility of these algorithms in practice is limited when the number of sequences is large, or the sequences are long because of the impractically long time required by these algorithms. We present a new algorithm with worst-case time complexity also O(2ns1s2...snr), but the algorithm avoids redundant computations in existing dynamic programming solutions. Experiments on both randomly generated strings and real data show that this algorithm is much faster than the existing algorithms. We present an analysis that explains the speed-up obtained in our experiments by our algorithm over the naive dynamic programming algorithm for constrained multiple sequence alignment of protein sequences. The speed-up is more significant when pattern is long, or n is large. For example in the case of constrained pairwise sequence alignment (the CMSA problem with n=2) when the pattern is sufficiently long for strings S1 and S2, the asymptotic time complexity is observed to be O(s1s2) instead of O(s1s2r). Main ideas in our algorithm can also be used in other constrained sequence alignment problems

Parallel progressive multiple sequence alignment on reconfigurable meshes

<p>Abstract</p> <p>Background</p> <p>One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. The most popular and proven best practice method to accomplish this task is aligning multiple sequences together. However, multiple sequence alignment is a computing extensive task. In addition, the advancement in DNA/RNA and Protein sequencing techniques has created a vast amount of sequences to be analyzed that exceeding the capability of traditional computing models. Therefore, an effective parallel multiple sequence alignment model capable of resolving these issues is in a great demand.</p> <p>Results</p> <p>We design <it>O</it>(1) run-time solutions for both local and global dynamic programming pair-wise alignment algorithms on reconfigurable mesh computing model. To align <it>m </it>sequences with max length <it>n</it>, we combining the parallel pair-wise dynamic programming solutions with newly designed parallel components. We successfully reduce the progressive multiple sequence alignment algorithm's run-time complexity from <it>O</it>(<it>m </it>× <it>n</it>⁴) to <it>O</it>(<it>m</it>) using <it>O</it>(<it>m </it>× <it>n</it>³) processing units for scoring schemes that use three distinct values for match/mismatch/gap-extension. The general solution to multiple sequence alignment algorithm takes <it>O</it>(<it>m </it>× <it>n</it>⁴) processing units and completes in <it>O</it>(<it>m</it>) time.</p> <p>Conclusions</p> <p>To our knowledge, this is the first time the progressive multiple sequence alignment algorithm is completely parallelized with <it>O</it>(<it>m</it>) run-time. We also provide a new parallel algorithm for the Longest Common Subsequence (LCS) with <it>O</it>(1) run-time using <it>O</it>(<it>n</it>³) processing units. This is a big improvement over the current best constant-time algorithm that uses <it>O</it>(<it>n</it>⁴) processing units.</p

Dynamic Programming Algorithms for Discovery of Antibiotic Resistance in Microbial Genomes

The translation of comparative genomics into clinical decision support tools often depends on the quality of sequence alignments. However, currently used methods of multiple sequence alignments suffer from significant biases and problems with aligning diverged sequences. The objective of this study was to develop and test a new multiple sequence alignment (MSA) algorithm suitable for the high-throughput comparative analysis of different microbial genomes. This algorithm employs an innovative tensor indexing method for partitioning the dynamic programming hyper-cube space for parallel processing. We have used the clinically relevant task of identifying regions that determine resistance to antibiotics to test the new algorithm and to compare its performance with existing MSA methods. The new method "mmDst" performed better than existing MSA algorithms for more divergent sequences because it employs a simultaneous alignment scoring recurrence, which effectively approximated the score for edge missing cell scores that fall outside the scoring region.Comment: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=d06cf32f66c6866e2867abdca587419d4958af1

Progressive multiple sequence alignment with the Poisson Indel Process

Sequence alignment lies at the heart of many evolutionary and comparative genomics studies. However, the optimal alignment of multiple sequences is NP-hard, so that exact algorithms become impractical for more than a few sequences. Thus, state of the art alignment methods employ progressive heuristics, breaking the problem into a series of pairwise alignments guided by a phylogenetic tree. Changes between homologous characters are typically modelled by a continuous-time Markov substitution model. In contrast, the dynamics of insertions and deletions (indels) are not modelled explicitly, because the computation of the marginal likelihood under such models has exponential time complexity in the number of taxa. Recently, Bouchard-Côté and Jordan [PNAS (2012) 110(4):1160-1166] have introduced a modification to a classical indel model, describing indel evolution on a phylogenetic tree as a Poisson process. The model termed PIP allows to compute the joint marginal probability of a multiple sequence alignment and a tree in linear time. Here, we present an new dynamic programming algorithm to align two multiple sequence alignments by maximum likelihood in polynomial time under PIP, and apply it a in progressive algorithm. To our knowledge, this is the first progressive alignment method using a rigorous mathematical formulation of an evolutionary indel process and with polynomial time complexity

Aligning Speakers: Evaluating and Visualizing Text-based Diarization Using Efficient Multiple Sequence Alignment (Extended Version)

This paper presents a novel evaluation approach to text-based speaker diarization (SD), tackling the limitations of traditional metrics that do not account for any contextual information in text. Two new metrics are proposed, Text-based Diarization Error Rate and Diarization F1, which perform utterance- and word-level evaluations by aligning tokens in reference and hypothesis transcripts. Our metrics encompass more types of errors compared to existing ones, allowing us to make a more comprehensive analysis in SD. To align tokens, a multiple sequence alignment algorithm is introduced that supports multiple sequences in the reference while handling high-dimensional alignment to the hypothesis using dynamic programming. Our work is packaged into two tools, align4d providing an API for our alignment algorithm and TranscribeView for visualizing and evaluating SD errors, which can greatly aid in the creation of high-quality data, fostering the advancement of dialogue systems.Comment: Accepted to the 35th IEEE International Conference on Tools with Artificial Intelligence (ICTAI) 202

MM-align: a quick algorithm for aligning multiple-chain protein complex structures using iterative dynamic programming

Structural comparison of multiple-chain protein complexes is essential in many studies of protein–protein interactions. We develop a new algorithm, MM-align, for sequence-independent alignment of protein complex structures. The algorithm is built on a heuristic iteration of a modified Needleman–Wunsch dynamic programming (DP) algorithm, with the alignment score specified by the inter-complex residue distances. The multiple chains in each complex are first joined, in every possible order, and then simultaneously aligned with cross-chain alignments prevented. The alignments of interface residues are enhanced by an interface-specific weighting factor. MM-align is tested on a large-scale benchmark set of 205 × 3897 non-homologous multiple-chain complex pairs. Compared with a naïve extension of the monomer alignment program of TM-align, the alignment accuracy of MM-align is significantly higher as judged by the average TM-score of the physically-aligned residues. MM-align is about two times faster than TM-align because of omitting the cross-alignment zone of the DP matrix. It also shows that the enhanced alignment of the interfaces helps in identifying biologically relevant protein complex pairs.Alfred P. Sloan Foundation; NSF Career Award (DBI 0746198); and the National Institute of General Medical Sciences (R01GM083107, R01GM084222). Funding for open access charge: Alfred P. Sloan Research Fellowship

Multiple sequence alignment augmented by expert user constraints

Sequence alignment has become one of the most common tasks in bioinformatics. Most of the existing sequence alignment methods use general scoring schemes. But these alignments are sometimes not completely relevant because they do not necessarily provide the desired information. It would be extremely difficult, if not impossible, to include any possible objective into an algorithm. Our goal is to allow a working biologist to augment a given alignment with additional information based on their knowledge and objectives.In this thesis, we will formally define constraints and compatible constraint sets for an alignment which require some positions of the sequences to be aligned together. Using this approach, one can align some specific segments such as domains within protein sequences by inputting constraints (the positions of the segments on the sequences), and the algorithm will automatically find an optimal alignment in which the segments are aligned together.A necessary prerequisite of calculating an alignment is that the constraints inputted be compatible with each other, and we will develop algorithms to check this condition for both pairwise and multiple sequence alignments. The algorithms are based on a depth-first search on a graph that is converted from the constraints and the alignment. We then develop algorithms to perform pairwise and multiple sequence alignments satisfying these compatible constraints.Using straightforward dynamic programming for pairwise sequence alignment satisfying a compatible constraint set, an optimal alignment corresponds to a path going through the dynamic programming matrix, and as we are only using single-position constraints, a constraint can be represented as a point on the matrix, so a compatible constraint set is a set of points. We try to determine a new path, rather than the original path, that achieves the highest score which goes through all the compatible constraint set points. The path is a concatenation of sub-paths, so that only the scores in the sub-matrices need to be calculated. This means the time required to get the new path decreases as the number of constraints increases, and it also varies as the positions of the points change. It can be further reduced by using the information from the original alignment, which can offer a significant speed gain.We then use exact and progressive algorithms to find multiple sequence alignments satisfying a compatible constraint set, which are extensions of pairwise sequence alignments. With exact algorithms for three sequences, where constraints are represented as lines, we discuss a method to force the optimal path to cross the constraint lines. And with progressive algorithms, we use a set of pairwise alignments satisfying compatible constraints to construct multiple sequence alignments progressively. Because they are more complex, we leave some extensions as future work

ASPIC: a novel method to predict the exon-intron structure of a gene that is optimally compatible to a set of transcript sequences

BACKGROUND: Currently available methods to predict splice sites are mainly based on the independent and progressive alignment of transcript data (mostly ESTs) to the genomic sequence. Apart from often being computationally expensive, this approach is vulnerable to several problems – hence the need to develop novel strategies. RESULTS: We propose a method, based on a novel multiple genome-EST alignment algorithm, for the detection of splice sites. To avoid limitations of splice sites prediction (mainly, over-predictions) due to independent single EST alignments to the genomic sequence our approach performs a multiple alignment of transcript data to the genomic sequence based on the combined analysis of all available data. We recast the problem of predicting constitutive and alternative splicing as an optimization problem, where the optimal multiple transcript alignment minimizes the number of exons and hence of splice site observations. We have implemented a splice site predictor based on this algorithm in the software tool ASPIC (Alternative Splicing PredICtion). It is distinguished from other methods based on BLAST-like tools by the incorporation of entirely new ad hoc procedures for accurate and computationally efficient transcript alignment and adopts dynamic programming for the refinement of intron boundaries. ASPIC also provides the minimal set of non-mergeable transcript isoforms compatible with the detected splicing events. The ASPIC web resource is dynamically interconnected with the Ensembl and Unigene databases and also implements an upload facility. CONCLUSION: Extensive bench marking shows that ASPIC outperforms other existing methods in the detection of novel splicing isoforms and in the minimization of over-predictions. ASPIC also requires a lower computation time for processing a single gene and an EST cluster. The ASPIC web resource is available at

An Improved Search Algorithm for Optimal Multiple-Sequence Alignment

Multiple sequence alignment (MSA) is a ubiquitous problem in computational biology. Although it is NP-hard to find an optimal solution for an arbitrary number of sequences, due to the importance of this problem researchers are trying to push the limits of exact algorithms further. Since MSA can be cast as a classical path finding problem, it is attracting a growing number of AI researchers interested in heuristic search algorithms as a challenge with actual practical relevance. In this paper, we first review two previous, complementary lines of research. Based on Hirschbergs algorithm, Dynamic Programming needs O(kN^(k-1)) space to store both the search frontier and the nodes needed to reconstruct the solution path, for k sequences of length N. Best first search, on the other hand, has the advantage of bounding the search space that has to be explored using a heuristic. However, it is necessary to maintain all explored nodes up to the final solution in order to prevent the search from re-expanding them at higher cost. Earlier approaches to reduce the Closed list are either incompatible with pruning methods for the Open list, or must retain at least the boundary of the Closed list. In this article, we present an algorithm that attempts at combining the respective advantages; like A* it uses a heuristic for pruning the search space, but reduces both the maximum Open and Closed size to O(kN^(k-1)), as in Dynamic Programming. The underlying idea is to conduct a series of searches with successively increasing upper bounds, but using the DP ordering as the key for the Open priority queue. With a suitable choice of thresholds, in practice, a running time below four times that of A* can be expected. In our experiments we show that our algorithm outperforms one of the currently most successful algorithms for optimal multiple sequence alignments, Partial Expansion A*, both in time and memory. Moreover, we apply a refined heuristic based on optimal alignments not only of pairs of sequences, but of larger subsets. This idea is not new; however, to make it practically relevant we show that it is equally important to bound the heuristic computation appropriately, or the overhead can obliterate any possible gain. Furthermore, we discuss a number of improvements in time and space efficiency with regard to practical implementations. Our algorithm, used in conjunction with higher-dimensional heuristics, is able to calculate for the first time the optimal alignment for almost all of the problems in Reference 1 of the benchmark database BAliBASE

Bit-parallel and SIMD alignment algorithms for biological sequence analysis

High-throughput next-generation sequencing techniques have hugely decreased the cost and increased the speed of sequencing, resulting in an explosion of sequencing data. This motivates the development of high-efficiency sequence alignment algorithms. In this thesis, I present multiple bit-parallel and Single Instruction Multiple Data (SIMD) algorithms that greatly accelerate the processing of biological sequences. The first chapter describes the BitPAl bit-parallel algorithms for global alignment with general integer scoring, which assigns integer weights for match, mismatch, and insertion/deletion. The bit-parallel approach represents individual cells in an alignment scoring matrix as bits in computer words and emulates the calculation of scores by a series of logic operations. Bit-parallelism has previously been applied to other pattern matching problems, producing fast algorithms. In timed tests, we show that BitPAl runs 7 - 25 times faster than a standard iterative algorithm. The second part involves two approaches to alignment with substitution scoring, which assigns a potentially different substitution weight to every pair of alphabet characters, better representing the relative rates of different mutations. The first approach extends the existing BitPAl method. The second approach is a new SIMD algorithm that uses partial sums of adjacent score differences. I present a simple partial sum method as well as one that uses parallel scan for additional acceleration. Results demonstrate that these algorithms are significantly faster than existing SIMD dynamic programming algorithms. Finally, I describe two extensions to the partial sums algorithm. The first adds support for affine gap penalty scoring. Affine gap scoring represents the biological likelihood that it is more likely for gaps to be continuous than to be distributed throughout a region by introducing a gap opening penalty and a gap extension penalty. The second extension is an algorithm that uses the partial sums method to calculate the tandem alignment of a pattern against a text sequence using a single pattern copy. Next generation sequencing data provides a wealth of information to researchers. Extracting that information in a timely manner increases the utility and practicality of sequence analysis algorithms. This thesis presents a family of algorithms which provide alignment scores in less time than previous algorithms