Fast, optimal alignment of three sequences using linear gap costs

Alignment algorithms can be used to infer a relationship between sequences when the true relationship is unknown. Simple alignment algorithms use a cost function that gives a fixed cost to each possible point mutation-mismatch, deletion, insertion. These algorithms tend to find optimal alignments that have many small gaps. It is more biologically plausible to have fewer longer gaps rather than many small gaps in an alignment. To address this issue, linear gap cost algorithms are in common use for aligning biological sequence data. More reliable inferences are obtained by aligning more than two sequences at a time. The obvious dynamic programming algorithm for optimally aligning k sequences of length n runs in O(n(k)) time. This is impractical if k>/=3 and n is of any reasonable length. Thus, for this problem there are many heuristics for aligning k sequences, however, they are not guaranteed to find an optimal alignment. In this paper, we present a new algorithm guaranteed to find the optimal alignment for three sequences using linear gap costs. This gives the same results as the dynamic programming algorithm for three sequences, but typically does so much more quickly. It is particularly fast when the (three-way) edit distance is small. Our algorithm uses a speed-up technique based on Ukkonen's greedy algorithm (Ukkonen, 1983) which he presented for two sequences and simple costs.     

Local multiple alignment by consensus matrix

A new algorithm for aligning several sequences based on thecalculation of a consensus matrix and the comparison of allthe sequences using this consensus matrix is described. Thisconsensus matrix contains the preference scores of each nucleotideøaminoacid and gaps in every position of the alignment. Two modificationsof the algorithm corresponding to the evolutionary and functionalmeanings of the alignment were developed. The first one solvesthe best-fitting problem without any penalty for end gaps andwith an internal gap penalty function independent on the gaplength. This algorithm should be used when comparing evolutionary-relatedproteins for identifying the most conservative residues. Theother modification of the algorithm finds the most similar segmentsin the given sequences. It can be used for finding those partsof the sequences that are responsible for the same biologicalJunction. In this case the gap penalty function was chosen tobe proportional to the gap length. The result of aligning aminoacid sequences of neutral proteases and a compilation of 65allosteric effectors and substrates of PEP carboxylase are presented.     

A greedy algorithm for aligning DNA sequences.

For aligning DNA sequences that differ only by sequencing errors, or by equivalent errors from other sources, a greedy algorithm can be much faster than traditional dynamic programming approaches and yet produce an alignment that is guaranteed to be theoretically optimal. We introduce a new greedy alignment algorithm with particularly good performance and show that it computes the same alignment as does a certain dynamic programming algorithm, while executing over 10 times faster on appropriate data. An implementation of this algorithm is currently used in a program that assembles the UniGene database at the National Center for Biotechnology Information.     

Constrained multiple sequence alignment tool development and its application to RNase family alignment

In this paper, we design a heuristic algorithm of computing a constrained multiple sequence alignment (CMSA for short) for guaranteeing that the generated alignment satisfies the user-specified constraints that some particular residues should be aligned together. If the number of residues needed to be aligned together is a constant alpha, then the time-complexity of our CMSA algorithm for aligning K sequences is O(alphaKn(4)), where n is the maximum of the lengths of sequences. In addition, we have built up such a CMSA software system and made several experiments on the RNase sequences, which mainly function in catalyzing the degradation of RNA molecules. The resulting alignments illustrate the practicability of our method.     

On comparing two structured RNA multiple alignments

We present a method, called BlockMatch, for aligning two blocks, where a block is an RNA multiple sequence alignment with the consensus secondary structure of the alignment in Stockholm format. The method employs a quadratic-time dynamic programming algorithm for aligning columns and column pairs of the multiple alignments in the blocks. Unlike many other tools that can perform pairwise alignment of either single sequences or structures only, BlockMatch takes into account the characteristics of all the sequences in the blocks along with their consensus structures during the alignment process, thus being able to achieve a high-quality alignment result. We apply BlockMatch to phylogeny reconstruction on a set of 5S rRNA sequences taken from fifteen bacteria species. Experimental results showed that the phylogenetic tree generated by our method is more accurate than the tree constructed based on the widely used ClustalW tool. The BlockMatch algorithm is implemented into a web server, accessible at http://bioinformatics.njit.edu/blockmatch. A jar file of the program is also available for download from the web server.     

Grammar-based distance in progressive multiple sequence alignment

Background  

We propose a multiple sequence alignment (MSA) algorithm and compare the alignment-quality and execution-time of the proposed algorithm with that of existing algorithms. The proposed progressive alignment algorithm uses a grammar-based distance metric to determine the order in which biological sequences are to be pairwise aligned. The progressive alignment occurs via pairwise aligning new sequences with an ensemble of the sequences previously aligned.     

A general method for fast multiple sequence alignment

We have developed a fast heuristic algorithm for multiple sequence alignment which provides near-to-optimal results for sufficiently homologous sequences. The algorithm makes use of the standard dynamic programming procedure by applying it to all pairs of sequences. The resulting score matrices for pair-wise alignment give rise to secondary matrices containing the additional charges imposed by forcing the alignment path to run through a particular vertex. Such a constraint corresponds to slicing the sequences at the positions defining that vertex, and aligning the remaining pairs of prefix and suffix sequences separately. From these secondary matrices, one can compute - for any given family of sequences - suitable positions for cutting all of these sequences simultaneously, thus reducing the problem of aligning a family of n sequences of average length l in a Divide and Conquer fashion to aligning two families of n sequences of approximately half that length.In this paper, we explain the method for the case of 3 sequences in detail, and we demonstrate its potential and its limits by discussing its behaviour for several test families. A generalization for aligning more than 3 sequences is lined out, and some actual alignments constructed by our algorithm for various user-defined parameters are presented.     

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.     

SimShift: identifying structural similarities from NMR chemical shifts

MOTIVATION: An important quantity that arises in NMR spectroscopy experiments is the chemical shift. The interpretation of these data is mostly done by human experts; to our knowledge there are no algorithms that predict protein structure from chemical shift sequences alone. One approach to facilitate this process could be to compare two such sequences, where the structure of one protein has already been resolved. Our claim is that similarity of chemical shifts thereby found implies structural similarity of the respective proteins. RESULTS: We present an algorithm to identify structural similarities of proteins by aligning their associated chemical shift sequences. To evaluate the correctness of our predictions, we propose a benchmark set of protein pairs that have high structural similarity, but low sequence similarity (because with high sequence similarity the structural similarities could easily be detected by a sequence alignment algorithm). We compare our results with those of HHsearch and SSEA and show that our method outperforms both in >50% of all cases.     

Learning scoring schemes for sequence alignment from partial examples

When aligning biological sequences, the choice of parameter values for the alignment scoring function is critical. Small changes in gap penalties, for example, can yield radically different alignments. A rigorous way to compute parameter values that are appropriate for aligning biological sequences is through inverse parametric sequence alignment. Given a collection of examples of biologically correct alignments, this is the problem of finding parameter values that make the scores of the example alignments close to those of optimal alignments for their sequences. We extend prior work on inverse parametric alignment to partial examples, which contain regions where the alignment is left unspecified, and to an improved formulation based on minimizing the average error between the score of an example and the score of an optimal alignment. Experiments on benchmark biological alignments show we can find parameters that generalize across protein families and that boost the accuracy of multiple sequence alignment by as much as 25%.     

GS-Aligner: a novel tool for aligning genomic sequences using bit-level operations

A novel algorithm, GS-Aligner, that uses bit-level operations was developed for aligning genomic sequences. GS-Aligner is efficient in terms of both time and space for aligning two very long genomic sequences and for identifying genomic rearrangements such as translocations and inversions. It is suitable for aligning fairly divergent sequences such as human and mouse genomic sequences. It consists of several efficient components: bit-level coding, search for matching segments between the two sequences as alignment anchors, longest increasing subsequence (LIS), and optimal local alignment. Efforts have been made to reduce the execution time of the program to make it truly practical for aligning very long sequences. Empirical tests suggest that for relatively divergent sequences such as sequences from different mammalian orders or from a mammal and a nonmammalian vertebrate GS-Aligner performs better than existing methods. The program and data can be downloaded from http://pondside.uchicago.edu/~lilab/ and http://webcollab.iis.sinica.edu.tw/~biocom.     

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.     

MACSE: Multiple Alignment of Coding SEquences accounting for frameshifts and stop codons

Until now the most efficient solution to align nucleotide sequences containing open reading frames was to use indirect procedures that align amino acid translation before reporting the inferred gap positions at the codon level. There are two important pitfalls with this approach. Firstly, any premature stop codon impedes using such a strategy. Secondly, each sequence is translated with the same reading frame from beginning to end, so that the presence of a single additional nucleotide leads to both aberrant translation and alignment.We present an algorithm that has the same space and time complexity as the classical Needleman-Wunsch algorithm while accommodating sequencing errors and other biological deviations from the coding frame. The resulting pairwise coding sequence alignment method was extended to a multiple sequence alignment (MSA) algorithm implemented in a program called MACSE (Multiple Alignment of Coding SEquences accounting for frameshifts and stop codons). MACSE is the first automatic solution to align protein-coding gene datasets containing non-functional sequences (pseudogenes) without disrupting the underlying codon structure. It has also proved useful in detecting undocumented frameshifts in public database sequences and in aligning next-generation sequencing reads/contigs against a reference coding sequence.MACSE is distributed as an open-source java file executable with freely available source code and can be used via a web interface at: http://mbb.univ-montp2.fr/macse.     

Constructing Sequence Alignments from a Markov Decision Model with Estimated Parameter Values

Current methods for aligning biological sequences are based on dynamic programming algorithms. If large numbers of sequences or a number of long sequences are to be aligned, the required computations are expensive in memory and central processing unit (CPU) time. In an attempt to bring the tools of large-scale linear programming (LP) methods to bear on this problem, we formulate the alignment process as a controlled Markov chain and construct a suggested alignment based on policies that minimise the expected total cost of the alignment. We discuss the LP associated with the total expected discounted cost and show the results of a solution of the problem based on a primal-dual interior point method. Model parameters, estimated from aligned sequences, along with cost function parameters are used to construct the objective and constraint conditions of the LP problem. This article concludes with a discussion of some alignments obtained from the LP solutions of problems with various cost function parameter values.     

Multiple sequence alignment by consensus.

An algorithm for multiple sequence alignment is given that matches words of length and degree of mismatch chosen by the user. The alignment maximizes an alignment scoring function. The method is based on a novel extension of our consensus sequence methods. The algorithm works for both DNA and protein sequences, and from earlier work on consensus sequences, it is possible to estimate statistical significance.     

Genomic multiple sequence alignments: refinement using a genetic algorithm

Background  

Genomic sequence data cannot be fully appreciated in isolation. Comparative genomics – the practice of comparing genomic sequences from different species – plays an increasingly important role in understanding the genotypic differences between species that result in phenotypic differences as well as in revealing patterns of evolutionary relationships. One of the major challenges in comparative genomics is producing a high-quality alignment between two or more related genomic sequences. In recent years, a number of tools have been developed for aligning large genomic sequences. Most utilize heuristic strategies to identify a series of strong sequence similarities, which are then used as anchors to align the regions between the anchor points. The resulting alignment is globally correct, but in many cases is suboptimal locally. We describe a new program, GenAlignRefine, which improves the overall quality of global multiple alignments by using a genetic algorithm to improve local regions of alignment. Regions of low quality are identified, realigned using the program T-Coffee, and then refined using a genetic algorithm. Because a better COFFEE (Consistency based Objective Function For alignmEnt Evaluation) score generally reflects greater alignment quality, the algorithm searches for an alignment that yields a better COFFEE score. To improve the intrinsic slowness of the genetic algorithm, GenAlignRefine was implemented as a parallel, cluster-based program.     

Aligning two sequences within a specified diagonal band

We describe an algorithm for aligning two sequences within adiagonal band that requires only O(NW) computation time andO(N) space, where N is the length of the shorter of the twosequences and W is the width of the band. The basic algorithmcan be used to calculate either local or global alignment scores.Local alignments are produced by finding the beginning and endof a best local alignment in the band, and then applying theglobal alignment algorithm between those points. This algorithmhas been incorporated into the FASTA program package, whereit has decreased the amount of memory required to calculatelocal alignments from O(NW) to O(N) and decreased the time requiredto calculate optimized scores for every sequence in a proteinsequence database by 40%. On computers with limited memory,such as the IBM-PC, this improvement both allows longer sequencesto be aligned and allows optimization within wider bands, whichcan include longer gaps.     

Post-processing long pairwise alignments

MOTIVATION: The local alignment problem for two sequences requires determining similar regions, one from each sequence, and aligning those regions. For alignments computed by dynamic programming, current approaches for selecting similar regions may have potential flaws. For instance, the criterion of Smith and Waterman can lead to inclusion of an arbitrarily poor internal segment. Other approaches can generate an alignment scoring less than some of its internal segments. RESULTS: We develop an algorithm that decomposes a long alignment into sub-alignments that avoid these potential imperfections. Our algorithm runs in time proportional to the original alignment's length. Practical applications to alignments of genomic DNA sequences are described.     

构建基于折叠核心的全α类蛋白取代矩阵

氨基酸残基取代矩阵是影响多序列比对效果的重要因素,现有的取代矩阵对低相似序列的比对性能较低.在已有的 BLOSUM 取代矩阵算法基础上,定义了基于蛋白质折叠核心结构的序列 结构数据块;提出一种新的基于全α类蛋白质折叠核心结构的氨基酸残基取代矩阵——TOPSSUM25,用于提高低相似度序列的比对效果.将矩阵TOPSSUM25导入多序列比对程序,对相似性小于25%的一组四螺旋束序列 结构数据块的测试结果表明,基于 TOPSSUM25的多序列比对效果明显优于BLOSUM30矩阵;基于一个BAliBASE子集的比对检验也进一步表明, TOPSSUM25在全α类蛋白质的两两序列比对上优于BLOSUM30矩阵.研究结果可为进一步的阐明低同源蛋白质序列 结构 功能关系提供帮助.     

Alignment of three biological sequences with an efficient traceback procedure

The major algorithms currently used for aligning biological sequences are those based on dynamic programming method. A dynamic programming algorithm consists of two major procedures, forward and traceback routines. This paper describes a dynamic programming algorithm for aligning three sequences at a time. Deletions and insertions are penalized according to their numbers and lengths. A forward process is accomplished in O(L3) computational steps, where L is the average sequence length. On the other hand, a traceback process is done in T steps, where T is the number of elementary configurations involved in the optimal alignment (usually T much less than L). The traceback procedure uses an effective technique for memory management, which is applicable to a wide range of sequence-matching methods.