Languages of lossless seeds

Several algorithms for similarity search employ seeding techniques to quickly discard very dissimilar regions. In this paper, we study theoretical properties of lossless seeds, i.e., spaced seeds having full sensitivity. We prove that lossless seeds coincide with languages of certain sofic subshifts, hence they can be recognized by finite automata. Moreover, we show that these subshifts are fully given by the number of allowed errors k and the seed margin l. We also show that for a fixed k, optimal seeds must asymptotically satisfy l ~ m^(k/(k+1)).Comment: In Proceedings AFL 2014, arXiv:1405.527

A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances

Spaced seeds have been recently shown to not only detect more alignments, but also to give a more accurate measure of phylogenetic distances (Boden et al., 2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower misclassification rate when used with Support Vector Machines (SVMs) (On-odera and Shibuya, 2013), We confirm by independent experiments these two results, and propose in this article to use a coverage criterion (Benson and Mak, 2008, Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both cases in order to design better seed patterns. We show first how this coverage criterion can be directly measured by a full automaton-based approach. We then illustrate how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance. At the end, for alignment-free distances, we propose an extension by adopting the coverage criterion, show how it performs, and indicate how it can be efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017

A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances

Spaced seeds have been recently shown to not only detect more alignments, but also to give a more accurate measure of phylogenetic distances (Boden et al., 2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower misclassification rate when used with Support Vector Machines (SVMs) (On-odera and Shibuya, 2013), We confirm by independent experiments these two results, and propose in this article to use a coverage criterion (Benson and Mak, 2008, Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both cases in order to design better seed patterns. We show first how this coverage criterion can be directly measured by a full automaton-based approach. We then illustrate how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance. At the end, for alignment-free distances, we propose an extension by adopting the coverage criterion, show how it performs, and indicate how it can be efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017

The Gapped-Factor Tree

International audienceWe present a data structure to index a specific kind of factors, that is of substrings, called gapped-factors. A gapped-factor is a factor containing a gap that is ignored during the indexation. The data structure presented is based on the suffix tree and indexes all the gapped-factors of a text with a fixed size of gap, and only those. The construction of this data structure is done online in linear time and space. Such a data structure may play an important role in various pattern matching and motif inference problems, for instance in text filtration

A unifying framework for seed sensitivity and its application to subset seeds

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem -- a set of target alignments, an associated probability distribution, and a seed model -- that are specified by distinct finite automata. The approach is then applied to a new concept of subset seeds for which we propose an efficient automaton construction. Experimental results confirm that sensitive subset seeds can be efficiently designed using our approach, and can then be used in similarity search producing better results than ordinary spaced seeds

Progressive Mauve: Multiple alignment of genomes with gene flux and rearrangement

Multiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms. We describe a method to align two or more genomes that have undergone large-scale recombination, particularly genomes that have undergone substantial amounts of gene gain and loss (gene flux). The method utilizes a novel alignment objective score, referred to as a sum-of-pairs breakpoint score. We also apply a probabilistic alignment filtering method to remove erroneous alignments of unrelated sequences, which are commonly observed in other genome alignment methods. We describe new metrics for quantifying genome alignment accuracy which measure the quality of rearrangement breakpoint predictions and indel predictions. The progressive genome alignment algorithm demonstrates markedly improved accuracy over previous approaches in situations where genomes have undergone realistic amounts of genome rearrangement, gene gain, loss, and duplication. We apply the progressive genome alignment algorithm to a set of 23 completely sequenced genomes from the genera Escherichia, Shigella, and Salmonella. The 23 enterobacteria have an estimated 2.46Mbp of genomic content conserved among all taxa and total unique content of 15.2Mbp. We document substantial population-level variability among these organisms driven by homologous recombination, gene gain, and gene loss. Free, open-source software implementing the described genome alignment approach is available from http://gel.ahabs.wisc.edu/mauve .Comment: Revision dated June 19, 200

CoveringLSH: Locality-sensitive Hashing without False Negatives

We consider a new construction of locality-sensitive hash functions for Hamming space that is covering in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius r . The construction is efficient in the sense that the expected number of hash collisions between vectors at distance  cr , for a given c &gt;1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (STOC’98). The efficiency of the new construction essentially matches their bound when the search radius is not too large—e.g., when cr = o (log ( n )/ log log n ), where n is the number of points in the dataset, and when cr = log ( n )/ k , where k is an integer constant. In general, it differs by at most a factor ln (4) in the exponent of the time bounds. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency. </jats:p

A FAST ALGORITHM FOR COMPUTING HIGHLY SENSITIVE MULTIPLE SPACED SEEDS

The main goal of homology search is to find similar segments, or local alignments, be­ tween two DNA or protein sequences. Since the dynamic programming algorithm of Smith- Waterman is too slow, heuristic methods have been designed to achieve both efficiency and accuracy. Seed-based methods were made well known by their use in BLAST, the most widely used software program in biological applications. The seed of BLAST trades sensitivity for speed and spaced seeds were introduced in PatternHunter to achieve both. Several seeds are better than one and near perfect sensitivity can be obtained while maintaining the speed. There­ fore, multiple spaced seeds quickly became the state-of-the-art in similarity search, being em­ ployed by many software programs. However, the quality of these seeds is crucial and comput­ ing optimal multiple spaced seeds is NP-hard. All but one of the existing heuristic algorithms for computing good seeds are exponential. Our work has two main goals. First we engineer the only existing polynomial-time heuristic algorithm to compute better seeds than any other program, while running orders of magnitude faster. Second, we estimate its performance by comparing its seeds with the optimal seeds in a few practical cases. In order to make the computation feasible, a very fast implementation of the sensitivity function is provided

Choosing the best heuristic for seeded alignment of DNA sequences

BACKGROUND: Seeded alignment is an important component of algorithms for fast, large-scale DNA similarity search. A good seed matching heuristic can reduce the execution time of genomic-scale sequence comparison without degrading sensitivity. Recently, many types of seed have been proposed to improve on the performance of traditional contiguous seeds as used in, e.g., NCBI BLASTN. Choosing among these seed types, particularly those that use information besides the presence or absence of matching residue pairs, requires practical guidance based on a rigorous comparison, including assessment of sensitivity, specificity, and computational efficiency. This work performs such a comparison, focusing on alignments in DNA outside widely studied coding regions. RESULTS: We compare seeds of several types, including those allowing transition mutations rather than matches at fixed positions, those allowing transitions at arbitrary positions ("BLASTZ" seeds), and those using a more general scoring matrix. For each seed type, we use an extended version of our Mandala seed design software to choose seeds with optimized sensitivity for various levels of specificity. Our results show that, on a test set biased toward alignments of noncoding DNA, transition information significantly improves seed performance, while finer distinctions between different types of mismatches do not. BLASTZ seeds perform especially well. These results depend on properties of our test set that are not shared by EST-based test sets with a strong bias toward coding DNA. CONCLUSION: Practical seed design requires careful attention to the properties of the alignments being sought. For noncoding DNA sequences, seeds that use transition information, especially BLASTZ-style seeds, are particularly useful. The Mandala seed design software can be found at

A unifying framework for seed sensitivity and its application to subset seeds (Extended abstract)

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem - a set of target alignments, an associated probability distribution, and a seed model - that are specified by distinct finite automata. The approach is then applied to a new concept of subset seeds for which we propose an efficient automaton construction. Experimental results confirm that sensitive subset seeds can be efficiently designed using our approach, and can then be used in similarity search producing better results than ordinary spaced seeds