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

Compressed Spaced Suffix Arrays

Spaced seeds are important tools for similarity search in bioinformatics, and using several seeds together often significantly improves their performance. With existing approaches, however, for each seed we keep a separate linear-size data structure, either a hash table or a spaced suffix array (SSA). In this paper we show how to compress SSAs relative to normal suffix arrays (SAs) and still support fast random access to them. We first prove a theoretical upper bound on the space needed to store an SSA when we already have the SA. We then present experiments indicating that our approach works even better in practice

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

Designing seeds for similarity search in genomic DNA

AbstractLarge-scale comparison of genomic DNA is of fundamental importance in annotating functional elements of genomes. To perform large comparisons efficiently, BLAST (Methods: Companion Methods Enzymol 266 (1996) 460, J. Mol. Biol. 215 (1990) 403, Nucleic Acids Res. 25(17) (1997) 3389) and other widely used tools use seeded alignment, which compares only sequences that can be shown to share a common pattern or “seed’’ of matching bases. The literature suggests that the choice of seed substantially affects the sensitivity of seeded alignment, but designing and evaluating seeds is computationally challenging.This work addresses the problem of designing a seed to optimize performance of seeded alignment. We give a fast, simple algorithm based on finite automata for evaluating the sensitivity of a seed in a Markov model of ungapped alignments, along with extensions to mixtures and inhomogeneous Markov models. We give intuition and theoretical results on which seeds are good choices. Finally, we describe Mandala, a software tool for seed design, and show that it can be used to improve the sensitivity of alignment in practice

Searching, clustering and evaluating biological sequences

The latest generation of biological sequencing technologies have made it possible to generate sequence data faster and cheaper than ever before. The growth of sequence data has been exponential, and so far, has outpaced the rate of improvement of computer speed and capacity. This rate of growth, however, makes analysis of new datasets increasingly difficult, and highlights the need for efficient, scalable and modular software tools. Fortunately most types of analysis of sequence data involve a few fundamental operations. Here we study three such problems, namely searching for local alignments between two sets of sequences, clustering sequences, and evaluating the assemblies made from sequence fragments. We present simple and efficient heuristic algorithms for these problems, as well as open source software tools which implement these algorithms. First, we present approximate seeds; a new type of seed for local alignment search. Approximate seeds are a generalization of exact seeds and spaced seeds, in that they allow for insertions and deletions within the seed. We prove that approximate seeds are completely sensitive. We also show how to efficiently find approximate seeds using a suffix array index of the sequences. Next, we present DNACLUST; a tool for clustering millions of DNA sequence fragments. Although DNACLUST has been primarily made for clustering 16S ribosomal RNA sequences, it can be used for other tasks, such as removing duplicate or near duplicate sequences from a dataset. Finally, we present a framework for comparing (two or more) assemblies built from the same set of reads. Our evaluation requires the set of reads and the assemblies only, and does not require the true genome sequence. Therefore our method can be used in de novo assembly projects, where the true genome is not known. Our score is based on probability theory, and the true genome is expected to obtain the maximum score

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