Best hits of 11110110111: model-free selection and parameter-free sensitivity calculation of spaced seeds

Abstract

Background Spaced seeds, also named gapped q-grams, gapped k-mers, spaced q-grams, have been proven to be more sensitive than contiguous seeds (contiguous q-grams, contiguous k-mers) in nucleic and amino-acid sequences analysis. Initially proposed to detect sequence similarities and to anchor sequence alignments, spaced seeds have more recently been applied in several alignment-free related methods. Unfortunately, spaced seeds need to be initially designed. This task is known to be time-consuming due to the number of spaced seed candidates. Moreover, it can be altered by a set of arbitrary chosen parameters from the probabilistic alignment models used. In this general context, Dominant seeds have been introduced by Mak and Benson (Bioinformatics 25:302–308, 2009) on the Bernoulli model, in order to reduce the number of spaced seed candidates that are further processed in a parameter-free calculation of the sensitivity.ResultsWe expand the scope of work of Mak and Benson on single and multiple seeds by considering the Hit Integration model of Chung and Park (BMC Bioinform 11:31, 2010), demonstrate that the same dominance definition can be applied, and that a parameter-free study can be performed without any significant additional cost. We also consider two new discrete models, namely the Heaviside and the Dirac models, where lossless seeds can be integrated. From a theoretical standpoint, we establish a generic framework on all the proposed models, by applying a counting semi-ring to quickly compute large polynomial coefficients needed by the dominance filter. From a practical standpoint, we confirm that dominant seeds reduce the set of, either single seeds to thoroughly analyse, or multiple seeds to store. Moreover, in http://bioinfo.cristal.univ-lille.fr/yass/iedera_dominance, we provide a full list of spaced seeds computed on the four aforementioned models, with one (continuous) parameter left free for each model, and with several (discrete) alignment lengths.

The number of k-mer matches between two DNA sequences as a function of k and applications to estimate phylogenetic distances

“…Spacedword matches or spaced seeds have been introduced in database searching as an alternative to exact k-mer matches [46][47][48]. The main advantage of spaced words compared to contiguous k-mers is the fact that results based on spaced words are statistically more stable than results based on k-mers [8,38,[49][50][51][52]. In short, neighbouring spaced-word matches are statistically less dependent from each other than neighbouring word matches; this is also the reason why spaced seeds lead to more sensitive results in database searching [53], compared with seeds that are defined as exact word matches as used, for example, in the original version of BLAST [54].…”

The number of spaced-word matches between twoDNAsequences as a function of the underlying pattern weight

“…Spacedword matches or spaced seeds have been introduced in database searching as an alternative to exact k-mer matches [8,34,31]. The main advantage of spaced words compared to contiguous k-mers is the fact that results based on spaced words are statistically more stable than results based on k-mers [24,13,10,9,36,38]. Quite obviously, approximations (4) and (5) remain valid if we define X k to be the number of spaced-word matches for a given pattern P of weight k, and we can generalize the definition of F (k) accordingly: if we consider a maximum pattern weight K and a given set of patterns {P k , 1 ≤ k ≤ K} where k is the weight of pattern P k , then we can define N k as the empirical number of spaced-word matches with respect to pattern P k between two observed DNA sequences.…”

Computation of exact probabilities associated with overlapping pattern occurrences

“…The many combinations of prefixes of words representing overlapping spaced seed hits and positions that may or may not be covered can render the number of states of an AMC to be extremely large, and the computation to be much more difficult than for sensitivity. Thus, there are relatively few studies where seed coverage is considered (see Benson & Mak, ; Martin, , ; Martin & Noé, ; Noé, and Noé & Martin, ). The setup of ϒ to compute the coverage distribution for a spaced seed of length k > m is discussed next, following Martin & Noé, , and Martin (, ).…”