Distributional regimes for the number of<i>k</i>-word matches between two random sequences

Lippert, Ross A.; Huang, Haiyan; Waterman, Michael S.

doi:10.1073/pnas.202468099

Cited by 107 publications

(140 citation statements)

References 25 publications

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“…Previous studies of the D 2 statistic used Kolmogorov-Smirnov tests [3] to compare the empirical distribution of D 2 with its theoretical asymptotic distributions (normal or compound-Poisson) [7,2]. These studies, however, have been in error for the following reason.…”

Section: Comparison Between Empirical and Hypothesised Distributionsmentioning

confidence: 99%

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Empirical distribution of k-word matches in biological sequences

Fôret¹,

Wilson²,

Burden³

2009

Pattern Recognition

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This study focuses on an alignment-free sequence comparison method: the number of words of length k shared between two sequences, also known as the D 2 statistic. The advantages of the use of this statistic over alignment-based methods are firstly that it does not assume that homologous segments are contiguous, and secondly that the algorithm is computationally extremely fast, the runtime being proportional to the size of the sequence under scrutiny. Existing applications of the D 2 statistic include the clustering of related sequences in large EST databases such as the STACK database. Such applications have typically relied on heuristics without any statistical basis. Rigorous statistical characterisations of the distribution of D 2 have subsequently been undertaken, but have focussed on the distribution's asymptotic behaviour, leaving the distribution of D 2 uncharacterised for most practical cases. The work presented here bridges these two worlds to give usable approximations of the distribution of D 2 for ranges of parameters most frequently encountered in the study of biological sequences.

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Section: Comparison Between Empirical and Hypothesised Distributionsmentioning

confidence: 99%

“…For pairs of Bernoulli texts with non-uniform letter distributions, the limiting distribution is compound Poisson in the regime k > 2 log b n + const. [7], and normal in the regime k < 1/2 log b n + const [2]. Here b = p 2 −1 .…”

Section: Introductionmentioning

confidence: 99%

Empirical distribution of k-word matches in biological sequences

Fôret¹,

Wilson²,

Burden³

2009

Pattern Recognition

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“…Repeat structure in large genomes has been analyzed without first constructing consensus repeat family sequences [11,12], including the use of oligonucleotide (hereafter "oligo") or lmer similarity, rather than sequence similarity [13,14], and analytical counting methods, such as RAP [15] and the method of Healy and colleagues [16]. There has been some statistical evaluation of oligo-based repeat region identification using these methods [15,16], but no comprehensive genomic annotation approaches have been developed for oligo-based repeat analysis.…”

Section: Introductionmentioning

confidence: 99%

Identification of repeat structure in large genomes using repeat probability clouds

Castoe

Hedges

et al. 2008

Analytical Biochemistry

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The identification of repeat structure in eukaryotic genomes can be time-consuming and difficult because of the large amount of information (~3×10 9 bp) that needs to be processed and compared. We introduce a new approach based on exact word counts to evaluate, de novo, the repeat structure present within large eukaryotic genomes. This approach avoids sequence alignment and similarity search, two of the most time-consuming components of traditional methods for repeat identification. Algorithms were implemented to efficiently calculate exact counts for any length oligonucleotide in large genomes. Based on these oligonucleotide counts, oligonucleotide excess probability clouds, or "P-clouds", were constructed. P-clouds are composed of clusters of related oligonucleotides that occur, as a group, more often than expected by chance. After construction, P-clouds were mapped back onto the genome, and regions of high P-cloud density were identified as repetitive regions based on a sliding window approach. This efficient method is capable of analyzing the repeat content of the entire human genome on a single desktop computer in less than half a day, at least 10-fold faster than current approaches. The predicted repetitive regions strongly overlap with known repeat elements, as well as other repetitive regions such as gene families, pseudogenes and segmental duplicons. This method should be extremely useful as a tool for use in de novo identification of repeat structure in large newly sequenced genomes.

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“…A.2 of Appendix A.6) additional computation time is required for the identi¯cation and classi¯cation of each maxmer and is proportional to the number of occurrences of this maxmer. In the worst case the number of occurrences of a given maxmer may be approximated by the integer value k at the maximum of a Poisson distribution, p ðkÞ ¼ k e À =ðk!Þ, where the interval is taken to be the sequence size n 45,46 ; however, since this quantity can only be determined empirically, the overall computation time order is estimated based on real computations. The full run time of the length distribution computation is plotted against the genome sequence size in Fig.…”

Section: Computational Complexitymentioning

confidence: 99%

EXHAUSTIVE COMPUTATION OF EXACT DUPLICATIONS VIA SUPER AND NON-NESTED LOCAL MAXIMAL REPEATS

Taillefer

Miller

2014

J. Bioinform. Comput. Biol.

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We propose and implement a method to obtain all duplicated sequences (repeats) from a chromosome or whole genome. Unlike existing approaches our method makes it possible to simultaneously identify and classify repeats into super, local, and non-nested local maximal repeats. Computation veri¯cation demonstrates that maximal repeats for a genome of several gigabases can be identi¯ed in a reasonable time, enabling us to identi¯ed these maximal repeats for any sequenced genome. The algorithm used for the identi¯cation relies on enhanced su±x array data structure to achieve practical space and time e±ciency, to identify and classify the maximal repeats, and to perform further post-processing on the identi¯ed duplicated sequences. The simplicity and e®ectiveness of the implementation makes the method readily extendible to more sophisticated computations. Maxmers can be exhaustively accounted for in few minutes for genome sequences of dozen megabases in length and in less than a day or two for genome sequences of few gigabases in length. One application of duplicated sequence identi¯cation is to the study of duplicated sequence length distributions, which our found to exhibit for large lengths a persistent power-law behavior. Variation of estimated exponents of this power law are studied among di®erent species and successive assembly release versions of the same species. This makes the characterization of the power-law regime of sequenced genomes via maximal repeats identi¯cation and classi¯cation, an important task for the derivation of models that would help us to elucidate sequence duplication and genome evolution.

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Distributional regimes for the number ofk-word matches between two random sequences

Cited by 107 publications

References 25 publications

Empirical distribution of k-word matches in biological sequences

Empirical distribution of k-word matches in biological sequences

Identification of repeat structure in large genomes using repeat probability clouds

EXHAUSTIVE COMPUTATION OF EXACT DUPLICATIONS VIA SUPER AND NON-NESTED LOCAL MAXIMAL REPEATS

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