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

ABSTRACT: We study the number Nk of length-k word matches between pairs of evolutionarily related DNA sequences, as a function of k. We show that the Jukes-Cantor distance between two genome sequences-i.e. the number of substitutions per site that occurred since they evolved from their last common ancestor-can be estimated from the slope of a function F that depends on Nk and that is affine-linear within a certain range of k. Integers kmin and kmax can be calculated depending on the length of the input sequences, such that the slope of F in the relevant range can be estimated from the values F(kmin) and F(kmax). This approach can be generalized to so-called Spaced-word Matches (SpaM), where mismatches are allowed at positions specified by a user-defined binary pattern. Based on these theoretical results, we implemented a prototype software program for alignment-free sequence comparison called Slope-SpaM. Test runs on real and simulated sequence data show that Slope-SpaM can accurately estimate phylogenetic distances for distances up to around 0.5 substitutions per position. The statistical stability of our results is improved if spaced words are used instead of contiguous words. Unlike previous alignment-free methods that are based on the number of (spaced) word matches, Slope-SpaM produces accurate results, even if sequences share only local homologies.

SUBMITTER: Rohling S

PROVIDER: S-EPMC7010260 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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

Röhling Sophie S Linne Alexander A Schellhorn Jendrik J Hosseini Morteza M Dencker Thomas T Morgenstern Burkhard B

PloS one 20200210 2

We study the number Nk of length-k word matches between pairs of evolutionarily related DNA sequences, as a function of k. We show that the Jukes-Cantor distance between two genome sequences-i.e. the number of substitutions per site that occurred since they evolved from their last common ancestor-can be estimated from the slope of a function F that depends on Nk and that is affine-linear within a certain range of k. Integers kmin and kmax can be calculated depending on the length of the input se ...[more]

PMID: 32040534

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Project description:BackgroundInversion Symmetry is a generalization of the second Chargaff rule, stating that the count of a string of k nucleotides on a single chromosomal strand equals the count of its inverse (reverse-complement) k-mer. It holds for many species, both eukaryotes and prokaryotes, for ranges of k which may vary from 7 to 10 as chromosomal lengths vary from 2Mbp to 200 Mbp. Building on this formalism we introduce the concept of k-mer distances between chromosomes. We formulate two k-mer distance measures, D1 and D2, which depend on k. D1 takes into account all k-mers (for a single k) appearing on single strands of the two compared chromosomes, whereas D2 takes into account both strands of each chromosome. Both measures reflect dissimilarities in global chromosomal structures.ResultsAfter defining the various distance measures and summarizing their properties, we also define proximities that rely on the existence of synteny blocks between chromosomes of different bacterial strains. Comparing pairs of strains of bacteria, we find negative correlations between synteny proximities and k-mer distances, thus establishing the meaning of the latter as measures of evolutionary distances among bacterial strains. The synteny measures we use are appropriate for closely related bacterial strains, where considerable sections of chromosomes demonstrate high direct or reversed equality. These measures are not appropriate for comparing different bacteria or eukaryotes. K-mer structural distances can be defined for all species. Because of the arbitrariness of strand choices, we employ only the D2 measure when comparing chromosomes of different species. The results for comparisons of various eukaryotes display interesting behavior which is partially consistent with conventional understanding of evolutionary genomics. In particular, we define ratios of minimal k-mer distances (KDR) between unmasked and masked chromosomes of two species, which correlate with both short and long evolutionary scales.Conclusionsk-mer distances reflect dissimilarities among global chromosomal structures. They carry information which aggregates all mutations. As such they can complement traditional evolution studies , which mainly concentrate on coding regions.

Dataset Information

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

Publications

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

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