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

Sophie Röhling; Alexander Linne; Jendrik Schellhorn; Morteza Hosseini; Thomas Dencker; Burkhard Morgenstern

doi:10.1371/journal.pone.0228070

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

PLoS One. 2020 Feb 10;15(2):e0228070. doi: 10.1371/journal.pone.0228070. eCollection 2020.

Authors

Sophie Röhling¹, Alexander Linne¹, Jendrik Schellhorn¹, Morteza Hosseini², Thomas Dencker¹, Burkhard Morgenstern^{1

3}

Affiliations

¹ University of Göttingen, Department of Bioinformatics, Göttingen, Germany.
² IEETA, University of Aveiro, Aveiro, Portugal.
³ Göttingen Center of Molecular Biosciences (GZMB), Göttingen, Germany.

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Phylogeny*
Sequence Alignment
Sequence Analysis, DNA*
Sequence Homology, Nucleic Acid

Grants and funding

The project was funded by VW Foundation, project VWZN3157 to BM, and by the Portuguese national funds through Foundation for Science and Technology (FCT), in the context of the project UID/CEC/00127/2019. We acknowledge support by the Open Access Publication Funds of Göttingen University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.