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A k-mer-Based Estimator of the Substitution Rate Between Repetitive Sequences

Authors Haonan Wu , Antonio Blanca , Paul Medvedev

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Subject Classification

ACM Subject Classification
  • Applied computing → Bioinformatics
  • Applied computing → Computational biology
Keywords
  • k-mers
  • sketching
  • mutation rates

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Abstract

K-mer-based analysis of genomic data is ubiquitous, but the presence of repetitive k-mers continues to pose problems for the accuracy of many methods. For example, the Mash tool (Ondov et al. 2016) can accurately estimate the substitution rate between two low-repetitive sequences from their k-mer sketches; however, it is inaccurate on repetitive sequences such as the centromere of a human chromosome. Follow-up work by Blanca et al. (2021) has attempted to model how mutations affect k-mer sets based on strong assumptions that the sequence is non-repetitive and that mutations do not create spurious k-mer matches. However, the theoretical foundations for extending an estimator like Mash to work in the presence of repeat sequences have been lacking.
In this work, we relax the non-repetitive assumption and propose a novel estimator for the mutation rate. We derive theoretical bounds on our estimator’s bias. Our experiments show that it remains accurate for repetitive genomic sequences, such as the alpha satellite higher order repeats in centromeres. We demonstrate our estimator’s robustness across diverse datasets and various ranges of the substitution rate and k-mer size. Finally, we show how sketching can be used to avoid dealing with large k-mer sets while retaining accuracy. Our software is available at https://github.com/medvedevgroup/Repeat-Aware_Substitution_Rate_Estimator.

Cite As Get BibTex

Haonan Wu, Antonio Blanca, and Paul Medvedev. A k-mer-Based Estimator of the Substitution Rate Between Repetitive Sequences. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WABI.2025.20

Author Details

Haonan Wu
  • Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA, USA
Antonio Blanca
  • Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA, USA
Paul Medvedev
  • Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA, USA
  • Department of Biochemistry and Molecular Biology, The Pennsylvania State University, University Park, PA, USA
  • Huck Institutes of the Life Sciences, The Pennsylvania State University, University Park, PA, USA

Funding

This material is based upon work supported by the National Science Foundation under Grants No. DBI2138585 and OAC1931531. Research reported in this publication was supported by the National Institute Of General Medical Sciences of the National Institutes of Health under Award Number R01GM146462. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Acknowledgements

We thank Amatur Rahman for initial work on the project and Qunhua Li and David Koslicki for helpful discussions. We thank Mahmudur Rahman for the helpful discussion about hash functions. We thank Bob Harris for the idea of using dynamic programming to compute the probability of the destruction of all k-spans.

Supplementary Materials

References

  1. Anton Bankevich, Andrey V. Bzikadze, Mikhail Kolmogorov, Dmitry Antipov, and Pavel A. Pevzner. Multiplex de Bruijn graphs enable genome assembly from long, high-fidelity reads. Nature Biotechnology, 40(7):1075-1081, 2022. Google Scholar
  2. Anton Bankevich, Sergey Nurk, Dmitry Antipov, Alexey A Gurevich, Mikhail Dvorkin, Alexander S Kulikov, Valery M Lesin, Sergey I Nikolenko, Son Pham, Andrey D Prjibelski, et al. SPAdes: a new genome assembly algorithm and its applications to single-cell sequencing. Journal of computational biology, 19(5):455-477, 2012. URL: https://doi.org/10.1089/cmb.2012.0021.
  3. Mahdi Belbasi, Antonio Blanca, Robert S Harris, David Koslicki, and Paul Medvedev. The minimizer jaccard estimator is biased and inconsistent. Bioinformatics, 38(Supplement_1):i169-i176, June 2022. URL: https://doi.org/10.1093/bioinformatics/btac244.
  4. G. Benson. Tandem repeats finder: a program to analyze DNA sequences. Nucleic Acids Research, 27(2):573-580, 1999. Google Scholar
  5. Antonio Blanca, Robert S Harris, David Koslicki, and Paul Medvedev. The statistics of k-mers from a sequence undergoing a simple mutation process without spurious matches. Journal of Computational Biology, 29(2):155-168, 2022. URL: https://doi.org/10.1089/cmb.2021.0431.
  6. George Casella and Roger L. Berger. Statistical inference. Duxbury, Pacific Grove, Calif., 2. ed. edition, 2002. Google Scholar
  7. Luca Denti, Marco Previtali, Giulia Bernardini, Alexander Schönhuth, and Paola Bonizzoni. MALVA: genotyping by Mapping-free ALlele detection of known VAriants. iScience, 18:20-27, 2019. Google Scholar
  8. Huan Fan, Anthony R Ives, Yann Surget-Groba, and Charles H Cannon. An assembly and alignment-free method of phylogeny reconstruction from next-generation sequencing data. BMC genomics, 16(1):522, 2015. Google Scholar
  9. Robert S. Harris and Paul Medvedev. Improved representation of Sequence Bloom Trees. Bioinformatics, 36(3):721-727, 2020. URL: https://doi.org/10.1093/bioinformatics/btz662.
  10. Bernhard Haubold, Fabian Klötzl, and Peter Pfaffelhuber. andi: Fast and accurate estimation of evolutionary distances between closely related genomes. Bioinformatics, 31(8):1169-1175, 2014. URL: https://doi.org/10.1093/bioinformatics/btu815.
  11. Mahmudur Rahman Hera, N Tessa Pierce-Ward, and David Koslicki. Deriving confidence intervals for mutation rates across a wide range of evolutionary distances using fracminhash. Genome research, 33(7):1061-1068, 2023. Google Scholar
  12. Chirag Jain, Luis M Rodriguez-R, Adam M Phillippy, Konstantinos T Konstantinidis, and Srinivas Aluru. High throughput ani analysis of 90k prokaryotic genomes reveals clear species boundaries. Nature communications, 9(1):1-8, 2018. Google Scholar
  13. Bryce Kille, Erik Garrison, Todd J Treangen, and Adam M Phillippy. Minmers are a generalization of minimizers that enable unbiased local Jaccard estimation. Bioinformatics, 39(9), 2023. URL: https://doi.org/10.1093/bioinformatics/btad512.
  14. Téo Lemane, Nolan Lezzoche, Julien Lecubin, Eric Pelletier, Magali Lescot, Rayan Chikhi, and Pierre Peterlongo. Indexing and real-time user-friendly queries in terabyte-sized complex genomic datasets with kmindex and ORA. Nature Computational Science, 4(2):104-109, 2024. URL: https://doi.org/10.1038/s43588-024-00596-6.
  15. Heng Li. Minimap2: pairwise alignment for nucleotide sequences. Bioinformatics, 34(18):3094-3100, 2018. URL: https://doi.org/10.1093/bioinformatics/bty191.
  16. Guillaume Marçais, Brad Solomon, Rob Patro, and Carl Kingsford. Sketching and sublinear data structures in genomics. Annual Review of Biomedical Data Science, 2(1):93-118, 2019. Google Scholar
  17. Shannon M McNulty and Beth A Sullivan. Alpha satellite DNA biology: finding function in the recesses of the genome. Chromosome research, 26:115-138, 2018. Google Scholar
  18. Burkhard Morgenstern, Bingyao Zhu, Sebastian Horwege, and Chris André Leimeister. Estimating evolutionary distances between genomic sequences from spaced-word matches. Algorithms for Molecular Biology, 10(1), 2015. Google Scholar
  19. Sergey Nurk, Sergey Koren, Arang Rhie, Mikko Rautiainen, Andrey V Bzikadze, Alla Mikheenko, Mitchell R Vollger, Nicolas Altemose, Lev Uralsky, Ariel Gershman, et al. The complete sequence of a human genome. Science, 376(6588):44-53, 2022. Google Scholar
  20. Brian D Ondov, Todd J Treangen, Páll Melsted, Adam B Mallonee, Nicholas H Bergman, Sergey Koren, and Adam M Phillippy. Mash: fast genome and metagenome distance estimation using MinHash. Genome Biology, 17(1):132, 2016. Google Scholar
  21. Arang Rhie, Sergey Nurk, Monika Cechova, Savannah J. Hoyt, Dylan J. Taylor, Nicolas Altemose, Paul W. Hook, Sergey Koren, Mikko Rautiainen, Ivan A. Alexandrov, Jamie Allen, Mobin Asri, Andrey V. Bzikadze, Nae-Chyun Chen, Chen-Shan Chin, Mark Diekhans, Paul Flicek, Giulio Formenti, Arkarachai Fungtammasan, Carlos Garcia Giron, Erik Garrison, Ariel Gershman, Jennifer L. Gerton, Patrick G. S. Grady, Andrea Guarracino, Leanne Haggerty, Reza Halabian, Nancy F. Hansen, Robert Harris, Gabrielle A. Hartley, William T. Harvey, Marina Haukness, Jakob Heinz, Thibaut Hourlier, Robert M. Hubley, Sarah E. Hunt, Stephen Hwang, Miten Jain, Rupesh K. Kesharwani, Alexandra P. Lewis, Heng Li, Glennis A. Logsdon, Julian K. Lucas, Wojciech Makalowski, Christopher Markovic, Fergal J. Martin, Ann M. Mc Cartney, Rajiv C. McCoy, Jennifer McDaniel, Brandy M. McNulty, Paul Medvedev, Alla Mikheenko, Katherine M. Munson, Terence D. Murphy, Hugh E. Olsen, Nathan D. Olson, Luis F. Paulin, David Porubsky, Tamara Potapova, Fedor Ryabov, Steven L. Salzberg, Michael E. G. Sauria, Fritz J. Sedlazeck, Kishwar Shafin, Valery A. Shepelev, Alaina Shumate, Jessica M. Storer, Likhitha Surapaneni, Angela M. Taravella Oill, Françoise Thibaud-Nissen, Winston Timp, Marta Tomaszkiewicz, Mitchell R. Vollger, Brian P. Walenz, Allison C. Watwood, Matthias H. Weissensteiner, Aaron M. Wenger, Melissa A. Wilson, Samantha Zarate, Yiming Zhu, Justin M. Zook, Evan E. Eichler, Rachel J. O’Neill, Michael C. Schatz, Karen H. Miga, Kateryna D. Makova, and Adam M. Phillippy. The complete sequence of a human y chromosome. Nature, 621(7978):344-354, 2023. Google Scholar
  22. Will P. M. Rowe. When the levee breaks: a practical guide to sketching algorithms for processing the flood of genomic data. Genome Biology, 20(1):199, 2019. Google Scholar
  23. Sophie Röhling, Alexander Linne, Jendrik Schellhorn, Morteza Hosseini, Thomas Dencker, and Burkhard Morgenstern. The number of k-mer matches between two dna sequences as a function of k and applications to estimate phylogenetic distances. Plos one, 15(2):e0228070, 2020. Google Scholar
  24. Shahab Sarmashghi, Kristine Bohmann, M Thomas P Gilbert, Vineet Bafna, and Siavash Mirarab. Skmer: assembly-free and alignment-free sample identification using genome skims. Genome Biology, 20(1):1-20, 2019. Google Scholar
  25. Tizian Schulz and Paul Medvedev. ESKEMAP: exact sketch-based read mapping. Algorithms for Molecular Biology, 19(1):19, 2024. URL: https://doi.org/10.1186/s13015-024-00261-7.
  26. Jim Shaw and Yun William Yu. Fast and robust metagenomic sequence comparison through sparse chaining with skani. Nature Methods, 20(11):1661-1665, 2023. Google Scholar
  27. Jim Shaw and Yun William Yu. Proving sequence aligners can guarantee accuracy in almost O(m log n) time through an average-case analysis of the seed-chain-extend heuristic. Genome Research, 33(7):1175-1187, 2023. Google Scholar
  28. Kai Song, Jie Ren, Gesine Reinert, Minghua Deng, Michael S Waterman, and Fengzhu Sun. New developments of alignment-free sequence comparison: measures, statistics and next-generation sequencing. Briefings in bioinformatics, 15(3):343-353, 2014. URL: https://doi.org/10.1093/bib/bbt067.
  29. Daniel S Standage, C Titus Brown, and Fereydoun Hormozdiari. Kevlar: a mapping-free framework for accurate discovery of de novo variants. iScience, 18:28-36, 2019. Google Scholar
  30. Chen Sun and Paul Medvedev. Toward fast and accurate snp genotyping from whole genome sequencing data for bedside diagnostics. Bioinformatics, 35(3):415-420, 2018. URL: https://doi.org/10.1093/bioinformatics/bty641.
  31. Gregory W Vurture, Fritz J Sedlazeck, Maria Nattestad, Charles J Underwood, Han Fang, James Gurtowski, and Michael C Schatz. Genomescope: fast reference-free genome profiling from short reads. Bioinformatics, 33(14):2202-2204, 2017. URL: https://doi.org/10.1093/bioinformatics/btx153.
  32. Haonan Wu, Antonio Blanca, and Paul Medvedev. Repeat-Aware_Substitution_Rate_Estimator. Software, (visited on 2025-08-04). URL: https://github.com/medvedevgroup/Repeat-Aware_Substitution_Rate_Estimator
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.24318
  33. Haonan Wu, Antonio Blanca, and Paul Medvedev. Reproducibility repository. URL: https://github.com/medvedevgroup/kmer-stats-repeat_Reproduce.
  34. Huiguang Yi and Li Jin. Co-phylog: an assembly-free phylogenomic approach for closely related organisms. Nucleic Acids Research, 41(7):e75-e75, 2013. Google Scholar
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