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Sequence-specific minimizers via polar sets

View ORCID ProfileHongyu Zheng, View ORCID ProfileCarl Kingsford, Guillaume Marçais
doi: https://doi.org/10.1101/2021.02.01.429246
Hongyu Zheng
1Computational Biology Department, Carnegie Mellon University, Pittsburgh, USA
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Carl Kingsford
1Computational Biology Department, Carnegie Mellon University, Pittsburgh, USA
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Guillaume Marçais
1Computational Biology Department, Carnegie Mellon University, Pittsburgh, USA
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  • For correspondence: gmarcais@cs.cmu.edu
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Abstract

Minimizers are efficient methods to sample k-mers from genomic sequences that unconditionally preserve sufficiently long matches between sequences. Well-established methods to construct efficient minimizers focus on sampling fewer k-mers on a random sequence and use universal hitting sets (sets of k-mers that appear frequently enough) to upper bound the sketch size. In contrast, the problem of sequence-specific minimizers, which is to construct efficient minimizers to sample fewer k-mers on a specific sequence such as the reference genome, is less studied. Currently, the theoretical understanding of this problem is lacking, and existing methods do not specialize well to sketch specific sequences. We propose the concept of polar sets, complementary to the existing idea of universal hitting sets. Polar sets are k-mer sets that are spread out enough on the reference, and provably specialize well to specific sequences. Link energy measures how well spread out a polar set is, and with it, the sketch size can be bounded from above and below in a theoretically sound way. This allows for direct optimization of sketch size. We propose efficient heuristics to construct polar sets, and via experiments on the human reference genome, show their practical superiority in designing efficient sequence-specific minimizers. A reference implementation and code for analyses under an open-source license are at https://github.com/kingsford-group/polarset.

Competing Interest Statement

Carl Kingsford is a co-founder of Ocean Genomics, Inc. Guillaume Marcais is V.P. of software development at Ocean Genomics, Inc.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted February 02, 2021.
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Sequence-specific minimizers via polar sets
Hongyu Zheng, Carl Kingsford, Guillaume Marçais
bioRxiv 2021.02.01.429246; doi: https://doi.org/10.1101/2021.02.01.429246
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Sequence-specific minimizers via polar sets
Hongyu Zheng, Carl Kingsford, Guillaume Marçais
bioRxiv 2021.02.01.429246; doi: https://doi.org/10.1101/2021.02.01.429246

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