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Joker de Bruijn: Covering k-Mers Using Joker Characters

Author(s)
Orenstein, Yaron; Yu, Yun William; Berger Leighton, Bonnie
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Creative Commons Attribution NonCommercial License 4.0 https://creativecommons.org/licenses/by-nc/4.0/
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Abstract
Sequence libraries that cover all k-mers enable universal and unbiased measurements of nucleotide and peptide binding. The shortest sequence to cover all k-mers is a de Bruijn sequence of length. Researchers would like to increase k to measure interactions at greater detail, but face a challenging problem: the number of k-mers grows exponentially in k, while the space on the experimental device is limited. In this study, we introduce a novel advance to shrink k-mer library sizes by using joker characters, which represent all characters in the alphabet. Theoretically, the use of joker characters can reduce the library size tremendously, but it should be limited as the introduced degeneracy lowers the statistical robustness of measurements. In this work, we consider the problem of generating a minimum-length sequence that covers a given set of k-mers using joker characters. The number and positions of the joker characters are provided as input. We first prove that the problem is NP-hard. We then present the first solution to the problem, which is based on two algorithmic innovations: (1) a greedy heuristic and (2) an integer linear programming (ILP) formulation. We first run the heuristic to find a good feasible solution, and then run an ILP solver to improve it. We ran our algorithm on DNA and amino acid alphabets to cover all k-mers for different values of k and k-mer multiplicity. Results demonstrate that it produces sequences that are very close to the theoretical lower bound. Keywords: de Bruijn sequence; microarray library design; peptide arrays; protein binding; proteinbinding microarrays
Date issued
2018-08-17
URI
https://hdl.handle.net/1721.1/122940
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Computational Biology
Publisher
Mary Ann Liebert Inc
Citation
Orenstein, Yaron et al. "Joker de Bruijn: Covering k-Mers Using Joker Characters." Journal of Computational Biology 25, 11 (2018): 1171-1178 © 2018 The Author(s)
Version: Final published version
ISSN
1557-8666

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