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A topological characterization of DNA sequences based on chaos geometry and persistent homology

Dong Quan Ngoc Nguyen, Phuong Dong Tan Le, Lin Xing, Lizhen Lin
doi: https://doi.org/10.1101/2021.01.31.429071
Dong Quan Ngoc Nguyen
1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
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  • For correspondence: dnguye15@nd.edu
Phuong Dong Tan Le
2Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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Lin Xing
1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
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Lizhen Lin
1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
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Abstract

Methods for analyzing similarities among DNA sequences play a fundamental role in computational biology, and have a variety of applications in public health, and in the field of genetics. In this paper, a novel geometric and topological method for analyzing similarities among DNA sequences is developed, based on persistent homology from algebraic topology, in combination with chaos geometry in 4-dimensional space as a graphical representation of DNA sequences. Our topological framework for DNA similarity analysis is general, alignment-free, and can deal with DNA sequences of various lengths, while proving first-of-the-kind visualization features for visual inspection of DNA sequences directly, based on topological features of point clouds that represent DNA sequences. As an application, we test our methods on three datasets including genome sequences of different types of Hantavirus, Influenza A viruses, and Human Papillomavirus.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • email: dongquan.ngoc.nguyen{at}nd.edu, email: pdle{at}uwaterloo.ca, email: lxing{at}nd.edu, email: lizhen.lin{at}nd.edu

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted February 01, 2021.
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A topological characterization of DNA sequences based on chaos geometry and persistent homology
Dong Quan Ngoc Nguyen, Phuong Dong Tan Le, Lin Xing, Lizhen Lin
bioRxiv 2021.01.31.429071; doi: https://doi.org/10.1101/2021.01.31.429071
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A topological characterization of DNA sequences based on chaos geometry and persistent homology
Dong Quan Ngoc Nguyen, Phuong Dong Tan Le, Lin Xing, Lizhen Lin
bioRxiv 2021.01.31.429071; doi: https://doi.org/10.1101/2021.01.31.429071

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