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. 2020 Feb 7;10:2079. doi: 10.1038/s41598-019-55660-3

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The LWPH based barcodes for different combinations of DNA base pairs. The weighted distance matrix in Eq. (8) is considered. Only the distances between two atoms from different nucleobases are set to be their Euclidean distance, while other distances are set to infinity. The shortest $β_{0}$ bars are distances between adjacent atoms from two bases. They characterize the hydrogen bonds between two nucleobases. For a single base pair (A-T or G-C) situation, the generated $β_{1}$ bars will never be “killed” as no 2-simplexes can be formed.