Hodge theory-based biomolecular data analysis
Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. Different from traditional graph-ba...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/160448 |
| _version_ | 1811692107167956992 |
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| author | Koh, Ronald Joon Wei Wee, Junjie Laurent, Valerie Evangelin Xia, Kelin |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Koh, Ronald Joon Wei Wee, Junjie Laurent, Valerie Evangelin Xia, Kelin |
| author_sort | Koh, Ronald Joon Wei |
| collection | NTU |
| description | Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. Different from traditional graph-based methods, biomolecular structures are represented as simplicial complexes, which can be viewed as a generalization of graph models to their higher-dimensional counterparts. Hodge Laplacian matrices at different dimensions can be generated from the simplicial complex. The spectral information of these matrices can be used to study intrinsic topological information of biomolecular structures. Essentially, the number (or multiplicity) of k-th dimensional zero eigenvalues is equivalent to the k-th Betti number, i.e., the number of k-th dimensional homology groups. The associated eigenvectors indicate the homological generators, i.e., circles or holes within the molecular-based simplicial complex. Furthermore, Hodge decomposition-based HodgeRank model is used to characterize the folding or compactness of the molecular structures, in particular, the topological associated domain (TAD) in high-throughput chromosome conformation capture (Hi-C) data. Mathematically, molecular structures are represented in simplicial complexes with certain edge flows. The HodgeRank-based average/total inconsistency (AI/TI) is used for the quantitative measurements of the folding or compactness of TADs. This is the first quantitative measurement for TAD regions, as far as we know. |
| first_indexed | 2024-10-01T06:30:31Z |
| format | Journal Article |
| id | ntu-10356/160448 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:30:31Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1604482023-02-28T20:02:29Z Hodge theory-based biomolecular data analysis Koh, Ronald Joon Wei Wee, Junjie Laurent, Valerie Evangelin Xia, Kelin School of Physical and Mathematical Sciences Science::Mathematics Chromosome Data Analysis Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. Different from traditional graph-based methods, biomolecular structures are represented as simplicial complexes, which can be viewed as a generalization of graph models to their higher-dimensional counterparts. Hodge Laplacian matrices at different dimensions can be generated from the simplicial complex. The spectral information of these matrices can be used to study intrinsic topological information of biomolecular structures. Essentially, the number (or multiplicity) of k-th dimensional zero eigenvalues is equivalent to the k-th Betti number, i.e., the number of k-th dimensional homology groups. The associated eigenvectors indicate the homological generators, i.e., circles or holes within the molecular-based simplicial complex. Furthermore, Hodge decomposition-based HodgeRank model is used to characterize the folding or compactness of the molecular structures, in particular, the topological associated domain (TAD) in high-throughput chromosome conformation capture (Hi-C) data. Mathematically, molecular structures are represented in simplicial complexes with certain edge flows. The HodgeRank-based average/total inconsistency (AI/TI) is used for the quantitative measurements of the folding or compactness of TADs. This is the first quantitative measurement for TAD regions, as far as we know. Ministry of Education (MOE) Nanyang Technological University Published version This work was supported in part by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG109/19 and Tier 2 MOE-T2EP20120-0013 and MOE-T2EP20220-0010. 2022-07-22T06:02:56Z 2022-07-22T06:02:56Z 2022 Journal Article Koh, R. J. W., Wee, J., Laurent, V. E. & Xia, K. (2022). Hodge theory-based biomolecular data analysis. Scientific Reports, 12(1), 9699-. https://dx.doi.org/10.1038/s41598-022-12877-z 2045-2322 https://hdl.handle.net/10356/160448 10.1038/s41598-022-12877-z 35690623 2-s2.0-85131819156 1 12 9699 en M4081842 RG109/19 MOE-T2EP20120-0013 MOE-T2EP20220-0010 Scientific Reports © 2022 The Author(s). 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/. application/pdf |
| spellingShingle | Science::Mathematics Chromosome Data Analysis Koh, Ronald Joon Wei Wee, Junjie Laurent, Valerie Evangelin Xia, Kelin Hodge theory-based biomolecular data analysis |
| title | Hodge theory-based biomolecular data analysis |
| title_full | Hodge theory-based biomolecular data analysis |
| title_fullStr | Hodge theory-based biomolecular data analysis |
| title_full_unstemmed | Hodge theory-based biomolecular data analysis |
| title_short | Hodge theory-based biomolecular data analysis |
| title_sort | hodge theory based biomolecular data analysis |
| topic | Science::Mathematics Chromosome Data Analysis |
| url | https://hdl.handle.net/10356/160448 |
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