PMID- 35690623
OWN - NLM
STAT- MEDLINE
DCOM- 20220614
LR  - 20220810
IS  - 2045-2322 (Electronic)
IS  - 2045-2322 (Linking)
VI  - 12
IP  - 1
DP  - 2022 Jun 11
TI  - Hodge theory-based biomolecular data analysis.
PG  - 9699
LID - 10.1038/s41598-022-12877-z [doi]
LID - 9699
AB  - 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.
CI  - (c) 2022. The Author(s).
FAU - Wei, Ronald Koh Joon
AU  - Wei RKJ
AD  - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, 
      Nanyang Technological University, Singapore, 637371, Singapore.
FAU - Wee, Junjie
AU  - Wee J
AD  - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, 
      Nanyang Technological University, Singapore, 637371, Singapore.
FAU - Laurent, Valerie Evangelin
AU  - Laurent VE
AD  - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, 
      Nanyang Technological University, Singapore, 637371, Singapore.
FAU - Xia, Kelin
AU  - Xia K
AD  - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, 
      Nanyang Technological University, Singapore, 637371, Singapore. 
      xiakelin@ntu.edu.sg.
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
DEP - 20220611
PL  - England
TA  - Sci Rep
JT  - Scientific reports
JID - 101563288
SB  - IM
MH  - *Chromosomes
MH  - *Data Analysis
MH  - Molecular Structure
PMC - PMC9188576
COIS- The authors declare no competing interests.
EDAT- 2022/06/12 06:00
MHDA- 2022/06/15 06:00
PMCR- 2022/06/11
CRDT- 2022/06/11 23:17
PHST- 2022/01/26 00:00 [received]
PHST- 2022/05/10 00:00 [accepted]
PHST- 2022/06/11 23:17 [entrez]
PHST- 2022/06/12 06:00 [pubmed]
PHST- 2022/06/15 06:00 [medline]
PHST- 2022/06/11 00:00 [pmc-release]
AID - 10.1038/s41598-022-12877-z [pii]
AID - 12877 [pii]
AID - 10.1038/s41598-022-12877-z [doi]
PST - epublish
SO  - Sci Rep. 2022 Jun 11;12(1):9699. doi: 10.1038/s41598-022-12877-z.