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Hodge theory-based biomolecular data analysis.

Ronald Koh Joon Wei1, Junjie Wee1, Valerie Evangelin Laurent1

  • 1Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore.

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This study introduces a novel method using Hodge theory and simplicial complexes to analyze biomolecular structures. This approach offers new insights into molecular folding and topological associated domains (TADs).

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Area of Science:

  • * Integrates differential geometry, algebraic topology, and functional analysis for biomolecular structure analysis.
  • * Applies Hodge theory, specifically Hodge Laplacian and decomposition, to understand complex molecular architectures.

Background:

  • * Traditional graph-based methods are limited for higher-dimensional biomolecular structures.
  • * Simplicial complexes offer a powerful generalization, capturing intricate topological features.
  • * Hodge theory provides a framework to analyze these complex structures.

Purpose of the Study:

  • * To develop a novel method for analyzing biomolecular structures using simplicial complexes and Hodge theory.
  • * To quantitatively measure the folding and compactness of molecular structures, particularly topological associated domains (TADs).
  • * To establish a new quantitative measurement for TAD regions using computational models.

Main Methods:

  • * Representing biomolecular structures as higher-dimensional simplicial complexes.
  • * Generating and analyzing Hodge Laplacian matrices from simplicial complexes to extract spectral information.
  • * Utilizing Hodge decomposition-based HodgeRank models for quantitative measurements of molecular folding and compactness.

Main Results:

  • * Spectral analysis of Hodge Laplacian matrices reveals intrinsic topological information, including Betti numbers and homological generators.
  • * HodgeRank model successfully characterizes molecular folding and compactness, applied to topological associated domains (TADs).
  • * Developed the first quantitative measurements (average/total inconsistency) for the folding and compactness of TADs.

Conclusions:

  • * Hodge theory and simplicial complexes provide a robust framework for analyzing complex biomolecular structures.
  • * The HodgeRank model offers a novel quantitative approach to assess molecular folding and TAD compactness.
  • * This work pioneers quantitative measurements for TAD regions, advancing structural biology and genomics.