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Weighted persistent homology for biomolecular data analysis.

Zhenyu Meng1, D Vijay Anand1, Yunpeng Lu2

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

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|February 9, 2020
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Summary
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Localized weighted persistent homology (LWPH) reveals biomolecular functional properties by analyzing local structures. This new method successfully differentiates DNA types and identifies configurational states, outperforming traditional geometric models.

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Area of Science:

  • Computational Biology
  • Biophysics
  • Data Science

Background:

  • Weighted persistent homology (WPH) models analyze biomolecular data by assigning weights to structural elements.
  • Existing WPH models treat biomolecules as inseparable systems, potentially missing localized functional properties.

Purpose of the Study:

  • To introduce the first localized weighted persistent homology (LWPH) model for biomolecular data analysis.
  • To enable the revelation of functional properties embedded in local biomolecular structures.

Main Methods:

  • Systematic review of weighted persistent homology (WPH) models.
  • Decomposition of biomolecules into overlapping local domains.
  • Application of persistent homology or WPH analysis on these local domains.
  • Development and application of LWPH-based principal component analysis (PCA).

Main Results:

  • LWPH features successfully discriminate between A-, B-, and Z-DNA types.
  • LWPH-PCA model identifies two distinct configurational states of DNA in ion liquid environments.
  • LWPH quantitatively characterizes structure information in arbitrary-sized regions, surpassing traditional geometric measurements.

Conclusions:

  • LWPH effectively captures local structure variations in biomolecules.
  • The LWPH model offers a powerful alternative to geometric models for analyzing complex biomolecular structures.
  • LWPH provides a versatile tool for quantitative structure-property relationship studies in biomolecular systems.