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Multidimensional persistence in biomolecular data.

Kelin Xia1, Guo-Wei Wei1,2,3

  • 1Department of Mathematics, Michigan State University, Michigan, 48824.

Journal of Computational Chemistry
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PubMed
Summary
This summary is machine-generated.

We introduce novel multidimensional persistence methods for analyzing complex data. These techniques enhance topological data analysis in fields like biomolecular science and materials science.

Keywords:
anisotropic filtrationmultidimensional persistencemultifiltrationmultiscale persistenceprotein flexibilityprotein foldingtopological denoising

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Area of Science:

  • Topological Data Analysis
  • Computational Biology
  • Materials Science

Background:

  • Persistent homology is key for simplifying complex datasets, especially in biomolecular applications.
  • Multidimensional persistence offers potential for integrating geometry and topology but faces construction challenges.

Purpose of the Study:

  • Introduce pseudomultidimensional persistence and multiscale multidimensional persistence.
  • Address the practical and robust construction of multidimensional persistence.
  • Demonstrate the utility and efficiency of these new topological methods.

Main Methods:

  • Pseudomultidimensional persistence: Repeated application of persistent homology filtration to high-dimensional data.
  • Multiscale multidimensional persistence: Construction using isotropic and anisotropic scales to generate new simplicial complexes.
  • Topological denoising using Laplace-Beltrami flow to separate noise from molecular signatures.

Main Results:

  • Demonstrated utility in protein folding, flexibility analysis, cryo-EM denoising, and nanoparticle scale dependence.
  • Observed topological transitions between folded and unfolded protein states.
  • Successfully separated noise from molecular topological fingerprints.

Conclusions:

  • The proposed pseudomultidimensional and multiscale multidimensional persistence methods are robust and efficient.
  • These methods provide insights into local and global topological features across different scales.
  • The techniques offer significant advancements for analyzing complex biological and material systems.