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Path Topology in Molecular and Materials Sciences.

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  • 1School of Advanced Materials, Peking University, Shenzhen Graduate School, Shenzhen518055, China.

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This study introduces persistent path topology (PPT) and path homology (PH) to mathematically link molecular structure to function. These topological tools offer new ways to design materials and understand biological systems.

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Area of Science:

  • Molecular and Materials Sciences
  • Computational Chemistry
  • Systems Biology

Background:

  • Understanding the structure-function relationship is crucial for designing molecules and materials.
  • Rational design is hindered by the lack of intrinsic mathematical descriptors for specific functions.

Purpose of the Study:

  • Introduce persistent path topology (PPT) for characterizing directed networks in functional units.
  • Utilize path homology (PH) to analyze amorphous solids and topological perturbation analysis (TPA) for biological systems.

Main Methods:

  • Persistent Path Topology (PPT) for network characterization.
  • Path Homology (PH) for analyzing amorphous solids and mirror-symmetric sublattices.
  • Topological Perturbation Analysis (TPA) for identifying critical targets in biological systems.

Main Results:

  • PPT effectively characterizes diverse functional units including isomers and catalysts.
  • PH deciphers the role of sublattices hindering periodicity in amorphous solids.
  • TPA reveals critical targets within the blood coagulation system.

Conclusions:

  • The developed topological tools provide a mathematical framework for structure-function relationships.
  • These methods have broad applicability in systems biology, omics sciences, topological materials, and machine learning.
  • This work advances the rational design of molecules and materials with desired functions.