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Topological graph description of multicellular dynamics based on vertex model.

Atsushi Hashimoto1, Atsuki Nagao2, Satoru Okuda3

  • 1Graduate School of Education, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan.

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Summary

This study introduces mathematically verified vertex models for multicellular dynamics. These rigorous 2D/3D models accurately capture topological changes, ensuring reliable biological insights.

Keywords:
2D/3D vertex modelGraph theoryMulticellular dynamicsOperational soundness and completeness

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Area of Science:

  • Computational Biology
  • Mathematical Modeling
  • Developmental Biology

Background:

  • Vertex models are widely used to simulate multicellular dynamics by representing tissues as networks.
  • The topological dynamics within these networks are crucial for model accuracy and biological relevance.
  • Current vertex models lack rigorous mathematical verification, potentially limiting their reliability.

Purpose of the Study:

  • To develop and mathematically verify rigorous two-/three-dimensional (2D/3D) vertex models for multicellular topological dynamics.
  • To establish conditions under which topological operators in vertex models can accurately represent multicellular rearrangements.
  • To provide a foundation for more reliable computational modeling of biological processes involving tissue dynamics.

Main Methods:

  • Classifying vertex models from a graph-theoretic perspective.
  • Performing mathematical analyses to identify conditions for accurate operator application.
  • Developing new 2D/3D vertex models based on graph theory and mathematical verification.

Main Results:

  • Identified conditions that ensure accurate application of topological operators without errors.
  • Demonstrated that under these conditions, operators can fully express multicellular topological dynamics.
  • Proposed novel, mathematically rigorous 2D/3D vertex models applicable to general multicellular dynamics.

Conclusions:

  • The proposed vertex models offer a mathematically validated framework for studying multicellular dynamics.
  • These models enhance the reliability of computational simulations in developmental biology and tissue engineering.
  • Clarified verification points for results obtained from previous, unverified vertex models.