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A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns.

José A Carrillo1, Hideki Murakawa2, Makoto Sato3

  • 1Mathematical Institute, University of Oxford, Oxford, United Kingdom.

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A new mathematical model explains how cell arrangements transition from hexagonal to tetragonal patterns during fruit fly brain development. This Adhesion-Repulsion-Attraction model offers insights into neural organization and biological pattern formation.

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Area of Science:

  • Developmental Biology
  • Computational Neuroscience
  • Mathematical Modeling

Background:

  • Differential adhesion drives neuronal spatial organization in early fruit fly brain development.
  • Columnar neuron arrangements form large-scale patterns in the fly visual center.
  • Hexagonal configurations are observed in the fly compound eye, with tetragonal patterns appearing in mutants.

Purpose of the Study:

  • To develop a mathematical framework for studying transitions between hexagonal and tetragonal cell arrangements.
  • To model the mechanisms underlying pattern changes in neural development.

Main Methods:

  • Proposed a new mathematical model based on macroscopic approximations of agent-based models.
  • Incorporated medium-range repulsion and longer-range attraction into existing cell sorting models.
  • Analyzed angular configurations using angle summary statistics and compared with experimental data.

Main Results:

  • The Adhesion-Repulsion-Attraction (ARA) model successfully reproduces the transition from hexagonal to tetragonal configurations.
  • Intermediate patterns between hexagonal and tetragonal are common in both experimental data and the ARA model.
  • The model shows qualitative agreement with experimental tile patterning.

Conclusions:

  • The ARA mathematical model provides a framework for understanding cell pattern transitions in biological systems.
  • The study opens new avenues for exploring pattern dynamics in neural development and other biological processes.
  • Further quantitative studies of ARA models are warranted.