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Related Experiment Video

Updated: Jun 3, 2025

Single Cell Durotaxis Assay for Assessing Mechanical Control of Cellular Movement and Related Signaling Events
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Single Cell Durotaxis Assay for Assessing Mechanical Control of Cellular Movement and Related Signaling Events

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Mechanical Cell Interactions on Curved Interfaces.

Pascal R Buenzli1, Shahak Kuba2, Ryan J Murphy3

  • 1School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia. pascal.buenzli@qut.edu.au.

Bulletin of Mathematical Biology
|January 8, 2025
PubMed
Summary
This summary is machine-generated.

We developed a mathematical model for cell mechanical relaxation in curved tissues. Curvature influences normal stress, allowing cells to sense tissue shape, but not tangential stress or relaxation speed in the continuum limit.

Keywords:
Coarse-grainingDiffusionMathematical modelMechanobiologySurface tensionTissue growthTissue mechanics

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Area of Science:

  • * Biophysics
  • * Mathematical Biology
  • * Cell Mechanics

Background:

  • * Existing models often simplify epithelial tissues as flat, neglecting curvature effects.
  • * Understanding cell behavior on curved surfaces is crucial for tissue development and disease modeling.

Purpose of the Study:

  • * To develop a mathematical model for mechanical relaxation of cells in curved epithelial layers.
  • * To investigate the influence of tissue curvature on cell mechanics and dynamics.

Main Methods:

  • * Developed a mathematical model representing cell mechanics using straight or curved springs.
  • * Derived a continuum limit by increasing cell number and springs.
  • * Analyzed cell density using a diffusion equation in arc length coordinates.

Main Results:

  • * Curved and straight spring models converge to diffusion dynamics in the continuum limit.
  • * Tissue curvature does not impact cell mechanical relaxation or tangential stress in the continuum limit.
  • * Cell normal stress depends on curvature, mediated by tangential forces and surface tension.

Conclusions:

  • * Cell normal stress allows sensing of substrate curvature at large scales.
  • * The model provides insights into how cells respond to curved geometries.
  • * Findings may explain curvature-dependent cellular behaviors observed in experiments.