Mechanical Cell Interactions on Curved Interfaces

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.