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Vertex model instabilities for tissues subject to cellular activity or applied stresses
Fernanda Pérez-Verdugo1, Jean-Francois Joanny2,3, Rodrigo Soto1
1Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile.
Physical Review. E
|December 17, 2020
Summary
Epithelial tissues become unstable when cell perimeters change or external stresses are applied, leading to cell deformation and potential model invalidity. This instability couples shear, rotation, and expansion modes, impacting tissue dynamics.
Area of Science:
- Biophysics
- Cell Biology
- Tissue Engineering
Background:
- The vertex model is a key tool for studying epithelial tissue dynamics.
- It incorporates biophysical parameters, offering simplicity and versatility.
- Understanding tissue stability under stress is crucial for developmental biology and regenerative medicine.
Purpose of the Study:
- To investigate the general conditions under which epithelial tissues described by the vertex model become unstable.
- To analyze the coupling of different deformation modes during instability.
- To determine the limits of the vertex model's validity in describing stressed or active tissues.
Main Methods:
- Analytical calculations for regular hexagonal tissues.
- Computational simulations for disordered tissues.
- Analysis of cell deformation, including ellipticity and nonconvexity.
Main Results:
- Tissue instability arises from modifications in cell equilibrium perimeter or external stresses.
- Instabilities couple shear/deviatoric modes with rotation and expansion modes.
- At longer timescales, cells can become nonconvex, indicating vertex model limitations.
Conclusions:
- The vertex model's validity is limited under conditions of cell activity or external stress.
- Observed instabilities and cell deformations are general phenomena in epithelial tissues.
- Homogenization at long wavelengths ensures excellent agreement between analytical and simulation results for disordered tissues.
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