Vertex model instabilities for tissues subject to cellular activity or applied stresses

• Published in: Physical review. E Vol. 102; no. 5-1; p. 052604
• Main Authors: Pérez-Verdugo, Fernanda, Joanny, Jean-Francois, Soto, Rodrigo
• Format: Journal Article
• Language: English
• Published: United States 01.11.2020
• Subjects: Biomechanical Phenomena; Computer Simulation; Models, Biological; Stress, Mechanical
• ISSN: 2470-0053
• DOI: 10.1103/PhysRevE.102.052604

The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their equilibrium perimeter due to their activity, or the tissue is subject to external stresses, the tissue becomes unstable with deformations that couple pure shear or deviatoric modes, with rotation and expansion modes. For short times, these instabilities deform cells, increasing their ellipticity, while at longer times cells become nonconvex, indicating that the vertex model ceases to be a valid description for tissues under these conditions. The agreement between the analytic calculations performed for a regular hexagonal tissue and the simulations of disordered tissues is excellent due to the homogenization of the tissue at long wavelengths.