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Linear viscoelastic properties of the vertex model for epithelial tissues

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  • Sijie Tong
  • Navreeta K Singh
  • Rastko Sknepnek
  • Andrej Košmrlj

Abstract

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.Author summary: Epithelial tissues line organs and cavities in the body, and serve as barriers that separate organisms from their environment. Epithelia are robust yet adaptable; they have the ability to change their own viscoelastic behavior in response to internal or external stimuli by actively tuning the mechanical properties of the constituent cells and interactions between them. The mesoscopic mechanics of epithelia are commonly described with the vertex model. Here we present a detailed study of the linear rheological properties of the vertex model for both regular hexagonal and disordered cell configurations over a wide range of driving frequencies. The linear viscoelastic responses of the vertex model are mapped to standard spring-dashpot models. Our work, therefore, shows that the vertex model is a suitable base model to study the rich rheological behavior of epithelial tissues.

Suggested Citation

  • Sijie Tong & Navreeta K Singh & Rastko Sknepnek & Andrej Košmrlj, 2022. "Linear viscoelastic properties of the vertex model for epithelial tissues," PLOS Computational Biology, Public Library of Science, vol. 18(5), pages 1-24, May.
    • Handle: RePEc:plo:pcbi00:1010135
    DOI: 10.1371/journal.pcbi.1010135
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    1. Matthew C. Gibson & Ankit B. Patel & Radhika Nagpal & Norbert Perrimon, 2006. "The emergence of geometric order in proliferating metazoan epithelia," Nature, Nature, vol. 442(7106), pages 1038-1041, August.
    2. Silke Henkes & Kaja Kostanjevec & J. Martin Collinson & Rastko Sknepnek & Eric Bertin, 2020. "Dense active matter model of motion patterns in confluent cell monolayers," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    3. D. Zeb Rocklin & Shangnan Zhou & Kai Sun & Xiaoming Mao, 2017. "Transformable topological mechanical metamaterials," Nature Communications, Nature, vol. 8(1), pages 1-9, April.
    4. Jennifer A. Mitchel & Amit Das & Michael J. O’Sullivan & Ian T. Stancil & Stephen J. DeCamp & Stephan Koehler & Oscar H. Ocaña & James P. Butler & Jeffrey J. Fredberg & M. Angela Nieto & Dapeng Bi & J, 2020. "In primary airway epithelial cells, the unjamming transition is distinct from the epithelial-to-mesenchymal transition," Nature Communications, Nature, vol. 11(1), pages 1-14, December.
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