https://doi.org/10.1140/epjp/s13360-021-02205-1
Regular Article
Modeling the mechanics of growing epithelia with a bilayer plate theory
1
Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005, Paris, France
2
Institut Universitaire de Cancérologie, Faculté de médecine, Sorbonne Université, 91 Bd de l’Hôpital, 75013, Paris, France
3
Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Turing Center for Living Systems, Marseille, France
Received:
14
July
2021
Accepted:
20
November
2021
Published online:
13
December
2021
Epithelia, which consists of cell sheets lying on a substrate, are prevalent structures of multicellular organisms. The physical basis of epithelial morphogenesis has been intensely investigated in recent years. However, as 2D mechanics focused most attention, we still lack a rigorous description of how the mechanical interactions between the cell layer and its substrate can lead to 3D distortions. This work provides a complete description of epithelial mechanics using the most straightforward model of an epithelium: a thin elastic bilayer. We first provide experimental evidence in Drosophila tissues that localized alterations of the cell substrate (the extracellular matrix) can lead to profound 3D shape changes in epithelia. We then develop an analytical model modifying the Föppl–von Kármán equation with growth for bilayers. We provide a complete description of all contributions from biophysical characteristics of epithelia. We show how any localized inhomogeneity of stiffness or thickness drastically changes the bending process when the two layers grow differently. Comparison with finite element simulations and experiments performed on Drosophila wing imaginal discs validates this approach for thin epithelia
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
