Abstract

We propose a minimal theoretical model of epithelial shape in 3D, based on cell adhesion and actomyosin contractility, which describes the various shapes of epithelial cells and the bending and buckling of epithelial sheets, as well as the relative stability of cellular tubes and spheres. We show that, to understand these processes, a full 3D description of the cells is needed, but that simple scaling laws can still be derived. The morphologies observed in vivo can be understood as stable points of mechanical equations and the transitions between them are either continuous or discontinuous. We then focus on epithelial sheet bending, a ubiquitous morphogenetic process. We calculate the curvature of an epithelium as a function of actin belt tension as well as of cell–cell and and cell–substrate tension.

Secondly, we incorporate in our model the stresses arising from cell division and death. When tissues grow in constrained environments, buckling instabilities are gener- ically expected, and we show that a simple biomechanical model can explain a wide variety of biological shapes, such as the intestinal wall or pathologies of biological tubes such as arteries and trachea.

We then apply these theories to the concrete example of the development of the Drosophila trachea, in collaboration with Bo Dong and Shigeo Hayashi (RIKEN Institute, Japan). Our findings demonstrate a mechanical role for the extracellular matrix and suggest that the interaction of the apical membrane and an elastic aECM determines the final morphology of biological tubes independent of cell shape.