A Model of Epithelial Invagination Driven by Collective Mechanics of Identical Cells

We propose a 2D mechanical model of a tubular epithelium resembling the early Drosophila embryo. The model consists of a single layer of identical cells with energy associated with the tension of cell cortex. Depending on the relative tersion of the apical, basal, and lateral sides of the cells, tissue thickness, and the degree of external constraint, the minimal-energy states of the epithelial cross section include circular shapes as well as a range of inward-buckled shapes. Some of the solutions are characterized by a single deep groove, which shows that an epithelium consisting of cells of identical mechanical properties can infold. This is consistent with what is seen in embryos of certain Drosophila mutants. To ensure that the infolding occurs at a predetermined section of the epithelium, we extend the model by increasing the cross-sectional area of a subset of cells, which is consistent with observations in wild-type embryos. This variation of cell parameters across the epithelium is sufficient to make it fold at a specific site. The model explores previously untested minimal conditions for tissue invagination and is devoid of specificity needed to accurately describe an in vivo situation in Drosophila.