Physics of epithelial flows and folds

The shape of a biological tissue is determined by mechanical stresses acting within the tissue cells. During embryonic morphogenesis, forces generated in the actomyosin cytoskeleton in the cell of epithelia result in cell deformation, cell rearrangements, and 3D bending of the epithelium. To understand tissue morphogenesis, force generation at the cellular scale must be related to flows and deformation occurring at the tissue scale. Here I will discuss how this relation can be captured by a 3D vertex model or by a continuum theory of active surfaces to understand epithelial fold formation during embryonic development. Using this framework, one finds that two different mechanisms, basal relaxation and lateral constriction, can account for fold formation in the Drosophila wing disc. I will also discuss how planar tissue flows are related to cell shape changes and cell division, and show how the growth of the Drosophila histoblast nests can be decomposed into basic cellular events.