Physics of epithelial folding

Three-dimensional deformations of epithelia play a fundamental role in tissue morphogenesis. The shape of an epithelium is determined by mechanical stresses acting within the tissue cells and from the outside environment. Here we discuss how patterned force generation in an epithelium can drive biological tissue folding. We discuss the formation of folds during the growth of the Drosophila wing disc, and show that two folds with similar shapes arise by two different physical mechanisms. We use three-dimensional vertex model simulations that take into account cell shapes and balance of forces in a tissue to show how patterned cellular surface tensions can drive tissue folding. A continuum theory of active surface allows to capture generic aspects of fold formation, which can be understood from the action of internal active bending moments resulting from apico-basal asymmetric forces.