Shape changes and elastic dewetting of adherent epithelia.

Epithelial tissues play a fundamental role in various morphogenetic events during development and early embryogenesis. Although epithelial monolayers are often modeled as two-dimensional (2D) elastic surfaces, they distinguish themselves from conventional thin elastic plates in three important ways: the presence of an apical-basal polarity, spatial control and variability of cellular thickness, and their nonequilibrium active nature. Here, we develop a minimal continuum model of a planar epithelial tissue as an active elastic material that incorporates all these features. We start from a full three-dimensional (3D) description of the tissue and derive an effective 2D model that captures both the apical-basal asymmetry and the spatial geometry of the tissue, through the curvature of the apical surface. By identifying four distinct sources of activity, we find that bulk active stresses arising from actomyosin contractility and growth compete with boundary active tensions due to localized actomyosin cables and lamellipodial activity, to generate the various states spanning the morphospace of a planar epithelium. Our treatment hence unifies elastic dewetting and 3D shape deformations of substrate-adhered tissues. Finally, we discuss the implications of our results for some biologically relevant processes such as tissue folding at the onset of lumen formation.