title: Theory of epithelial sheet morphology in three dimensions.
abstract: Morphogenesis during embryo development requires the coordination of mechanical forces to generate the macroscopic shapes of organs. We propose a minimal theoretical model, 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. The model allows for a comparison of the relative stabilities of spherical or cylindrical cellular structures (acini or tubes). Finally, we propose a unique type of buckling instability of epithelia, driven by a flattening of individual cell shapes, and discuss experimental tests to verify our predictions.
authors.affiliation: Physicochimie Curie (Institut Curie/Centre National de la Recherche Scientifique-Unité Mixte de Recherche 168/UPMC), Institut Curie, Centre de Recherche, 75248 Paris Cedex 05, France.
authors.forename: Edouard
authors.initials: E
authors.lastname: Hannezo
authors.forename: Jacques
authors.initials: J
authors.lastname: Prost
authors.forename: Jean-Francois
authors.initials: JF
authors.lastname: Joanny
mesh_terms: D000199:Actins / Q000737:chemistry; D000205:Actomyosin / Q000737:chemistry / Q000378:metabolism; D000818:Animals; D017209:Apoptosis; D002448:Cell Adhesion; D002450:Cell Communication; D048430:Cell Shape; D004330:Drosophila; D004548:Elasticity; D004847:Epithelial Cells / Q000166:cytology*; D004848:Epithelium / Q000254:growth & development*; D021621:Imaging, Three-Dimensional; D008962:Models, Theoretical; D009024:Morphogenesis; D014921:Wings, Animal / Q000473:pathology; D014981:Xenopus
chemical_list: D000199:Actins; D000205:Actomyosin
keywords: active foams; biophysics; mathematical modeling