Epithelial tissue as a self-sculpting, viscoelastic slab

Epithelial tissues are cell monolayers composed of adhering columnar cells. During embryonic development, in a process called morphogenesis, epithelia actively alter their shape to create various body parts of the animal, making epithelia one of the most active and critical structures in early animal development. Even though epithelial cells exist and move in three dimensions, mathematical models frequently describe them as two-dimensional. With the importance of the third dimension in mind, we have developed a self-sculpting, three-dimensional model of epithelia whose dynamics are driven by active forces on its surface. Our model describes mechanical properties such as viscoelasticity, biologically relevant tissue geometry, fluid surroundings, and active forces that come from the localization of molecular motors to cell surfaces. We represent epithelial tissue as a thick slab, a 3D continuum comprised of a Stokes fluid with extra viscoelastic stress. Employing this model, we can make quantitative predictions about cell shapes, cell dynamics, and the tissue's response to force in a three-dimensional setting, allowing for physics-based studies of animal morphogenesis.