Geometric aspects of epithelial tissue mechanics

An epithelial tissue is a two-dimensional layer composed of biological cells adhered to each other, forming a structure similar to thin elastic sheet. In contrast with thin sheets elasticity, epithelial tissue mechanics is highly nonlinear, mostly due to the strong coupling between mechanics and biological activity. However, mechanics of epithelial tissues is poorly understood because even the simpler problem, of formulating a continuum theory for an inanimate cellular tissue, is still unsolved. In this talk I will show that the main property of inanimate epithelial tissues that distinguishes it from other materials is the presence of sets of local zero modes. Incorporating these zero modes into an elastic theory results in a generalized mechanical formalism that reproduces the salient characteristics observed in experiments and simulations. The continuum description is a powerful tool and the analysis bears many fruits: First, In a certain regime of parameters the theory allows an exact mapping to the mechanics of amorphous solids, a field from which we can port knowledge and predictions, and test against numerical and experimental realizations of epithelia. Second, a surprising prediction of the theory is the ability of epithelia to curve in three dimensions without stretching it. Third, the continuum description of materials with local zero-modes opens a venue for new problems of epithelial tissue, such as the melting transition in 2D and shaping mechanisms.