Mechanical effects of cell anisotropy on epithelia.

Theoretical, numerical and experimental methods are used to develop a comprehensive understanding of how cell shape affects the mechanical characteristics of two-dimensional aggregates such as epithelia. This is an important step in relating the mechanical properties of tissues to those of the cells of which they are composed. Statistical mechanics is used to derive formulas for the in-plane stresses generated by tensions gamma along cell-cell interfaces in sheets with anisotropic cellular fabric characterized by average cell aspect ratio kappa. These formulas are then used to investigate self-deformation (strain relaxation) of an anisotropic sheet composed of cells of thickness h and having effective viscosity mu. Finite element simulations of epithelia and of isolated cells and novel relaxation studies of specimens of embryonic epithelia reported herein are consistent with the predictions of the theory. In all cases, geometric factors cause the relaxation responses to be more complex than a single decaying exponential.