Necking of epithelial tissues with cellular topological transition.

As the cover of embryos and adult organisms, epithelial tissues are subjected to substantial mechanical forces in tissue morphogenesis. However, the finite deformation behaviors of epithelial tissues remain largely unexplored. This study combines discrete vertex simulations with an analytical constitutive model to investigate the necking behavior of epithelial tissues. In this model, the shape changes and topological transitions of single cells are associated with the elastic and inelastic components of tissue deformation via a mean-field formulation. Our results show that the necking bifurcation of a stretched tissue strongly associated with cellular topological transitions. The bifurcation condition and the steady state of necking propagation are predicted from the constitutive model and validated by vertex simulations. Furthermore, we find that topological defects in disordered tissues facilitate necking bifurcation but impede its propagation. These defects also induce the necked region to collapse into a thin thread, as observed in real tissues. Finally, our simulations show that necking also occurs under various tissue surface tensions and configurations (e.g., tubular geometry), demonstrating the generality of this behavior. Together, our work provides valuable insights into the deformation behaviors of epithelial tissues.