Topological Floppy Modes in Epithelial Tissue Network

The ordering, structure formation, and mechanical response in epithelial cells are essential to the functioning of many tissues. In this talk, we explore topological mechanics in a simple epithelial cell sheet starting described by a vertex model. We find that floppy modes in this model can become polarized based on the geometry of the cells, and domain boundaries with localized floppy modes can be observed. This simple model indicates a possible role for epithelial cell structure in directing mechanical responses. This topological mechanical polarization may be related to the mechanism of formation of Planar Cell Polarization (PCP), an intriguing phenomenon often seen in animal development, which is a polarization of a field of cells within the plane of a cell sheet to obtain directional information that is essential for diverse cellular processes.