Numerical study of dynamic zigzag patterns in migrating epithelial tissue

Collective cell migration plays a crucial role in embryonic development, metastasis, and wound healing. Nevertheless, to the best of our knowledge, how the coordination between the cell motility and deformations affects the collective motion of epithelial cells is not fully understood. In this work, we propose a modified self-propelled Voronoi model for epithelial cell migration incorporating the coupling between the self-propulsion of cells and the polarization of the cell elongation. At a high coupling strength,we observe the emergence of backward traveling band structures formed by highly aligned cells, which can be regulated by cell elongations or shape anisotropy. Increasing the cell shape anisotropy, we find that large bands split into multiple small microbands. The latter essentially forms a dynamic zigzag pattern, in which the angle between the polarization direction of the bands and the migration direction switches alternatively between π/4 and-π/4 because the cells are forced to move preferentially in the anterior direction. We also analyzed the disclinations in the cell monolayer, force distribution near the domain boundaries and the shape alignment of the epithelial monolayer during the formation of this dynamic pattern. The present findings may further our understanding of stripe pattern formations in living systems and inspire potential designs for cell sorting.