How topology influences force chains in networks of epithelial cells

In some epithelial tissues under external mechanical stress cells are arranged in a stationary brick-like pattern where the cells form rows parallel to the high stress axis. This facilitates the creation of multicellular action-myosin cables which oppose the external stress. However, when an external mechanical stress causes calls to flow past one another they exchange neighbors in a way that forms rows of cells perpendicular to the high stress axis. We propose a metric for distinguishing between these two orientations for cells in a disordered tissue based on geometric properties of the cells as they are strained with fixed edge length. We also describe the different types of coordinated topological changes that cells can undergo to move between the two distinct patterns.