Hydrodynamics of shape-driven rigidity transitions in motile confluent tissues

In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell polarization and motility might be governed by the internal shear stiffness of nearby tissue, deemed ``plithotaxis''. Meanwhile, other work has demonstrated that there is a direct relationship between cell shapes and tissue shear modulus in confluent tissues. Joining these two ideas, we develop a hydrodynamic model that couples cell shape, and therefore tissue stiffness, to collective cell motility. Linear stability analysis indicates that the formation of aster-like and banding patterns in these tissues is controlled by a composite ``morphotaxis'' parameter which encapsulates the influence of inhomogeneities in cell shape on collective cell migration and vice versa.