  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
cell motility and polarization. Using linear stability analysis and numerical
simulations, we find that tissue behavior can be tuned between largely
homogeneous states and patterned states such as asters, controlled by a
composite "morphotaxis" parameter that encapsulates the nature of the coupling
between shape and polarization. The control parameter is in principle
experimentally accessible, and depends both on whether a cell tends to move in
the direction of lower or higher shear modulus, and whether sinks or sources of
polarization tend to fluidize the system.
