Generating convergent-extension flows in a model epithelial tissue with active feedback

Epithelial tissues undergo significant structural changes during development. An example is convergent-extension, which is observed during gastrulation and germ band extension. This involves tissue elongation in one direction, accompanied by narrowing in the perpendicular direction, mediated by active processes acting on mechanical or chemical tissue polarisation. However, we lack a mechanical understanding of how these changes occur. Here, we present a continuum model for an epithelial tissue with catch-bond type feedback for the actomyosin cortex, due to an anisotropic distribution of myosin molecular motors regulated by tension. We add this to a viscoelastic model tissue which is embedded in a background fluid that provides friction, inspired by physics of chick embryo gastrulation. Using an explicit numerical solution of the two-dimensional model, we find steady-state solutions with anomalous viscoelastic coefficients, as well as oscillations of the tissue that are triggered at sufficiently strong activity. We complement these findings with a linear response theory of this system, which shows that shear modes dominate the instability.