  Morphogenetic dynamics of tissue sheets require coordinated cell shape
changes regulated by global patterning of mechanical forces. Inspired by such
biological phenomena, we propose a minimal mechanochemical model based on the
notion that cell shape changes are induced by diffusible biomolecules that
influence tissue contractility in a concentration-dependent manner -- and whose
concentration is in turn affected by the macroscopic tissue shape. We perform
computational simulations of thin shell elastic dynamics to reveal propagating
chemical and three-dimensional deformation patterns arising due to a sequence
of buckling instabilities. Depending on the concentration threshold that
actuates cell shape change, we find qualitatively different patterns. The
mechanochemically coupled patterning dynamics are distinct from those driven by
purely mechanical or purely chemical factors. Using numerical simulations and
theoretical arguments, we analyze the elastic instabilities that result from
our model and provide simple scaling laws to identify wrinkling morphologies.
