Active morphogenesis of epithelial monolayers.

During typical early-stage embryo development, single-cell-thick tissues of tightly bound epithelial cells autonomously generate profound changes in their shape, forming the basis of organism anatomy. We report on a (covariant) active-hydrodynamic theory of such monolayer morphogenesis that is closed under its shape-changing dynamics-i.e., the degrees of freedom that encode monolayer geometry appear properly as broken-symmetry variables. In our theory, the salient physics of tissue-scale deformations emerges from a balance between the displacement and/or shear of a low-Reynolds-number embedding fluid (the "yolk") and cell-autonomous stresses, themselves a result of combining apical contractile stresses with an elastic-like mechanical response under the constraint of constant cell volume. The leading-order hydrodynamic instabilities include both passive constrained-buckling and active deformation, which can be further categorized by cell shape changes that are either "squamous to columnar" or "regular-prism to truncated-pyramid." The deformations resulting from the latter qualitatively reproduce in vivo observations of the onset of both mesoderm and posterior midgut invaginations, which take place during gastrulation in the model organism Drosophila melanogaster.