A Mean-Field Model for Active Plastic Flow of Epithelial Tissue

During morphogenesis, epithelial sheets drastically remodel to form tissues and organs. We rethink tissue mechanics in the limit where actively generated tension dominates over passive elasticity. Instead of being tied to cell shape via a constitutive relation, tensions are controlled by biomechanical feedback. Morphogenetic dynamics takes place on a timescale much slower than relaxation to force balance through adiabatic remodeling of active stresses. We call this behavior active plasticity. In force balance, we can represent the key cell scale degrees of freedom – internal active tensions – geometrically by a triangulation dual to the polygonal cell tiling. Motivated by experimental data from Drosophila, we study a key motif of epithelial morphogenesis, convergent extension by cell rearrangement. We use tension geometry to identify the relevant hydrodynamic variables that determine the morphogenetic behavior at large scales and systematically derive a mean field model for internally driven tissue flow. We show how local mechanical feedback couples to order in cell geometry, explaining the self-limiting nature of feedback-driven tissue flow observed in experiments and simulations, and predict how morphogenetic dynamics couples to external fields such as planar cell polarity and external forces.