The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.

Planar cell polarity (PCP) proteins form polarized cortical domains that govern polarity of external structures such as hairs and cilia in both vertebrate and invertebrate epithelia. The mechanisms that globally orient planar polarity are not understood, and are investigated here in the Drosophila wing using a combination of experiment and theory. Planar polarity arises during growth and PCP domains are initially oriented toward the well-characterized organizer regions that control growth and patterning. At pupal stages, the wing hinge contracts, subjecting wing-blade epithelial cells to anisotropic tension in the proximal-distal axis. This results in precise patterns of oriented cell elongation, cell rearrangement and cell division that elongate the blade proximo-distally and realign planar polarity with the proximal-distal axis. Mutation of the atypical Cadherin Dachsous perturbs the global polarity pattern by altering epithelial dynamics. This mechanism utilizes the cellular movements that sculpt tissues to align planar polarity with tissue shape.

Summary Axis elongation in Drosophila occurs through polarized cell rearrangements driven by actomyosin contractility. Myosin II promotes neighbor exchange through the contraction of single cell boundaries, while the contraction of myosin II structures spanning multiple pairs of cells leads to rosette formation. Here we show that actomyosin cables form at a higher frequency than expected by chance during elongation, indicating that cable assembly is an active process. Multicellular cables are sites of increased mechanical tension as measured by laser ablation. Fluorescence recovery after photobleaching experiments show that myosin II is stabilized at the cortex in regions of increased tension. Myosin II is recruited in response to an ectopic force and relieving tension leads to a rapid loss of myosin, indicating that tension is necessary and sufficient for cortical myosin localization. These results demonstrate that myosin II dynamics are regulated by tension in a positive feedback loop that leads to actomyosin cable formation and efficient tissue elongation.

Epithelia are sheets of cells that are dynamically remodelled by cell division and cell death during development. Here we describe the cell shapes and packings as networks of polygons: stable and stationary network configurations obey force balance and are represented as local minima of a potential function. We characterize the physical properties of this vertex model, including the set of ground states, and the energetics of topological rearrangements. We furthermore discuss a quasistatic description of cell division that allows us to study the mechanics and dynamics of tissue remodelling during growth. The biophysics of cells and their rearrangements can account for the morphology of cell packings observed in experiments.

The agreement between our results and modeling suggests that the force generators themselves have the intrinsic capability of generating oscillations when opposing forces exceed a threshold.