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.

How tissue shape emerges from the collective mechanical properties and behavior of individual cells is not understood. We combine experiment and theory to study this problem in the developing wing epithelium of Drosophila. At pupal stages, the wing-hinge contraction contributes to anisotropic tissue flows that reshape the wing blade. Here, we quantitatively account for this wing-blade shape change on the basis of cell divisions, cell rearrangements and cell shape changes. We show that cells both generate and respond to epithelial stresses during this process, and that the nature of this interplay specifies the pattern of junctional network remodeling that changes wing shape. We show that patterned constraints exerted on the tissue by the extracellular matrix are key to force the tissue into the right shape. We present a continuum mechanical model that quantitatively describes the relationship between epithelial stresses and cell dynamics, and how their interplay reshapes the wing.DOI: http://dx.doi.org/10.7554/eLife.07090.001

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.

Epithelial tissues develop planar polarity that is reflected in the global alignment of hairs and cilia with respect to the tissue axes. The planar cell polarity (PCP) proteins form asymmetric and polarized domains across epithelial junctions that are aligned locally between cells and orient these external structures. Although feedback mechanisms can polarize PCP proteins intracellularly and locally align polarity between cells, how global PCP patterns are specified is not understood. It has been proposed that the graded distribution of a biasing factor could guide long-range PCP. However, we recently identified epithelial morphogenesis as a mechanism that can reorganize global PCP patterns; in the Drosophila pupal wing, oriented cell divisions and rearrangements reorient PCP from a margin-oriented pattern to one that points distally. Here, we use quantitative image analysis to study how PCP patterns first emerge in the wing. PCP appears during larval growth and is spatially oriented through the activities of three organizer regions that control disc growth and patterning. Flattening morphogen gradients emanating from these regions does not reduce intracellular polarity but distorts growth and alters specific features of the PCP pattern. Thus, PCP may be guided by morphogenesis rather than morphogen gradients.