Background: Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms that likely control the biophysical properties of cells and their interactions.
Results: To understand how physical cellular properties and proliferation determine cell-packing geometries, we use a vertex model for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations. The model takes into account cell elasticity and junctional forces arising from cortical contractility and adhesion. By numerically simulating proliferation, we generate different network morphologies that depend on physical parameters. These networks differ in polygon class distribution, cell area variation, and the rate of T1 and T2 transitions during growth. Comparing theoretical results to observed cell morphologies reveals regions of parameter space where calculated network morphologies match observed ones. We independently estimate parameter values by quantifying network deformations caused by laser ablating individual cell boundaries.
Conclusions: 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.