Cell size heterogeneity controls crystallization of the developing fruit fly wing

A transition from disordered to hexagonally ordered crystalline cellular packing occurs during the development of fruit fly wing. We investigate the biophysical mechanisms underlying this crystallization. While shear induced crystallization has been proposed as a mechanism for this disorder to order transition, our findings reveal that ordering could still occur even in the absence shear flows. Instead, we suggest that cell size heterogeneity controls crystallization in the developing fly wing. In particle systems, packing is disordered above a critical value of size heterogeneity and becomes crystalline below it. Similarly, using a vertex model of epithelial tissue, we demonstrate that when cell size heterogeneity exceeds a critical value, cellular packing remains disordered, whereas reducing it below this value induces a phase transition to crystalline packing. In the fruit fly wing, cell size heterogeneity decreases during development, promoting crystallization, while in a perturbed wing where heterogeneity remains high, packing remains disordered. Although shear flows are not the primary driver of the disorder to order transition, they support the process by aligning locally ordered regions, thereby enhancing tissue-scale order.