Abstract
The physiological functions of several organs rely on branched epithelial tubule networks bearing specialized structures for secretion, gas exchange, or filtration. Little is known about conflicts in development between building enough tubules for adequate function and geometric constraints imposed by organ size. We show that the mouse embryonic kidney epithelium negotiates a physical packing conflict between increasing tubule tip numbers through branching and limited organ surface area. Through imaging of whole kidney explants, combined with computational and soft material modeling of tubule families, we identify six possible geometric packing phases, including two defective ones. Experiments in explants show that a radially oriented tension on tubule families is necessary and sufficient for them to switch to a vertical packing arrangement that increases surface tip density while avoiding defects. These results reveal developmental contingencies in response to physical limitations and create a framework for classifying congenital kidney defects.