Geometric coordination of endothelial invasion and vascular patterning during epithelial morphogenesis
As organs grow and remodel in three dimensions, developing vascular networks extend through the tissue while maintaining spatial coordination and establishing connections between distant sprouts. How local endothelial behavior generates vascular patterns within such deforming environments remains poorly understood. Here, using the developing mouse epididymis, we combine two-photon live microscopy, pharmacological perturbations, and mathematical modeling to investigate angiogenesis alongside epithelial tubule folding. Endothelial cells invade the organ interior while maintaining proximity to the deforming tubule. Live imaging reveals dynamic protrusions directed toward the epithelium and a characteristic sequence in which endothelial fronts approach the tubule, stop, and maintain their separation despite continued folding. ERK activity promotes endothelial extension and declines during the transition to distance maintenance. From these observations, we derive a minimal follow-and-stop rule that captures endothelial positioning relative to the changing epithelium. Extending this model to three dimensions reveals how epithelial folding can bring otherwise distant endothelial fronts together, creating opportunities for vascular connection. Explants exhibiting greater three-dimensional folding also show a higher observed frequency of endothelial connections. Our findings support a geometric framework in which local endothelial dynamics and tissue-scale deformation can jointly contribute to vascular patterning during organ morphogenesis.