Boundary geometry controls a topological defect transition that determines lumen nucleation in embryonic development

Topological defects determine the collective properties of anisotropic materials. Nonetheless, it is not fully understood how their configurations are controlled, especially in three dimensions. In living matter, contributions of two-dimensional topological defects to biological functions have been demonstrated, but whether three-dimensional polar defects have any biological relevance is unclear. Here we report a charge-preserving transition between three-dimensional defect configurations driven by boundary geometry and independent of material parameters. Moreover, we find that three-dimensional polar defects in the mouse embryo are the sites where fluid-filled lumina form, essential structures for subsequent development. We validate these findings by experimentally perturbing embryo shape beyond the transition point, which results in the creation of additional lumen initiation sites near predicted defect locations. Overall, our results reveal how boundary geometry controls polar defects, and how embryos use this mechanism for shape-dependent lumen formation. We expect this defect-control principle to apply broadly to systems with orientational order.