From Topological Defects to Embryos — How Surface Geometry Controls Bulk Organisation

Anna Erzberger

Despite their central importance in ordered systems including living matter, how topological defects are controlled in three dimensions remains unclear. We investigated 3D defect configurations in boundary-aligned polar fluids, and found that boundary geometry controls charge-preserving transitions in the number and type of defects. Applying our findings to living matter, we discovered that 3D polar defect positions determine the sites of lumen formation in embryonic development -- structures important for embryo viability. Experimentally perturbing embryo shape beyond the transition point results in additional lumen initiation sites at the predicted positions. Our work reveals how surface geometry can control 3D polar defect configurations, 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.