Dynamic Morphoskeletons in Development

Morphogenetic flows in developmental biology are characterized by the coordinated motion of thousands of cells that organize into tissues, naturally raising the question of how this collective organization arises. Using only the Lagrangian kinematics of tissue deformation, which naturally integrates local and global mechanisms along cell paths, we can identifying the Dynamic Mor- phoskeletons (DM) behind morphogenesis, i.e., the evolving centerpieces of multi-cellular trajectory patterns. The DM is model and parameter-free, frame-invariant, robust to measurement errors, and can be computed from unfiltered cell velocity data. It reveals the spatial attractors and repellers of the embryo, objects that cannot be identified by simple trajectory inspection or Eulerian meth- ods that are local and typically frame-dependent. Computing the DM underlying primitive streak formation in chicken embryo and early gastrulation in the whole fly embryo, we find that the DM captures the early footprint of known morphogenetic features, and reveals new ones, providing a geometric framework to analyze tissue organization.