Defect Driven Morphogenesis: Active Cell Division Generates Four-Fold Order

The generation of 2D hexagon-dominated topologies has been well studied in thermally equilibrated systems. Six-fold coordinated patterns also frequently arise in living matter far from equilibrium as a result of cell proliferation. We present a quantitative profile of exotic non-equilibrium pattern formation in the crustacean Parhyale hawaiensis. Active orchestration of cell proliferation transforms an initially disordered epithelial tissue into a regular rectangular lattice that cannot be explained by cell packing or randomly oriented divisions. Using light-sheet microscopy and computer vision techniques, we extract the dynamics of cell proliferation in the growing Parhyale embryo and quantify the spatiotemporal dependence of orientational order. In vivo cell tracking and lineage reconstruction together with simulation and theoretical modeling reveal the relationship between division axis orientation and both the emergence and preservation of order. Disorder introduced into the lattice by divisions must be mitigated by the active control of subsequent divisions in order to maintain the lattice structure in a program we call defect driven morphogenesis.