Vortices, space-time braids and loops in the membrane of a living cell

Topological defects determine the structure and function of matter over a wide range of scales. Many advances have been made in understanding and controlling the defect dynamics in active and passive non-equilibrium fluids. Yet, it remains unknown whether the statistical laws which govern the dynamics of defects in classical or quantum fluids extend to active living matter. Here, we show a defect-mediated turbulence underlies the complex wave propagation patterns of Rho-GTP signaling proteins on the membrane of starfish oocytes. Our experiments reveal that the phase-velocity field extracted from Rho-GTP concentration patterns exhibits vortical defect motions and annihilation dynamics reminiscent of those seen in quantum systems. Space-time analyses of defect trajectories reveal the existence of two characteristic types of braids: loops braided by multiple pairwise creation and annihilation events, and long-lived defect pairs that wiggle and form braid groups. Several key statistics and scaling laws of the defect dynamics, braids and loops can be captured by a generic complex Landau-Ginzburg continuum theory, suggesting space-time braids and loops are useful topological measures for unraveling information scrambling and transmission in dissipative living systems.