Topological turbulence in the membrane of a living cell

Topological defects determine the structure and function of physical and biological matter over a wide range of scales, from the turbulent vortices in planetary atmospheres, oceans or quantum fluids to bioelectrical signalling in the heart(1-3) and brain(4), and cell death(5). Many advances have been made in understanding and controlling the defect dynamics in active(6-9) and passive(9,10) non-equilibrium fluids. Yet, it remains unknown whether the statistical laws that govern the dynamics of defects in classical(11) or quantum fluids(12-14) extend to the active matter(7,15,16) and information flows(17,18) in living systems. Here, we show that a defect-mediated turbulence underlies the complex wave propagation patterns of Rho-GTP signalling protein on the membrane of starfish egg cells, a process relevant to cytoskeletal remodelling and cell proliferation(19,20). Our experiments reveal that the phase velocity field extracted from Rho-GTP concentration waves exhibits vortical defect motions and annihilation dynamics reminiscent of those seen in quantum systems(12,13), bacterial turbulence(15) and active nematics(7). Several key statistics and scaling laws of the defect dynamics can be captured by a minimal Helmholtz-Onsager point vortex model(21) as well as a generic complex Ginzburg-Landau(22) continuum theory, suggesting a close correspondence between the biochemical signal propagation on the surface of a living cell and a widely studied class of two-dimensional turbulence(23) and wave(22) phenomena. Activity in certain living systems can lead to swirling flows akin to turbulence. Here, the authors connect the dynamics of topological defects in starfish oocyte membranes to vortex dynamics in 2D Bose-Einstein condensates.