Topological braiding and bosonic phases on the cell membrane

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and has been extensively studied in the context of topological quantum computation. By contrast, braiding of topological defects in the signaling waves of living systems remains poorly understood. Here, we investigate the self-organized Rho-GTP protein waves formed on the membrane of starfish egg cells during cell division. We show that the worldlines of spiral wave cores embedded in the signaling waves undergo rich spontaneous braiding dynamics, and are also capable of forming intricate loop structures. The worldline creation and annihilation events, topological entropy and braiding exponents, as well as loop statistics correlate with cellular activity and exhibit universal scaling behaviors, in agreement with predictions from a generic complex Ginzburg-Landau continuum theory with a tunable activity parameter. Our analysis further reveals that the braiding dynamics is dominated by same-sign defect pairs displaying bosonic exchange symmetry, suggesting an unexpected parallel between information processing processes in quantum and living matter, which can be further investigated using optical controls in this biological system.