Direct observation of topological turbulence in the oocyte membrane

Living systems self-organize local interactions into global structures and dynamics. Despite prevalence of such features across biological entities, the underlying self-organization principles have not been fully understood. Here we report on direct observation of a class of biochemical patterns formed during early development in starfish oocytes. The observed patterns maintain long-live structures despite short molecular turn-over times, and each pattern has distinguishing wavelength and orientation in spite of sharing the same local interaction rules. Through field analysis, we find that phase singularity dynamics in the chemical field dominates evolution of observed patterns. The pair interactions between the point singularities drive topological turbulence in phase velocity field. Such topological turbulence shares the same characteristic vortex size across observed patterns, reminiscent of quantum turbulence feature. An Onsager vortex model with pairwise interaction potential captures the essential features of the experimentally observed phase singularity dynamics. We propose topological turbulence in phase velocity field underlies dynamics of the observed self-organized biochemical patterns, propagating order from local molecular to global cellular scales.