Active geometrodynamics predicts the emergence of cytokinesis

Cell division accomplishes the segregation of genetic material and involves remarkable changes in the cellular geometry culminating in cytokinesis: the cleavage of a mother cell giving rise to two daughter cells. Cytokinesis in animal cells is driven by flows resulting from cortical tension gradients in the actomyosin cortex. Here, we combine a theory for the active geometrodynamics of the cortical surface and quantitative measurements in the C. elegans zygote to reveal the physical principles of cytokinesis. At high activity, we observe the spontaneous emergence of ring-like patterns of myosin concentration and cell shape in the theory. The constriction dynamics of this self-organized pattern agrees with the ingression of the cytokinetic furrow and concomitant myosin accumulation during the first division in the C. elegans embryo. Through RNAi perturbations, we quantitatively test our theoretical predictions of myosin accumulation rates linearly varying with the ingression rate, and the emergence of asymmetric ingression. Our work suggests that the self-organised geometrodynamics of active fluid surfaces underlies cytokinesis.