Model of Membrane Delivery and Flow During Cytokinesis

During cytokinesis the cell surface area increases by up to 20%, requiring plasma membrane delivery to the division plane to prevent rupture through global stretching. As tension gradients develop, the plasma membrane must also undergo two-dimensional fluid-like deformations while preserving mechanical integrity. To understand membrane mechanics and hydrodynamics during cytokinesis, we focused on fission yeast where the rate of contractile ring constriction and spatial distribution and rates of exocytosis and endocytosis have been experimentally measured. We model the cell membrane as a 2D fluid with forces by cell wall and osmotic pressure pinning its shape along a curved shape. The contractile ring/septum growth provides a moving boundary condition of speed varying with time as measured in prior experiments. Conservation of mass and balance of forces determine time evolution local membrane density and flow. We find that membrane strain is higher at early stages of cytokinesis, which may relate to recent observations of Ca spikes primarily at these stages of division. Delivery of vesicles, especially the “rim” of the division plane through the TRAPP-II and exocyst complex pathways, leads to divergent flows with an outward flow pattern away from the division plane, as was recently observed with low mobility peripheral membrane proteins, and inward flows closer to the contractile ring. We discuss the importance of the spatiotemporal pattern of lipid trafficking in relationship to the unknown drag forces exerted by transmembrane proteins anchored to the cell wall, which determine the rate of membrane tension propagation and maximum strain. Overall, these theoretical results provide insights into how cells maintain membrane integrity for successful division.