Design principles for robust vesiculation in clathrin-mediated endocytosis

Abstract A critical step in cellular trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a snapthrough instability in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to “snap” from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions. Significance statement Plasma membrane tension plays an important role in various biological processes. In particular, recent experimental studies have shown that membrane tension inhibits membrane budding processes like clathrin-mediated endocytosis (CME). We have identified a mathematical relationship between the curvature-generating capability of the protein coat and membrane tension that can predict whether the coat alone is sufficient to produce closed buds. Additionally, we show that a combination of increased coat rigidity and applied force from actin polymerization can produce closed buds at high membrane tensions. These findings are general to any membrane budding process, suggesting that biology has evolved to take advantage of a set of physical design principles to ensure robust vesicle formation across a range of organisms and mechanical environments. Author Contributions J.E.H., G.O., and P.R. designed research. J.E.H. performed research. J.E.H., D.G.D., and P.R. analyzed data. J.E.H., G.O., D.G.D., and P.R. wrote the paper.