Design Principles for Robust Vesiculation in Clathrin-Mediated Endocytosis

Budding of membranes by protein coats is a universal phenomenon that is critically important in cellular trafficking pathways. Recent experiments have demonstrated that elevated membrane tension inhibits the ability of protein coats to deform membranes into buds. However, the robustness of 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 design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a modified Helfrich model for membrane mechanics and membrane protein interaction, we have 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 robust 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. Through systematic analyses of the different parameters contributing to membrane budding, we have identified potential ways of overcoming the energy barrier associated with the instability. For example, increasing the bending rigidity of the coat smooths out this instability, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can induce the transition from an open to a closed bud, bypassing the instability. Finally, a combination of increased coat rigidity and force from actin polymerization ensures robust vesiculation, even at high membrane tensions.