Co-authors: Sebastian Aland (UC Irvine/TU Dresden), Jun Allard (UC Irvine)

Many cell processes involve the formation of membrane vesicles from a larger membrane, including endocytosis, inter-organelle transport and virus entry. These events are typically orchestrated by curvature-inducing molecules attached to the membrane, such as clathrin and bar-domain proteins. Recent reports demonstrate that in some circumstances vesicles can form de novo in a few milliseconds, e.g., ultrafast endocytosis at the neurological synapse. Membrane dynamics at these scales (millisecond, nanometer) are dominated by hydrodynamic interactions, as the membrane pushes the intracellular and extracellular fluids around to accommodate curvature. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. A new feature of this work is the implementation of the local inextensibility condition by using a local Lagrange multiplier harmonically extended off the interface. To make the method even more robust, we develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. This is critical to accurately capturing hydrodynamic effects during endocytosis. By varying the membrane coverage of curvature-inducing molecules, we find that there is a cri tical (smallest) neck radius and a critical (fastest) budding time.