(117a) Invited: Theoretical Modeling of Clathrin Self-Assembly On an Undulating Membrane

Clathrin proteins stabilize the budding and curvature of cell membranes that are characteristic of endocytosis, the process by which cells internalize cargo. These elastic, three-legged, pinwheel-like triskelia are also capable of aggregating into a diverse array of two- and three-dimensional nanostructures. Observations of clathrin aggregation on membranes in vivo show the proteins forming two distinct structures, depending on membrane conditions. Specifically, large, crystalline “plaques” are observed predominantly where the underlying membrane is adhered to a rigid substrate, while short-lived, high-curvature “pits” are found on all membranes. Such findings indicate a pathway through which intercellular transport is modulated by the surrounding environment. We develop a simplified physical model of clathrin self-assembly to address the physical mechanisms that underlie the observed experimental behavior. In this model, the proteins bind to one another to form honeycomb lattices (6-membered rings) on flat surfaces, and insert non-6-membered defects and void spaces into this lattice depending on the elastic properties and binding affinities of the subunits. Our model also predicts the lattice’s response to membrane indentations, such as those occurring in the initial stages of endocytosis. When a spherical indentation is imposed on a crystalline lattice, the structure tears apart and gives way to a void space around the indentation. We observe the opposite effect when an indentation is imposed on a fluid clathrin phase, as the proteins aggregate into a localized crystalline patch. These conditions mimic those found often in cells undergoing endocytosis. During this process, the bulk of the membrane is freely fluctuating, while a localized patch wraps intercellular cargo. Our results indicate that the physical structure of the clathrin subunit is ideal for facilitating cell uptake, and the modulation of forces felt by the membrane plays a critical role in this process.