Modeling the Flat to Curved Transition during Clathrin Mediated Endocytosis

Abstract

Clathrin-mediated endocytosis is essential for the cellular uptake of receptors and nutrients. Although under investigation since decades, the exact sequence of structural and molecular events remains elusive. There are two basic models that have been suggested for the way it proceeds. In the constant curvature model, it is assumed that clathrin-coated pits grow with constant curvature, determined by the geometry of clathrin triskelia. In the constant area model, it is assumed that clathrin triskelia first assemble into flat hexagonal arrays that later invaginate at constant surface area. This second model implicitly assumes that during bending, some hexagons are converted into pentagons. Here, we integrate data sets from correlative electron and light microscopy and quantify the sequence of ultrastructural rearrangements of the clathrin coat during endocytosis in mammalian cells with the help of some simple mathematical growth laws. Our main assumption is that the clathrin domain can grow only over the boundary. In the case of flat arrays, this requires some balancing process to prevent a run-away process, which we assume to grow in proportion to the domain area. In the case of curved arrays, pit closure is sufficient to limit growth and thus an additional process is not required. Our analysis shows that clathrin-coated structures initially grow flat but start to acquire curvature when 70% of the final clathrin content is reached. We find that this transition correlates with a change in the ratio of clathrin to adaptor protein AP2, and that membrane tension suppresses this transition. Hence, our analysis suggests that elements of both suggested models are present and that mechanical and cellular factors will decide about the relative weights of growth versus curvature formation.