Eden growth models for flat clathrin lattices with vacancies

Abstract

Clathrin-mediated endocytosis is one of the major pathways by which cells internalise cargo molecules. Recently it has been shown that clathrin triskelia can first assemble as flat lattices before the membrane starts to bend. However, for fully assembled clathrin lattices high energetic and topological barriers exist for the flat-to-curved transition. Here we explore the possibility that flat clathrin lattices grow with vacancies that are not visible in traditional imaging techniques but would lower these barriers. We identify the Eden model for cluster growth as the most appropriate modeling framework and systematically derive the four possible variants that result from the specific architecture of the clathrin triskelion. Our computer simulations show that the different models lead to clear differences in the statistical distributions of cluster shapes and densities. Experimental results from electron microscopy and correlative light microscopy provide first indications for the model variants with a moderate level of lattice vacancies.

The structure and spontaneous curvature of clathrin lattices at the plasma membrane

“…This is consistent with visibly broken lattices observed in platinum replica data. In agreement with a recently introduced model, 39 our ultrastructural analysis suggests flat clathrin are also not fully saturated with triskelia at each vertex. With the loss of a flattening force, and the aid of curvature inducing proteins, the lattice spontaneously assumes the curved state to form a vesicle.…”

“…Therefore, we support a model where flat lattices are not saturated with triskelia. 39 Beyond these breaks, holes in the lattice differed in size and were not organized according to regular hexagonal lattice packing. Such packing would maintain equal sides and angles and linear arrays of holes.…”

Superresolution microscopy reveals partial preassembly and subsequent bending of the clathrin coat during endocytosis

“…To overcome this frustration, they would have to adjust their positions relative to their neighbors, such that their free energy is getting more favorable. Second, lattice vacancies could be filled up with new triskelia, as predicted theoretically [4]. Note that these vacancies would not necessarily relate to patch area, because the clathrin lattice consists of many overlapping arms.…”

“…It is however likely that the properties of the clathrin coat change during endocytosis, e.g. by coat stiffening or increasingly tight interactions between triskelia (Frey and Schwarz, 2020; Frey et al, 2020; Sochacki et al, 2021).…”

More than just a barrier: using physical models to couple membrane shape to cell function

“…123,124 The assembly of flat and invaginated clathrin lattices was suggested to result from triskelia which occur in a flat and curved configuration and from lattices that exhibit lattice vacancies. 125,126 The dynamics of clathrin coat assembly can be modeled by kinetic growth equations. A comparison of this model with the experimentally measured size and shape distribution of clathrin coated membranes suggests that clathrin coats first assemble flat before they start to curve.…”