(746e) Theoretical Modeling of the Weaving of Clathrin Into Nanoscale Baskets

Clathrin is a protein that plays a major role in the creation of membrane-bound transport vesicles in cells. Clathrin forms soccer-ball-shaped lattices that coat a new vesicle as it forms. The clathrin molecule is known to take the shape of a triskelion, a pinwheel-shaped structure with three bent legs. In vitro assembly of clathrin within a solution results in closed, nanoscale assemblies with various shapes and sizes. To understand how clathrin functions, particularly how it forms the lattice, we develop a theoretical model for the thermodynamics and kinetics of clathrin assembly in order to guide experiments toward the design of targeted nanoscale structures. Our model addresses the behavior in 2 and 3 dimensions, relevant to membrane/surface and bulk assembly, respectively. The clathrin triskelions are modeled as effective flexible pinwheels that form leg-leg associations and resist bending, twisting and stretching deformations. Thus, the pinwheels are capable of forming a range of ring structures, including 5-, 6-, and 7-member rings that are observed experimentally. Our theoretical model employs Brownian dynamics to track the motion of clathrin pinwheels at sufficiently long time scales to achieve complete assembly. With this theoretical model, we predict the phase diagram for clathrin assembly incorporating binding interactions, elastic deformation, and defect-pair coupling, utilizing the Kosterlitz?Thouless theory of defect-induced melting in 2 dimensions. In two-dimensional system, we account for the existence of topological defects whose interactions diverge logarithmically with separation distance between defects, which is determined through large scale energy optimization of our model. To verify the phase diagram, we perform dynamic simulations for a range of quenches into the phase diagram and compare phase separation across the binodal curve. We show that the resulting Brownian dynamics simulations exhibit the hallmark behavior of spinodal decomposition with subsequent coarsening of ordered domains. These simulations demonstrate the effect of quench rate and leg elasticity on the final configurations of the lattice network and cluster-size distribution. The three dimensional pinwheel model exhibits cage formation upon sudden increase of leg-leg associations, consistent with experimental observations. Our simulated size distribution of assembled cages will be compared with experimental distributions attained from light scattering (Heilshorn lab, Department of Materials Science and Engineering, Stanford University). We will then proceed to discuss the assembly of specific nanoscale structures.