Theoretical Modeling of the Weaving of Clathrin into Nanoscale Baskets

Abstract

Many biological systems are capable of spontaneously assembling a diverse set of molecular architectures from a single subunit, without the need to pre-pattern the assembly. Cellular uptake of external substances is accomplished by a highly adaptive endocytosis process that accommodates a wide range of cargo shapes and sizes. Clathrin-mediated endocytosis involves the formation of a pit that is surrounded by a honeycomb coating whose pinwheel-shaped subunit is a clathrin-protein complex. We develop a theoretical model for the thermodynamics and kinetics of clathrin assembly, addressing the behavior in 2 and 3 dimensions, relevant to membrane and bulk assembly, respectively. The clathrin triskelions are modeled as effective flexible pinwheels that form leg-leg associations and resist elastic deformation. 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 Monte Carlo simulations to address thermodynamic behavior and Brownian dynamics simulations 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 Kosterlitz-Thouless theory of defect-induced melting in 2 dimensions. Using analytical theory and computational simulations, we explore the role of binding strength and clathrin elasticity in the ability for clathrin lattices to dynamically reorganize due to local changes in membrane elasticity and tension. We then proceed to discuss the dynamics of lattice reorganization during the process of a clathrin-coated membrane wrapping around a nanoscale cargo.