Statistical mechanical model of the energetics of coated vesicle formation

Adsorptive endocytosis is mediated by a structural transformation of a two-dimensional hexagonal lattice to a polyhedron or coated vesicle. Clathrin is the structural protein involved in this process. A theoretical model that focuses on the energetics of clathrin in coated vesicle formation is presented. Fisher's cluster model of phase transitions is applied to this problem. The equilibrium constant for the process of converting a large two-dimensional patch to a coated vesicle and a smaller patch is calculated. There are three energetic contributions to be considered. They are the surface energy, the interior or lattice energy, and a loop entropy. Features of the Ising model are introduced into this model by scaling the critical exponents. In determining the configurational partition functions required for equilibrium constant calculations, the polyhedron is represented as a planar graph with no surfaces. The equilibrium constants are extremely sensitive to changes in the lattice and surface energies. The loop entropy contributions favor bimodal distributions in vesicle size under certain conditions. Conditions can also be established where the energy required to form the vesicle is small.