Modeling Self-Assembly of Objective Structures

Virus capsids have evolved for millions of years to efficiently self-assembled out of many protein sub-units. We wish to understand and model the fundamentals of this assembly to further synthetic self-assembly and hinder undesired virus assembly. All viruses have a symmetric structure, in the sense that each sub-unit sees the exact same environment in the assembled state. We call the class of all such structures "objective structures" and these can be characterized by translations and rotations of the sub-unit. To model the equilibrium and dynamics of assembly, the three-dimensional rotation and translation of each sub-unit must be included. Simulations using the overdamped Langevin equation with rotation show the equilibrium distribution as a function of temperature. The temperature at which an objective structure undergoes a phase transformation between disordered and assembled compare favourably to predictions from a Smoluchowski equation with rotation, which we derive. This equation could also be used to model the dynamics of assembly.