Assembly of viruses and the pseudo-law of mass action.

The self-assembly of the protein shell ("capsid") of a virus appears to obey the law of mass action (LMA) despite the fact that viral assembly is a nonequilibrium process. In this paper we examine a model for capsid assembly, the "assembly line model," that can be analyzed analytically. We show that, in this model, efficient viral assembly from a supersaturated solution is characterized by a shock front propagating in the assembly configuration space from small to large aggregate sizes. If this shock front can reach the size of assembled capsids, then capsid assembly follows either the LMA or a "pseudo" LMA that describes partitioning of capsid proteins between assembled capsids and a metastable, supersaturated solution of free proteins that decays logarithmically slowly. We show that the applicability of the LMA and the pseudo-LMA is governed by two dimensionless parameters: the dimensionless nucleation rate and the dimensionless line energy of incomplete capsids.