Understanding the Concentration Dependence of Viral Capsid Assembly Kinetics - the Origin of the Lag Time and Identifying the Critical Nucleus Size

The kinetics for the assembly of viral proteins into a population of capsids can be measured in vitro with size exclusion chromatography or dynamic light scattering, but extracting mechanistic information from these studies is challenging. For example, it is not straightforward to determine the critical nucleus size or the elongation time (the time required for a nucleated partial capsid to grow completion). We show that, for two theoretical models of capsid assembly, the critical nucleus size can be determined from the concentration dependence of the assembly reaction half-life and the elongation time is revealed by the length of the lag phase. Furthermore, we find that the system becomes kinetically trapped when nucleation becomes fast compared to elongation. Implications of this constraint for determining elongation mechanisms from experimental assembly data are discussed.