Effects of rim fluctuations in classical nucleation theory of virus capsids

Most spherical viruses exhibit icosahedral symmetry, yet the growth of viral shells remains poorly understood due to the short lifetimes and broad size distribution of assembly intermediates. Classical nucleation theory has been widely applied to describe this process, but it treats the boundary of a growing shell as rigid and structureless. Here, we extend classical nucleation theory by incorporating thermal fluctuations of the capsid rim using both discrete and continuum descriptions. Allowing the rim of a partially formed capsid to undergo small geometric undulations, we show that these fluctuations generate an entropic contribution that renormalizes the effective line tension. As a result, rim fluctuations can either promote or hinder capsid closure, depending on the subunit-subunit binding free energy, temperature, and fluctuation amplitude. We find that fluctuations generally lower the nucleation barrier when the binding free energy is below a threshold value, while for sufficiently strong binding, they can instead raise the barrier by stabilizing incomplete capsids through a finite-size entropy penalty associated with rim closure. By moving beyond the idealized capillarity approximation, our results provide a controlled extension of classical nucleation theory that clarifies how boundary fluctuations influence capsid nucleation and growth.