On the morphology of viral capsids: elastic properties and buckling transitions

The morphology of icosahedral viruses ranges from highly spherical to highly faceted, and for some viruses a shape transition occurs during the viral life cycle. This phenomena is predicted from continuum elasticity, via the buckling transition theory by Nelson (Phys. Rev. E 2003, 68, 051910), in which the shape is dependent on the Foppl-von Kármán number (γ), which is a ratio of the two-dimensional Young's modulus (Y) and the bending modulus (κ). However, until now, no direct calculations have been performed on atomic-level capsid structures to test the predictions of the theory. In this study, we employ a previously described multiscale method by May and Brooks (Phys. Rev. Lett. 2011, 106, 188101) to calculate Y and κ for the bacteriophage HK97, which undergoes a spherical to faceted transition during its viral life cycle. We observe a change in γ consistent with the buckling transition theory and also a significant reduction in κ, which facilitates formation of the faceted state. We go on to examine many capsids from the T = 3 and 7 classes using only elastic network models, which allows us to calculate the ratio Y/κ, without the expense of all-atom molecular dynamics. We observe for the T = 7 capsids, there is strong correlation between the shape of the capsid and γ; however, there is no such correlation for the smaller T = 3 viruses.