Form, symmetry and packing of biomacromolecules. V. Shells with boundaries at anti-nodes of resonant vibrations in icosahedral RNA viruses

The RNA viruses cowpea chlorotic mottle, satellite tobacco mosaic, pariacoto and MS2, already considered in part IV of this series of papers [Janner, A. (2011a), Acta Cryst. A67, 517–520], are investigated fur­ther, with the aim to arrive at a possible physical basis for their structural properties. The shell structure of the filled capsid is analyzed in terms of successive spherical boundaries of the sets of icosahedral equivalent chains. By inversion in the sphere enclosing the capsid, the internal boundaries are trans­formed into external ones, which are more easily visualized. This graphical procedure reveals the presence of regularly spaced shells with boundaries fitting with anti-nodal surfaces of the virus considered as an elastic resonator. The centers of gravity of the various chains occur in the nodal regions of eigen­vibrations with wavelength λ = R₀/K₀, where R₀ is the radius of the virus and K₀ takes one of the values 12, 6, 4, 3, depending on the mode. The resonator model is consistent with practically all spherical shell boundaries, whereas deviations are observed for the icosahedral axial modes, which apparently play a secondary role with respect to the spherical ones. Both the spherical and the axial anti-nodal surfaces fit very well with the packed structure of the viruses in the crystal which, accordingly, is expected to have eigenfrequencies related to those of the virus. These results open the way to a better understanding of the possibility of breaking the capsid using resonant forced oscillations excited, for example, by an applied elastic shock or by irradiation with femtosecond laser pulses, as already realised by K.-T. Tsen and co-workers. An alternative `ply­wood' model connected to the extreme elastic properties of the capsid is also considered.