From an affine extended icosahedral group towards a toolkit for viral architecture

The affine extensions (there are 55 different ones) of the icosahedral group developed by T. Keef and R. Twarock of the York Centre for Complex Systems Analysis of the University of York [see in particular Keef et al. (2013). Acta Cryst. A69, 140-150], and applied to the investigation of the architecture of a number of icosahedral viruses, are here considered in the framework of molecular crystallography. The basic ideas of such molecular description involve positions with rational indices which approximate backbone positions in viral polypeptide and RNA chains. The test case of the Pariacoto virus suggests that the best-fit algorithm used in the York group's approach should be adapted to a more specific toolkit suited for the investigation of the architecture of icosahedral viruses. Typical problems which could be solved by means of such a toolkit are exemplified and put in the perspective of viral properties.