Crystallographic structural organization of human rhinovirus serotype 16, 14, 3, 2 and 1A

The architecture of the human rhinovirus is shown to be based on a crystallographic polyhedron (the ico-dodecahedron) with 60 triangular facets and 32 vertices at points of a body-centered icosahedral lattice. The ico-dodecahedron is only slightly different from the T = 3 icosadeltahedron of Caspar & Klug [Cold Spring Harbor Symp. Quant. Biol. (1962), 27, 1-24]. The capsid of the virion is encapsulated between two ico-dodecahedra in scaling relation by a factor tau, the golden number. Clusters with axial symmetry of the coat proteins VP1, VP2, VP3 and VP4 are considered (decamers, pentamers, hexamers, trimers and tetramers). Their crystallographic enclosing forms obey the same laws as a number of axial-symmetric proteins, involving planar and linear crystallographic scaling relations and having vertices at points of lattices with an integral metric tensor. These properties also occur for the icosahedral cluster of each coat protein viewed along the symmetry axes (fivefold, threefold and twofold, respectively). The structural organization of the rhinovirus in terms of all these enclosing forms is independent of the serotype (16, 14, 3, 2, 1A) and is typical for a strongly correlated system, as it depends on one single free parameter, taken to be the icosahedral lattice parameter a0, which relates the geometry with the real structure (up to small variations).