Introduction to capsid architecture

protein molecule that is big enough to cover the entire genome-for a simple reason that one amino acid is coded by three nucleotides; hence, protein is always smaller than its gene. Therefore, multiple copies of coat protein are needed to enclose the genome. Since in many cases all coat protein monomers are identical, Watson and Crick reasoned that they are presumably engaged in the same protein-protein interactions with each other; that is, each monomer has identical protein environment [1]. Mathematically, there are only two ways to enclose a part of space by identical objects in identical environments. First, objects can be arranged in a helical fashion, thereby enclosing a cylindrical region of space. Second, objects can be arranged in facets of polyhedron, enclosing roughly spherical volume. There are only five regular polyhedrons (also called Platonic solids). Each face of the polyhedron can be divided into three (for tetrahedron, octahedron, and icosahedron), four (for cube), or five (for dodecahedron) identical triangles (Figure 1.1a). Therefore, tetrahedron, having 32 symmetry, can be regarded as built from 12 identical triangular units, cube and octahedron, having 432 symmetry-from 24 units, dodecahedron and icosahedron, both having 532 symmetry (Figure 1.1b)-from 60 units. Therefore, identical subunits enclose the biggest volume in 532 symmetrical arrangement. Viruses utilize both helical and icosahedral arrangement of subunits, although the latter seems to be more common.