Molecular biology by numbers … five

Watson and Crick are famous for the discovery of the double helix but there is a less widely known Ciba Symposium paper by Crick and Watson that puts forward a general theory of virus structure based on principles of assembly of subunits. Few people remember that Jim Watson came to Cambridge to work on the X-ray crystallography of tobacco mosaic virus; I suspect that had he not been distracted by DNA and genes he might have become a great force in structural biology. The argument in the Crick and Watson paper was that if the coats of viruses (now called capsids) are built of identical protein subunits, there would be a limited number of ways of assembling these to produce the regular structures found. Thus helical symmetry, where the subunits are related by a translation and a rotation, would generate rod-shaped viruses. In theory, these could grow to infinite length; Crick and Watson suggested that the fixed length of such viruses is determined by the length of the enclosed RNA molecule. For the assembled subunits of spherical viruses to enclose space, they argued, only three classes of symmetry are possible: 3:2 (as found in the tetrahedron), 4:3:2 (cube or octahedron) and 5:3:2. They concentrated on the last class, as it provides structures that approximate better to the spherical shells of viruses such as poliovirus. 5:3:2 is the symmetry found in the eicosahedron, which has 20 triangular faces (3-fold symmetry), 30 2-fold edges and 12 vertices through which the 5-fold axes pass. The same symmetry is shown by the dodeca-hedron, the dual of the eicosahedron, which has 12 pentagonal faces and 20 3-fold vertices. If one placed three subunits on each triangular face of an eicosahedron, they would be related by 5-fold symmetry at each vertex, 3-fold on the faces and 20-fold at the edges, hence 5:3:2. Crick and Watson therefore predicted that spherical virus coats would contain 60 identical protein molecules, or some multiple thereof, because the subunits may themselves be composed of dimers or trimers. The predictions of Crick and Watson have been completely vindicated by subsequent research on virus structure by electron microscopy and X-ray crystallography methods. The 5-fold way has come to stay. In conversation, I have speculated from time to time that these symmetry elements may be used in cells to build components where only one entity is required. This would circumvent the problem that it …