Viruses and the physics of soft condensed matter.

Almost 50 years ago, Francis Crick and James Watson observed that “almost all small viruses are either spheres or rods” and put forth the hypothesis that such viruses were symmetrical arrays of subunits (1). In the following paper in that issue of Nature , Donald Caspar demonstrated that tomato bushy stunt virus had at least cubic symmetry and provided the first evidence for icosahedral symmetry in a biological molecule (2). About half of all virus families share icosahedral geometry, even though they may have nothing else in common. In this issue of PNAS, Zandi et al. (3) have investigated the physical basis for the prevalence of icosahedral symmetry by using a simplest case model: circular elements tiling the surface of a more or less spherical solid. The resulting model can produce the complex behavior observed in solution experiments. Their results strongly support a corollary implicit in Crick's hypothesis: the physical properties of icosahedra lead to their prevalence in biology. Here, I will briefly discuss the paper by Zandi et al. and compare it to some recent theoretical and biochemical studies of virus structure and assembly. To understand the nature and application of Zandi et al. 's argument, it is probably best to start with a description of icosahedral symmetry. An icosahedron is 20-sided solid, where each facet has threefold symmetry (Fig. 1 A ). To build an icosahedron out of protein, each face must be made of at least three proteins, because an individual protein cannot have intrinsic threefold symmetry. In an icosahedron, the proteins are related by exact two-, three-, and fivefold symmetry axes. It turns out that few spherical viruses are built of 60 subunits (3 × 20), but most …