In developing their theories about virus structure, Caspar and Klug used graphic illustrations of capsid subunits, such as the net of flat hexagons shown at the top left of panel A in the figure. Each hexagon represents a hexamer, with identical subunits shown as equilateral triangles. When all subunits assemble into such hexamers, the result is a flat sheet, or lattice, which can never form a closed structure. To introduce curvature, and hence form three-dimensional structures, one triangle is removed from a hexamer to form a pentamer in which the vertex and faces project above the plane of the original lattice (A, far right). As an icosahedron has 12 axes of fivefold symmetry, 12 pentamers must be introduced to form a closed structure with icosahedral symmetry. If 12 adjacent hexamers are converted to pentamers, an icosahedron of the minimal size possible for the net is formed. This structure is built from 60 equilateral-triangle asymmetric units and corresponds to a T = 1 icosahedron (Fig. 4.9B). Larger structures with icosahedral symmetry are built by including a larger number of equilateral triangles (subunits) per face (Fig. 4.10). In the hexagonal lattice, this is equivalent to converting 12 nonadjacent hexamers to pentamers at precisely spaced and regular intervals.
To illustrate this operation, we use nets in which an origin (O) is fixed and the positions of all other hexamers are defined by the coordinates along the axes labeled h and k, where h and k are any positive integer (A, left). The hexamer (h, k) is therefore defined as that reached from the origin (O) by h steps in the direction of the h axis and k steps in the direction of the k axis. In the T = 1 structure, h = 1 and k = 0 (or h = 0 and k = 1), and adjacent hexamers are converted to pentamers. When h = 1 and k = 1, pentamers are separated by one step in the h and one step in the k direction. Similarly, when h = 2 and k = 0 (or vice versa), two steps in a single direction separate the pentamers.
The triangulation number, T, is the number of asymmetric units per face of the icosahedron constructed in this way. It can be shown, for example by geometry, that
T = h2 + hk + k2
Therefore, when both h and k are 1, T = 3, and each face of the icosahedron contains three asymmetric units. The total number of units, which must be 60T, is 180. When T = 4, there are four asymmetric units per face and a total of 240 units (Fig. 4.10).
As the integers h and k describe the spacing and spatial relationships of pentamers, that is, of fivefold vertices in the corresponding icosahedra, their values can be determined by inspection of electron micrographs of virus particles or their constituents (B). For example, in the bacteriophage p22 capsid (B, top), one pentamer is separated from another by two steps along the h axis and one step along the k axis, as illustrated for the bottom left pentamer shown. Hence, h = 2, k = 1, and T = 7. In contrast, pentamers of the herpes simplex virus type 1 (HSV-1) nucleocapsid (bottom) are separated by four and zero steps along the directions of the h and k axes, respectively. Therefore, h = 4, k = 0, and T = 16.
Recent application of the principles applied by Caspar and Klug to other uniform lattices that can form icosahedra has generalized the theory of quasiequivalence to account for structures of virus particles that appeared as exception, for example, T = 2 protein shells.
Cryo-electron micrographs of bacteriophage p22 and HSV-1 courtesy of B.V.V. Prasad and W. Chiu, Baylor College of Medicine, respectively.
EXPERIMENTS
Viral chain mail: not the electronic kind
The mature capsid of the tailed, double-stranded DNA bacteriophage HK97 is a T = 7 structure built from hexamers and pentamers of a single viral protein, Gp5. The first hints of the remarkable and unprecedented mechanism of stabilization of this particle came from biochemical experiments, which showed the following:
A previously unknown covalent protein-protein linkage forms in the final reaction in the assembly of the capsid: the side chain of a lysine in every Gp5 subunit forms a covalent isopeptide bond with an asparagine in an adjacent subunit. Consequently, all subunits are joined covalently to each other.
This reaction is autocatalytic, depending only on Gp5 subunits organized in a particular conformational state: the capsid is enzyme, substrate, and product.
HK97 mature particles are extraordinarily stable and cannot be disassembled into individual subunits by boiling in strong ionic detergent.
It was therefore proposed that the cross-linking also interlinks the subunits from adjacent structural units to catenate rings of hexamers and pentamers. The determination of the structure of the HK97 capsid to 3.6-Å resolution by X-ray crystallography has confirmed the formation of such capsid “chain mail” (figure, panel A), akin to that widely used in armor (B) until the development of the crossbow. The HK97 capsid is the first example of a protein catenane (an interlocked ring). This unique structure has been shown to increase the stability of the virus particle, and it may be necessary as the capsid shell is very thin. The delivery of the DNA genome to host cells via the tail of the particle obviates the need for capsid disassembly.
Chain mail in the bacteriophage HK97 capsid. (A) The exterior of the HK97 capsid is shown at the top, with structural units of the Gp5 protein in gray. The segments of subunits that are cross-linked into rings are colored the same, to illustrate the formation of catenated rings of subunits. The cross-linking is shown in the more detailed view below, down a quasithreefold axis with three pairs of cross-linked subunits. The isopeptide bonds are shown in yellow. The cross-linked monomers (shown in blue) loop over a second pair of covalently joined subunits (green), which in turn cross over a third pair (magenta). Adapted from Wikoff WR et al. 2000. Science 289:2129–2133, with permission. Courtesy of J. Johnson, The Scripps Research Institute. (B) Chain mail armor and schematic illustration of the rings that form the chain mail.
Duda RL. 1998. Protein chainmail: catenated protein in viral capsids. Cell 94:55–60.
Wikoff WR, Liljas L, Duda RL, Tsuruta H, Hendrix RW, Johnson JE. 2000. Topologically linked protein rings in the bacteriophage HK97 capsid. Science 289:2129–2133.
Structurally Simple Capsids
Several nonenveloped animal viruses are small enough to be amenable to high-resolution analysis by X-ray crystallography. To illustrate the molecular foundations of icosahedral architecture, we have chosen three examples, the parvovirus adenovirus-associated virus 2, the picornavirus poliovirus, and the polyomavirus simian virus 40.
Figure 4.11 Structure of the parvovirus adeno-associated virus 2. (A) Ribbon diagram of the single coat subunit of the T = 1 particle. The regions of the subunit that interact around the five-, three-, and twofold axes indicated by the lines labeled 5, 3, and 2, respectively, of icosahedral symmetry are shown in blue, green, and yellow, respectively. The red segments form peaks that cluster around the threefold axes. (B) Surface view of the 3-Å-resolution structure determined by