3.3 THE STRUCTURE OF ISOMETRIC VIRUS PARTICLES

A second way of constructing a symmetrical particle would be to arrange the smallest number of subunits possible around the vertices or faces of an object with cubic symmetry, e.g. tetrahedron, cube, octahedron, dodecahedron (constructed from 12 regular pentagons), or icosahedron (constructed from 20 equilateral triangles). Figure 3.3 shows possible arrangements for objects with triangular and square faces. Multiplying the minimum number of subunits per face by the number of faces gives the smallest number of subunits which can be arranged around such an object. The minimum number of subunits is determined by the symmetry element of the face, i.e. a square face will have four subunits, a triangular face will have three subunits, etc.

For a tetrahedron the smallest number of subunits is 12, for a cube or octahedron it is 24 subunits, and for a dodecahedron or icosahedron it is 60 subunits. Although it may not be immediately apparent, these represent the few ways in which an asymmetrical object (such as a protein molecule) can be placed symmetrically on the surface of an object resembling a sphere. (This can be checked by using a ball and sticking on bits of paper of the shape shown in Fig. 3.3.) Examination of electron micrographs reveals that many viruses appear spherical in outline, but actually have icosahedral symmetry rather than octahedral, tetrahedral, or cuboidal symmetry. There are two possible reasons for the selection of icosahedral symmetry over the others. Firstly, since it requires a greater number of subunits to provide a sphere of the same volume, the size of the repeating subunits can be smaller, thus economizing on genetic information. Secondly, there appear to be physical restraints which prevent the tight packing of subunits required by tetrahedral and octahedral symmetry. Symmetry of an icosahedron An icosahedron is made up of 20 triangular faces, five at the top, five at the bottom and 10 around the middle, with 12 vertices (Fig. 3.4c). Each triangle is symmetrical and it can be inserted in any orientation (Fig. 3.4a). An icosahedron has three axes of symmetry: fivefold, threefold, and twofold (Fig. 3.4b). However, many viruses are icosahedral and yet achieve a much greater size than can apparently be accomplished with this simple arrangement (Box 3.1). The triangulation of spheres – or how to make bigger virus particles It is possible to enumerate all the ways in which this subdivision can be carried out. This can be demonstrated with a simple example. Starting with an icosahedron, arranging the subunits around the vertices will generate 12 groups of five subunits (Fig. 3.6a). Subdividing each triangular face into four smaller and identical equilateral triangular facets and incorporation of subunits at the vertices of those smaller triangles gives a structure containing a total of 240 subunits (Fig. 3.6b). At the vertices of each of the original icosahedron faces there will be rings of five subunits, called pentamers (dark spheres). However, at all the other (new) vertices generated by the triangular facets will be rings of six subunits, called hexamers (light spheres). Since some of the subunits are arranged as pentamers and others as hexamers, it should be apparent that they cannot be equivalently related; hence they are called quasi-equivalent, but this still represents the minimum-energy shape. Thus with the subunit being kept a constant size, greater subdivision allows the formation of larger virus particles. T = 1: the smallest virus particle – satellite tobacco necrosis virus In its simplest form one subunit used in the construction of a virus particle subunit is one protein. However no independently replicating virus is known to consist of only 60 protein subunits, but satellite viruses do (Table 3.1). These encode one coat protein but depend upon coinfection with a helper virus to provide missing replicative functions (Appendix 5). The single-stranded RNA genome of satellite tobacco necrosis virus is about 1000 nt. Presumably the volume of a 60-subunit structure is too small to accommodate the larger genome that is needed by an independent virus. The virion is only 17 nm in diameter, compared to the 30 nm of small independent viruses. Box 3.2 Calculating the number of subunits in a virus particle The way in which each triangular face of the icosahedron can be subdivided into smaller, identical equilateral triangles is governed by the law of solid geometry. This can be calculated from the expression: T = Pf 2 where T, the triangulation number, is the number of smaller, identical equilateral triangles, P is given by the expression h2 + hk + k2 . In this expression, h and k are any pair of integers without common factors, i.e. h and k cannot be multiplied or divided by any number to give the same values, f = 1, 2, 3, 4, etc. For viruses so far examined, the values of P are 1 (h = 1, k = 0), 3 (h = 1, k = 1), and 7 (h = 1, k = 2). Representative values of T are shown in Table 3.1. Once the number of triangular subdivisions is known, the total number of subunits can easily be determined since it is equal to 60T. 36 PART I WHAT IS A VIRUS

Detailed determination of the structure of a virus depends primarily on being able to grow crystals of purified virus, although valuable but lower resolution information can be obtained from cryoelectron microscopic examination of virus frozen in vitreous ice. The conditions required for crystallization of virus particles or proteins are not fully understood, and many will not form crystals at all. Large stable crystals are required that are then bombarded with X-rays. These are diffracted by atoms within the virion, and the image captured. Knowledge of the amino acid sequence of the proteins which comprise the particle makes it possible to determine the three-dimensional crystal structure. X-ray analysis gives resolution to around 0.3 nm and cryoelectron microscopy to around 15 nm. Both processes require high-powered computers which are used to make the necessary calculations and for image reconstruction. The morphological units seen by electron microscopy are called capsomers and the number of these need not be the same as the number of protein subunits. The numbers of morphological units seen will depend on the size and physical packing of the subunits and on the resolution of electron micrographs. A repeating subunit may consist of a complex of several proteins, such as the four structural proteins of poliovirus (see below and Section 11.3), or a fraction of a protein, such as the adenovirus hexon protein, half of which is considered to be a single repeating subunit. = 3: the molecular basis for quasi-equivalent packing of chemically identical polypeptides – tomato bushy stunt virus Some plant virus particles achieve the T = 3, 180-subunit structure (Fig. 3.7) while encoding only a single virion polypeptide. They compensate for the physical asymmetry of quasi-equivalence by each polypeptide adopting one of three subtly different conformations. The virion polypeptide of tomato bushy stunt virus has three domains P, S, and R (Fig. 3.8a): this is folded so that P and S are external and hinged to each other, while R is inside the virion and has a disordered structure. An arm (a) connects S to R, h connects S and P (Fig. 3.8b). Each triangular face is made of three identical polypeptides, but these are in different conformations to accommodate the quasi-equivalent packing. For example, the C subunit has the S and P domains orientated differently from the A and B subunits (Fig. 3.8c), while the arm (a) is ordered in C and disordered in A and B (not shown). The S domains form the viral shell with tight interactions, while the P domains (total = 180) interact across the twofold axes of symmetry to form 90 dimeric protrusions. This virion is 33 nm in diameter and can accommodate a single-stranded RNA genome about fourfold larger than that of the satellite viruses. Thus a larger particle can be achieved without any more genetic cost. T = 3: with icosahedra constructed of four different polypeptides – picornaviruses Picornaviruses are made of 60 copies of each of four polypeptides: VP1, VP2, VP3, and VP4. VP4 is entirely internal. The repeating subunit of picornaviruses is the complex of VP1, VP2, and VP3. This should generate a T = 1 particle. However despite the significant differences in amino acid sequence, the proteins adopt very similar conformations and, in geometric terms, appear as separate repeating subunits. For this reason the assembled picornavirus particles appear to have a T = 3 structure; more accurately this is a pseudo T = 3 (compare Figs 3.10 and 3.7). The pentamers contain 15 polypeptides, with five molecules of VP1 forming a central vertex. These pentamers are the building blocks in the cell from which the virion is assembled. Use of three polypeptides gives a chemically more diverse structure and may be an adaptation to cope with the immune system of animal hosts. The cell receptor attachment site of picornavirus particles Many virus proteins including the VP1, VP2, and VP3 of picornaviruses, have the same type of structure – an antiparallel β barrel also known as a “jelly-roll” (Fig. 3.9). Crystallographic, biochemical, and immunological data have together identified a depression within the β barrel of VP1, which is thought to be the attachment site of picornaviruses. There are 60 attachment sites per virion. Apart from its intrinsic interest, the structure of the attachment site is important as the prime target for antiviral drugs (e.g. pleconaril – see Section 21.8) which can stop attachment of virus to the host cell. The arrangement of the β strands of VP1 is such that an annulus is formed around each fivefold axis of symmetry (Fig. 3.10). In the rhino (common cold) viruses, this is particularly deep and is called a “canyon.” The canyon lies within the structure of the β barrel. Amino acids within the canyon are invariant, as expected from their requirement if they have to interact with the cell receptor, while amino acids on the rim of the canyon are variable. Only the latter interact with antibody. It is thought that the floor of the canyon has evolved so that it physically cannot interact with antibody. This avoids immunological pressure to accumulate mutations in order to escape from reaction with antibody, since these would at the same time render the attachment site nonfunctional, and hence be lethal to the virus. An unknown structure – virus particles with 180 + 1 subunits and no jelly-roll β barrel – RNA bacteriophages The leviviruses are 24 nm icosahedral RNA bacteriophages, and include MS2, R17, and Qβ. They encode two coat proteins. There are 180 subunits of one of these arranged with T = 3, but only a single copy of the second “A” protein in each particle. This is the attachment protein. It is not known how the single subunit is incorporated into the particle. The main coat protein does not form a jelly-roll β barrel like the others described above, but instead has five antiparallel β strands arranged like the vertical elements of battlements. Two subunits interact to form a sheet consisting of 10 antiparallel β strands. T = 25: more complex animal virus particles – adenoviruses Careful examination of electron micrographs of adenoviruses shows that T = 25. There are 240 hexamers and 12 pentamers, and a fiber projects from each vertex of the virus (Fig. 3.11a,b). The fibers, the pentamers and the hexamers are all constructed from different proteins. We are thus faced with the problem of arranging not one, but three different proteins in a regular fashion, while adhering to the design principles outlined above. This can be achieved by arranging the pentamers and the fibers at the vertices of the icosahedron and the hexamers on the faces of the icosahedron (Fig. 3.11c). However the formula 60T gives the number of subunits as 1500 (Table 3.1). How is this difference resolved? The 240 hexons are composed of three identical polypeptides and each functions as two repeating subunits. Thus there are 1440 hexon subunits. The 12 pentons are formed from five identical polypeptides and each functions as a subunit, making 60 of these. Thus 1440 hexon subunits + 60 penton subunits makes up the 1500 predicted subunits. Actually the hexamers are not all spatially equivalent, as those surrounding the vertex pentamers contact five other hexons, while the others contact six hexons. Double-shelled particles: a capsid within a capsid – reoviruses A different and very complex structural arrangement is found in another class of isometric viruses, the reoviruses, which are composed of a capsid within a capsid. The diameter of the inner and the outer capsid being 51 nm and 73 nm respectively. Reovirus synthesizes 11 polypeptides. Of these eight are located in the virion, three forming the outer capsid and five forming the inner capsid (Table 3.2). Both capsids have icosahedral