Icosahedral subunits

The propensity of boron to form polyhedral structures is reflected also in the structures of elemental boron and boron-rich metal borides. In hydrocarbon chemistry, benzene is characterized by its extra stability the thermodynamically most stable allotrope of carbon, namely, graphite is formed by the condensation of benzene units. This beautiful relationship between compounds and allotropes exists in boron chemistry as well, where the stable allotropes of elemental boron and many of the boron-rich metal borides are made up of icosahedral subunits. 

The number of helical turns in these structures is larger than those found so far in two-sheet p helices. The pectate lyase p helix consists of seven complete turns and is 34 A long and 17-27 A in diameter (Figure 5.30) while the p-helix part of the bacteriophage P22 tailspike protein has 13 complete turns. Both these proteins have other stmctural elements in addition to the P-helix moiety. The complete tailspike protein contains three intertwined, identical subunits each with the three-sheet p helix and is about 200 A long and 60 A wide. Six of these trimers are attached to each phage at the base of the icosahedral capsid. 

Any symmetric object is built up from smaller pieces that are identical and that are related to each other by symmetry. An icosahedron can therefore be divided into a number of smaller identical pieces called symmetry-related units. Protein subunits are asymmetric objects hence, a symmetry axis cannot pass through them. The minimum number of protein subunits that can form a virus shell with icosahedral symmetry is therefore equal to... 

Can any number of identical subunits be accommodated in the asymmetric unit while preserving specificity of interactions within an icosahedral arrangement This question was answered by Don Caspar then at Children s Hospital, Boston, and Aaron Klug in Cambridge, England, who showed in a classical paper in 1962 that only certain multiples (1, 3, 4, 7...) of 60 subunits are likely to occur. They called these multiples triangulation numbers, T. Icosahedral virus structures are frequently referred to in terms of their trian-gulation numbers a T = 3 virus structure therefore implies that the number of subunits in the icosahedral shell is 3 x 60 = 180. 

Figure 16.6 A T = 3 icosahedral virus structure contains 180 subunits in its protein shell. Each asymmetric unit (one such unit is shown in thick lines) contains three protein subunits A, B, and C. The icosahedral structure is viewed along a threefold axis, the same view as in Figure 16.5. One asymmetric unit is shown in dark colors.

In the T = 4 structure there are 240 subunits (4 x 60) in four different environments, A, B, C, and D, in the asymmetric unit. The A subunits interact around the fivefold axes, and the D subunits around the threefold axes (Figure 16.7). The B and C subunits are arranged so that two copies of each interact around the twofold axes in addition to two D subunits. For a T = 4 structure the twofold axes thus form pseudosixfold axes. The A, B, and C subunits interact around pseudothreefold axes clustered around the fivefold axes. There are 60 such pseudothreefold axes. The T = 4 structure therefore has a total of 80 threefold axes 20 with strict icosahedral symmetry and 60 with pseudosymmetry. 

The S domains form the viral shell by tight interactions in a manner predicted by the Caspar and Klug theory and shown in Figure 16.8. The P domains interact pairwise across the twofold axes and form protrusions on the surface. There are 30 twofold axes with icosahedral symmetry that relate the P domains of C subunits (green) and in addition 60 pseudotwofold axes relating the A (red) and B (blue) subunits (Figure 16.9). By this arrangement the 180 P domains form 90 dimeric protrusions. 

The fact that spherical plant viruses and some small single-stranded RNA animal viruses build their icosahedral shells using essentially similar asymmetric units raises the possibility that they have a common evolutionary ancestor. The folding of the main chain in the protein subunits of these viruses supports this notion. 

One of the most striking results that has emerged from the high-resolution crystallographic studies of these icosahedral viruses is that their coat proteins have the same basic core structure, that of a jelly roll barrel, which was discussed in Chapter 5. This is true of plant, insect, and mammalian viruses. In the case of the picornaviruses, VPl, VP2, and VP3 all have the same jelly roll structure as the subunits of satellite tobacco necrosis virus, tomato bushy stunt virus, and the other T = 3 plant viruses. Not every spherical virus has subunit structures of the jelly roll type. As we will see, the subunits of the RNA bacteriophage, MS2, and those of alphavirus cores have quite different structures, although they do form regular icosahedral shells. 

X-ray studies at 22.5 A resolution of murine polyomavlrus by 1. Rayment and D.L.D. Caspar at Brandeis University confirmed the presence of these 72 capsomers at the expected positions, but even at low resolution the pentagonal shape of all 72 capsomers was evident (Figure 16.22). They concluded that each capsomer must be a pentameric assembly of the major viral subunit, known as viral protein 1 (VPl). Each of the 60 icosahedral asymmetric units contains 6 VPl subunits, not 7, and the complete shell contains 360 VPl subunits. The 12 VPl pentamers centered on icosahedral fivefold axes are identically related to their five neighbors, but the 60 pentamers centered on pseudosixfold positions "see" each of their 6 neighbors quite differently (Figure 16.23). How can such diversity of interaction be incorporated into the bonding properties of just one type of protein subunit, without compromising specificity and accuracy of assembly ... 

Small spherical viruses have a protein shell around their nucleic acid that is constructed according to icosahedral symmetry. Objects with icosahedral symmetry have 60 identical units related by fivefold, threefold, and twofold symmetry axes. Each such unit can accommodate one or severed polypeptide chains. Hence, virus shells are built up from multiples of 60 polypeptide chains. To preserve quasi-equivalent symmetry when packing subunits into the shell, only certain multiples (T = 1, 3, 4, 7...) are allowed. 

Figure 5.6 A simple icosahedral virus. Each face has three subunits. A single subunit consists of one or more proteins, (a) Whole virus particle, (b) Virus particle opened up nucleic acid released.

One of the most intriguing recent examples of disordered structure is in tomato bushy stunt virus (Harrison et ah, 1978), where at least 33 N-terminal residues from subunit types A and B, and probably an additional 50 or 60 N-terminal residues from all three subunit types (as judged from the molecular weight), project into the central cavity of the virus particle and are completely invisible in the electron density map, as is the RNA inside. Neutron scattering (Chauvin et ah, 1978) shows an inner shell of protein separated from the main coat by a 30-A shell containing mainly RNA. The most likely presumption is that the N-terminal arms interact with the RNA, probably in a quite definite local conformation, but that they are flexibly hinged and can take up many different orientations relative to the 180 subunits forming the outer shell of the virus particle. The disorder of the arms is a necessary condition for their specific interaction with the RNA, which cannot pack with the icosahedral symmetry of the protein coat subunits. 

Electron microscopic studies have suggested that the alphavirus particle has icosahedral symmetry (see below). The triangulation number is not certain, however (Murphy, 1980). Previous estimates for the molecular weight were compatible with 240 subunits per virus particle, and electron micrographs appear to show a T = 4 surface lattice (von Bons-dorff and Harrison, 1975). More information is now needed to determine the surface organization, since compositional data show fewer than 240 subunits. 

FIGURE 4-24 Rotational symmetry in proteins, (a) In cyclic symmetry, subunits are related by rotation about a single n-fold axis, where n is the number of subunits so related. The axes are shown as black lines the numbers are values of n. Only two of many possible Cn arrangements are shown, (b) In dihedral symmetry, all subunits can be related by rotation about one or both of two axes, one of which is twofold. D2 symmetry is most common, (c) Icosahedral symmetry. Relating all 20 triangular faces of an icosahedron requires rotation about one or more of three separate rotational axes twofold, threefold, and fivefold. An end-on view of each of these axes is shown at the right. 

Figure 7-15 (A) Schematic diagram of the icosahedral shell of a human rhinovirus showing the arrangement of the three subunits VP1, VP2, and VP3, each present as 60 copies. (B) Stereoscopic view of an image of the virus "decorated" by the binding of two immunoglobulinlike domains of the intercellular adhesion molecule ICAM-1, a natural receptor for the virus.

Many virus coats have 180 subunits or a number that is some other multiple of 60. However, in these coats the subunits cannot all be in identical environments. Two cases may be distinguished. If all of the subunits have identical amino acid sequences they probably exist in more than one distinct conformation that permit them to pack efficiently. (Next section) Alternatively, two or more subunits of differing sequence and structure may associate to form 60 larger subunits that do pack with icosahedral symmetry. For example, the polioviruses (diameter 25 nm) contain three major coat proteins (a, P, and y or VP1, VP2, and VP3). These are formed by cleavage of a large precursor protein into at least four pieces.76 77 Tire three largest pieces of 33-, 30-, and 25-kDa mass (306,272, and 238 residues, respectively) aggregate as (aPy)60. Sixty copies of a fourth subunit of 60 residues are found within the shell. 

Quasi-equivalence in virus coats. A large number of icosahedral viruses have coats consisting of 180 identical subunits. For example, the small RNA-containing bacteriophage MS 2 consists of an eicosahedral shell of 180 copies of a 129-residue protein that encloses one molecule of a 3569-residue RNA.89 Tire virus also contains a single molecule of a 44-kDa protein, the A protein, which binds the virus to a bacterial pilus to initiate infection. Related bacteriophages GA, fr, f2, and QP90"1 have a similar... 

Figure 7-19 Schematic icosahedrally symmetric structure with 180 subunits. The quasi-equivalent units A, B, and C are necessarily somewhat differently positioned with respect to their neighbors and must therefore assume different conformations in order to fit together tightly. From Harrison.68...

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