Icosahedral

Plenary 4. George J Thomas Jr et at, e-mail address thomasgj ,cctr.mnkc.edu (RS). Protein folding and assembly into superstructures. (Slow) time resolved RS probing of virus construction via protein assembly into an icosahedral (capsid) shell. 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

Miehle W, Kandler O, Leisner T and Echt O 1989 Mass spectrometric evidence for icosahedral structure in large rare gas clusters Ar, Kr, Xe J. Chem. Phys. 91 5940... 

C. C. Chancey and M. C, M. O Brien, The Jahn-Teller Effect in ttnd other Icosahedral Complexes, Princeton University Press, FYinceton, NJ, 1997. 

Molecules with icosahedral symmetry are not new but the discovery of the newest of them, Ceo or buckminsterfiillerene, has had such a profound effect on chemistry in recent years that 1 thought it useful fo include a discussion of fhe icosahedral poinf group fo which Ceo belongs. 

Fig. 8. Electron micrograph showing crystallization of icosahedral phase from glassy Pd—U—Si alloy.

Nonicosahedral carboranes can be prepared from the icosahedral species by similar degradation procedures or by reactions between boranes such as B H q and B H with acetylenes. The degradative reactions for intermediate C2B H 2 species (n = 6-9) have been described in detail (119). The small closo-Qr Yi 2 species (n = 3-5 are obtained by the direct thermal reaction (500—600°C) of B H using acetylene in a continuous-flow system. The combined yields approach 70% and the product distribution is around 5 5 1 of 2,4-C2B3H2 [20693-69-0] to l,6-C2B Hg [20693-67-8] to 1,5-C2B3H3 [20693-66-7] (120). A similar reaction (eq. 60) employing base catalysts, such as 2 6-dimethylpyridine at ambient temperature gives nido-2 >-(Z, ... 

The silacarborane analogue of C,C-dimethyl-o / o-carborane, closo-l]l-((C i]) -l]lSi[ fri [128270 8 ] h.3.s been reported (179). This o-sdacarborane, which has an icosahedral framework much like o-carborane and is reported to be stable to air and moisture, was obtained in low yield from the reaction of decaborane and bis (dimethyl amino)metbyl silane in refluxing benzene. 

Representative icosahedral metaUacarborane carbonyl complexes are prepared as shown (193). 

Rhodacarborane catalysts have been immobilized by attachment to polystyrene beads with appreciable retention of catalytic activity (227). A 13-vertex /oj iJ-hydridorhodacarborane has also been synthesized and demonstrated to possess catalytic activity similar to that of the icosahedral species (228). Ak-oxidation of closo- >(2- P((Z [) 2 - i- > l[l-Bih(Z, results in a brilliant purple dimer. This compound contains two formal Rh " centers linked by a sigma bond and a pak of Rh—H—B bridge bonds. A number of similar dimer complexes have been characterized and the mechanism of dimer formation in these rhodacarborane clusters have been studied in detail (229). 

Main Group Element Carborane Derivatives. Main group element carborane derivatives have been reviewed (231). Only a few alkaline-earth element metaHacarborane derivatives have been characterized. The icosahedral beryUacarborane, /(9j (9-3-[(CH3)3N]-3,l,2-BeC2B H, shown in Figure 24a, has been prepared via the reaction of nido-1 and Be(CH3)2 [0(C2H3)2]2 followed by reaction of the diethyletherate product and... 

To date, the most extensively studied polyboron hydride compounds in BNCT research have been the icosahedral mercaptoborane derivatives Na2[B22H22SH] and Na [(B22H22S)2], which have been used in human trials with some, albeit limited, success. New generations of tumor-localizing boronated compounds are being developed. The dose-selectivity problem of BNCT has been approached using boron hydride compounds in combination with a variety of deUvery vehicles including boronated polyclonal and monoclonal antibodies, porphyrins, amino acids, nucleotides, carbohydrates, and hposomes. Boron neutron capture therapy has been the subject of recent reviews (254). 

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. 

The protein shells of spherical viruses have icosahedral symmetry... 

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... 

The asymmetric unit of an icosahedron can contain one or several polypeptide chains. The protein shell of a spherical virus with icosahedral symmetry... 

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. 

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