Shell icosahedral

Key Words —Fullerenes, mass spectrometry, clusters, eieclroiiic shells, icosahedral layers. 

Thus, Ih Ceo is the first of an infinite magic-number series of neutrals and / , C20 the first of a series with closed-shell dications but open-shell neutrals. Inspection of the two series shows a general geometrical relationship in that any open-shell icosahedral fullerene C with n = 60k + 20 = 20(3k + 1) canbe converted into a larger icosahedral fullerene C3 with 3n = 60(3k + 1) by a specific transformation, and all icosahedral closed-shell neutrals are so produced. The conversion operation is the so-called... 

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. 

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.

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. 

M. PeUarin, B. Baguenard, J. L. Vialle, J. Lerme, M. Broyer, J. Miller and A. Perez, Evidence for icosahedral atomic shell structure in nickel and cobalt clusters. Comparison with iron clusters , Chem. Phys. Lett. 217 349 (1994). 

For icosahedral packing, the transition from an inner core of one spheron to one of two spherons would be expected to take place between V = 90 and N = 92. The effect of the shell structure (completed mantle at 31 rather than 32 spherons) may explain why the transition occurs over the range 88 to 92 rather than more sharply at 90 to 92. 

Lithium has been alloyed with gaUium and small amounts of valence-electron poorer elements Cu, Ag, Zn and Cd. like the early p-block elements (especially group 13), these elements are icosogen, a term which was coined by King for elements that can form icosahedron-based clusters [24]. In these combinations, the valence electron concentrations are reduced to such a degree that low-coordinated Ga atoms are no longer present, and icosahedral clustering prevails [25]. Periodic 3-D networks are formed from an icosahedron kernel and the icosahedral symmetry is extended within the boundary of a few shells. 

Reoviruses Rotavirus An inner core is surrounded by tv/o concentric icosahedral shells producing particles 70nm in diameter A very common cause of gastroenteritis in infants. It is spread through poor water supplies and when standards of general hygiene are low. In developing countries it is responsible for about a million deaths each year... 

Pyykkd, P. and Runeberg, N. (2002) Icosahedral WAU]2 A Predicted Closed-Shell Species, Stabilized by Aurophilic Attraction and Relativity and in Accord with the 18-Electron Rule. Angewandte... 

Virus symmetry The nucleocapsids of viruses are constructed in highly symmetrical ways. Symmetry refers to the way in which the protein morphological units are arranged in the virus shell. When a symmetrical structure is rotated around an axis, the same form is seen again after a certain number of degrees of rotation. Two kinds of symmetry are recognized in viruses which correspond to the two primary shapes, rod and spherical. Rod-shaped viruses have helical symmetry and spherical viruses have icosahedral symmetry. 

All the active metals in Tsai-type clusters lie on and define only the icosahedral shell. As a result, the global percentages of the active metals in Tsai-type phases are always — 157/, in contrast to that in Bergman-type phases ( 32%, below). 

Bergman- and Tsai-type clusters have the same geometric types for the second, third, and fifth shells, with the innermost and the penultimate shells being different. Particularly, the third (icosahedral) shell and the outmost triacontahedral shell define comparably sized spheres for both, but the other three shells for Tsai types are about 1.0 A smaller in diameter than for Bergman types. 

The nature of the electronic states for fullerene molecules depends sensitively on the number of 7r-electrons in the fullerene. The number of 7r-electrons on the Cgo molecule is 60 (i.e., one w electron per carbon atom), which is exactly the correct number to fully occupy the highest occupied molecular orbital (HOMO) level with hu icosahedral symmetry. In relating the levels of an icosahedral molecule to those of a free electron on a thin spherical shell (full rotational symmetry), 50 electrons fully occupy the angular momentum states of the shell through l = 4, and the remaining 10 electrons are available... 

---