Asymmetric unit

The symmetry properties of an icosahedron are not restricted to the surface but extend through the whole volume. An asymmetric unit is therefore a part of this volume it is a wedge from the surface to the center of the icosahedron. Sixty such wedges completely fill the volume of the icosahedron. 

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

Figure 16.4 The division of the surface of an icosahedron into asymmetric units, (a) One triangular face is divided into three asymmetric units into which an object is placed. These are related by the threefold symmetry axis.

Figure 16.S Schematic illustration of the way the 60 protein subunits are arranged around the shell of safellite tobacco necrosis virus. Each subunit is shown as an asymmetric A. The view is along one of the threefold axes, as in Figure 16.3a. (a) Three subunifs are positioned on one triangular tile of an Icosahedron, in a similar way to that shown in 16.4a. The red lines represent a different way to divide the surface of the icosahedron into 60 asymmetric units. This representation will be used in the following diagrams because it is easier to see the symmetry relations when there are more than 60 subunits in the shells, (b) All subunits are shown on the surface of the virus, seen in the same orientation as 16.4a. The shell has been subdivided into 60 asymmetric units by the red lines. When the corners are joined to the center of the virus, the particle is divided into 60 triangular wedges, each comprising an asymmetric unit of the virus. In satellite tobacco necrosis virus each such unit contains one polypeptide chain...

Complex spherical viruses have more than one polypeptide chain in the asymmetric unit... 

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. 

When they form the three subunits A, B, and C of the asymmetric unit, the identical polypeptides adopt different three-dimensional structures. The C subunit in particular is distinct from the A and B structures, its hinge region assuming a different conformation so that the S and P domains are... 

The asymmetric unit contains one copy each of the subunits VPl, VP2, VP3, and VP4. VP4 is buried inside the shell and does not reach the surface. The arrangement of VPl, VP2, and VP3 on the surface of the capsid is shown in Figure 16.12a. These three different polypeptide chains build up the virus shell in a way that is analogous to that of the three different conformations A, C, and B of the same polypeptide chain in tomato bushy stunt virus. The viral coat assembles from 12 compact aggregates, or pen tamers, which contain five of each of the coat proteins. The contours of the outward-facing surfaces of the subunits give to each pentamer the shape of a molecular mountain the VPl subunits, which correspond to the A subunits in T = 3 plant viruses, cluster at the peak of the mountain VP2 and VP3 alternate around the foot and VP4 provides the foundation. The amino termini of the five VP3 subunits of the pentamer intertwine around the fivefold axis in the interior of the virion to form a p stmcture that stabilizes the pentamer and in addition interacts with VP4. 

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. 

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 ... 

M03S7X4 (X = Cl, Br), monoclinic (P2i/c). Figure 24 shows the asymmetrical unit of the crystal structure. The three, independent molybdenum atoms form an almost equilateral triangle. Six of the seven sulfur atoms occur in three S2 groups, each one bridging one Mo-Mo... 

Fig. 23. Two asymmetric units forming the translational element along the o axis of M0S2CI3. (Redrawn from J. D. Marcoll, A. Rabenau, D. Mootz, and M. Wunderlich, Rev. Chim. Miner. 11, 607 (1974), Fig. 1, p. 611.)...

Depending on the size and packing (space group) of the asymmetric unit in the crystal and the resolution available, many tens of thousands of diffraction spots must be recorded to determine a structure. 

Rossmann MG, Blow DM. Detection of sub-units within crystallographic asymmetric unit. Acta Cryst 1962 15 24-31. 

Fig.8 The molecular structure of Cp2Zr(Me)0B[0Si(0 Bu)3]2 generated from the crystallographic data of 1 of the 18 independent molecules from the asymmetric unit, with all hydrogen atoms omitted for clarity...

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