The Asymmetric Unit

Introduction to Macromolecular Crystallography, Second Edition By Alexander McPherson Copyright 2009 John Wiley Sons, Inc. 

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

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. 

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. 

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... 

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. 

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...

The crystal structure of the complex [PhCH2PPh3][Au(C6F5)Cl] has been determined by X-ray diffraction it consists of an anion-cation pair where the anion shows a two coordinate Au(I) atom bonded to a Cl atom and a C Fs ring and the coordination is almost linear (molecules with two different angles were found but the differences between the two molecules in the asymmetric unit are not significant 177.8(5) and 179.8(4) A) [78]. 

In addition to halogen bonded complexes or ionic salts, it is also possible for sulfur and selenium electron donors to form complexes in which the electron donor atom inserts into the X2 bond, giving a hypervalent donor atom with a T-shaped geometry. It has been recently reported [147] that for dibromine and selenium, this type of complex is favored over halogen bonded complexes. While no purely halogen bonded complex is reported for dibromine, there is one complex (IRABEI) in which one selenium atom of each of several selenanthrene molecules in the asymmetric unit does insert into a Br2 bond, but for one of the molecules, the other selenium atom forms a halogen bond with a Br2 molecule to form a simple adduct (A). 

Z = 8 D, = 1.84 R = 0.059 for 2,587 intensities. In the asymmetrical unit, there are two molecules that have similar conformations. The glycosyl dispositions are anti (45.8°, 40.9°) in both molecules. The D-ribosyl conformation is 2Tj (157.6°, 32.1°) in one molecule, and 2T3 (165.1°, 31.9°) in the other. The exocyclic, C-4 -C-5 bond torsion-angles are gauche+ (51.9°, 53.9°) in both molecules, and the C-5 -0-5 bond torsion-angles are trans (172.5°, 176.6°). The two UDP molecules form a dimer coordinated by three K+ ions. There is no metal-ion or water bridge between the pyrophosphate chain and the uracil base of the same molecule. The three K+ ions are coordinated by oxygen atoms of... 

C2 Z = 4 Dx = 1.41 R = 0.102 for 4,115 intensities. The structure is a 3 2 complex of proflavine and CpG. The asymmetrical unit contains one CpG molecule, 1.5 proflavine molecules, 0.5 sulfate ion, and 11 5 water molecules. Two CpG molecules form an antiparallel, Watson-Crick, miniature duplex, with a proflavine intercalated between the base pairs through the wide groove. The double helix has exact (crystallographic), two-fold symmetry, and the crystallographic, two-fold axis passes through the C-9-N-10 vector of the intercalated proflavine. A second and a third molecule of proflavine are stacked on top of the C - G pairs ... 

The core and valence monopole populations used for the MaxEnt calculation were the ones of the reference density (electrons in the asymmetric unit iw = 12.44 and nvalence = 35.56). The phases and amplitudes for this spherical-atom structure, union of the core fragment and the NUP, are already very close to those of the full multipolar model density to estimate the initial phase error, we computed the phase statistics recently described in a multipolar charge density study on 0.5 A noise-free data [56],... 

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