Crystallographic symmetry, asymmetric unit

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 ... 

To the extent that a crystal is a perfectly ordered structure, the specificity of a reaction therein is determined by the crystallographic symmetry. A crystal is built up by repeated translations, in three dimensions, of the contents of the unit cell. However, the space group usually contains elements additional to the pure translations, such as a center of inversion, rotation axis, and mirror plane. These elements can interrelate molecules within the unit cell. The smallest structural unit that can develop the whole crystal on repeated applications of all operations of the space group is called the asymmetric unit. This unit can consist of a fraction of a molecule, sometimes fractions of two or more molecules, a single whole molecule, or more than one molecule. If, for example, a molecule lies on a crystallographic center of inversion, the asymmetric unit will contain half... 

There are a number of possible explanations for the formation of more than one photodimer. First, due care is not always taken to ensure that the solid sample that is irradiated is crystallographically pure. Indeed, it is not at all simple to establish that all the crystals of the sample that will be exposed to light are of the same structure as the single crystal that was used for analysis of structure. A further possible cause is that there are two or more symmetry-independent molecules in the asymmetric unit then each will have a different environment and can, in principle, have contacts with neighbors that are suited to formation of different, topochemical, photodimers. This is illustrated by 61, which contrasts with monomers 62 to 65, which pack with only one molecule per asymmetric unit. Similarly, in monomers containing more than one olefinic bond there may be two or more intermolecular contacts that can lead to different, topochemical, dimers. Finally, any disorder in the crystal, for example due to defective structure or molecular-orientational disorder, can lead to formation of nontopochemical products in addition to the topochemical ones formed in the ordered phase. This would be true, too, in those cases where there is reaction in the liquid phase formed, for example, by local melting. 

The asymmetric unit mentioned above, with the coordinates given by Mitra et al. (based on iduronate rings) was then surrounded, according to the crystallographic symmetry, by all the atoms up to a cutoff distance of 0.6 nm. All of the partial residues arising from the above selection were completed, and the sodium atoms needed to ensure neutrality were added. The resulting microcrystal contains about 5200 atoms, but due to symmetry, only 215 atoms have independent coordinates for a total of 645 variables in the minimization (see Figure 3). 

Figure 3. Schematic representation of the microcrystal considered in the computations/ the asymmetric unit (4 DeS residues, 5 Na ions and 16 water molecules, evidenced by heavy lines) is reproduced according to the crystallographic symmetry note the two ions and the water molecule in special position (on the diagonal 2-axis at -c/8). Hydrogen atoms in the polymer and lone-pairs are omitted in the drawing.

Non-crystallographic symmetry. Many protein crystals contain multiple copies of one or more molecules within the asymmetric unit. Often the conformations of such chemically indistinguishable but crystallographically non-equivalent molecules are sufficiently alike to treat them as identical. In this case, we can improve the signal to noise ratio of the electron density of our molecule of interest by averaging the density of the multiple copies in the asymmetric unit. 

The refined coordinates will correspond to either the icosahedral asymmetric unit or the crystallographic asymmetric unit, hence symmetry operations must be applied to generate the whole capsid. A useful repository of virus structure information is the website http // viperdb.scripps.edu/ where portions of the viral capsid can be generated. 

The structure of di-p-xylylene was first shown to be (59) by Brown and Farthing s (1949) X-ray analysis. The compound crystallizes in the tetragonal system, space group P42/mwm, with two C16H16 molecules in the unit cell. A consequence of this is that mmm molecular symmetry is a crystallographic requirement and the three carbon atoms in the asymmetric unit are completely specified by seven coordinates. The conformation of the molecule is shown in Fig. 6. If the benzene rings... 

The first structure of a dimeric DmNcd construct (PDB code 2NCD amino acids 281-700 Sablin et al., 1998) turned out to be perfectly symmetric (by contrast to dimers of rat kinesin-1) the two molecules of a dimer are related by a crystallographic twofold axis. The symmetry axis coincides with the axis of the coiled-coil (Fig. 3C). A similar construct (PDB code 1CZ7 amino acids 295-700 Kozielski et al., 1999) crystallized in a different space group with two dimers per asymmetric unit. Although none of the dimers has a proper twofold symmetry, their conformation is not far from that. The deviation from perfect symmetry can be described by 2- and 10-degree torsions, respectively. 

Three independent anions in the crystallographic asymmetric unit. 6Two independent anions in the crystallographic asymmetric unit. Anion has mirror symmetry. 

Figure 75. Diagrams showing (a) the crystallographic asymmetric unit of (Cp2MoH2)-[Ag(S2CO—i-Pr)]4 oo in which the Ag - Ag interactions are not shown for clarity the Mo—H atoms were not located in the X-ray study, and (b) supramolecular aggregation, viewed down the c axis, showing only the Ag—S—C(O)—S and (C5H5)2Mo groups, for clarity. Symmetry operations i,...

A crystal structure usually is described by the unit cell dimensions, space group and coordinates of the atoms (or orientation and position of the molecules) in the asymmetric unit. This, in fact, is the order in which the information is obtained when a crystal structure is determined by X-ray or neutron diffraction experiments. However, an equivalent way to describe a structure is to place the center of a molecule at the origin of an orthogonal coordinate system and to specify its molecular surroundings. This alternative is especially powerful in crystals with one molecule per asymmetric unit because the orientations of the surrounding molecules are related to the central molecule by crystallographic symmetry. The coordination sphere or environment of the structure then is defined as those surrounding molecules which are in van der Waals contact, or nearly in contact, with the central molecule. 

To describe the contents of a unit cell, it is sufficient to specify the coordinates of only one atom in each equivalent set of atoms, since the other atomic positions in the set are readily deduced from space group symmetry. The collection of symmetry-independent atoms in the unit cell is called the asymmetric unit of the crystal structure. In the International Tables, a portion of the unit cell (and hence its contents) is designated as the asymmetric unit. For instance, in space group P2 /c, a quarter of the unit cell within the boundaries 0asymmetric unit. Note that the asymmetric unit may be chosen in different ways in practice, it is preferable to choose independent atoms that are connected to form a complete molecule or a molecular fragment. It is also advisable, whenever possible, to take atoms whose fractional coordinates are positive and lie within or close to the octant 0 < x < 1/2,0 < y < 1/2, and 0 < z < 1 /2. Note also that if a molecule constitutes the asymmetric unit, its component atoms may be related by non-crystallographic symmetry. In other words, the symmetry of the site at which the molecule is located may be a subgroup of the idealized molecular point group. 

Today, we do not know the physical reason why there may be more than one asymmetric unit in the unit cell, nor do we have definite answer to the question When is the symmetry of the free molecule reduced by the condensation into a solid and when is this symmetry preserved Typical examples are the substituted 2,4,6-trichloro-l-X-benzenes. The symmetry of the gaseous molecule is preserved in the solid in so far as the Cl atoms in positions 2 and 6 are crystallographically equivalent for X = N02 and X = Br. Sites 2 and 6 of the molecule, however, are inequivalent in the solid for X = I, Cl, OH, and all other compounds for which the NQR spectrum is known. In the vast majority of molecules, the symmetry is reduced by condensation. We shall take the frequency splitting of NQR resonances due to this breakdown of symmetry as a qualitative measure of the crystal field effect. 

MIPS crystal structure is characterized by a homotetrameric association, with a 222 symmetry where two monomers are related by a non crystallographic twofold axis in an asymmetric unit and two such molecules are related by a crystallographic two-fold axis at one end. The holoenzyme seems to have three well defined domains, where the N and C terminal ends are a part of the central domain which is involved in subunit interactions, an NAD binding domain containing a modified Rossman fold and a catalytic domain which contains the active site amino acids and residues that occur at the tetrameriza-tion interface (Jin et al., 2004 Majumder et al., 2003 Stein and Geiger, 2002). 

---