Noncrystallographic symmetries

The X-ray diffraction pattern of a quasicrystal exhibits noncrystallographic symmetry. In addition, the number of observable reflections increases more and more the more intense the X-ray radiation is or the longer the exposure time is (in a similar way to the number of stars visible in the sky with a more potent telescope). 

The [16]annulene is nonplanar, with almost complete bond alternation. The single bonds (1.454 A) are alternately trans and gauche, and the double bonds (1.337 A) cis and trans. The average torsion angle at a gauche C—C bond is 41°. The molecule is therefore relatively flat with S4 noncrystallographic symmetry, and the structure confirms the lack of aromaticity in this [4n] annulene. 

The football-shaped hexamer is made up of two identical trimers. The two NCI trimers are related by a two-fold noncrystallographic symmetry axis lying in the equatorial plane and perpendicular to the pseudo-three-fold axis (Figure 20). The interface, which covers about 4400 A of solvent-accessible area per trimer, is formed by the nearly flat surfaces of the two trimers. The polar (45.5%) and nonpolar atoms (54.5%) in the interface are in almost equal proportions, underscoring the importance of both types of interactions in the hexamer stabilization. ... 

Crystals of pronase-released heads of the N2 human strains of A/Tokyo/3/67 [44] and A/RI/5+/57 were used for an x-ray structure determination. The x-ray 3-dimensional molecular structure of neuraminidase heads was determined [45] for these two N2 subtypes by a novel technique of molecular electron density averaging from two different crystal systems, using a combination of multiple isomorphous replacement and noncrystallographic symmetry averaging. The structure of A/Tokyo/3/67 N2 has been refined [46] to 2.2 A as has the structures of two avian N9 subtypes [47-49]. Three influenza type structures [50] have also been determined and found to have an identical fold with 60 residues (including 16 conserved cysteine residues) being invariant. Bacterial sialidases from salmonella [51] and cholera [52] have homologous structures to influenza neuraminidase, but few of the residues are structurally invariant. 

Molecular replacement method The use of rotation and translation functions (q.v.), of noncrystallographic symmetry (q.v.), or of structural information from related structures, to determine a protein crystal structure. 

Noncrystallographic symmetry Symmetry within an asymmetric unit in a crystal structure that is not accounted for by any space group symmetry. For examph one asymmetric unit of a crystalline protein may contain a dimer whose two subunits... 

Noncrystallographic symmetry and density modification PATTERSON METHODS... 

If an asymmetric unit possesses high symmetry, as is often the case for large macromolecu-lar complexes such as the pyruvate dehydrogenase enzyme complex, or icosahedral viruses, then another approach to solving the phase problem becomes available. Viruses, in particular, are amenable because their symmetry operators are very precise and their orientations are well defined. Asymmetric units also occassionally contain redundant copies of a protein that are related by noncrystallographic symmetry through proper or improper rotations and translations. 

The means for improving the real space, electron density map may involve a combination of ideas, but by far the most powerful is application of noncrystallographic symmetry. If the asymmetric unit contains noncrystallographic symmetry, then its electron density map does as well. If the dispositions of the noncrystallographic symmetry operators are known, then the electron density map can be self-averaged using these operators. 

The presence of rotational or screw symmetry means that the unit cell has internal symmetry. Therefore, only part of the unit cell, known as the asymmetric unit, is needed to uniquely define the unit cell. (The asymmetric unit may also contain more than one molecule, related by movements — symmetry operations — that are not part of the crystal symmetry - noncrystallographic symmetry operators. This can be very important in determining the protein structure, as discussed in Section 9.03.9.3). 

Every second protein domain in PDB is represented by more than one PDB entry 20% of proteins have two structures, and the remaining 30% more than two structures. Some of them are mutants (e.g., 400 of T4 lysozyme structures from Brian Matthews s laboratory) but in most cases, these multiple structures represent snapshots of the pocket conformational diversity. Furthermore, many entries contain more than one chain in an asymmetric unit. These protein structures related by noncrystallographic symmetry can also be used as a source of multiple pocket conformations. The noncrystallographic symmetry-related subunits increase the number of domains already represented by multiple experimental conformations from 50% to the overall level of 75% (Fig. 2). About 5% of the domains are represented by more than 30 copies. 

Fig. 2. A histogram of experimental structural variability of the 11,168 protein domains in the Protein databank (PDB). Twenty-five percent of protein domains are represented by a single structure, and 5% are represented by more than 30 structures. Three-quarters of the domains are represented by more than one conformation. The additional conformers are found in either different PDB entries or noncrystallographic symmetry-related domains of the same entry.

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