Resolution of a crystal

Resolution of a crystal structure The process of distinguishing two close objects as separate entities rather than as a single, blurred object. 

The resolution of a crystal, how far it diffracts into reciprocal space, is a good measure of crystal order. It tells us immediately to what limit of precision we can expect to structurally characterize the molecules that make up the crystal. This is highly variable between protein crystals, and often between different crystal forms of the same macromolecule. Consider the diffraction patterns in Figure 6.23. 

Fig. 26. The resolution of a crystal structure shown on the left is the appearance of a small molecule at various resolutions and on the right a diagram of the relative number of Bragg reflections included in the calculation.

Figure 12 2 Resolving power and energy resolution of a crystal spectrometer as a function of X-ray energy (data used n - I, d = 0.2 nm, A0 = j°).

The crystallographic world was stunned when at a meeting in Erice, Sicily, in 1982, Hartmut Michel of the Max-Planck Institute in Martinsried, Germany, displayed the x-ray diagram shown in Figure 12.12. Not only was this the first x-ray picture to high resolution of a membrane protein, but the crystal was... 

It is well known that spontaneous resolution of a racemate may occur upon crystallization if a chiral molecule crystallizes as a conglomerate. With regard to sulphoxides, this phenomenon was observed for the first time in the case of methyl p-tolyl sulphoxide269. The optical rotation of a partially resolved sulphoxide (via /J-cyclodextrin inclusion complexes) was found to increase from [a]589 = + 11.5° (e.e. 8.1%) to [a]589 = +100.8 (e.e. 71.5%) after four fractional crystallizations from light petroleum ether. Later on, few optically active ketosulphoxides of low optical purity were converted into the pure enantiomers by fractional crystallization from ethyl ether-hexane270. This resolution by crystallization was also successful for racemic benzyl p-tolyl sulphoxide and t-butyl phenyl sulphoxide271. 

Aleshin and coworkers (49) have reported the X-ray crystal structure at 2.2-A resolution of a G2-type variant produced by Aspergillus awamori. Meanwhile, an attempt was made to determine the amino acid residues that participate in the substrate binding and catalysis provided by G2 of A. niger (52). The results of the chemical approach indicated that the Asp-176, Glu-179, and Glu-180 form an acidic cluster crucial to the functioning of the enzyme. This conclusion was then tested by site-specific mutagenesis of these amino acid residues, which were replaced, one at a time, with Asn, Gin, and Gin, respectively (53). The substitution at Glu-179 provided an inactive protein. The other two substitutions affected the kinetic parameters but were not of crucial importance to the maintenance of activity. The crystal structure (49) supports the conclusion that Glu-179 functions as the catalytic acid but Asp-17 6 does not appear to be a good candidate for provision of catalytic base. Thus, there still exists considerable uncertainty as to how the disaccharide is accepted into the combining site for hydrolysis. Nevertheless, the kind of scheme presented by Svensson and coworkers (52) almost surely prevails. 

Although varying considerably in molecular size, any GPCR polypeptide sequence contains seven hydrophobic a-helices that span the lipid bilayer and dictate the typical macromolecule architecture. Seven transmembrane domains bundled up to form a polar internal tunnel and expose the N-terminus and three interconnecting loops, to the exterior, and the C-terminus with a matching number of loops, to the interior of the cell [1-3]. This structural information was recently confirmed by the resolution of the crystal structure of rhodopsin [4,5]. 

Resolution of a racemic mixture is still a valuable method involving fractional crystallization [113], chiral stationary phase column chromatography [114] and kinetic resolutions. Katsuki and co-workers demonstrated the kinetic resolution of racemic allenes by way of enantiomer-differentiating catalytic oxidation (Scheme 4.73) [115]. Treatment of racemic allenes 283 with 1 equiv. of PhIO and 2 mol% of a chiral (sale-n)manganese(III) complex 284 in the presence of 4-phenylpyridine N-oxide resulted... 

In this chapter we discuss double-crystal topography, in which we obtain a map of the diffracting power of a crystal compared to that of a reference. We first treat the principles and geometries, the mechanisms of image contrast and resolution and the ttse of laboratory and synchrotron radiation. We then discuss applicatiorrs wafer inspection, strain contour mapping, topography of curved crystals. 

The surface of a crystal often shows irregularities such as steps, Idnks and holes. As microscopic resolution increases, smaller and smaller irregularities become visible. If similar surface morphologies are observed on all scales, regardless of magnification, these surfaces are termed self similar or self affine. 

In CBED, zone-axis patterns (ZAP) can be recorded near the relevant zone axis and the pattern may also include a higher-order Laue zone (referred to as a HOLZ). The radius of the first HOLZ ring G is related to the periodicity along the zone axis [c] and the electron wavelength, by = 2/kc. CBED can thus provide reciprocal space data in all three (x,y,z) dimensions, typically with a lateral resolution of a few nanometres. As in any application, corroborative evidence from other methods such as HRTEM and single-crystal x-ray diffraction, where possible, can be productive in an unambiguous structural determination of complex and defective materials such as catalysts. We illustrate some examples in later sections. 

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