Resolution of a crystal structure

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

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.

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]. 

X-ray crystallography has provided some details of the location, structure, and protein environment of the Mn4Ca2+ cluster. However, because of the low resolution of the crystal structures reported to date, and the possibility of radiation damage at the catalytic centre, the precise position of each metal ion remains a matter of debate. To some extent these problems have been overcome by applying spectroscopic techniques [22],... 

This example illustrates the derivation of a crystal structure based on a suspected analogy with related compounds followed by geometry optimization to enhance and improve the deduced structural model. Such a complex approach in this case has been adopted because of poor crystallinity of the material, which results in a low resolution of its powder diffraction pattern (see Figure 6.33), where the full widths at half maximum range from 0.25 to 0.55°. Furthermore, the pattern is relatively complex, with as many as 255 Bragg reflections possible for 20 < 37.5° when Mo Ka radiation is employed. 

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. 10. (a) Frequency of helical backbone torsional angles in PDB structure with resolutions between 1 and 1.49 A resolution, (b) Difference plot between frequencies of helical backbone torsional angles in PDB structures with resolution between 1 and 1.49 A resolutions and those with resolutions between 2 and 2.49 A. Note loss of observations at O, = -61, -40 seen in high-resolution data and enhanced observations at classical (Pauling) ex-helical torsion angles (0, P = -57, -47) with lower-resolution data. The implication of this plot is that data from lower-resolution (>2 A) crystal structures of proteins is biased toward the classical alpha-helix because the electron density of the protein backbone is not adequately resolved by density data. In such cases, electron density fitting is usually supplemented by force field calculations that utilize monopole electrostatics. 

The advances of our capability in this area were aided by a number of remarkable new developments in analytical instrumentation. These new characterization tools include, among many, NMR, which provides information on the local environment of atoms in the structure (16-17), synchrotron XRD, which provides very high resolution x-ray data from powders (18-19), the application of Rietveld analysis of x-ray or neutron diffraction data to zeolite structure determination (20), and STEM, which provides atomic resolution of the crystal structure and its chemical composition (21), to name just a few. 

The low resolution of a protein structure determination implies limited accuracy. Therefore any discussion of bond-length variations should be complemented with data from small molecule crystal structures. Tris-di(thiocarbamate)lron(III) complexes show a high-spin/low-spin equilibrium in the solid state [141, 142]. This process involves a systematic change in Fe-S bond length and affects the atomic displacement parameters [141]. In the low-spin configuration there are no an-... 

J -3-Keto isomerase catalyzes the isomerization of J -3-ketosteroids to zl -3-ketosteroids by stereospecific transfer of a hydrogen atom from C(4) to C(6). There is considerable evidence that it is the 40- and 6/5-hydrogens that are involved and that the reaction proceeds via an enolic intermediate. A low resolution (6 A) crystal structure determination has been published and the probable steroid-binding site identified via a bound inhibitor, 4-acetoxy-mercuric estradiol. The results of a higher resolution study (2.5 A) combined with the results of NMR studies and analysis of activity of mutant forms of the enzyme have helped to further define the probable active site of the enzyme [64]. 

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