Lattice data collection

Reflection data can be checked for completeness when made available to the PLATON validation software as an FCF file along with the CIF file. Inadequate data collection procedures may result in an incomplete survey of the reciprocal lattice. Data collection on a CCD or image-plate based diffractometer may require more than one scan in order to avoid a cusp of missing data. ... 

The presence of a covalent acyl-enzyme intermediate in the catalytic reaction of the serine proteases made this class of enzymes an attractive candidate for the initial attempt at using subzero temperatures to study an enzymatic mechanism. Elastase was chosen because it is easy to crystallize, diffracts to high resolution, has an active site which is accessible to small molecules diffusing through the crystal lattice, and is stable in high concentrations of cryoprotective solvents. The strategy used in the elastase experiment was to first determine in solution the exact conditions of temperature, organic solvent, and proton activity needed to stabilize an acyl-enzyme intermediate for sufficient time for X-ray data collection, and then to prepare the complex in the preformed, cooled crystal. Solution studies were carried out in the laboratory of Professor A. L. Fink, and were summarized in Section II,A,3. Briefly, it was shown that the chromophoric substrate -carbobenzoxy-L-alanyl-/>-nitrophenyl ester would react with elastase in both solution and in crystals in 70 30 methanol-water at pH 5.2 to form a productive covalent complex. These... 

Present-day diffraction facilities provide easy access to very low-temperature data collection and hence to an accurate determination of electron densities in crystals. Application of standard theorems of classical physics then provides an evaluation of the Coulombic interaction energies in crystal lattices [27]. These calculations are parameter-less and hence are as accurate as the electron density is. Moreover, for highly polar compounds, typically aminoacid zwitterions and the like, a fortunate coincidence cancels out all other attractive and repulsive contributions, and the Coulombic term almost coincides with the total interaction energy. 

The detailed experimental procedure on the synthesis of Sn-incorporated analogues, physicochemical characterization and the catalytic POM reaction can be obtained from our earlier reports [1,2, 5]. Lattice parameters of the samples were calculated from the XRD data collected between 5 to 70° 20 employing a scan speed of 0.5° 20/min. 

Fig. 1.3. Data for og,0 Rg as function of logl0n. From above polystyrene- toluene P- me t h yhncthacry-1 ate-acetone self avoiding walks on a simple cubic lattice. The data collect. results from different groups. Tull lin s axe fits to Eq, (1.3). The broken line represents the behavior at the 0-point (Fjq. (1.2))...

If the unit-cell contents are symmetric, then the reciprocal lattice is also symmetric and certain sets of reflections are equivalent. In theory, only one member of each set of equivalent reflections need be measured, so awareness of unit-cell symmetry can greatly reduce the magnitude of data collection. In practice, modest redundancy of measurements improves accuracy, so when more than one equivalent reflection is observed (measured), or when the same reflection is observed more than once, the average of these multiple observations is considered more accurate than any single observation. 

The unit-cell dimensions determine the reciprocal-lattice dimensions, which in turn tell us where we must look for the data. Methods like oscillation photography require that we know precisely which reflections will fall completely and partially within a given oscillation angle so that we can collect as many reflections as possible without overlap. So we need the unit-cell dimensions in order to devise a strategy of data collection that will give us as many identifiable (by index), measurable reflections as possible. 

As mentioned earlier, the unit-cell space group can be determined from systematic absences in the the diffraction pattern. With the space group in hand, the crystallographer can determine the space group of the reciprocal lattice, and thus know which orientations of the crystal will give identical data. All reciprocal lattices possess a symmetry element called a center cf symmetry or point of inversion at the origin. That is, the intensity of each reflection hkl is identical to the intensity of reflection -h k -1. To see why, recall from our discussion of lattice indices (Section II.B) that the the index of the (230) planes can also be expressed as (-2 -3 0). In fact, the 230 and the —2 -3 0 reflections come from opposite sides of the same set of planes, and the reflection intensities are identical. (The equivalence of Ihkl and l h k l is called Friedel s law,but there are exceptions. See Chapter 6, Section IV.) This means that half of the reflections in the reciprocal lattice are redundant, and data collection that covers 180° about any reciprocal-lattice axis will capture all unique reflections. 

Figure 22. Resonance Raman spectra of reduced samples of Rh. sphaemides DMSOR (a) Dithionite-reduced (b) DMS-reduced after oxidation with DMS O (c) DMS-reduced after oxidation with DMSlsO The lsO downshifts of 29 and 18 cm are observed for the bands at 862 and 497 cm 1, respectively. The spectra were recorded using 530-nm excitation and the data collection and handling procedures are as described in Fig. 21. Bands marked by an asterisk correspond to lattice modes of ice and bands marked with P correspond to nonresonantly enhanced protein modes.

The third approach to solving this problem (Farber, 1999) involves the preparation of an enzyme-intermediate complex at high substrate concentration for X-ray data collection. Under such a condition active sites in the crystal lattice will be filled with intermediates. Using a combination of flow cell experiments and equilibrium experiments, it is possible to obtain the structure of important intermediates in an enzyme reaction (Bolduc et al., 1995). It was also discovered that some enzyme crystals can be transformed from their aqueous crystallization buffer to nonaqueous solvents without cross-linking the crystals before the transfer (Yennawar et. al., 1995). It is then possible to regulate the water concentration in the active site. The structure of the first tetrahedral intermediate, tetrapeptide -Pro-Gly-Ala-Tyr- in the y-chymotrypsin active site obtained by this method is shown in Fig. 1.1. 

Up to now we have seen how lattice distortions are detected and characterized. This does not provide a direct observation of the molecular translations, rotations, and deformations associated with the distortion. However, for a few compounds it has been possible to measure a large enough number of satellite or superstructure reflections so that the distorted structure can be parametrized and refined (rigid-body or full structural study). We consider below four examples, taken from materials selected in Section IV. A, which show that such studies are not easy and that the data collection requires special attention. Indeed, it is generally difficult to measure enough satellite reflections, especially if several kinds of the latter coexist (e.g., 2kp and 4kF satellites, high-order satellites, etc.). 

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