Use of anomalous scattering

The structure factor amplitude of the reflection (hkl) is equal to the structure factor amplitude of the centro-symmetrically related reflection (HliT), i.e., 

In the presence of an anomalous scatterer this relation no longer holds (Fig. 7). In vector terms we may write 

from application of the cosine rule it may be shown that 

pH can be determined and consequently the angle ap can be found from the 

Atomic scattering factors and absorption edges for selected atoms of interest to protein crystallographers 

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The resulting increase in data quality is illustrated in Fig. 5, which shows a comparison of ADX and EDX data from the same sample of InSb. The quality achieved was such that more sophisticated techniques could be applied, such as the use of anomalous scattering to distinguish similarly-scattering elements, like In (Z = 49) and Sb (Z = 51) [164, 165]. And the combination of the high-resolu-tion 2D data and the GUI software made it possible to distinguish mixed phases simply from the difference in appearance of the diffraction rings [164, 245]. 

The generation of a first-order difference by the use of anomalous scattering methods (either X-ray or neutron) offers the advantage that only a single sample is required. However, little use has been made of this possibility so far. On the other hand, extended X-ray absorption fine structure (EXAFS) spectroscopy has been used to investigate, in a limited way, gMo( ) and the existence of inner-sphere complexing 69). 

Direct methods are likely to increase in importance and have more widespread application for several reasons. As experimental tools become more powerful, and we learn to grow better crystals, atomic resolution data for proteins of increasing size will become more common. As the use of anomalous scattering approaches expands, the opportunities for their application to deduce the constellations and substmctures will increase as well. Finally, as the algorithms strengthen and computing methods become even more powerful, the direct methods themselves will become more effective. 

The first X-ray photographs of a protein crystal were described 50 years ago by Bernal and Crowfoot [1], These remarkable photographs indicated that a wealth of structural information was available for protein molecules once methods for the solution of the patterns had been developed. At that time the determination of atomic positions even in the crystals of small molecules was a difficult task. In 1954, Perutz and his colleagues [2] showed that the technique of heavy atom isomorphous replacement could be used to solve the phase problem. The method was put on a sound systematic basis by Blow and Crick [3] and extended to include the use of anomalous scattering [4,5]. Until recently, these methods provided the basis for all protein structure determinations. They have been remarkably effective (as illustrated below) and new developments have both increased the size of the problem solvable and provided greater insights. 

Until recently, the use of anomalous scattering had been restricted to those proteins which contained iron or heavy atom derivatives for which anomalous scattering was appreciable at CuK, wavelengths (Table 1). Synchrotron radiation provides a tuneable source of X-rays so that the wavelength may be varied to optimise anomalous scattering for the particular atom present in the crystal (section 3(d)). 

P212121 Z = 4 D = 2.01 R = 0.04 for 1,611 intensities. The compound is a minor product in the synthesis of methyl tyveloside. The pyranose conformation is a distorted 4, with Q = 66 pm 6= 162° (p=H8a. The (methylthio)carbonyl side-chain is extended. The C-S bond-lengths are 174.8, 179.1 pm. The C-I bond-length is 215.2 pm. The absolute configuration was confirmed by using the anomalous-scattering factors of the iodine atoms. 

The f3i(h) values thus derived can be used to determine the positions of anomalous scatterers through computation of a Patterson s)mthesis, or by other methods. This step leads to the knowledge of %A(h), and since Arj) < )T(h) — A(h), the %r(h) for each reflection can be computed. All of these steps are implemented in the MADSYS (Hendrickson, 1991) system of programs. 

The absolute structure of (-)-(M)-39 and the major isomer (+)-(IS, 4R)-4( was determined by X-ray structural analysis using an anomalous scattering method (Figure 4-a and Figure 4-b). Figure 5 shows the superimposed structure of both absolute structures which was drawn with the overlay program included in CSC Chem3D. The sulfur and the alkenyl carbon atoms are closely placed to make the C-S bond easily, and subsequent cyclization of biradical BR needs the rotation of the radical center like path a to yield (1S,4R)-40. The molecular transformation from (-)-39 to (+)-40 needs... 

Our IBM 7040 least-squares programme was modified to cope with this situation. After several cycles of refinement of the gold atomic parameter, a c-axis difference electron-density projection was computed. On the resulting map it WM possible to locate the fluorine atoms there are only two independent fluorines, one in the general position x, y, z), 12(c), and the other in the special position (J, 0, 0), 6(o). Structure factors were calculated by use of the scattering factors of the International Tables for Au and F, that for gold being corrected for the real part of the anomalous dispersion effect B was taken as 2-0 A. ... 

Anomalous scattering can also be used directly if the protein is small and a suitable anomalous scatterer can be used. The three-dimensional structure of the small protein, crambin, was determined by W ayne A. Hendrickson and Martha Teeter by the use of anomalous dispersion measurements. This protein contains 45 amino acid residues and diffracts to 0.88 A resolution. It crystallizes with 72 water and four ethanol molecules per protein molecule. Since there is a sulfur atom in the protein molecule, the use of its anomalous scattering was made. The nearest absorption edge of sulfur lies at 5.02 A, but for Cu Ka radiation, wavelength 1.5418 A, values of A/ and A/" for sulfur are 0.3 and 0.557, respectively. Friedel-related pairs of reflections were measured to 1.5 A resolution, and sulfur atom positions were computed from difference Patterson maps. The structure is now fully refined and a portion of an a helix was shown in Figure 12.27 (Chapter 12). 

The Patterson synthesis (Patterson, 1935), or Patterson map as it is more commonly known, will be discussed in detail in the next chapter. It is important in conjunction with all of the methods above, except perhaps direct methods, but in theory it also offers a means of deducing a molecular structure directly from the intensity data alone. In practice, however, Patterson techniques can be used to solve an entire structure only if the structure contains very few atoms, three or four at most, though sometimes more, up to a dozen or so if the atoms are arranged in a unique motif such as a planar ring structure. Direct deconvolution of the Patterson map to solve even a very small macromolecule is impossible, and it provides no useful approach. Substructures within macromolecular crystals, such as heavy atom constellations (in isomorphous replacement) or constellations of anomalous scattered, however, are amenable to direct Patterson interpretation. These substructures may then be used to solve the phase problem by one of the other techniques described below. 

Excellent and detailed treatments of the use of anomalous dispersion data in the deduction of phase information can be found elsewhere (Smith et al., 2001), and no attempt will be made to duplicate them here. The methodology and underlying principles are not unlike those for conventional isomorphous replacement based on heavy atom substitution. Here, however, the anomalous scatterers may be an integral part of the macromolecule sulfurs (or selenium atoms incorporated in place of sulfurs), the iron in heme groups, Ca++, Zn++, and so on. Anomalous scatterers can also be incorporated by diffusion into the crystals or by chemical means. With anomalous dispersion techniques, however, all data necessary for phase determination are collected from a single crystal (but at different wavelengths) hence non-isomorphism is less of a problem. 

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