Uses of anomalous dispersion

The use of anomalous dispersion has led to many results of interest in chemistry and biochemistry such as the steric course of certain chemical reactions.The uses for detailed studies of chirality and for protein relative phase determination will now be discussed. 

FIGURE 14.26. Absolute structure of deuterated lithium glycolate and its biochemical implications (Ref. 114). (a) Some neutron dispersion data are listed for lithium-6 S-glycolate-2-d. Values are given for 100(/4. — I-)/ I+ + I-) — 100 difference/sum = 100 D/S (see Equations 14.2 and 14.3). Calc. = calculated value from the absolute structure found, and Obs. = measured value from the Bragg reflections, (b) The structure of the glycolate ion, together with its chemical formula, and (c) the steric course of the enzymatic reaction deduced from this X-ray diffraction study. 

Anomalous dispersion can also be used as an aid in the determination of phase angles. It was realized early on that anomalous scattering from the heavy atom in a derivative could be used to resolve the phase ambiguities if a single heavy-atom derivative is all that is available. 

but now the vectors between atoms have a distinguishable direction. When peaks in the sine-Patterson map are positive they represent A- X vectors, while the holes (troughs) in the map represent X- A vectors. 

FIGURE 14.27. (a) The cosine (normal) and (b) the sine Patterson maps of potassium isocitrate (Ref. 13). Peaks in these maps are marked with filled circles if they are positive and open circles if they are negative. Note that the high K- -K peaks at u = 0.25, V — 0.50 and u = 0.50, v = 0.0 (present in the cosine Patterson map), are missing in the sine Patterson map. Note that each vector in the sine Patterson map has a sign (positive or negative). 

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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). 

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. 

The preceding characterization of anomalously dispersive transit pulses aroused considerable interest, both from a theoretical and an experimental viewpoint. Attention focused on the latter was stimulated by the possibility of using the log-log display technique to identify ft in cases where the dispersion was such as to obscure any change of gradient in conventionally displayed transit pulses. However, it became necessary to question the validity of such measurements of ft under conditions where individual carrier transit times vary over such a wide range. 

Solution and Refinement of the Structure. Scattering factors for the hydrogen (14) and nonhydrogen (15) atoms are those used previously. Anomalous dispersion terms (16) were included in Fc for rhodium and phosphorus atoms. For the processing of the data and solution and refinement of the structure procedures and computer programs standard in this laboratory were used. (See, e.g., Ref. 17).) Trial absorption corrections calculated for a random selection of reflections gave transmission factors in the range 0.71 to 0.73 therefore a full absorption correction was considered to be unnecessary. 

Carrasco, N., Buzin, Y., Tyson, E., Halpert, E., and Huang, Z. (2004). Selenium derivati-zation and crystallization of DNA and RNA oligonucleotides for X-ray crystallography using multiple anomalous dispersion. Nucleic Acids Res. 32, 1638—1646. 

Note that an equivalent stmeture is obtained when the positions of the Zn and S atoms are interchanged, but in this case the polar direction of the crystal is reversed. This arises because Pfymc is a polar space group, and historically the polar sense of a single crystal of ZnS has been used to demonstrate the breakdown of Friedel s law under conditions of anomalous dispersion. 

More than 150 years later Mach and co-workers (4) used TIR to demonstrate the existence of anomalous dispersion. They reported a method for projecting the dispersion curve n = n(X) directly. 

Fig. 1 Top Behavior of the electronic linear chiroptical response in the vicinity of an excitation frequency. Re = real part (e.g., molar rotation [< ]), Im = imaginary part (e.g., molar ellipticity [0]). Without absorption line broadening, the imaginary part is a line-spectrum (5-functions) with corresponding singularities in the real part at coex. A broadened imaginary part is accompanied by a nonsingular anomalous OR dispersion (real part). A Gaussian broadening was used for this figure [37]. Bottom Several excitations. Electronic absorptions shown as a circular dichroism spectrum with well separated bands. The molar rotation exhibits regions of anomalous dispersion in the vicinity of the excitations [34, 36, 37]. See text for further details...

The optics of angular dispersive small angle scattering cameras differ according to the field of application. Thus the double monochromator camera is mainly used for anomalous dispersion experiments (Fig. 21) By varying the Bragg angle of two... 

Scattering factors for neutral F, Xe, and Pd were taken from Doyle and Turner" and Cromer and Waber." Cromer and Liberman s values" of Af and A/" were used for anomalous dispersion corrections. ... 

Three-dimensional Patterson functions showed the positions of the Xe and As atoms. Subsequent least-squares rerinements, Fourier calculations, and difference Fourier calculations revealed the fluorine atom positions. Least-squares refinements, in which the function EwdfJ -was minimized, converged rapidly to the final structures. Scattering factors of Doyle and Turner were used, and anomalous dispersion corrections were applied. The resulting R factors are given in Table I. 

Polarity or polar character is one-dimensional chirality for example, a spear or arrow has direction and it is always clear which is the head of the arrow. One of the first uses of the breakdown of Friedel s law as a result of anomalous dispersion was in the determination of the polarity of zinc blende. In this crystal structure layers of zinc atoms and layers of sulfur atoms are arranged in pairs through the crystal. The polarity of zincblende is expressed with respect to some observable physical property (for example, the appearance of crystal faces at different ends of the crystal). The question is whether the zinc or the sulphur layers are on the shiny-face side of these pairs. Anomalous scattering of Au La X rays was used to determine the polarity of the arrangement of these layers. 

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