Resolved anomalous phasing

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. 

For more than 50 years it has been known that the barely measurable differences between Fhki and F-n-k-t contained useful phase information. For macromolecular crystals lacking anomalous scattering atoms, this phase information was impossible to extract and use because it was below the measurement error of reflections. Anomalous dispersion was, however, sometimes useful in conjunction with isomorphous replacement where the heavy atom substitutent provided a significant anomalous signal. The difference between F ki and F-h-k-i was, for example, employed to resolve the phase ambiguity when only a single isomorphous derivative could be obtained (known as single isomorphous replacement, or SIR) or used to improve phases in MIR analyses. 

For example, if we have another heavy atom isomorphous derivative available with heavy atom sites different from those found in the first derivative, when the preceding process is repeated, we will get two solutions, one true and one false for each reflection from the second derivative as well. The true solutions should be consistent between the two derivatives while the false solution should show a random variation. Thus, by comparing the solutions obtained from these two calculations, one (the computer) can establish which solution represents the true phase angle. This is the principle of the MIR method. One can also utilize the anomalous scattering (AS) data of the first derivative to resolve the phase ambiguity. In this case, the technique is called the SIRAS approach. If two derivatives and anomalous data are used, then it is called the MIRAS approach. 

In principle, one can also resolve free from bound probes, and, in fact, an interesting phenomenon occurs in these types of measurements which can be used to determine binding isotherms. Namely, if the lifetime of the fluorophore increases on binding, in addition to its rotational rate, then one may observe, at particular modulation frequencies, anomalous phase delays, that is, negative values for the phase delay between the parallel and perpendicular components, which provide a sensitive measure... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Application. Anomalous X-ray diffraction (AXRD), anomalous wide-angle X-ray scattering (AWAXS), and anomalous small-angle X-ray scattering (ASAXS) are scattering methods which are selective to chemical elements. The contrast of the selected element with respect to the other atoms in the material is enhanced. The phase problem of normal X-ray scattering can be resolved, and electron density maps can be computed. 

SOLVE/RESOLVE is a program system that permits automation of all the steps between processed data and interpretation of phased maps. These include scaling of data measured at multiple wavelengths, location of anomalous scatterers. 

Because of the ambiguity in the cos" term, there are two possible values for ap (Fig. 6b). The ambiguity can be resolved by a second heavy atom derivative. For some reflections, two derivatives may be sufficient to solve the phase problem. In general, more than two derivatives and/or the use of anomalous data are required, because of the effects of errors in the measurements on the phase determination. 

Anomalous scattering can be used to solve protein structures without the need for other information. There are two methods. In the first the normal scattering contributions of the anomalous scatterer are used as a partial structure to resolve the ambiguity inherent in the phase information from the anomalous scatterer. This... 

For instance, three-beam diffraction (one transmitted and two diffracted beams) is used for determination of triplet phases (see Direct Methods) and provides also a means of resolving the enantiomorphism problem without the need for anomalous scattering. 

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