Anomalous difference

The selection of labelling need not affect the "blind" nature of the analysis since Q.C. samples do not have to be identified until analyses are completed. Treating the Q.C. samples in "blind" fashion is often important to ensure that they do not receive special treatment. These samples are used as surrogate replicates for real samples and are used to evaluate method performance in lieu of routine unknown sample replicates. Therefore, they must not receive special operator attention or handling. However, the "blind" requirement may be relaxed when sample preparation has been minimal or well controlled, or when automated instrument performance is the sole subject of scrutiny. It may be argued that "blind" labelling is unecessary even when the detection device is under human operator control since any attempt to "adjust" the determination of either Q.C. sample to match its pair mate will be expressed as an anomalous difference D. 

Table 9.3 Number of peak-wavelength anomalous difference data pairs for 1JC4 remaining after successive application of the various DIFFE significance tests...

Even if anomalous dispersion data are involved in the substructure determination process, it is the magnitude of the anomalous differences that are used, and the substructures of the biologically occurring macromolecule and its enantiomer are both consistent with the data. The probability that the substructure obtained by direct methods can be developed into a protein model with L-amino acids and right-handed a helices is 50%. Therefore, before proceeding further, other information must be used to determine the correct hand. 

When a solution contains multiple ionic species, ASAXS can be used to determine the fractional contribution of each cationic species to the ion atmosphere around nucleic acids. As an illustration, we show monovalent and trivalent ion competition around DNA. Figure 19.8A displays anomalous difference signal from Rb+ ions bound to DNA in two solutions. In a... 

The radial Patterson inversion of the anomalous difference signal is calculated using... 

Figure 19.10 RNA ASAXS data compared with APBS predictions. This figure shows the measured anomalous difference signal for Rb-RNA in comparison with predictions generated using APBS. To obtain good agreement, the finite size of the ion must be included. In this case, an ion probe radius of 3 or 4 A (pictured) optimizes the...

As with the isomorphous replacement method, the locations x, y, z in the unit cell of the anomalous scatterers must first be determined by Patterson techniques or by direct methods. Patterson maps are computed in this case using the anomalous differences Fi,u — F-h-k-i-Constructions similar to the Harker diagram can again be utilized, though probability-based mathematical equivalents are generally used in their stead. 

As with the isomorphous replacement technique it is necessary to identify the positions, the x, y, z coordinates of the anomalous scatterers. This can be done by anomalous difference Patterson maps, which are Patterson syntheses that use the anomalous differences Fhki — F—h—k—i as coefficients (Blow and Rossmann, 1961). These maps are interpreted identically to isomorphous difference Patterson maps (see Chapter 9). Rapidly surpassing Patterson approaches, particularly for selenomethionine problems and others where the number of anomalous scatterers tends to be large, are direct methods (see below). These are strictly mathematical methods that have proved to be surprisingly effective in revealing the constellation of anomalous scatterers in a unit cell. 

As an aside, let us return for a moment to SIR. How can anomalous scattering be used to break the phase ambiguity of SIR if both methods have similar Harker constructions Fortunately, the information from the isomorphous differences and the anomalous differences is not the same, but complementary. If, as is usually the case, the heavy atom is the only anomalous scatterer, the substructure is the same, that is, we can use the same AH for a reflection h, k, l. When the anomalous difference/" and its inverse are added to Fh, we can draw two circles of radii FPh + and FPh centered at the ends of each vector (Figure 24). With the FP -circle centered at the origin, these three circles only intersect at one point, which defines the phase of FP. This method is Single Isomorphous Replacement with Anomalous Scattering - or SIRAS. 

Figure 23 The Harker construction for the SAD method. The anomalous differences f" are drawn from the end of FH, giving rise to two circles. These two circles intersect at two points (just like in SIR), leaving the phase of FP (not shown for clarity) ambiguous.

It is usual to define the quantity known as an anomalous difference, ano given by... 

The anomalous difference for each reflection, AA 0(hk ), can be used, along with the isomorphous difference to determine its phase, aP (figure 2.13(b)). 

The effect of absorption on the reflection intensities is obviously to reduce them in the absence of a correction this would affect the estimation of individual atomic temperature factors in refinement. The absorption corrections applied to individual reflections are usually different from one to another. In the case where a single data set is made up of several crystals (because of radiation damage), each of variable shape, then the lack of an absorption correction will leave systematic errors in the data. Even when a single crystal is used for a complete native data set and an identically shaped and mounted crystal is used as the heavy atom derivative, the lack of an absorption correction can seriously affect the measured isomorphous or anomalous differences. 

One check of these expressions, for the reader, is to take the standard anomalous difference, at a particular wavelength, by subtracting equation (9.16) from (9.15). The resulting expression may then be compared directly with equation (2.20).)... 

The caesium derivative was isomorphous to a potassium derivative. Data were collected on the potassium derivative on a conventional source at CuKa wavelength. Data were also collected at 2.47 A at the peak of the absorption of the caesium Lm edge where/" is a maximum. Data extended to a resolution of 3.8 A. The isomorphous and anomalous differences gave phases, which allowed an electron density map to be calculated the sense of progression of an a-helix was clearly recognisable from the map. 

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