Section 2.4.4.5. Use of anomalous scattering in phase evaluation

When anomalous-scattering data have been collected from derivative crystals, and can be formally treated as arising from two independent derivatives. The corresponding Harker diagram is shown in Fig. 2.4.4.4. Thus, in principle, protein phase angles can be determined using a single derivative when anomalous-scattering effects are also made use of. It is interesting to note that the information obtained from isomorphous differences, , and that obtained from anomalous differences, , are complementary. The isomorphous difference for any given reflection is a maximum when and are parallel or antiparallel. The anomalous difference is then zero, if all the anomalous scatterers are of the same type, and is determined uniquely on the basis of the isomorphous difference. The isomorphous difference decreases and the anomalous difference increases as the inclination between and increases. The isomorphous difference tends to be small and the anomalous difference tends to have the maximum possible value when and are perpendicular to each other. The anomalous difference then has the predominant influence in determining the phase angle.

Figure 2.4.4.4 | top | pdf | Harker construction using anomalous-scattering data from a single derivative.

Although isomorphous and anomalous differences have a complementary role in phase determination, their magnitudes are obviously unequal. Therefore, when and are treated as arising from two derivatives, the effect of anomalous differences on phase determination would be only marginal as, for any given reflection, is usually much smaller than . However, the magnitude of the error in the anomalous difference would normally be much smaller than that in the corresponding isomorphous difference. Firstly, the former is obviously free from the effects of imperfect isomorphism. Secondly, and are expected to have the same systematic errors as they are measured from the same crystal. These errors are eliminated in the difference between the two quantities. Therefore, as pointed out by North (1965), the r.m.s. error used for anomalous differences should be much smaller than that used for isomorphous differences. Denoting the r.m.s. error in anomalous differences by E′, the new expression for the probability distribution of protein phase angle may be written as where and Here is the phase angle of [see (2.4.4.19) and Fig. 2.4.4.2]. is the anomalous difference calculated for the assumed protein phase angle . may be taken as the average of and for calculating using (2.4.4.20).