Section 18.4.2. Data

As can be seen from equation (18.4.1.2), the measure of information about all or part of the crystal contents depends strongly on the quality and quantity of the data. Of course, before the experiment is carried out some questions should be answered. Firstly, what is the aim of the experiment? Secondly, what is the cost of the experiment and what are the available resources? With modern techniques, if synchrotron radiation (SR) is used with an efficient detector, the cost of the experiment for different resolutions does not vary greatly (provided that a suitable quality crystal is available). In practice, the apparent increase in cost to attain high-resolution data will generally provide a saving in terms of the time spent by the investigator, since the interpretation of the resulting electron density is much easier and faster. In general, to answer the same question is much easier and cheaper if high-resolution data are available. In addition, high-resolution data mean that answers to some of the questions which may arise during analysis of the experiment will already be addressable. In contrast, low-resolution data not only make it difficult to answer the question currently being asked, but may also necessitate further experiments to address other problems that arise.

While the information content of the data appears to depend quantitatively on the nominal resolution, in fact it is dependent on the data quality throughout the resolution range, and both high- and low-resolution completeness and their statistical significance affect the information content of the data and derived model. High-intensity low-resolution terms remain important for refinement at atomic resolution, as they define the contrast in the density maps between solvent and protein, and because their omission biases the refinement, especially that of parameters such as the ADPs. The rejection of low-intensity observations will have a similar biasing effect. In particular, all the maps calculated for visual or computer inspection by Fourier transformation are diminished in quality by omission of any terms, but are especially affected by omission of strong low-resolution data. This is particularly true in the early stages of structure solution, where low-resolution data can be vital. Although most phase-improvement algorithms rely on relations between all reflections, terms involving low-resolution reflections will be large, will be involved in many relations and will play a dominant role. Hence, omission of these terms will severely degrade the power of these methods, which may indeed converge to solutions that have nothing whatsoever to do with the real structure.

The intensity data from a crystal may display anisotropy, i.e., the intensity fall-off with resolution will vary with direction, and may be much higher along one crystal axis than along another. If the structure is to be refined with an isotropic atomic model (either because there are insufficient data or the programs used cannot handle anisotropic parameters), then the fall-off of the calculated values will, of necessity, also be isotropic. In this situation, an improved agreement between observed and calculated values can be obtained either by using anisotropic scaling during data reduction to the expected Wilson distribution of intensities, or by including a maximum of six overall anisotropic parameters during refinement. This will result in an isotropic set of values. For crystals with a high degree of anisotropy in the experimental data, this can lead to a substantial drop of several per cent in R and R_free (Sheriff & Hendrickson, 1987; Murshudov et al., 1998).

This ambiguity effectively disappears with use of an anisotropic atomic model. The individual ADPs, including contributions from both static and thermal disorder, take up relative individual displacements, but also the overall anisotropy of the experimental values. The significance of the overall anisotropy is a point of some contention, and its physical meaning is not clear. It may represent asymmetric crystal imperfection or anisotropic overall displacement of molecules in the lattice related to TLS parameters. Refinement of TLS parameters, which can be performed using, for example, RESTRAIN (Driessen et al., 1989), removes the overall crystal contribution to the ADP.