Section 18.1.9. Evaluation of the model

Refinement-program output listings will normally provide some information on atoms that are showing non-standard bond lengths, bond angles or B factors. In addition, there is other software which can help identify non-standard or unusual geometry, such as PROCHECK (Laskowski et al., 1993) and WHAT IF (Vriend, 1990). These are very useful in identifying questionable regions of structure but should not be completely relied on to identify errors or how the molecular models may be improved. Overall, the constraints in the model must be satisfied exactly, and the restraints should have a statistically reasonable distribution of deviations from the ideal values.

Refinement of the model to improve the agreement between the observed and calculated diffraction data and the associated calculated phases should result in improved electron-density and ΔF maps. Unexplained features in the electron-density map or difference map are a clear indication that the model is not yet complete or accurate. Careful examination of the Fourier maps is essential. Interactive graphics programs such as XtalView (McRee, 1993) and O contain a number of analysis tools to aid in the identification of errors in the models.

There are several different types of Fourier maps that can be useful in the correction of the models. This topic is discussed extensively in Chapter 15.2 . Usual maps include maps, ΔF maps and maps. The Fourier coefficients used to compute the maps should be weighted by estimates of the degree of bias as described in Chapter 15.2 . While ΔF maps are very useful in highlighting areas in the maps that reflect the greatest difference between the 's and 's in Fourier space, they do not show the electron density of the unit cell. Positive and negative regions of a ΔF map may be the result of positional errors of an atom or group of atoms, B-factor errors, completely misplaced atoms or missing atoms. maps show the electron density but are biased by the current model. A map is a combination of an map and a ΔF map which results in a map better showing the changes due to errors. Some investigators prefer using further amplified ΔF contributions by using a map or higher-order terms.

The contribution of the disordered solvent continuum has been discussed previously. Macromolecular crystals also contain significant quantities of discrete or partially discrete solvent molecules (i.e. water). Care needs to be taken in adding solvent to a model. Errors in models generate peaks in Fourier maps that can be interpreted as solvent peaks. Hence, adding solvent peaks too early in the refinement process may, in fact, lead to model errors. Automatic water-adding programs are becoming more common; examples include SHELXL98 and ARP/wARP (Lamzin & Wilson, 1997). These programs check if the waters are with in reasonable bonding distances of hydrogen-bonding atoms. There is a distribution of solvent molecules ranging from ones with low B factors at unit occupancy to ones with very large B factors. Various criteria are used to decide on a cutoff in the discrete solvent contribution. A rule of thumb for ambient-temperature data sets is frequently about one solvent molecule per residue in a protein molecule. As more data are being collected at cryogenic temperatures, this ratio is tending to go up. Noise is being fitted if too many peaks in a ΔF map are being assigned as solvent molecules. This can also contribute to reducing R factors on incorrect models. Solvent sites may not be fully occupied. Because of the large B factors and limited range of the diffraction data, the B factors and occupancy are highly correlated. Refinement of occupancy does not usually contribute either to improving a model or to reduction of R factors in structures with up to 2.0 Å resolution data. Beyond 1.5 Å data, it may be possible to refine solvent water occupancies and B factors. At even higher resolution, some programs, such as SHELXL98, provide anisotropic refinement methods which may further improve the solvent model while reducing R factors including R_free.

Cross validation is a powerful tool for avoiding over-interpretation of the data by a too elaborate model. The introduction of cross validation to crystallography (Brünger, 1992) has been responsible for significant improvement in the quality of structure determinations. A subset of the reflections, chosen randomly, is segregated and not used in the refinement. If the model is correct and the only errors are statistical, these reflections should have an R factor close to that of the reflections used in the refinement. Changes to the model should affect both R and R_free similarly. Kleywegt & Jones (1997) have pointed out that it is necessary to treat the selection of free reflections very carefully in the presence of noncrystallographic symmetry.