Section 21.2.3.1.3. Quality assessment based on surveys across structures

As for the evaluation of the geometric and stereochemical parameters of the model, surveying the same quality indicators across many structures is crucial. It allows one to establish the ranges of expected values for each indicator and to identify structures with unexpected features – those for which the values of one or more quality indicators are outside their standard range.

The global quality indicators computed by SFCHECK are the nominal resolution (d spacing), the R factor, , the minimal and maximal errors in atomic positions, the DPI, and the correlation coefficient . Another type of global quality indicator can be obtained by computing the average values of local quality measures across a given structure. This can be done for the per-residue (or per-group) atomic displacement and the Density correlation and B factor parameters as well as for the Density index and Connect parameters.

Many of the geometric and stererochemical quality indicators vary as a function of resolution – some linearly and some not (Laskowski et al., 1993). This is also the case for most of the global quality indicators described here. Examples of this dependence are given in Fig. 21.2.3.4, which shows how the correlation coefficient, the maximal error, the average atomic displacement and average density index vary as a function of resolution in the 104 nucleic acid structures surveyed. This variation is approximately linear for all four parameters. The density correlation and average density index decrease, whereas the maximal error and average atomic displacements increase, as the resolution gets poorer. In all four plots of Fig. 21.2.3.4, the points tend to display significant scatter as the d spacing increases, and at least three points, corresponding to the same three structures, appear as outliers in all plots. These structures also appear as outliers in the analysis of other parameters. A closer examination revealed that in the vast majority of the cases, the abnormal behaviour of these structures could be traced back to problems with data formats or errors that occurred during data deposition and entry processing.

Figure 21.2.3.4| top | pdf | Variation of global quality indicators with the nominal resolution (d spacing) of the crystallographic data. The following quality indicators were computed by SFCHECK for each of the 104 nucleic acid crystal structures considered in the study of Das et al. (2001): (a) correlation coefficient, (b) maximal error, (c) average atomic displacement and (d) average density index. For the meaning of the various quantities see Table 21.2.3.2. The three structures for which the reported and re-computed R factors differ by more than 10% are highlighted as black circles. The NDB (PDB) codes for these structures are ADFB72 (256D), ADF073 (257D) and ADJ081 (320D).

As the number of structures with deposited structure-factor data becomes large enough, plots such as those of Fig. 21.2.3.4 could be used to define the expected range of values for a quality indicator in a structure determined at a given resolution or refined under given conditions. Structures yielding quality indicators outside this range could then be identified as unusual on a more solid statistical basis.

The main purpose for computing the four local quality measures, the B factor, the Density index, the atomic displacement (Shift) and the Density correlation (Table 21.2.3.3), is to identify problem regions in a model. In order to do this effectively, it is necessary to evaluate the degree of redundancy between these measures and to establish the standard ranges for their values. The latter task, in particular, is not straightforward since it depends crucially on the quality of the experimental data and biases introduced by the scaling procedure and refinement protocol. In this regard, several issues are presently still under investigation.

A preliminary investigation of the mutual relations between the above-mentioned local measures has been performed in several protein and nucleic acid structures taken individually. This shows that that the B factor is strongly correlated with the density index, as illustrated in Fig. 21.2.3.5(a), and to a lesser extent with the atomic displacement (Fig. 21.2.3.5b). A weaker correlation was detected between the latter three measures and the residue density correlation (data not shown).

Figure 21.2.3.5| top | pdf | Pairwise correlations between the various local quality indicators computed by SFCHECK. (a) Correlation between the average residue B factor and the density index, and (b) between the B factor and the atomic displacement. The values displayed were computed for residues in the crystal structure of carboxypeptidase (1YME). The meaning of the parameters displayed is given in Table 21.2.3.3.

Analyses across structures could, in principle, be carried out for all four local measures computed by SFCHECK, provided these measures are not subject to systematic biases due to differences in scaling procedures and refinement practices. Such biases are, however, well known for the B factors of individual atoms or residues. This is illustrated in Fig. 21.2.3.6(a). This figure plots, side-by-side, the average residue B factors in 21 protein structures determined at different d spacings. It shows that for proteins determined at poorer resolution (d spacing above 2 Å), the B factors of different structures are systematically shifted relative to one another. Such systematic shifts are much smaller for structures determined at 2 Å resolution or better (Fig. 21.2.3.6a). This is not surprising, since in lower-resolution structures, is often too low (< 4) to yield meaningful values for the B factors.

Figure 21.2.3.6| top | pdf | B factors and density indices for residues across different structures. (a) Average B values in residues of 21 protein structures; (b) average density indices of the same set of residues and structures. The 21 protein structures analysed are from the following PDB entries: 1YME, 1MCT, 1PDO, 1VHH, 1WBA, 1CNS, 1RG7, 1UCO, 1BRO, 1EMB, 1FXI, 1KBA, 1XSM, 1HIB, 1IVF, 1QRS, 1AGX, 1NSN, 1ZOO, 1TGK, 1JCK.

Interestingly, the residue Density index, a very different parameter from the B factor, which measures the level of electron density at the atomic positions, does not display the systematic shifts observed for the B factors (Fig. 21.2.3.6b), despite the fact that the two measures are rather strongly correlated in individual structures. An indicator such as this one, and ultimately the atomic s.u.'s themselves, should be better suited for analysing and comparing the trends in the quality of specific regions of the model across different structures.