Better models by discarding data?

Abstract

In macromolecular X-ray crystallography, typical data sets have substantial multiplicity. This can be used to calculate the consistency of repeated measurements and thereby assess data quality. Recently, the properties of a correlation coefficient, CC1/2, that can be used for this purpose were characterized and it was shown that CC1/2 has superior properties compared with `merging' R values. A derived quantity, CC*, links data and model quality. Using experimental data sets, the behaviour of CC1/2 and the more conventional indicators were compared in two situations of practical importance: merging data sets from different crystals and selectively rejecting weak observations or (merged) unique reflections from a data set. In these situations controlled `paired-refinement' tests show that even though discarding the weaker data leads to improvements in the merging R values, the refined models based on these data are of lower quality. These results show the folly of such data-filtering practices aimed at improving the merging R values. Interestingly, in all of these tests CC1/2 is the one data-quality indicator for which the behaviour accurately reflects which of the alternative data-handling strategies results in the best-quality refined model. Its properties in the presence of systematic error are documented and discussed.

Keywords: R value; correlation coefficient; data quality; model quality; outlier rejection.

Figure 1

Scheme documenting the relationships of correlation coefficients calculated between squared observed and calculated amplitudes. This figure was adapted from Diederichs & Karplus (2013 ▶).

Figure 2

Data statistics for CDO3 (blue), CDO3b (green) and CDO3c (red).

Figure 3

Example demonstrating the possibility of negative CC_1/2 when rejecting reflections with negative intensities from a data set. The plots show ∊₁ versus ∊₂ for simulated data having Gaussian noise and no signal (τ = 0). (a) 1000 unique reflections, each represented by two observations; no rejections. The correlation of ∊₁ and ∊₂ is near zero. (b) From the 1000 unique reflections, those with negative intensity (∊₁ + ∊₂ < 0) were rejected. The resulting correlation between ∊₁ and ∊₂ is about −0.47. (c) From the 1000 unique reflections, those with negative ∊₁ or negative ∊₂ were rejected, also resulting in positive (merged) intensity. The resulting correlation between ∊₁ and ∊₂ is near zero.