Linking crystallographic model and data quality

Abstract

In macromolecular x-ray crystallography, refinement R values measure the agreement between observed and calculated data. Analogously, R(merge) values reporting on the agreement between multiple measurements of a given reflection are used to assess data quality. Here, we show that despite their widespread use, R(merge) values are poorly suited for determining the high-resolution limit and that current standard protocols discard much useful data. We introduce a statistic that estimates the correlation of an observed data set with the underlying (not measurable) true signal; this quantity, CC*, provides a single statistically valid guide for deciding which data are useful. CC* also can be used to assess model and data quality on the same scale, and this reveals when data quality is limiting model improvement.

Figure 1

Higher resolution data, even if weak, improves refinement behaviour. For each incremental step of resolution from X->Y (top legend), the pair of bars gives the changes in overall R_work (blue) and R_free (red) for the model refined at resolution Y with respect to those for the model refined at resolution X, with both R values calculated at resolution X. The first pair of bars shows that R_work and R_free dropped 0.38 and 0.34% upon isotropic refinement, respectively, when the refinement resolution limit was extended from 2.0 to 1.9 Å; the other pairs of bars show the improvement upon anisotropic refinement.

Figure 2

Data quality R values behave differently than those from crystallographic refinement, and useful data extend well beyond what standard cutoff criteria would suggest. R_meas (squares) and R_pim (circles) are compared with R_work (blue) and R_free (red) from 1.42 Å resolution refinements against the EXP dataset. $<\stackrel{‒}{\mathrm{I}}∕\sigma \left(\stackrel{‒}{\mathrm{I}}\right)>$ (grey X) is also plotted. Inset is a close-up of the plot beyond 2 Å resolution.

Figure 3

Signal as a function of resolution as measured by correlation coefficients. Plotted as a function of resolution for the EXP data is CC_1/2 (diamonds) and the CC for a comparison with the 3ELN reference dataset (triangles). $<\stackrel{‒}{\mathrm{I}}∕\sigma \left(\stackrel{‒}{\mathrm{I}}\right)>$ (grey) is also shown. All determined CC_1/2 values shown have expected standard errors of <0.025 (21, 22).

Figure 4

The CC_1/2 / CC* relationship and the utility of comparing CC* with CC_work and CC_free from a refined model. (A) Plotted is the analytical relationship (eqn. 3) between CC_1/2 and CC* (black curve). Also roughly following the CC* curve are the CC values for the EXP data compared with 3ELN (triangles) as a function of CC_1/2. (B) Plotted as a function of resolution are CC* (black solid) for the EXP dataset as well as CC_work (blue dashed) and CC_free (red dashed) calculated on intensities from the 1.42 Å refined model. Also shown are CC_work (blue dotted) and CC_free (red dotted) between the 1.42 Å refined model and the 3ELN dataset.