International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 21.1, pp. 500-501
Section 21.1.7.1.1. Merging R values ^{a}Department of Cell and Molecular Biology, Uppsala University, Biomedical Centre, Box 596, SE-751 24 Uppsala, Sweden |
Possibly the most common mistake in papers describing protein crystal structures is an incorrectly quoted formula for the merging R value (calculated during data reduction), where the outer sum (h) is over the unique reflections (in most implementations, only those reflections that have been measured more than once are included in the summations) and the inner sum (i) is over the set of independent observations of each unique reflection (Drenth, 1994). This statistic is supposed to reflect the spread of multiple observations of the intensity of the unique reflections (where the multiple observations may derive from symmetry-related reflections, different images or different crystals). Unfortunately, R_{merge} is a very poor statistic, since its value increases with increasing redundancy (Weiss & Hilgenfeld, 1997; Diederichs & Karplus, 1997), even though the signal-to-noise ratio of the average intensities will be higher as more observations are included (in theory, an N-fold increase of the number of independent observations should improve the signal-to-noise ratio by a factor of N ^{1/2}). At high redundancy, the value of R_{merge} is directly related to the average signal-to-noise ratio (Weiss & Hilgenfeld, 1997): R_{merge} ≃ 0.8/<I/σ(I)>.
Diederichs & Karplus (1997) have suggested a number of alternative measures that lack most of the drawbacks of R_{merge}. Their statistic R_{meas} is similar to R_{merge}, but includes a correction for redundancy (m), Another statistic, the pooled coefficient of variation (PCV), is defined as Since PCV = 1/<I/σ(I)>, this quantity also provides an indication as to whether the standard deviations σ(I) have been estimated appropriately. Finally, the statistic R_{mrgd-F}, used for assessing the quality of the reduced data, enables a direct comparison of this merging R value with the refinement residuals R and R_{free}.
Ideally, merging statistics should be quoted for all resolution shells (which should not be too broad), as well as for the entire data set. However, as a minimum, the values for the two extreme (low- and high-resolution) shells and for the entire data set should be reported.
References
Diederichs, K. & Karplus, P. A. (1997). Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Biol. 4, 269–275.Google ScholarDrenth, J. (1994). Principles of protein X-ray crystallography. New York: Springer–Verlag.Google Scholar
Weiss, M. S. & Hilgenfeld, R. (1997). On the use of the merging R factor as a quality indicator for X-ray data. J. Appl. Cryst. 30, 203–205.Google Scholar