Bias in cross-validated free R factors: mitigation of the effects of non-crystallographic symmetry

Current methods of free R factor cross-validation assume that the structure factors of the test and working sets are independent of one another. This assumption is only an approximation when the modeled structure occupies anything less than the full asymmetric unit. Through progressive elimination of reflections from the working set, starting with those expected to be most correlated to the test set, small biases in free R can be measured, presumably because of over-sampling of the Fourier transform owing to bulk solvent in the crystal. This level of bias may be of little practical importance, but it rises to significant levels with increasing non-crystallographic symmetry owing to wider correlations between structure factors than hitherto appreciated. In the presence of 15-fold non-crystallographic symmetry, with resolutions commonly attainable in macromolecular crystallography, it may not be possible to calculate an unbiased free R factor. Methods are developed for the calculation of reduced-bias free R factors through elimination of the strongest correlations between test and working sets. With 180-fold non-crystallographic symmetry they may not be an accurate indicator of absolute quality, but they do yield the correct optimal weighting for stereochemical restraints.