Free R value: a novel statistical quantity for assessing the accuracy of crystal structures

Abstract

The determination of macromolecular structure by crystallography involves fitting atomic models to the observed diffraction data. The traditional measure of the quality of this fit, and presumably the accuracy of the model, is the R value. Despite stereochemical restraints, it is possible to overfit or 'misfit' the diffraction data: an incorrect model can be refined to fairly good R values as several recent examples have shown. Here I propose a reliable and unbiased indicator of the accuracy of such models. By analogy with the cross-validation method of testing statistical models I define a statistical quantity (R(free) (T) that measures the agreement between observed and computed structure factor amplitudes for a 'test' set of reflections that is omitted in the modelling and refinement process. As examples show, there is a high correlation between R(free) (T) and the accuracy of the atomic model phases. This is useful because experimental phase information is usually inaccurate, incomplete or unavailable. I expect that R(free) (T) will provide a measure of the information content of recently proposed models of thermal motion and disorder, time-averaging and bulk solvent.