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 data¹. The traditional measure of the quality of this fit, and presumably the accuracy of the model, is theR value. Despite stereochemical restraints², 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 shown³. Here I propose a reliable and unbiased indicator of the accuracy of such models. By analogy with the cross-validation method^4,5 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^6–8, time-averaging⁹ and bulk solvent¹⁰.