Assessment of phase accuracy by cross validation: the free R value. Methods and applications

Analogies between the free R statistic [Brünger (1992). Nature (London), 355, 472-474] and the statistical methods of cross validation and bootstrap are discussed. Several new applications which make use of the previously observed correlation between the free R value and the phase accuracy of crystal structures are presented. One application concerns the relative weighting of individual restraint classes in macromolecular refinement. The free R value provides an objective statistical basis for the optimal choice of the weights. The results for the refinement of a penicillopepsin crystal structure at 1.8 A resolution indicate that overall bond length and bond angle weights, derived from uncertainties observed in small-molecule crystal structures, appear to be transferable to macromolecules. In another application, the landscape of the R value around the crystal structure was investigated for unrestrained modeling of diffraction data with equal atomic scatterers. Others have suggested applications to ab initio phasing because of the simplicity of the liquid-like system of equal atomic scatterers. However, there are a large number of incorrect configurations of the scatterers whose R values at 1.8 A resolution are close to that of the correct configuration given by the positions of the non-hydrogen atoms in the penicillopepsin crystal structure. A substantial number of the incorrect configurations have higher free R values than the correct one. It is therefore conceivable that the free R value could be used as a selection criterion to distinguish between certain incorrect configurations and configurations close to the correct one.