Phase improvement by cross-validated density modification

Solvent flattening is a useful constraint for the early stages of crystallographic structure determination. However, sometimes it fails to produce significant improvement of poor experimental or molecular-replacement phases. This often occurs as a result of incorrect parameterization. In addition, the potential of overfitting or misinterpretation of the data exists. We have implemented a cross-validated (or free) R value in order to reduce this risk. The free R value was calculated between the experimental F_obs(h) and the calculated structure factors, F_sf(h), obtained by inverse Fourier transformation of the solvent-flattened electron density. Because of the sensitivity of the free R value to the test set selection at low resolution complete cross-validation may be required. The reliability of this approach was assessed by examining the correlation between the free R value and the known phase errors for two test cases. A high correlation was found upon variation of the extent of negative density elimination, figure of merit estimation, and the relative weighting in the phase combination procedure. The free R value can be used to optimize parameters of density-modification procedures when independent phase error estimates are unavailable.