Abstract
Density modification often suffers from an overestimation of phase quality, as seen by escalated figures of merit. A new cross-validation-based method to address this estimation bias by applying a bias-correction parameter 'β' to maximum-likelihood phase-combination functions is proposed. In tests on over 100 single-wavelength anomalous diffraction data sets, the method is shown to produce much more reliable figures of merit and improved electron-density maps. Furthermore, significantly better results are obtained in automated model building iterated with phased refinement using the more accurate phase probability parameters from density modification.
Highlights
Density modification (DM) can significantly improve an electron-density map by incorporating features that are expected to appear in the map, such as flatness or disorder of the solvent region (Wang, 1985), the similarity of regions related by noncrystallographic symmetry (Bricogne, 1974) and the similarity of the density-map histogram to histograms of deposited macromolecules (Zhang & Main, 1990)
In order to reduce the effect of the introduced errors, the modified map is recombined with the original experimental information and the resulting combined map is passed to the cycle of density modification
While the likelihood function of the experimental phases and a corresponding estimation of their errors is known from experimental phasing, the errors in the density-modified phases can be estimated from the agreement between the observed and modified amplitudes
Summary
Density modification (DM) can significantly improve an electron-density map by incorporating features that are expected to appear in the map, such as flatness or disorder of the solvent region (Wang, 1985), the similarity of regions related by noncrystallographic symmetry (Bricogne, 1974) and the similarity of the density-map histogram to histograms of deposited macromolecules (Zhang & Main, 1990). In an extreme case of ‘null’ modification (Cowtan & Main, 1996), the density-modified map is equal to the experimental map and a perfect agreement exists between the null-modified and observed amplitudes. The combined phases become biased towards the modified phases, which is referred to as model bias It leads to statistical bias in the estimation of the resulting phase quality as the measure of combined phase quality, the figure of merit, becomes overestimated. Despite this distinction, the source of both types of bias is the same and a single term ‘bias’ will be used to describe the negative consequences of consistent underestimation of errors in the modified phases. This assumption is incorrect for the reasons explained above, which further amplifies the problem of bias in density-modification procedures
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