Frequency-restrained structure-factor refinement. I. Histogram simulation

An analysis of the frequencies of different values encountered in protein electron-density syntheses reveals characteristic shapes for their distributions (histograms). This property can be used to refine ill-defined phases (and, perhaps, some of the moduli) of structure factors, and thus to obtain more-interpretable electron-density maps. A simple empirical model is designed which can predict the histogram for a protein with an undetermined structure provided its unit-cell volume and charge are known. The parameters of the histogram model are derived from a set of proteins with known spatial structures. The application of the simulated histogram is illustrated by an improved electron-density map for the `dry' form of the protein γ-crystallin IIIb.