A method for predicting the position of protein molecules in the unit cell is presented. This prediction is based on the structure-factor amplitudes of the very low order reflections and packing considerations. With very low resolution data, the calculated electron density is very blurred, such that a protein molecule may well be approximated as a sphere. A sphere with the same volume as the unknown protein was translated in small (2–3 Å) steps in the corresponding Cheshire cell until maximum overlap between the amplitudes calculated from the sphere and the true protein structure was found. A molecular packing can be calculated to restrain the allowable regions. This makes the positioning of the protein molecule even more reliable. Structure factors of the ten or so lowest resolution reflections were calculated with a sphere at the best position. These structure factors agreed closely with those of the true protein structure. The translation algorithm has been successfully tested for 16 proteins. For 12 out of 16 proteins tested, the position of the centre of the molecule was correctly predicted to within 5 Å. A qualitative deduction of deviations from the spherical model can be gained by comparing structure factors from the spherical model and the true protein. The very low resolution phasing obtained by this method may be used as powerful starting set for phase-extension methods such as maximum entropy.
Low-resolution phase extension using wavelet analysis
