Direct structure analysis in protein electron crystallography via the density histogram: deoxycholate-treated purple membrane

The crystal structure of bacteriorhodopsin in purple membrane treated with sodium deoxycholate (plane group p3, a = 57.3 Angstrom) was solved ab initio in projection from previously published electron diffraction amplitudes to 6.2 Angstrom by direct methods for crystallographic phase determination. The best solution from the Sayre equation was identified by minimizing the skew properties of the cross-correlation of the experimental density histogram with the expected histogram. After Fourier refinement: the overall mean phase error is 43.3 degrees for all 35 unique reflections or 16.9 degrees for the 14 most intense maxima. For six clearly identified helix sites, the mean deviation of positions, when compared to the original model, was 0.7 Angstrom.