Direct phase determination in protein electron crystallography: The pseudo-atom approximation

The crystal structure of halorhodopsin is determined directly in its centrosymmetric projection using 6.0-Å-resolution electron diffraction intensities, without including any previous phase information from the Fourier transform of electron micrographs. The potential distribution in the projection is assumed a priori to be an assembly of globular densities. By an appropriate dimensional re-scaling, these “globs” are then assumed to be pseudo-atoms for normalization of the observed structure factors. After this treatment, the structure is determined directly by conventional direct methods, followed by Fourier refinement, leading to a mean phase deviation of only 20° (from the values originally found from the image transform) for the 45 most intense reflections.