Density histograms in protein electron crystallography—direct phase determination of bacteriorhodopsin at 6 Å resolution

Abstract

Direct methods for crystallographic phase determination have been used to solve the projected structure of native glucose-embedded bacteriorhodopsin (plane group p3, a=62.4 Å) to 6 Å, without accepting any information from electron micrographs. After defining the origin and enantiomorph and adding one algebraic phase term to the basis set, expansions into the complete set of 50 unique reflections via the Sayre equation, testing four possible values of the algebraic term, could be screened with figures of merit based on the protein density histogram, where the auto-correlation function of the ideal histogram is an endpoint for the cross-correlation of experimental histogram with this ideal distribution. Initial phase determination, followed by Fourier refinement and some additional phase permutation, yields a solution with an overall mean phase error of 60.8 or 35.4° for the 18 most intense reflections.