Direct Methods in Protein Electron Crystallography: the Ab Initio Structure Determination of Two Membrane Protein Structures in Projection using Maximum Entropy and Likelihood

Using maximum entropy and likelihood, an ab initio phase determination was carried out in projection at ca 6–10 Å resolution for two dissimilar membrane proteins: the Omp F porin from the outer membrane of E. coli (largely β-sheet) and halorhodopsin (largely α-helix). Accurate phase information found for the most likely solutions enabled potential maps to be calculated that contained most of the essential structural details of these macromolecules without the need for any image, derived phases as a starting set for phase extension or the necessity to use envelopes or electron-density histograms. A comparison with earlier calculations using the Sayre–Hughes equation coupled with phase annealing and the Luzzati flatness criterion used as a figure of merit is made.