Direct phasing in protein electron crystallography--phase extension and the prospects for ab initio determinations

Zonal diffraction amplitudes and crystallographic phases, derived from an averaged electron micrograph of two-dimensionally crystalline E. coli Omp F outer membrane porin (plane group p31m, a = 72 A), embedded in glucose, were used as a model data set to test the feasibility of direct phase extension and ab initio direct phase determination. If 17 phase terms derived from e.g. a 10 A (diffraction) resolution image are expanded to 6 A by the Sayre-Hughes equation, the unknown phases are found with reasonable accuracy (mean error 43 degrees for 25 reflections). This, however, is not the most optimal starting point. As a function of initial image resolution, the accuracy of the phase extension to 6 A is approximately a parabolic function. That is, an optimal basis resolution, found at 11 A (i.e. 14 defined reflections), produces a least mean error of 18 degrees for 28 new reflections. In addition, ab initio phase determination is possible via a multisolution technique, using a test for density flatness as a figure of merit. The success of the determination, again is sensitive to the size of the starting basis set generated from the permuted unknown reflections. If an annealing step is used to improve the basis set, the test for flatness will identify which reflections should be changed in phase. However, this figure of merit is not absolutely reliable for finding the exact value of the unknown phases.