'Peakiness' test functions

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 Å) was solved ab initio in projection from previously published electron diffraction amplitudes to 6.2 Å by direct methods for crystallographic phase determination. The best solution form 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° for all 35 unique reflections of 16.9° 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 Å.

The charge flipping algorithm

This paper summarizes the current state of charge flipping, a recently developed algorithm ofab initiostructure determination. Its operation is based on the perturbation of large plateaus of low electron density but not directly on atomicity. Such a working principle radically differs from that of classical direct methods and offers complementary applications. The list of successful structure-solution cases includes periodic and aperiodic crystals using single-crystal and powder diffraction data measured with X-ray and neutron radiation. Apart from counting applications, the paper mainly deals with algorithmic issues: it describes and compares new variants of the iteration scheme, helps to identify and improve solutions, discusses the required data and the use of known information. Finally, it tries to foretell the future of such an alternative among well established direct methods.

Direct structure determination by electron crystallography: protein data sets

Applications of the Sayre equation to the electron crystallographic analysis of protein structures are demonstrated. Starting with a lower-resolution basis phase set obtained from the Fourier-transform of an electron micrograph, it is possible, for example, to extend directly to the higher resolution of the electron diffraction pattern. Examples of such analyses include bacteriorhodopsin, halorhodopsin and the Omp F porin from the outer membrane of Escherichia coli. If a multisolution approach is taken, it may also be possible to carry out ab initio phase determinations, as demonstrated with low-resolution diffraction amplitudes from a negatively-stained membrane protein crystal.