Direct determination of crystallographic phases for diffraction data from lipid bilayers. II. Refinement of phospholipid structures

Direct structure analysis in protein electron crystallography: crystallographic phases for halorhodopsin to 6-A resolution

The crystal structure of halorhodopsin was determined in (centrosymmetric) projection to 6-A resolution by direct methods that use only the amplitudes of the electron diffraction pattern. A multisolution technique was used to generate initial 15-A-resolution basis sets, and after selection of the best phase set (by the closest match of magnitude of Eobs and magnitude of Ecalc), annealing of individual reflections was used to improve its accuracy. The Sayre equation was then used to expand the phase terms to 10 A, followed again by phase annealing. A final expansion with the Sayre equation enlarged this corrected phase set to 6 A. When the condition of density flatness was used to locate the best phase solution after each extension, a final structure could be observed that was quite similar to the one found earlier by analysis of electron micrographs.

The Sayre equation in electron crystallography

The Sayre equation was evaluated as a technique for phase refinement in electron crystallography. Atomic-resolution electron diffraction data from copper perchlorophthalocyanine were assigned phase values from the Fourier transforms of various experimental electron micrographs, including one at 2.3 A, containing errors due to lens astigmatism. In each case, an atomic-resolution structure could be found after Fourier refinement. In addition, it was possible to begin with a basis set derived from symbolic addition for phase extension. Such a source of phases was also found to be useful for extending zonal electron diffraction sets from six polymer crystals, even though there was considerable overlap of atomic positions in the projection down the chain axes. Other tests of the Sayre equation were made with zonal protein data sets (bacteriorhodopsin, halorhodopsin) to evaluate what difficulties are to be expected when direct phasing techniques are to be used in macromolecular electron crystallography. Comparison to known values indicated that the low-resolution range (e.g. to 6 A) was reasonably stable for phase extension from a 10-15 A resolution image. Only when a minimum in average intensity was approached (near 5 A) did the direct extension encounter serious difficulties. If this minimum was treated as a "phase node" to generate two possible solutions, a model more similar to the true phase set was found. In general, this rather simple convolutional technique for phase extension seems to be particularly suitable for a variety of electron crystallographic applications.

Direct determination of layer packing for a phospholipid solid solution at 0.32-nm resolution

Electron diffraction intensity data were collected from a 2:3 binary solid solution of two homologous phosphatidylethanolamines (1,2-dimyristoyl-sn-glycerophosphoethanolamine and 1,2-dipalmitoyl-sn-glycerophosphoethanolamine) epitaxially oriented by cocrystallization with naphthalene. The layer packing was determined directly by predicting the value of 12 of the 17 phases from sigma 1- and sigma 2-triplet invariants in space group P1. A reverse Fourier transform of the resulting potential maps provides estimates for three other phases and the two remaining ones were found by generating maps for the 2(2) = 4 possible phase combinations and then testing the smoothness of the potential profile of the hydrocarbon chain packing. The same phase solution can be found by translating a molecular model (based on the known x-ray crystal structure of a shorter homologue) past the unit cell origin. The solid solution is found to retain a stable polar group packing while the statistical occupancy of two terminal-chain carbons is expressed by a reduced potential profile at the nonpolar interface at the bilayer center.

Electron crystallography of organic and biological molecules--techniques and comparison to X-ray crystallographic results

In this review, it is shown how ab initio analyses of molecular crystal structures can be carried out with electron diffraction intensities and high-resolution, low-dose, electron micrographs, dispelling the long-held myth that such determinations are not possible. The results for small organics, polymethylene compounds, various polymers, and even intregral membrane proteins, are in good agreement with independent X-ray crystal structure determinations, which, however, were not needed to solve the crystallographic phase problem from the electron scattering data. The concept of electron crystallography benefits from the utility of electron micrographs for providing phase information, in addition to the standard 'direct' methods used nowadays by all crystallographers.