Direct determination of crystallographic phases for diffraction data from lipid bilayers. I. Reliability and phase refinement

Abstract

Direct analysis of lipid lamellar packing based on the probabilistic estimate of sigma 1- and sigma 2-triplet phase invariants is evaluated here for a large variety of bilayer structures than examined in an original study of this problem (Dorset, D.L., 1990. Biophys. J. 58:1077-1087). Using x-ray crystal structures of five phospholipids, three glycerides and two cerebrosides, lamellar diffraction data were generated at the approximately 3 A resolution often found experimentally from oriented multilayers. For structures where no significant density occurs at the unit cell origin, the ab initio phase determination is successful for six of the ten structures. A seventh structure can be solved if a limited set of sigma 2-triples are used to determine the initial phase set based on the hierarchy of the A2 values. Bilayers, e.g., with solvent at the origin, can be analyzed if a modified criterion for accepting phase estimates for sigma 1-triples is used, as suggested by the distribution of normalized structure factors and the number of probable single-valued phase domains. In all cases, partial phase determinations can be refined effectively by density modification ("flattening") of the hydrocarbon region in real space. A figure of merit suggested by Luzzati et al. (Luzzati, V., A. Tardieu, and D. Taupin. 1972. J. Mol. Biol. 64:269-286) used to evaluate the success of such refinement can be supplemented by an evaluation of density smoothness, which can also detect the presence of near structure homomorphs not identified by the former test for density flatness.

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

“…A Fourier transform of p(z) was then calculated, at the same time flattening a section of the structure corresponding to the packing of acyl chains, as described (17,18). The procedure is equivalent to the solvent-flattening procedure used in Table 2 Table 1 (,6estl).…”

“…This was again transformed back to give a new estimate of the missing phases, resulting in no change from the list in Table 1. Since another reflection lies in a likely homogeneous phase domain determined by the intensity envelope (17,18), a value 4009 = ir was accepted to produce another map (Fig. 3, trace c).…”

“…The mixed chain packing, on the other hand, is betrayed by a lower potential density in the chain end region. This is readily seen when the profile is compared to the determination ofthe L-DHPE structure, after correction ofthe electron diffraction intensities for dynamical scattering, or also by comparison to recent analyses of phospholipids from x-ray diffraction data (17,18). Thus, as mentioned above, this result is also similar to the crystallographic results from cholesteryl ester solid solutions where the packing of sterol nuclei serves to immobilize one part of the molecule such as the hydrogenbonding intensities do for the phosphatidylethanolamine binary.…”

“…In this earlier work, measurements of lamellar spacings for several-binary combinations ofphosphatidylethanolamines, for which chain lengths and linkages were varied, were used to demonstrate continuous cosolubility in the crystalline and (thermotropic) smectic phases. Since the lamellar electron diffraction data often extend to reasonably high resolution (e.g., 0.34 nm), it should be possible to determine the layer packing by using analytical techniques developed in the past few years by this laboratory (16)(17)(18). Such a direct quantitative study of a binary phospholipid solid solution layer packing is presented in this paper.…”

Direct Phasing in Protein Electron Crystallography – Phase Extension and the Prospects forAb InitioDeterminations

“…(However, annealing reflections with weak amplitudes also is not useful.) False minima of q occur, therefore, and also shallow ones, as experienced before when this figure of merit was used to direct the phase refinement of phospholipid bilayers (Dorset, 1991). Thus, while this concept seems to provide a useful starting point, there may be other FOM's that will prove to be more useful for identification of correct phase changes.…”