Detailed procedures for solving small crystal structures ab initio with the maximum-entropy (ME) methods using X-ray powder diffraction data are described by determining the structure of the low-pressure phase of magnesium boron nitride, Mg3BN3(L), which was previously solved by one of the authors and co-workers using the Patterson method and the direct methods. The simple ME method devised by Gull, Livesey, and Sivia failed to correctly phase the structure-factor data, leading to noninterpretable electron-density maps. This method, maximizing the entropy under the constraints of the observed structure factors with subsequent incorporation of strong extrapolates in the basis set, trapped the solution in a local entropy maximum, from which there is no way to move. The multisolution method of phase determination by entropy maximization and likelihood evaluation, developed by Bricogne and Gilmore, successfully located all the Mg, B, and N atoms in one cycle of phase extension. The correct solution had a highest log-likelihood gain, but a minimum entropy, among the multisolutions generated by phase permutation.

Amorphous 1–2-nm-wide intergranular films in ceramics dictate many of their properties. The detailed investigation of structure and chemistry of these films pushes the limits of today's transmission electron microscopy. We report on the reconstruction of the one-dimensional potential profile across the film from an experimentally acquired tilt series of energy-filtered electron diffraction patterns. Along with the potential profile, the specimen thickness, film orientation with respect to the grain lattice and specimen surface, and the absolute specimen orientation with respect to the laboratory frame of reference are retrieved.

The solution of the crystallographic macromolecular phase problem requires incorporation of heavy atoms into protein crystals. Several 2′-halogenated nucleotides have been reported as potential universal phasing tools for nucleotide binding proteins. However, only limited data are available dealing with the effect of 2′-substitution on recognition by the protein. We have determined equilibrium dissociation constants of 2′-halogenated ATP analogues for the ATP binding proteins UMP/CMP kinase and the molecular chaperone DnaK. Whereas the affinities to UMP/CMP kinase are of the same order of magnitude as for unsubstituted ATP, the affinities to DnaK are drastically decreased to undetectable levels. For 2′-halogenated GTP analogues, the kinetics of interaction were determined for the small GTPases p21ras(Y32W) (fluorescent mutant) and Rab5. The rates of association were found to be within about one order of magnitude of those for the nonsubstituted nucleotides, whereas the rates of dissociation were accelerated by factors of ∼100 (p21ras) or ∼105 (Rab5), and the resulting equilibrium dissociation constants are in the nm or μM range, respectively. The data demonstrate that 2′halo-ATP and -GTP are substrates or ligands for all proteins tested except the chaperone DnaK. Due to the very high affinities of a large number of GTP binding proteins to guanine nucleotides, even a 105-fold decrease in affinity as observed for Rab5 places the equilibrium dissociation constant in the μM range, so that they are still well suited for crystallization of the G-protein:nucleotide complex.