Individual Temperature Factors Research Articles

Debye—Waller factors of stoichiometric and Al-rich γ-TiAl alloys

Abstract Average room temperature Debye—Waller factors B and individual (isotropic) temperature factors B Ti and B Al of γ-TiAl alloys containing 51, 54 and 56 at.% Al have been determined by conventional powder X-ray diffraction. The B values for Ti—50 at.% Al and Ti—56 at.% Al were also measured by the critical voltage method in electron diffraction. The temperature factors were calculated from the X-ray intensities using both free-atom relativistic Hartree—Fock structure factors as well as a set of structure factors obtained from first principles local density calculations for the equiatomic γ-TiAl alloy. The B values determined from the X-ray intensities using the free-atom structure factors were found to be in poor agreement with those determined by electron diffraction whereas the B values calculated from the X-ray intensities using structure factors obtained from first-principles calculations were found to be in good agreement with the electron diffraction data. This difference appears to arise because many of the low-angle structure factors of γ-TiAl (up to hkl = 224) are significantly different from the free-atom values owing to crystal bonding. It was found to be difficult to determine the individual temperature factors B Ti and B Al with high accuracy, particularly for the 54 and 56 at.% Al alloys. This is ascribed to the static contributions to the Debye—Waller factors associated with the excess Al atoms on Ti sites and to the ordering of these excess Al atoms on the Ti sublattice as discussed in recent single-crystal X-ray work on this topic.

Atomic thermal parameters of TiN by powder elastic neutron diffraction

For the first time, the difference between the thermal parameters of metal and nonmetal ions has been positively established by high-resolution neutron diffraction measurements on a powder sample of TiN. Measurements were made on a double- as well as triple-axis neutron spectrometer. The data were analysed by the Rietveld method. The refined occupancy factor indicated a chemical composition of TiN0.95 (1). The values of the individual temperature factors were BTi = 0.209 (13) A2 and BN = 0.271 (7) A2. The results of the present investigation are compared with the values obtained by X-ray and neutron diffraction techniques.

Crystal structure of cytochrome c3 from Desulfovibrio desulfuricans Norway at 1·7 Å resolution

The crystal structure of cytochrome c 3 ( M r 13,000) from Desulfovibrio desulfuricans (118 residues, four heme groups) has been crystallographically refined to 1.7 Å resolution using a annealing method, based on the structure-model at 2.5 Å resolution, already published. The final R-factor for 10,549 reflections was 0·198 covering the range from 5·5 to 1·7 Å resolution. The individual temperature factors were refined for a total of 1059 protein atoms, together with 126 bound solvent molecules. The structure has been analyzed with respect to its detailed conformational properties, secondary structure features, temperature factor behaviour, bound solvent sites and heme geometery and ligation. The characteristic secondary structures of the polypeptide chain of this molecule are one extended α-helix, a short β-strand and 13 reverse turns. The four heme groups are located in different structural environments, all highly exposed to solvent. The particular structural features of the heme environments are compared to the four hemes of the cytochrome c 3 from Desulfovibrio vulgaris Miyazaki.

Crystallographic refinement and structure of ribulose-1,5-bisphosphate carboxylase from Rhodospirillum rubrum at 1.7 Å resolution

The amino acid sequence of ribulose-1,5-bisphosphate carboxylase/oxygenase from Rhodospirillum rubrum has been fitted to the electron density maps. The resulting protein model has been refined to a nominal resolution of 1.7 Å using the constrained-restrained least-squares refinement program of Sussman and the restrained least-squares refinement program of Hendrickson & Konnert. The crystallographic refinement, based on 76,452 reflections with F >σ(F) in the resolution range 5.5 to 1.7 Å resulted in a crystallographic R-factor of 18.0%. The asymmetric unit contains one dimeric ribulose-1,5-biphosphate carboxylase molecule, consisting of 869 amino acid residues and 736 water molecules. The geometry of the refined model is close to ideal, with root-mean-square deviations of 0.018 Å in bond lengths and 2.7 ° in bond angles. Two loop regions, comprising residues 54 to 63 and 324 to 335, and the last ten amino acid residues at the C terminus are disordered in our crystals. The expected trimodal distribution is obtained for the side-chain χ1-angles with a marked preference for staggered conformation. The hydrogen-bonding pattern in the N-terminal β-sheet and the parallel sheet in the βα-barrel is described. A number of hydrogen bonds and salt bridges are involved in domain-domain and subunit-subunit interactions. The subunit-subunit interface in the dimer covers an area of 2800 Å2. Considerable deviations from the local 2-fold symmetry are found at both the N terminus (residues 2 to 5) and the C terminus (residues 422 to 457). Furthermore, loop 8 in the ββ-barrel domain has a different conformation in the two subunits. A number of amino acid side-chains have different conformations in the two subunits. Most of these residues are located at the surface of the protein. An analysis of the individual temperature factors indicates a high mobility of the C-terminal region and for some of the loops at the active site. The positions and B-factors for 736 solvent sites have been refined (average B: 45·9 Å2). Most of the solvent molecules are bound as clusters to the protein. The active site of the enzyme, especially the environment of the activator Lys191 in the non-activated enzyme is described. Crystallographic refinement at 1.7 Å resolution clearly revealed the presence of a cis-proline at the active site. This residue is part of the highly conserved region Lys166-Pro167-Lys168.

Structure-activity relationships of methionyl-tRNA synthetase: graphics modelling and genetic engineering

The 3D structure of the methionyl-tRNA synthetase from E. coli has been investigated using X-ray analysis 1,2 at a resolution 1.8Å. 90% of the molecule is now well defined and the zinc atom has been identified in a buried region of the molecule, close to the active site. At the same time, the refinement of the complex ATP-MetRS at 2.5 Å has been carried out. The crystallographic R factor has been assigned a value of 25% at 2.5Å with an overall temperature factor of 9Å 2 and 22% when the individual temperature factors are refined. A Fourier difference map clearly reveals the electron density of the bound ATP, showing the phosphate groups deeply plunging into the active site. In parallel, the synthetase gene has been used to probe some of the enzyme structure-activity relationships. A series of 60 modified enzymes truncated at the C-terminus have been constructed in vitro and assayed for activity. In agreement with the graphics model, the results show that a minimum of 534 residues is necessary to sustain the aminoacylation reaction. A programme of site-directed mutagenesis is in progress: residues thought to be important for the catalytic activity, the metal coordination and tRNA interaction are being modified. Preliminary results are discussed in the light of the crystallographic model.

Determination by X-ray diffraction of interstitial concentrations of vanadium ions in disordered VOx

Integrated intensities were measured from VOx single crystals with x = 0.80, 0.94, 1.01, 1.11 and 1.25. A least-squares refinement was carried out for the scale factor and the isotropic temperature factors of vanadium and oxygen ions for each composition, for a range of interstitial vanadium contents. The R values after the refinement were 0.04-0.05. There are vanadium ions at tetrahedral interstitial sites, the concentration of which changes from 0-0.5% to 3% with composition x; this confirms quantitatively previous studies which employed dynamical electron diffraction effects. The temperature factors of vanadium (BV) and oxygen (BO) increase with x; BV = 1.02-1.38 A2 and BO = 0.58-1.24 A2. The composition dependence of the overall temperature factor is similar to that of the lattice parameter. The 002 structure factor for electrons U002 and the critical voltage Ec at which the second-order Kikuchi line disappears were calculated for VO0.82 and VO1.20, using the individual temperature factors determined by this study. The 002 structure factors measured by the critical-voltage and the intersecting-Kikuchi-line method [Watanabe, Andersson, Gjonnes & Terasaki (1974). Acta Cryst. A30, 772-776] were in agreement within less than 2%. The results support the idea that the ionic state of the cation lies between neutral and singly ionized.

Refinement of the structure of carp muscle calcium-binding parvalbumin by model building and difference fourier analysis

The structure of carp muscle calcium-binding parvalbumin has been refined to an overall residual, ( Σ¦F 0 − F c¦ Σ¦F 0¦ ), of 0.25 by a combination of model building and difference Fourier analyses. The atomic positions were allowed to vary up to 0.25 Å from their idealized positions; individual temperature factors ranged from 2 to 150; and 138 solvent peaks were included in this final structure factor calculation. The effects of varying these parameters were analyzed. The treatment of low-order reflections and the influence of solvent have been analyzed in terms of Babinet's principle. These procedures and results are applicable to other protein refinement problems. The errors in co-ordinates are estimated to range from 0.15 Å for the Ca 2+ ions to 0.30 Å for internal side chain atoms. A van der Waals' radii study indicates that 42% of the crystal volume is occupied by solvent. There are 16 intermolecular contacts. Of the 108 main chain peptide hydrogen atoms, 15 are neither in contact with solvent nor involved in hydrogen bonds. These “lost” hydrogen bonds are considered to be important to the proposed model of function.

Neutron diffraction study of sodium thiosulphate pentahydrate, Na2S2O3.5H2O

A single-crystal neutron-diffraction investigation of sodium thiosulphate pentahydrate, Na2S203.5H20, has been made with three sets of zonal data. The structure was refined by least-squares techniques, with individual temperature factors, to an R value of 8.2%. The geometry of the $203 group and sodium-oxygen framework agree with those of X-ray studies. The positional parameters of some of the atoms differ from those p3stulated from the X-ray and nuclear magnetic resonance studies. The O-H and H-H bond distances and the H-O-H valence angle of all the five water molecules were found to be normal. The hydrogen-bond scheme falls into four classes: two strong water-thiosulphate oxygen, two weak water-thiosulphate oxygen, two water-water, and three water-sulphur hydrogen bonds. From the geometry of its surroundings one of the hydrogen atoms H(9) may be regarded as not participating in hydrogen bonding.

Refinement of the crystal structure of scandium oxide

The crystal structure of Sc2O3 (C-type; a0 = 9.8459 ± 15 Å at 20 ± 2 °C) was refined from X-ray powder diffractometer data. Isotropic individual temperature factors were used in full-matrix F (19 reflections) and F2 (41 reflections) programs. The positional parameters were determined as u(Sc) = −0.0355 ± 1, x(O) = 0.3933 ± 3, y(O) = 0.1513 ± 3, and z(O) = 0.3835 ± 3. The merits and limitations of refining from careful powder diffractometer data are briefly discussed.

A method for seeking an appropriate model of complicated organic crystal structure based on two-dimensional least squares refinement

In crystals of complicated organic substances of all atoms having approximately the same weights most of the atoms overlap in projections and therefore it is impossible to verify the correctness of a proposed model of structure and to improve it by Fourier projections. As the three-dimensional Fourier syntheses are rather time-consuming, two-dimensional least squares refinement of coordinates and individual temperature factors is used.

Chalcogenides of the transition elements. V. Crystal structures of the disulfides and ditellurides of ruthenium and osmium

The crystal structures of RuS2, OsS2, RuTe2, and OsTe2were refined isotropically by least squares from powder diffractometer data using individual temperature factors. The resulting positional parameters of the chalcogen atoms in these C2-type structures are 0.3879 ± 14, 0.3865 ± 19, 0.3739 ± 9, and 0.3725 ± 18 respectively (for meaning of the uncertainty limits see Table II and text). The structure of Ir3Te8was refined from Hockings and White's published data to give x(Te) = 0.3702 ± 18. The shortest metal–chalcogen distances in these structures are Ru—S 2.351 ± 3 Å, Os—S 2.352 d ± 5 Å, Ru–Te 2.647 ± 3 Å, Os–Te 2.647 ± b 3 Å, and Ir—Te 2.651 ± 4 Å (not corrected for thermal motion). The shortest S–S distances (in the S2groups) are 2.179 ± 30 Å in RuS2and 2.210 ± 46 Å in OsS2. The corresponding shortest Te—Te distances are 2.791 ± fc 35 Å in RuTe2, 2.826 ± 38 Å in OsTe2, and 2.872 ± 30 Å in Ir3Te8(not corrected for thermal motion). Within the stated uncertainty limits the shortest metal–chalcogen distances are independent of the nature of the metal. The shortest chalcogen–chalcogen distances are so sensitive to variations in x that even the above relatively narrow uncertainty limits preclude meaningful statements to be made about the effect of the metal on these distances, with the possible marginal exception of the nonstoichiometric C2 structure Ir3Te8.