Direct-methods Program Research Articles

Serial electron crystallography: merging diffraction data through rank aggregation

Serial electron crystallography is being developed as an alternative way to collect diffraction data on beam-sensitive polycrystalline materials. Merging serial diffraction data from a large number of snapshots is difficult, and the dynamical nature of electron diffraction prevents the use of existing methods that rely on precise measurement of kinematical reflection intensities. To overcome this problem, an alternative method that uses rank aggregation to combine the rankings of relative reflection intensities from a large number of snapshots has been developed. The method does not attempt to accurately model the diffraction intensity, but instead optimizes the most likely ranking of reflections. As a consequence, the problem of scaling individual snapshots is avoided entirely, and requirements for the data quality and precision are low. The method works best when reflections can be fully measured, but the benefit over measuring partial intensities is small. Since there were no experimental data available for testing rank-based merging, the validity of the approach was assessed through a series of simulated serial electron diffraction datasets with different numbers of frames and varying degrees of errors. Several programs have been used to show that these rank-merged simulated data are good enough for ab initio structure determination using several direct methods programs.

Assessment of methods for estimation of effective atomic numbers of common human organ and tissue substitutes: waxes, plastics and polymers

We calculated mass attenuation coefficients, effective atomic numbers and Kerma relative to air for human organ and tissue substitutes (i.e. wax, plastic and polymer materials). The effective atomic numbers of the tissue substi- tutes were calculated by the direct method, interpolation method, Auto-Zeff software and single value XMuDat program and then compared. The calculated effective atomic numbers were also compared with available experimental data and a good agreement was observed. A large difference in effective atomic numbers calculated by the direct and interpola- tion methods was observed in photoelectric and pair-production regions. The direct method was found to be appropriate for effective atomic number computation in low-(>10 keV) and medium-(0.1 ≤ E ≤ 10 MeV) photon energy regions. Kerma relative to air of the selected tissue substitutes was found to be dependent upon the atomic number and element compositions, which show a sharp peak due to K-edge absorption.

Hafnium-Silicon Precipitate Structure Determination in a New Heat-Resistant Ferritic Alloy by Precession Electron Diffraction Techniques

The structure determination of an HfSi4 precipitate has been carried out by a combination of two precession electron diffraction techniques: high precession angle, 2.2°, single pattern collection at eight different zone axes and low precession angle, 0.5°, serial collection of patterns obtained by increasing tilts of 1°. A three-dimensional reconstruction of the associated reciprocal space shows an orthorhombic unit cell with parameters a = 11.4 Å, b = 11.8 Å, c = 14.6 Å, and an extinction condition of (hkl) h + k odd. The merged intensities from the high angle precession patterns have been symmetry tested for possible space groups (SG) fulfilling this condition and a best symmetrization residual found at 18% for SG 65 Cmmm. Use of the SIR2011 direct methods program allowed solving the structure with a structure residual of 18%. The precipitate objects of this study were reproducibly found in a newly implemented alloy, designed according to molecular orbital theory.

A robust tangent procedure

Third-generation direct methods programs are based on a phasing algorithm (e.g.the tangent or the parameter shift method) and on dual space refinement techniques. The two spaces may be alternated during the phasing procedure or used in a sequential way: for example, first phase and after extend and refine. The tangent approach inSIR2011belongs to the second category: phases are first estimated by the tangent formula, then their extension and refinement is performed in direct spaceviaelectron density modification techniques. In this article a number of new algorithms are described, with the aim of improving theSIR2011tangent step and allowing more efficient phase extension and refinement. New criteria were chosen for defining the number of reflections to phase, for modifying the tangent weighting scheme, and for fixing the active use of the psi-0 triplets and of the quartet invariants. Each tangent trial may now be submitted to the RELAX procedure, a tool for moving to the correct position a well oriented but misplaced structural model. The resulting procedure shows surprising efficiency, testified by a wide set of applications. The experimental results have been compared with the tangent and VLD (vive la différence) approaches implemented inSIR2011.

Combining SAD/SIR iteration and MR iteration in partial-model extension of proteins

There are two kinds of dual-space partial-model extensions which involve the direct-method program OASIS. The first kind, named SAD/SIR iteration, uses SAD/SIR information, while the second kind, named molecular replacement (MR) iteration, does not use that information. In general, the SAD/SIR iteration is more powerful since more experimental information is used. However, in most cases when protein structures are solved with the molecular replacement method, SAD/SIR information is not available. Thus the MR iteration is particularly useful for the completion of models from molecular replacement. The SAD/SIR iteration will be automatically used in OASIS for data sets containing SAD/SIR signals, while the MR iteration will be dedicated to data sets without SAD/SIR signals. The present paper shows that for data containing SAD/SIR signals, a combination of SAD/SIR iteration and MR iteration could lead to significantly better results than that obtained from the SAD/SIR iteration alone.

A comparative study of crystal structure of a Cu(II) dicyanamide compound determined independently from X-ray powder- and single-crystal analyses

Abstract The dicyanamido diethelenetriamine copper (II) compound, C8H13CuN9 (I), has been synthesized, and structurally characterized independently using X-ray powder- and single-crystal diffraction data. The direct methods program package EXPO-2004 has been used for structure solution from laboratory powder diffraction data. Intermolecular N—H···N hydrogen bonds in (I) generate R2 2(16) rings, which are fused forming molecular columns propagating along the [100] direction. Further linking of parallel columns through N—H···N hydrogen bonds results into a three-dimensional supramolecular network.

What can be done with a good crystal and an accurate beamline?

X-ray single-wavelength anomalous diffraction (SAD) data from a crystal of proteinase K were collected using synchrotron radiation of 0.98 A wavelength at SER-CAT 22-ID beamline, Advanced Photon Source, Argonne National Laboratory. At this wavelength, the expected Bijvoet ratio resulting from the presence of one calcium, one chloride and ten S atoms in the 279-residue protein is extremely small at approximately 0.46%. The direct-methods program SHELXD located 11 anomalous sites using data truncated to 2 A resolution. SHELXE was used to produce an easily interpretable electron-density map. This study shows that an accurate beamline and a good-quality crystal provide the possibility of successfully using a very weak anomalous signal of sulfur measured at a short wavelength for phasing a protein structure, even if a small degree of radiation damage is present.

Use of an ion-binding site to bypass the 1000-atom limit to structure determination by direct methods.

Proteins with more than 1000 non-H atoms and without heavy-atom prosthetic groups are very difficult to solve by ab initio direct methods. T4 lysozyme is being used to explore these limits. The protein has 1309 non-H atoms, seven S atoms, no disulfide bonds and no heavy-atom prosthetic group. It is recalcitrant to structure determination by direct methods using X-ray diffraction data to 0.97 A. It is shown here that it is possible to obtain a truly ab initio structure determination of a variant of the protein that has an Rb+ (Z = 37) binding site. Using diffraction data to 1.06 A resolution, the direct-methods programs SIR2002 and ACORN independently solved the structure in about 20 h. The bound Rb+, which contributes about 1.7% of the total scattering, does not appear to distort the structure or to inhibit refinement (R factor 12.1%). The phases obtained via SIR2002 or ACORN are in good agreement with those from a reference structure obtained from conventional molecular-substitution and refinement procedures (average error in the figure-of-merit-weighted phases of less than 25 degrees). Thus, proteins with more than 1000 atoms that include halide-binding or other such sites may be amenable to structure determination by ab initio direct methods. The direct-methods approaches are also compared with structure determination via use of the anomalous scattering of the Rb+ ion. As shown by examples, high-resolution structures determined by direct methods can be useful in highlighting regions of strain in the protein, including short hydrogen bonds and non-planar peptide groups.

Away from the edge: SAD phasing from the sulfur anomalous signal measured in-house with chromium radiation.

Anomalous scattering with soft X-ray radiation opens new possibilities in phasing for macromolecular crystallography. Anomalous scattering from S atoms collected on an in-house chromium radiation source (lambda = 2.29 A) was used to phase the X-ray diffraction data of thaumatin (22 kDa) and trypsin (24 kDa) crystals. The contribution to the anomalous term, Deltaf" = 1.14 e(-), from sulfur for Cr Kalpha radiation is doubled compared with that for Cu Kalpha radiation, Deltaf" = 0.56 e(-). The direct-methods programs RANTAN or SHELXD successfully found sulfur positions using data sets with resolution limited to 3.5 A. The statistical phasing program SHARP was used to produce the electron-density maps using the sulfur anomalous signal alone at low resolution ( approximately 3.5 A). An interpretable electron-density map for each structure was obtained solely from the phases derived from single-wavelength anomalous dispersion (SAD) data obtained using Cr Kalpha radiation. Much fewer data (that is, lower redundancy) are required for this sulfur SAD phasing procedure compared with the highly redundant data reported in the sulfur SAD phasing procedure with Cu Kalpha radiation. Cr Kalpha radiation can also improve the strength of anomalous scattering of many other intrinsic elements in macromolecules, such as calcium, zinc and phosphorus, because of the increased Deltaf". Furthermore, the anomalous scattering of selenium is increased substantially from 1.14 e(-) with Cu Kalpha radiation to 2.28 e(-) with Cr Kalpha radiation. In order to measure the small Bijvoet differences accurately, several devices were developed for the experiment, including an Osmic Confocal MaxFlux optic optimized for Cr Kalpha radiation, a helium path and a beam stop. In the cases studied here, radiation damage to the samples and reduction of anomalous signal were observed in some long exposure time data sets. Therefore, an adequate data-collection strategy to maximize the completeness in a short scan range was used in subsequent data collections. The results show that the anomalous signal of S atoms can be collected quickly. Since the absorption of solvent and the loop may no longer be negligible with Cr Kalpha radiation, the orientation of the crystal and exposure time were taken into account in order to minimize the effects of radiation damage and absorption. This experimental study shows that using Cr Kalpha radiation from an in-house rotating-anode X-ray generator can provide sufficient phasing power from sulfur anomalous signals to routinely phase protein diffraction data.

SAPI: a direct-methods program for finding heavy-atom sites with SAD or SIR data

SAPIis aCCP4-format program that applies a direct-methods procedure to find heavy-atom sites using single-wavelength anomalous dispersion (SAD) or single-isomorphous replacement (SIR) data. The program is designed to run in a fast (typical CPU time consumed is less than 1 min) and simple way. User input is kept to a minimum and the default parameter values are adequate in most cases. It can also be used to solve general small-molecule structures.

SAD manganese in two crystal forms of glucose isomerase.

Glucose isomerase from Streptomyces rubiginosus was crystallized in two forms: I222, with one molecule of 44 kDa in the asymmetric unit, and P2(1)2(1)2, with two unique molecules. The I222 structure is known, but the P2(1)2(1)2 form has not been solved before. X-ray diffraction data for the P2(1)2(1)2 form were collected at a wavelength of 1.54 A and data for the I222 form were collected at three different wavelengths: 1.34, 1.07 and 0.98 A. The amount of anomalous signal from one Mn and eight S atoms in these data sets varies from 1.24% to as low as 0.56%. The dual-space direct-methods program SHELXD, run against the Bijvoet differences, gave a clear solution of all anomalous scatterers for all data sets. The Mn positions only were used for SAD phasing of all four data sets. The electron-density map after density modification, resulting from the phasing of a single-wavelength data set and based purely on the anomalous deltaf" contribution, was clearly interpretable; an almost complete model of the protein was built by wARP without human intervention in all four cases. As far as is known, this is the first time that an anomalous signal as low as 0.6% has successfully been used to determine the structure of a macromolecule.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

Abstract The direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c6, a heme-containing redox protein with 89 amino acids, a Fe atom and 151 solvent water molecules in the asymmetric unit and data to 1.1 Å resolution. The crystal system is rhombohedral with space group R3, cell parameters a = b = c = 40.43(10) Å, α = β = γ = 80.25(5)°. Starting with initially random phases, useful phase sets could be obtained from multiple trials of direct methods based on reciprocal space. The E-map corresponding to the phase set with the lowest mean phase error, 45.4°, showed a distorted octahedral coordination around the Fe site. The phase estimates from the metal atom and a few neighbouring atoms in the initial E-map have been improved by density modification procedure (PERP) operating in direct space. The resulting electron density map can be interpreted readily by an automated procedure to build up the protein structure.

Towards automated protein structure determination: BnP, the SnB-PHASES interface

Abstract The direct-methods program SnB provides an efficient means for solving protein substructures containing many heavy-atom sites (current record: 160). In order to meet the high-throughput requirements of structural genomics projects, substructure determination needs to be tightly integrated with other aspects of the protein-phasing process. This has been accomplished through the design of a common Java interface, BnP, for SnB and components of PHASES, a popular and proven program suite that provides all the tools necessary to proceed from substructure refinement to the computation of an unambiguous protein electron-density map. Therefore, BnP will facilitate a high degree of automation and enable rapid structure determination by both experienced and novice crystallographers.

A quick solution:ab initiostructure determination of a 19 kDa metalloproteinase usingACORN

A data set from the metalloproteinase deuterolysin was collected at atomic resolution (1.0 A) with synchrotron radiation. The high resolution allowed the structure to be solved with the new direct-methods program ACORN using the coordinates of the Zn atom as a starting point. The phases obtained from ACORN were of sufficient quality to allow automated building to be carried out in ARP/wARP. Minimal manual rebuilding of the model was required and the structure determination was completed using the maximum-likelihood refinement program REFMAC. The whole process, starting from the processed and merged data and ending with a refined model, required less than 6 h of computational time.

A direct-methodab initiophasing of a protein, cupredoxin amicyanin, at 1.31 Å resolution

The direct-methods program MULTAN88 has been applied successfully to redetermine the structure of a protein, cupredoxin amicyanin, containing 808 non-H atom sites, one Cu atom and 132 ordered water molecules in the asymmetric unit using data at 1.31 A resolution. Starting with initially random phases, useful phase sets selected by figures of merit could be obtained from multiple trials. The E maps corresponding to the best eight phase sets in order of combined figures of merit (CFOM2) revealed a distorted tetrahedral geometry around the Cu site. The phase estimates from the metal and a few neighbouring atoms in the initial E map corresponding to the set with the highest CFOM2 could be improved by the density-modification procedure PERP and led to an interpretable electron-density map.

Crystal structure a cobalt molybdate type φx: NaCo2OH(H2O)(MoO4)2

A cobalt molybdate with the formula NaCo2OH(H2O)(MoO4)2 was synthesized by hydrothermal reaction at 200°C in 3 days. The structure was determined from powder data by means of the EXPO direct methods program and refined with GSAS. The purple solid crystallizes in the monoclinic space group C2/m with a=9.3789(3), b=6.3330(1), c=7.6280(2) Å, and β=115.833(2)a. Octahedral cobalt atoms, centered at 1/4b and 3/4b, share edges to create endless chains running parallel to the b axis. The chains are connected through molybdenum tetrahedra, which share two vertices with consecutive octahedra in one chain and extend the third vertex to an adjacent chain; the fourth vertex protrudes into the interlayer space. This arrangement repeats itself indefinitely in the ab plane to create a layered structure.

Synthesis and structure of a porous zinc vanadate, Zn3(VO4)2·3H2O

A zinc vanadate with the formula Zn3(VO4)2·3H2O was synthesized by hydrothermal reaction of a gel of composition [(CH3CO2)2Zn·2H2O] : 0.5V2O5: 0.4 [1,3-diaminepropane] : 1.5 NaOH : 114 H2O, held at 170°C for 24 hours. The structure was determined ab initio by means of the EXPO direct methods program and refined with GSAS. The pale yellow solid crystallizes in the hexagonal space group P-6 with a= 6.07877(8), c= 7.1827(2) A. The structure consists of vanadium tetrahedra bonded to distorted octahedral zinc atoms to create one dimensional columnar passageways for molecules. Though occupied by water in the as synthesized form, the passages could host other small molecules.

A direct-methodab initiophasing of a protein, pseudoazurin, at 1.55 Å resolution

The direct-method program MULTAN88 has been applied to solve a known protein, pseudoazurin, space group P6(5), unit-cell parameters a = b = 50.0 (1), c = 98.5 (3) A, with 917 protein atoms, a Cu atom and 93 solvent water molecules in the asymmetric unit (>6,000 non-H atoms in the unit cell) and data at 1.55 A resolution. One of several trials with sets of initially random phases yielded phase estimates for 1,000 reflections with a mean phase error of 68.3 degrees that was recognized as the best available solution by the figure of merit being used. Phase extension to 2,000 largest Es showed a distorted tetrahedral geometry around the Cu site. Density modification was applied to improve the phases and the quality of the maps, starting with phases calculated from the atomic positions indicated by the first map.

Structure and function of S-adenosylhomocysteine hydrolase.

In mammals, S-adenosylhomocysteine hydrolase (AdoHcyase) is the only known enzyme to catalyze the breakdown of S-adenosylhomocysteine (AdoHcy) to homocysteine and adenosine. AdoHcy is the product of all adenosylmethionine (AdoMet)-dependent biological transmethylations. These reactions have a wide range of products, and are common in all facets of biometabolism. As a product inhibitor, elevated levels of AdoHcy suppress AdoMet-dependent transmethylations. Thus, AdoHcyase is a regulator of biological transmethylation in general. The three-dimensional structure of AdoHcyase complexed with reduced nicotinamide adenine dinucleotide phosphate (NADH) and the inhibitor (1'R, 2'S, 3'R)-9-(2',3'-dihyroxycyclopenten-1-yl)adenine (DHCeA) was solved by a combination of the crystallographic direct methods program, SnB, to determine the selenium atom substructure and by treating the multiwavelength anomalous diffraction data as a special case of multiple isomorphous replacement. The enzyme architecture resembles that observed for NAD-dependent dehydrogenases, with the catalytic domain and the cofactor-binding domain each containing a modified Rossmann fold. The two domains form a deep active site cleft containing the cofactor and bound inhibitor molecule. A comparison of the inhibitor complex of the human enzyme and the structure of the rat enzyme, solved without inhibitor, suggests that a 17 degrees rigid body movement of the catalytic domain occurs upon inhibitor/substrate binding.

XLENS, a direct methods program based on the modulus sum function: Its application to powder data

XLENS is a traditional direct methods program working exclusively in reciprocal space. The distinctive feature of XLENS is the use of the modulus sum function as target function for the phase refinement. Due to its efficiency, robustness, and no need of weighting schemes, this function is specially well suited for treating powder diffraction data. The mathematical basis as well as the significance of the most important control parameters of the program will be described here. To illustrate how XLENS works, three different examples will be shown. Due to its simplicity, the modulus sum function can be easily combined with real-space filtering procedures to produce even more efficient crystal structure solving strategies.