ALBERT

Notes: Owing to the two-dimensional periodicity of a superstructure on the crystal surface, the intensity in reciprocal space is continuously distributed along rods normal to the sample surface. The analysis of rod scans in surface X-ray diffraction provides information about the structure parameters normal to the sample surface. For high resolution to be achieved, the measurements must extend to momentum transfers q⊥ that are as large as possible. At large exit angles, the conventional Lorentz factor must be modified to take account of the finite aperture of the detector and the continuous intensity along the lattice rod. For two types of Z-axis diffractometer used in surface X-ray crystallography, an analytical expression for the resolution correction of rod-scan intensity data has been developed. It takes into account an anisotropic detector resolution T(ΔΘ, ΔΦ), the finite width of the diffracted beam and the primary-beam divergence parallel to the sample surface, Δτ. The calculation of the convolution functions is simplified by a projection onto the q⊥ = 0 plane. The effects of different detector settings and the influences of the primary-beam divergence and the sample quality on the measured intensity are demonstrated for several examples.

Notes: A four-circle diffractometer system has been built around the Huber model 5042. The scintillation detector and associated electronics were assembled from commercially available standard modules. A comprehensive control program has been developed. It runs on a cheap personal computer that also incorporates a fast multichannel scaler board for automatic histogram production from continuous or step intensity scans. The software can handle the complete unit-cell determination and data collection in an automatic mode but for the experienced user who wishes to tailor the experiment to his or her particular needs, there are more than 100 commands available.

Notes: A suite of computer programs (REPLACE) for crystal-structure determination by the molecular-replacement method has been developed. It currently includes a general (locked) rotation-function program (GLRF) and a translation-function program (TF). The rotation-function program can carry out ordinary as well as locked self- or cross-rotation-function calculations. It can also optimize non-crystallographic symmetry parameters based on the maximal electron-density overlap of the subunits related by the non-crystallographic symmetry. The translation search can be based on R-factors, correlation coefficients, Patterson correlation and electron-density-correlation criteria. The packing of the molecular structure in the unit cell can be checked as well.

Notes: This paper describes the characterization of an image-plate readout system used to calculate small-angle-scattering intensities as cross sections per unit volume. The raw data are the latent phosphorescent excitations stored on an image plate. Self-decay, self exposure, resolution, smearing, dynamic range and sensitivity are measured. Preliminary experiments show that an inexpensive neutron-imaging system can be obtained when the plates are placed behind a suitable neutron-to-X-ray converter.

Notes: On the basis of the expressions given by Rossmanith [Acta Cryst. (1992), A48, 596–610; (1993), A49, 80–91], a simple approximation is derived for the half-widths of Bragg intensity profiles measured with a triple-crystal diffractometer at a synchrotron-radiation source. This new formula facilitates insight into the effects of four parameters – divergence, wavelength spread, mosaic spread and mosaic block size – on the widths of the profiles.

Notes: An approximate experimental correction of electron diffraction intensities from an epitaxically crystallized phospholipid bilayer for dynamical scattering is described. This correction, which is useful for certain low-angle centrosymmetric data sets, compares intensities recorded at high and low electron-accelerating voltages to ascertain which reflections are most affected by n-beam interactions. When applied to experimental intensity data from 1,2-dihexadecyl-sn-glycerophosphoethanolamine (DHPE), the correction facilitates a direct phase determination based on the probabilistic estimate of three-phase invariants because a more accurate estimate of the hierarchy of |El| values is obtained. When a multisolution technique is used, incorporating algebraic unknowns for certain phase values, the best phase assignment can be assessed by comparison of the single convolution of phased structure factors to the observed structure-factor magnitudes for the low-voltage data. This approach exploits an approximate analogy made earlier by Moodie between the Sayre equation and the phase grating series and is valid as long as the single convolution adequately models experimental low-voltage data (a condition favored by light-atom structures in a low-angle region of reciprocal space). In real space, the correct structure can also be readily identified as the one having the smoothest density profile.

Notes: An automated structure-refinement program has been developed for X-ray powder diffraction data collected on disordered carbons. The program minimizes the difference between the observed and calculated diffraction profiles in a least-squares sense by optimizing model parameters analogously to the popular Rietveld refinement method. Unlike the Rietveld method, which is designed for crystalline materials, this program allows the quantification of the finite size, strain and disorder present in disordered carbon fibers and cokes. For example, the structural model used includes the probability of a random translation parallel to adjacent carbon layers as a refinable parameter describing turbostratic disorder. Other parameters are used to describe finite size, fluctuations in the spacing between adjacent layers, average lattice constants, background and other important quantities. The structural model, combined with the refinement program, acceptably describes the diffraction patterns from disordered carbons such as pitch heated near 823 K, cokes, fibers, heat-treated cokes and synthetic graphite.

Notes: The pressure sensor proposed by Shen, Gregorian & Holzapfel [High Press. Res. (1991), 7, 73–75], based on the pressure-dependent shift of the luminescence line due to the 5D0−7F0 electronic transition of Sm2+ in a matrix of BaFCl, has been tested in a diamond-anvil cell and calibrated against the R1−R2 doublet shift of ruby and the known NaCl equation of state, in the pressure range between 0.0001 and 4.3 GPa. The parabolic dependence of the shift from the pressure can be approximated by the equation Δ(nm) = 1.46P − 0.047P2, where the shift, Δ, is in nm and the pressure, P, in GPa. The estimated error in the pressure measurements is 5%. The Sm2+: BaFCl luminescence sensor can be advantageously used in the low to moderate pressure range (0.0001–5 GPa or more).

Notes: Perturbations from crystal perfection will result in diffuse X-ray scattering, which can be imaged by topography to yield defect information without the swamping contribution of perfect-crystal scattering. This paper illustrates the importance of the probe shape for obtaining topographic images in this diffuse region not only to aid interpretation but to isolate the contributors to this scattering. The diffuse scattering in the vicinity of the Bragg peaks of GaAs, Si and Ge substrate crystals has been mapped to very high resolution and the diffuse scattering has been imaged by topography. It was found that the majority of the scattering emanates from surface damage and dislocations and not point defects or thermal diffuse scattering (TDS). These latter two components are found to be second-order effects in general and are only just discernable as a very weak background intensity in highly perfect crystals. This topography method is very sensitive to surface damage. This is because the associated diffuse scattering close to a Bragg peak can be used to form an image. Therefore, this relatively intense scattering provides a topograph within a few hours for assessing substrate-surface quality. The sensitivity of the method is illustrated with images of surface defects and dislocations in very perfect semiconductors. A procedure for measuring the diffuse scattering emanating from microdefects is also presented.

Notes: Spectroscopic measurements on crystals during X-ray data collection provide additional information on the composition of the crystal and can be used in the interpretation of structural data. This paper describes a portable microspectrophotometer to obtain UV–visible–near-IR spectra from single crystals during X-ray measurements. The instrument consists of a deuterium lamp, optical fibres, a pair of mirror lenses and a monochromator equipped with a photodiode array detector. Spectra can be recorded in short periods of time (a few milliseconds) from a measurement area of 0.10 mm diameter or smaller. The device can be used to monitor spectral changes in crystals during time-resolved X-ray experiments so that the X-ray camera can be triggered at the right moment as determined by the spectrum, thereby eliminating much of the present guesswork from such studies.

Notes: The construction of a new high-pressure cell is presented. It is a piston-cylinder type of apparatus. The entrance and exit of X-rays or light are possible through two parallel diamond-plate windows placed on V-shaped slits covering almost the whole range of reflection angles. This makes the cell particularly suitable for X-ray diffraction examinations of monocrystals. The potential accuracy of absolute-bulk-modulus determination by lattice-constant measurements using the Bond method [Bond (1960). Acta Cryst. 13, 814–816] at pressures of 108–109 Pa can be estimated at 1–2%. The cell enables the simultaneous examination of two samples, which makes possible the comparison of their compressibilities with an accuracy of 0.01–0.1%. As examples, the results of compressibility measurements on GaAs and GaN are given.

Notes: A modification is described of the singular value decomposition (SVD) method suitable for underdetermined linear least squares (LLS). When a set of data to be fitted is incomplete and does not allow an independent determination of all model parameters, the modified method automatically merges a previously available approximate solution into the LLS results. The solution so produced is more appropriate to the particular problem than the usual SVD solution, while still being a LLS estimate of the whole set of parameters. The method is discussed with reference to the LLS determination of unit-cell dimensions during the step-by-step assignment of h, k, l indices of a diffraction pattern.

Notes: The use of position-sensitive area detectors with high-flux radiation sources demands high-rate data-acquisition systems. Ideally, such devices should be commercially available and machine independent. In this paper, the basic features of such a system are described. The steps are highlighted that determine the counting rates of present-day addressing-logic and computer-bus speeds. The improvements expected with a new industrial standard bus system are briefly described.

Notes: The PIPEX system, an inexpensive pipetting station for the preparation of protein crystallization buffers, is described. The system, built around a computer-controlled motorized pipette, contains a spreadsheet application for the planning of experiments in, for example, standard Linbro plates, a program for the control of the pipette and a customized electronic interface. The PIPEX system performs most of the software tasks offered by current automatic crystallization systems.

Notes: With the assumption that both size- and strain-broadened profiles of the pure-specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren–Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the `hook' effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from 1̃.31, for the minimum allowed Cauchy content, to 2, when the size-broadened profile is given solely by a Cauchy function. If the distortion Subscripts coefficient is approximated by a harmonic term, mean-square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance.

Notes: The one-dimensional contrast modulation along the b axis of [001] high-resolution reverse images of the compounds Bi2Sr2(Ca1 − xNdx)Cu2O8 + δ (x = 0.05 + 0.1n; n = 1, 2, 6 and 7) is examined closely using the density distribution recorded from a wide area of the negative film by microphotometric densitometry. Three typical short units of the density distribution, of lengths 4.5b0, 5b0 and 4b0, characterized by twin peaks or a single maximum peak with subpeaks in the middle of the unit, are discerned. The density distributions of the three units and the contrast modulations of their images are reproduced well by computer simulations, using three structure models modulated with longitudinal displacement waves along the b axis of the metal atoms. The one-dimensional contrast modulation is attributed to sinusoidal changes in the effective scattering amplitudes for the [001] electron beam of the metal-atom chains along the c axis. The results of the simulation are applied to investigation of the (2, 1)5 and (3, 1)4 modulation modes in the modulated structure.

Notes: Theoretical calculation shows that suitable approximations of the line-shape asymmetry in powder diffraction profiles should be represented by functions having limited codomains.

Notes: (0{\bar 1}11) twin boundaries of Y-cut synthetically grown quartz crystals are studied by means of X-ray section topographs. The images show an anomalous contrast and no extinction condition can be found. Simulated images demonstrate that the twin boundaries are not simple planar defects. They may be described as lamellae of a non-diffracting material. Their thickness is of the order of 15 μm and, within these boundaries, the Fourier components of the dielectric susceptibility are drastically reduced by one order of magnitude.

Notes: A set of cylindrical vacuum chambers made of a carbonaceous composite material coated with a thin layer of aluminium is described. Its performance with a Displex cryostat and Mo Kα radiation has been tested.

Notes: PEDX is a newly developed interactive computer program for the radial-distribution-function analysis of measured energy-dispersive X-ray diffraction (EDXD) data from disordered systems. The program is furnished with efficient computing procedures and all the standard data for 96 neutral atoms necessary for the calculations. With the help of PEDX, the rather involved EDXD data processing is reduced to a routine operation.

Notes: Diffusion in Ni–Ti multilayers with periods of 120 Å is studied in the temperature range 293–743 K by grazing-angle unpolarized neutron reflectometry. The effective diffusion coefficient, Deff, of nickel into titanium and its corresponding activation energy, Qa, are determined by measurement of the decay of the reflectivity of the first Bragg peak, which arises from the nuclear scattering-length density modulation, as a function of annealing temperature at constant time. The direction of diffusion is determined by simulation of the Kiessig fringes located between the total-reflection plateau and the first Bragg peak. Two diffusion regimes with a transition temperature Tc ∼ 543 K are observed in this Ni–Ti multilayer; the corresponding activation energy values are 0.21 and 0.43 eV, respectively.

Notes: A sample environment apparatus, such as a diamond-anvil cell (DAC), cryostat or furnace, presents a unique problem for the crystallographer because some of the diffraction data are shadowed by its components. The first algorithm for sorting diffraction data from a sample consisting of several crystals enclosed in a sample environment apparatus is described. This algorithm requires no previous knowledge of the crystal structure of the sample, so it can be used to solve the structures of substances when the growth of one unstrained crystal is unsuccessful. An example is given to illustrate the development and the implementation of this algorithm: the identification of the unit cell of a high-pressure phase of oxygen known as epsilon-oxygen (ε-O2). The ε-O2 sample contains at least seven individual crystals and is enclosed in a DAC. The ε-O2 unit cell is monoclinic, it contains eight molecules per unit cell and the lattice constants at 19.7 GPa and room temperature are a = 3.642, b = 5.491, c = 7.705 Å and β = 116.2°. In the example, monochromatic X-ray diffraction data from this high-pressure sample are sorted, but the algorithm is a general-purpose technique; it can also be used to sort single-crystal time-of-flight neutron diffraction data. Additionally, this method may be used to sort reflections from several crystal samples containing a mixture of materials. The algorithm is given in symbolic logic so that it can be translated and inserted into available crystallographic software packages.

Notes: Two crystals of monoclinic hen egg-white lysozyme were irradiated in a monochromatic synchrotron X-ray beam (λ = 1.488 Å), the first as a rapidly frozen crystal mounted at the end of a glass fiber at low temperature (120 K) and the second mounted in a capillary tube at ambient temperature (298 K). Comparison of oscillation photographs, extending in resolution to 1.85 Å, and taken from both crystals at zero time and again after a period of exposure in the synchrotron beam (60 min exposure at 120 K; 8 min at 298 K), reveals that radiation-induced decay is not observed at 120 K but is observed, particularly at high resolution, at 298 K. In a separate set of experiments, data sets to 1.9 Å resolution at 100 and 298 K were collected from two monoclinic and two tetragonal hen egg-white lysozyme crystals using a rotating-anode source (λ = 1.5418 Å). Before inclusion of solvent molecules, the monoclinic and tetragonal structures at low temperature, where data were collected from rapidly frozen crystals, refined to R = 27.5 and 25.2%, respectively. The structures at ambient temperature, however, where crystals were mounted in capillary tubes, refined to significantly lower values of R = 20.9 and 20.6%. After inclusion of solvent, the R values at convergence were 20.3 and 17.6% for the monoclinic and tetragonal low-temperature structures and 17.9 and 16.2% for the room-temperature structures. Approximately twice the number of water molecules were included in the low-temperature structures at convergence (406 and 237) than could be assigned in the room-temperature structures (191 and 100). These results suggest that data sets from rapidly frozen crystals might generally be expected to yield higher initial R factors, compared to similar room-temperature structures, but that this difference should diminish appreciably as ordered solvent is included in the model. Apart from the general reduction in atomic temperature factors, the enhancement in resolution observed in diffraction patterns obtained from rapidly frozen crystals is probably due, to some significant degree, to the increase in the ordered-solvent content of the low-temperature structures.

Notes: A new method has been developed for the improved intensity assignment of severely or exactly overlapping Bragg reflections in a powder diffraction pattern. This fast iterative Patterson squaring (FIPS) method addresses, in particular, the systematic lack of small and large normalized intensities (|E| values) in severely overlapping powder data, which causes (a) the intensity statistics to be strongly acentric (even when the structure itself is centrosymmetric) and (b) the under-estimation of strong structure-invariant relationships. Direct methods for structure determination are more likely to succeed with FIPS-improved data than with conventionally used equipartitioned data (ratio of |E| values for overlapping reflections set to 1.0). In the case of the molecular sieve AFR (in which 65% of the reflections severely overlap), the ab initio structure solution was only possible after a redistribution of the intensities by the FIPS method.

Notes: Thin films of β-FeSi2, grown on Si(111) by the technique of solid-phase epitaxy (SPE) in ultra-high vacuum (UHV) conditions, were analysed by transmission electron microscopy (TEM). The expected epitaxies, β-FeSi2(101)/Si(111) and β-FeSi2(110)/ Si(111), were detected for film thicknesses smaller than 2̃50 Å. The present analysis reveals an unusual microstructure: the films are composed of very thin lamellae (5–30 Å) of both orientations induced by planar defects. Such lamellar films are strained, with a parameter shift estimated to be about 0.4%. For these films, grain sizes in the μm range were obtained and the interface roughness increased with increasing film thickness. An unexpected film orientation, β-FeSi2(100)/Si(111), was also found.

Notes: Reflection curves of bent crystals were calculated using the Takagi–Taupin theory of dependence on bending radius, wavelength, crystal thickness and Bragg angle. The reflection properties of bent crystals were measured for bending radii down to 90 mm. Usually, for the measurement of rocking curves of crystals with large bending radii, the double-crystal diffractometer was used in parallel position (n, −n). A special achromatic diffractometer consisting of a plane and a bent crystal is proposed. It is used to measure rocking curves of bent crystals with small bending radii (R 〈 1 m). Experimental values show close agreement with the theory. The reflection properties are important for X-ray microscopy with two-dimensionally bent crystals and for X-ray spectroscopy with bent crystals.

Notes: MEED (maximum-entropy electron density) is a program package to calculate the electron-density distribution from a set of structure-factor data by the maximum-entropy method. MEED is an upgraded version of the original maximum-entropy program, MEMTARO, which was used in the first study to use the maximum-entropy method (MEM) on silicon [Sakata & Sato (1990). Acta Cryst. A46, 263–270]. MEED is applicable to any space group and can cope with both single-crystal and powder X-ray diffraction data, whereas MEMTARO can only after modification. Another upgraded feature is the speed of calculation. By employing a new algorithm, MEED is much faster than MEMTARO for the same calculation. Computing time depends on various factors, such as the number of reflection data, accuracy of data and the number of symmetry operations. It is estimated that MEED is typically 100 times faster than MEMTARO. In an extreme case like the beryllium powder-data case, MEED is 600 times faster than MEMTARO. MEED is coded in Fortran77 for both a scaler computer, FACOM M780, and a vector computer, FACOM VP2600, which are mainframe computers at the Computation Center of Nagoya University. MEED enables the electron-density distribution to be calculated for any crystalline material, with a fine pixel size, e.g. with 128 × 128 × 128 pixels to a unit cell, provided that accurate diffraction data are available. MEED can overcome, to some extent, one of the biggest drawbacks of MEM analysis, the vast computing time required.

Notes: An inexpensive system has been designed that eliminates most of the collisions that might occur between the goniostat and the stationary items and complements the Rigaku RU 200 X-ray generator, Huber goniostat, Blake Industries' 2θ mechanism and San Diego multiwire area detector used in the CABM/Waksman X-ray crystallography laboratory.

Notes: Owing to the breakdown of Friedel's law when anomalous scatterers are present, unique values of the three-phase structure invariants in the whole range from 0 to 2π are determined by measured values of diffraction intensities alone. Two methods are described for going from presumed known values of these invariants to the values of the individual phases. The first, dependent on a scheme for resolving the 2π ambiguity in the estimate ωHK of the triplet φH + φK + φ−H−K, solves by least squares the resulting redundant system of linear equations φH + φK + φ−H−K = ωHK. The second attempts to minimize the weighted sum of squares of differences between the true values of the cosine and sine invariants and their estimates. The latter method is closely related to one based on the `minimal principle' which determines the values of a large set of phases as the constrained global minimum of a function of all the phases in the set. Both methods work in the sense that they yield values of the individual phases substantially better than the values of the initial estimates of the triplets. However, the second method proves to be superior to the first but requires, in addition to estimates of the triplets, initial estimates of the values of the individual phases.

Notes: Conventional small-molecule methods of solving the phase problem from native data alone, without the use of heavy-atom derivatives, known fragment geometries or anomalous dispersion, have been tested on 0.9 Å resolution data for two small proteins: rubredoxin, from Desulfovibrio vulgaris, and crambin. The presence of three disulfide bridges in crambin and an FeS4 unit in rubredoxin enabled automated Patterson interpretation as well as direct methods to be tried. Although both structures were already well established, the known structures were not used in the phasing attempts, except for identifying successful solutions. Direct methods were not successful for crambin, although the correct phases were stable to phase refinement and gave figures of merit clearly superior to any obtained in the ca 500 000 random starting phase sets that were refined. It appears that the presence of an iron atom in rubredoxin reduces the scale of the search problem by many orders of magnitude, but at the cost of producing `over-consistent' phase sets that overemphasize the iron atom and involve partial loss of enantiomorph information. However, about 1% of direct-methods trials were successful for rubredoxin, giving mean phase errors of about 56° (for all E 〉 1.2) that could be reduced to about 20° by standard E-Fourier recycling methods. Limiting the resolution of the data degraded the quality of the solutions and suggested that the limiting resolution for routine direct-methods solution of rubredoxin is about 1.2 Å. With the 0.9 Å data, automated Patterson interpretation convincingly finds the three disulfide bridges in crambin and the FeS4 unit in rubredoxin, and in both cases E-Fourier recycling starting from these `heavier' atoms yields almost the complete structure. Whereas crambin could only be solved in this way at very high resolution, rubredoxin could be solved by Patterson interpretation down to 1.6 Å. These results emphasize the benefits of collecting protein data to the highest possible resolution, and indicate that when a few `heavier' atoms are present, it may prove possible in favorable cases to solve the phase problem from a single native data set collected to `atomic resolution'.

Notes: An automated refinement procedure (ARP) for protein models is proposed, and its convergence properties discussed. It is comparable to the iterative least-squares minimization/difference Fourier synthesis approach for small molecules. ARP has been successfully applied to three proteins, and for two of them resulted in models very similar to those obtained by conventional least-squares refinement and rebuilding with FRODO. In real time ARP is about ten times faster than conventional refinement. In its present form ARP requires high (2.0 Å or better) resolution data, which should be of high quality and a starting protein model having about 75% of the atoms in roughly the correct position. For the third protein at 2.4 Å resolution, ARP was significantly less powerful but nevertheless gave definite improvement, in the density map at least.

Notes: A knowledge-based approach to crystal structure determination is presented. The approach integrates direct-methods and artificial-intelligence strategies to rephrase the structure determination process as an exercise in scene analysis. A general joint probability distribution framework, which allows the incorporation of isomorphous replacement, anomalous scattering and a priori structural information, forms the basis of the direct-methods strategies. The accumulated knowledge on crystal and molecular structures is exploited through the use of artificial-intelligence strategies, which include techniques of knowledge representation, search and machine learning.

Notes: A complementary relationship between the entropy (S) and the variance (σ2) of an electron-density map is derived by approximating the logarithmic term in the entropy expression by a series expansion around the average map density. The resulting expression is S ∼ ln N − {1 \over 2}σ2, where N is the number of grid points and σ is the r.m.s. deviation from the mean in a map normalized to unit mean. The algebraic expression is of interest because it is consistent with and allows numerical evaluation of the surprising argument that noise decreases the entropy of a map. The argument is that a noise contribution by itself generates a certain variance that is independent of the atomic structure and that adds to the variance due to the structure. Increased variance corresponds to decreased entropy. This property of noise provides an intuitively reasonable justification for maximizing the entropy of an electron-density map in the quest for more readily interpretable maps of macromolecules. The entropy–variance relationship also extends the range of applicability of the entropy concept to maps with a limited amount of negative density. The approximation which leads to the entropy–variance relationship is most applicable where it is most likely to be useful – in experimental maps of relatively low structure definition.

Notes: A practical generally applicable procedure for exponential modeling to maximum likelihood of macromolecular data sets constrained by a moderately large basis set of reliable phases and a molecular envelope is described, based on the computer program MICE [Bricogne & Gilmore (1990). Acta Cryst. A46, 284–297]. Procedures were first tested with simulated data sets. Exact and randomly perturbed amplitudes and phases were generated, together with a known envelope for solvent-free protein and for protein in an electron-dense crystal mother liquor typical of many real protein crystals. These experiments established useful guidelines and values for various parameters. Tests with basis sets chosen from the largest amplitudes indicate that exponential models with considerable correct extrapolated phase and amplitude information can be constructed from as few as 16% of the total number of reflections, with mean phase errors of about 30°, at resolution limits of either 5 or 3 Å. When the shape of the solvent channels in macromolecular crystals is known, it offers an important additional source of information. MICE was, therefore, adapted to average the density outside the molecular boundary defined by an input envelope. This flattening process imposes a uniform density distribution in solvent-filled channels as an additional constraint on the exponential model and is analogous to the treatment of solvent in conventional solvent flattening. Experimental data for cytidine deaminase, a structure recently solved by making extensive use of conventional solvent flattening, provides an example of the performance of maximum-entropy methods in a real situation and a compelling comparison of this method to standard procedures. Exponential models of the electron density constrained by the most reliable phases obtained by multiple isomorphous replacement with anomalous scattering (MIRAS) (figure of merit 〉 0.7, representing 34% of the total number of reflections) and by the envelope give rise to centroid electron-density maps which are quantitatively superior by numerous statistical criteria to conventionally solvent-flattened density. Similarity of these maps to the 2Fobs − Fcalc map calculated with phases obtained after crystallographic refinement of the model implies that maximum-entropy extrapolation provides better phases for the remaining 66% of the reflections than the original centroid MIRAS distributions. Importantly, the solvent-flattened electron density, although it did permit interpretation of the map which was not readily accomplished with the MIRAS map, contains substantial errors. It is proposed that errors of this sort may account for previously noted deficiencies of the solvent-flattening method [Fenderson, Herriott & Adman (1990). J. Appl. Cryst. 23, 115–131] and for the occasional tendency of incorrect interpretations to be `locked in' by crystallographic refinement [Brändén & Jones (1990). Nature (London), 343, 687–689, and references cited therein]. Solvent flattening with combined maximization of entropy and likelihood represents a phase-refinement path independent of atomic models, using the experimental amplitudes and the most reliable phases. It should, therefore, become a valuable and generally useful procedure in macromolecular crystal structure determination.

Notes: The crystal structure of a complex of ribonuclease from Streptomyces aureofaciens (RNase Sa) with guanosine-2′-monophosphate (2′-GMP) has been refined against synchrotron data recorded from a single crystal using radiation from beamline X31 at EMBL, Hamburg, and an imaging plate scanner. The crystals are in space group P212121 with cell dimensions a = 64.7, b = 78.8 and c = 39.1 Å. The structure has two enzyme molecules in the asymmetric unit, complexed with 2′-GMP inhibitor with occupancies of 1 and {2 \over 3} (different to the 3′-GMP complex crystal structure where only one of the two independent RNase Sa molecules binds nucleotide), 492 associated water molecules and one sulfate ion, and was refined using all data between 10.0 and 1.7 Å to a final crystallographic R factor of 13.25%. Binding of the base to the enzyme confirms the basis for the guanine specificity but the structural results still do not provide direct evidence of the identity and role of the particular residues involved in the catalytic process. New native RNase Sa data to 1.8 Å were recorded to provide a reference set measured under comparable experimental conditions. The crystals are in the same space group and have the same lattice as those of the 2′-GMP complex. The native structure with 423 water molecules was refined in a similar manner to the complex to a final R factor of 13.87%. 1.77 Å resolution data were independently measured on a 2′-GMP complex crystal at UCLA using an R-AXIS II image plate scanner mounted on a conventional source. The cell dimensions were essentially the same as above. 2′-GMP was bound more fully to molecule A than to molecule B of the RNase Sa. The structure was refined to an R factor of 14.64% with 388 water molecules. This work follows on from the structure determination of native RNase Sa and its complex with 3′-GMP [Sevcik, Dodson & Dodson (1991). Acta Cryst. B47, 240–253].

Notes: . Sulfur atoms, an integral part of many proteins, are possible candidates for anomalous scattering in phase determination by multiple-wavelength methods. The main difficulty encountered is that a wavelength of about 5 Å is required to obtain a large anomalous signal from these atoms, leading to very large absorption effects. Initial experiments have been carried out using a synchrotron X-ray source, evacuated beam tubes, a diffractometer inside a vacuum chamber, a special sample holder and a suitable scattering geometry. The results are encouraging, showing that Bragg reflections can be measured, and that changes in their intensities around the absorption edge are observable.

Notes: The previous paper described a phase-refinement strategy for protein crystallography which exploited the information that proteins consist of connected linear chains of atoms. Here the method is applied to a molecular-replacement problem, the structure of the protease inhibitor ecotin bound to trypsin, and a single isomorphous replacement problem, the structure of the N-terminal domain of apolipoprotein E. The starting phases for the ecotin-trypsin complex were based on a partial model (trypsin) containing 61% of the atoms in the complex. Iterative skeletonization gave better results than either solvent flattening or twofold non-crystallographic symmetry averaging as measured by the reduction in the free R factor [Brünger (1992). Nature (London), 355, 472–474]. Protection of the trypsin density during the course of the refinement greatly improved the performance of both skeletonizing and solvent flattening. In the case of apolipoprotein E, previous attempts using solvent flattening had failed to improve the SIR phases to the point of obtaining an interpretable map. The combination of iterative skeletonization and solvent flattening decreased the phase error with respect to the final refined structure, significantly more than solvent flattening alone. The final maps generated by the skeletonization procedure for both the ecotin–trypsin complex and apolipoprotein E were readily interpretable.

Notes: In an earlier study [Heinemann & Hahn (1992). J. Biol. Chem. 267, 7332–7341], the crystal structure of the double-stranded B-DNA decamer d(CCAGGCm5CTGG) was refined with NUCLSQ to R = 17.4% against 3799 2σ structure amplitudes in the resolution range 8–1.7 Å. This structure has now been re-refined against the same diffraction data using either TNT or X-PLOR in order to determine to what extent the resulting DNA conformations would differ and to examine the suitability of these programs for the refinement of oligonucleotide structures. The R value from the NUCLSQ refinement could not be reached with either TNT or X-PLOR, although both programs yield reasonably refined DNA models showing root-mean-square deviations against the NUCLSQ model of the decamer duplex of 0.25 and 0.32 Å, respectively. Some derived local structure parameters differ depending on the refinement procedure used. This holds true for several exocyclic torsion angles of the sugar-phosphate backbone, whereas sugar puckers as well as helical and base-pair stacking parameters are only weakly influenced. A subset of 15 solvent sites with low temperature factors is conserved in all three models.

Notes: A survey of 129 protein crystal structures with more than one molecule per asymmetric unit shows that local (non-crystallographic) symmetry axes are not randomly oriented. When compared to the crystal cell edges, face diagonals, body diagonal and reciprocal cell edges, 65% of the local symmetry axes are found to be parallel to one of the reference directions to within 15°; another 18% are orthogonal to within 3°; only 17% are in general orientations. In monoclinic, trigonal and hexagonal crystals, a majority of the local symmetry axes are orthogonal to the unique axis, while preferred orientations are parallel to the cell edges in orthorhombic crystals.

Notes: A conventional direct method, using the Sayre equation as a basis, has been shown to be capable of solving a small protein with data of 3.0 Å resolution or better. An analysis of the Sayre equation, with data of various resolutions and with different lower limits of |E| for the contributors in the summation, shows that its effectiveness for phasing is independent of structural complexity but does decline as the resolution becomes worse. It is suggested that a practicable lower limit for the application of conventional direct methods is about 3.5 Å. For large macromolecular structures the number of contributors to the summation in the Sayre equation becomes too large to handle and it is suggested that real-space methods should be used instead.

Notes: The entropy-dynamics method seeks maxima for the entropy of the electron density for N atoms in a crystal cell, when the Fourier amplitudes are fixed, but their phases are unknown. By analogy with molecular dynamics, the effective potential energy is the negative entropy V = −NS. The kinetic energy is proportional to the squared velocities of the electron densities at grid points in the map. It reduces to a sum of Fourier-mode rotor energies. Each rotor angle experiences a couple equal to the phase gradient of S, and local dynamical equilibrium yields a Boltzmann distribution of S. Discrete phase angles (e.g. signs) are treated as quantized rotor modes. The distributions depend on a popularity function of the entropy histogram. Trial calculations have been made of phase averages and correlations in a centrosymmetric projection of the membrane protein bacteriorhodopsin. The maximum-entropy solution and the correct solution do not always coincide.

Notes: Xtal3.2, a crystallographic software package, is an international development project involving about 40 researchers over a full spectrum of crystallographic interests. This development has been supported by many national and international agencies and commercial institutions since the first version in 1983. The 1992 release, Xtal3.2, contains software for 95 different calculations. These range from the processing of raw diffraction data to interactive molecular graphics, atomic charge estimation, electronic publication preparation, and the structure solution and refinement of small and large molecules. Tests of the Xtal programs for phase determination and phase refinement by the application of `maximum entropy' are presented.

Notes: Synchrotron radiation has been used extensively to overcome a variety of technical challenges involved in data collection from macromolecular crystals. The next generation of such sources offer a higher brilliance at much shorter wavelengths than hitherto available. Hence, the quality of X-ray diffraction data from crystals of biological macromolecules will be further improved in terms of reduced systematic and random errors, in conjunction with a very high degree of completeness of, and multiple measurements within, the data set. Real data sets should be able to approach closely the quality of ideal data sets. Tests at CHESS are described of the feasibility of recording protein crystal diffraction patterns at ultra-short wavelengths (λ = 0.3 Å) and very-short wavelengths (λ = 0.5 Å), in monochromatic rotating crystal geometry.

Notes: The molecular structure of calf γB-crystallin (previously called γII), a lens-specific protein, has been refined to a crystallographic R factor of 18.1% for all reflection data, between 8.0 and 1.47 Å, 25 959 hkl measured at 293 (1) K. 230 water molecules have been defined by difference Fourier techniques and included in a restrained least-squares refinement. Difference Fourier maps clearly indicated the presence of multiple sites for the sulfur atoms of Cys 18 and Cys 22 which were therefore given coupled second-site occupancies during the refinement. The sulfur atom in the major position of Cys 22 is in the reduced state. Either of the Cys 18 sites can form a high-energy disulfide bridge with the minor position of Cys 22. The position of the carboxy terminus and many other surface side chains have been further defined including the RGD signal peptide. The hydration of the backbone and the interdomain region has been analysed. 27 water molecules make extensive contacts to a single protein molecule and thus contribute to its stability.

Notes: Ferredoxin I from Azotobacter vinelandii (AvFdI) is an iron–sulfur protein composed of 106 amino acids, seven Fe atoms and eight inorganic S* atoms. A crystallographic redetermination of its structure showed the originally reported structure to be incorrect. We report here the crystal structure of AvFdI at pH 6.5. Extensive refinement has led to a final R value of 0.170 for all 6986 non-extinct reflections in the range 10–2.3 Å using a solvent model which includes 98 discrete solvent atoms with occupancies between 0.3 and 1.0 and an average B value of 22.5 Å2. The first half of the peptide chain closely resembles that of the 55-residue ferredoxin from Peptococcus aerogenes (PaFd), while the remainder consists of three turns of helix and a series of loops which form a cap over part of the molecular core. Despite the similarities in structure and surroundings, the corresponding 4Fe4S* clusters in PaFd and AvFdI have strikingly different redox potentials; a possible explanation has been sought in the differing hydration models for the two molecules.

Notes: The white-beam Laue-diffraction method is a useful tool for rapid measurement of crystallographic intensities with synchrotron radiation. Considerations of the signal-to-noise ratio to be expected from scattering of X-rays within a limited wavelength range suggest that it will pay to limit that range to something like an octave. This rule-of-thumb has the added advantage that there will be significantly fewer diffraction spots that are overlapping harmonics of one another. To maximize the number of reflections recorded in a single stationary-crystal exposure, one should choose this octave of wavelengths in a region where the curvature of the Ewald sphere is greatest, that is at the longest wavelength allowable after other considerations are taken into account.

Notes: The low-density elimination method for phase extension and refinement [Shiono & Woolfson (1992). Acta Cryst. A48, 451–456] has been improved by substituting a smoother density-modification procedure for the original sharp cut-off function. In addition, better criteria have been found for limiting the number of refinement cycles, which gives a better final result for much less work. The effectiveness of the process has been illustrated by phase refinement for a protein with high-resolution (1.17 Å) data containing 808 independent non-H atoms plus 83 water molecules in the asymmetric unit; the unweighted mean-phase error was reduced from 74 to 39.3°. Phase extension and refinement was also demonstrated for pig 2Zn insulin starting with multiple isomorphous replacement (MIR) phases at 1.9 Å and extending out to 1.5 Å. There was a significant improvement of phases and the final map had a correlation coefficient of 0.540.

Notes: The crystal structure of bovine seminal ribonuclease, a homodimeric enzyme closely related to pancreatic ribonuclease, has been refined at a nominal resolution of 1.9 Å employing data collected on an electronic area detector. The final model consists of two chains containing 1990 non-H atoms, seven sulfate anions and 113 water molecules per asymmetric unit. The unit-cell parameters are a = 36.5 (1), b = 66.7 (1) and c = 107.5 (2) Å, space group P22121. The R factor is 0.177 for 16 492 reflections in the resolution range 6.0–1.9 Å and the deviations from ideal values of bond lengths and bond angles are 0.020 Å and 3.7°, respectively. The molecule is formed by two pancreatic like chains, which have their N-terminal segments interchanged so that each active site is formed by residues from both subunits. The two chains are related by a non-crystallographic twofold symmetry and are covalently linked by two consecutive disulfide bridges, which form an unusual sixteen-membered ring across the dimer interface. The deviations from the molecular symmetry, the hydration shell and the sulfate-binding sites are also discussed in relation to the known structure of the pancreatic enzyme.

Notes: The structure of triosephosphate isomerase (TIM) from the organism Escherichia coli has been determined at a resolution of 2.6 Å. The structure was solved by the molecular replacement method, first at 2.8 Å resolution with a crystal grown by the technique of hanging-drop crystallization from a mother liquor containing the transition-state analogue 2-phosphoglycolate (2PG). As a search model in the molecular replacement calculations, the refined structure of TIM from Trypanosoma brucei, which has a sequence identity of 46% compared to the enzyme from E. coli, was used. An E. coli TIM crystal grown in the absence of 2PG, diffracting to 2.6 Å resolution, was later obtained by application of the technique of macro-seeding using a seed crystal grown from a mother liquor without 2PG. The final 2.6 Å model has a crystallographic R factor of 11.9%, and agrees well with standard stereochemical parameters. The structure of E. coli TIM suggests the importance of residues which favour helix initiation for the formation of the TIM fold. In addition, TIM from E. coli shows peculiarities in its dimer interface, and in the packing of core residues within the β-barrel.

Notes: The OP-G2 monoclonal antibody binds to the platelet integrin, gpIIb/IIIa, in a mode that mimics fibrinogen binding. The specificity of this antibody is mediated by the third complementarity-determining region (CDR3) loop of the immunoglobulin heavy chain which contains a sequence (RYD) related to the RGD recognition sequence of fibrinogen. The OP-G2 Fab fragment has been crystallized by vapor diffusion from solutions containing polyethylene glycol and imidazole malate (pH 5.6). The crystals belong to space group P21212 with a = 93.1, b = 83.8 and c = 53.7 Å. One Fab molecule is present in the asymmetric unit. A complete data set to 2.0 Å resolution has been collected.