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1.  Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool 
A new concept in virology provides insights into structural constraints on virus structure, extending Caspar–Klug theory to include predictions across all radial levels of the virus particle including genome organization. The predictive power of the new tool is demonstrated for a range of viruses, revealing a previously unrecognized structural interdependence of shapes and sizes of different viral components.
Understanding the fundamental principles of virus architecture is one of the most important challenges in biology and medicine. Crick and Watson were the first to propose that viruses exhibit symmetry in the organization of their protein containers for reasons of genetic economy. Based on this, Caspar and Klug introduced quasi-equivalence theory to predict the relative locations of the coat proteins within these containers and classified virus structure in terms of T-numbers. Here it is shown that quasi-equivalence is part of a wider set of structural constraints on virus structure. These constraints can be formulated using an extension of the underlying symmetry group and this is demonstrated with a number of case studies. This new concept in virus biology provides for the first time predictive information on the structural constraints on coat protein and genome topography, and reveals a previously unrecognized structural interdependence of the shapes and sizes of different viral components. It opens up the possibility of distinguishing the structures of different viruses with the same T-number, suggesting a refined viral structure classification scheme. It can moreover be used as a basis for models of virus function, e.g. to characterize the start and end configurations of a structural transition important for infection.
PMCID: PMC3571114  PMID: 23403965
virus structure; genome organization; structural constraints; affine-extended symmetry group; tiling theory
2.  Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing 
A semi-transparent central stop has been used for ptychographic coherent diffractive imaging to increase the effective dynamic range in the recording of the far-field diffraction patterns. In this way, the high flux density provided by nano-focusing Kirkpatrick–Baez mirrors can be fully exploited for high resolution and quantitative phase reconstructions.
A ptychographic coherent X-ray diffractive imaging (PCDI) experiment has been carried out using 7.9 keV X-rays and Kirkpatrick–Baez focusing mirrors. By introducing a semi-transparent central stop in front of the detector the dynamic range on the detector is increased by about four orders of magnitude. The feasibility of this experimental scheme is demonstrated for PCDI applications with a resolution below 10 nm. The results are compared with reference data and an increase of resolution by a factor of two is obtained, while the deviation of the reconstructed phase map from the reference is below 1%.
PMCID: PMC3744854
ptychography; Kirkpatrick–Baez mirrors; semi-transparent central stop; semi-transparent beam stop; coherent diffractive imaging; phase reconstruction
3.  Digital electron diffraction – seeing the whole picture 
Computer control of beam tilt and image capture allows the collection of electron diffraction patterns over a large angular range, without any overlap in diffraction data and from a region limited only by the size of the electron beam. This results in a significant improvement in data volumes and ease of interpretation.
The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters.
PMCID: PMC3686228  PMID: 23778099
electron diffraction; symmetry determination; CBED; LACBED; computer control
4.  High-resolution study of (002, 113, 11−1) four-beam diffraction in Si 
A high-resolution study of (002, 113, 11−1) four-beam diffraction in Si was performed both experimentally and theoretically. Excellent coincidence between theory and experiment was achieved. The forbidden two-beam 002 reflection was excited with the maximum reflectivity of 80%.
The results of a high-resolution study of the (002, 113, ) four-beam diffraction in Si are presented. The incident synchrotron radiation beam was highly monochromated and collimated with a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes, in an attempt to experimentally approach plane-wave incident conditions. The Renninger scheme was used with the forbidden reflection reciprocal-lattice vector 002 normal to the crystal surface. The azimuthal and polar rotations were performed in the crystal surface plane and the vertical plane correspondingly. The polar angular curves for various azimuthal angles were measured and found to be very close to theoretical computer simulations, with only a small deviation from the plane monochromatic wave. The effect of the strong two-beam 002 diffraction was observed for the first time with the maximum reflectivity close to 80%. The structure factor of the 002 reflection in Si was experimentally determined as zero.
PMCID: PMC3329769  PMID: 22514065
X-ray multiple diffraction; silicon; high resolution; forbidden reflections
5.  The early development of neutron diffraction: science in the wings of the Manhattan Project 
Early neutron diffraction experiments performed in 1944 using the first nuclear reactors are described.
Although neutron diffraction was first observed using radioactive decay sources shortly after the discovery of the neutron, it was only with the availability of higher intensity neutron beams from the first nuclear reactors, constructed as part of the Manhattan Project, that systematic investigation of Bragg scattering became possible. Remarkably, at a time when the war effort was singularly focused on the development of the atomic bomb, groups working at Oak Ridge and Chicago carried out key measurements and recognized the future utility of neutron diffraction quite independent of its contributions to the measurement of nuclear cross sections. Ernest O. Wollan, Lyle B. Borst and Walter H. Zinn were all able to observe neutron diffraction in 1944 using the X-10 graphite reactor and the CP-3 heavy water reactor. Subsequent work by Wollan and Clifford G. Shull, who joined Wollan’s group at Oak Ridge in 1946, laid the foundations for widespread application of neutron diffraction as an important research tool.
PMCID: PMC3526866  PMID: 23250059
neutron diffraction; Manhattan Project
6.  Equivalence of superspace groups 
The standard settings of (3 + d)-dimensional superspace groups are determined for a series of modulated compounds, especially concentrating on d = 2 and 3. The coordinate transformation in superspace is discussed in view of its implications in physical space.
An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool on , providing the transformation of any user-given superspace group to the standard setting of this superspace group in . It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.
PMCID: PMC3553647  PMID: 23250064
symmetry; superspace groups; two-dimensionally modulated crystals; three-dimensionally modulated crystals
7.  Some B eq are more equivalent than others 
B eq is a well defined entity that represents one property, mean-square displacement, of the anisotropic atomic displacement parameter tensor from which it is derived. B eq is not, however, the best estimate of the B factor that would result from isotropic model refinement. A new entity B est is proposed to serve this purpose.
Crystallographic structural models for macromolecules have typically included an isotropic displacement parameter B iso for each atom. In cases where the structural model instead includes anisotropic displacement parameters U ij, the derived quantity B eq can be substituted for B iso for many purposes. B eq is not, however, the best predictor of the value B iso that would hypothetically have been obtained by direct refinement of an isotropic model. A new entity B est is proposed that represents an estimate for B iso that minimizes the Kullback–Leibler divergence from a paired anisotropic model. In general B est/B eq < 1, with the difference between the two values becoming larger for atoms that are more anisotropic. Although this difference does not affect direct refinement of either isotropic or anisotropic models, it is relevant to any analysis that compares isotropic and anisotropic models of the same underlying structure. In particular, it may lead to improved selection of multi-group TLS models based on analysis of an initial isotropic refinement.
PMCID: PMC3211245  PMID: 22011466
macromolecular refinement; TLS; anisotropy
8.  Mathematical aspects of molecular replacement. I. Algebraic properties of motion spaces 
Search spaces in the method of molecular replacement are shown to be coset spaces of the Lie group of rigid-body motions by the chiral space group of a crystal. The resulting ‘motion space’ can be endowed with a quasigroup operation that has interesting properties which are explored here.
Molecular replacement (MR) is a well established method for phasing of X-ray diffraction patterns for crystals composed of biological macromolecules of known chemical structure but unknown conformation. In MR, the starting point is known structural domains that are presumed to be similar in shape to those in the macromolecular structure which is to be determined. A search is then performed over positions and orientations of the known domains within a model of the crystallographic asymmetric unit so as to best match a computed diffraction pattern with experimental data. Unlike continuous rigid-body motions in Euclidean space and the discrete crystallographic space groups, the set of motions over which molecular replacement searches are performed does not form a group under the operation of composition, which is shown here to lack the associative property. However, the set of rigid-body motions in the asymmetric unit forms another mathematical structure called a quasigroup, which can be identified with right-coset spaces of the full group of rigid-body motions with respect to the chiral space group of the macromolecular crystal. The algebraic properties of this space of motions are articulated here.
PMCID: PMC3171898  PMID: 21844648
rigid-body motion; coset space; quasigroup; fundamental domain; molecular replacement
9.  The development of Laue techniques for single-pulse diffraction of chemical complexes: time-resolved Laue diffraction on a binuclear rhodium metal-organic complex 
A modified Laue technique suitable for time-resolved diffraction is described in which profile-independent integration is used, the RATIO method is applied and multi-crystal data are normalized to a common scale. The method is applied in single-pulse pump–probe studies of a binuclear Rh complex, showing Rh—Rh bond shortening of 0.136 (8) Å on excitation.
A modified Laue method is shown to produce excited-state structures at atomic resolution of a quality competitive with those from monochromatic experiments. The much faster data collection allows the use of only one or a few X-ray pulses per data frame, which minimizes crystal damage caused by laser exposure of the samples and optimizes the attainable time resolution. The method has been applied to crystals of the α-modification of Rh2(μ-PNP)2(PNP)2 (BPh4)2 [PNP = CH3N(P(OCH3)2)2, Ph = phenyl]. The experimental results show a shortening of the Rh—Rh distance in the organometallic complex of 0.136 (8) Å on excitation and are quantitatively supported by quantum-mechanical (QM)/molecular-mechanics (MM) theoretical calculations which take into account the confining effect of the crystal environment, but not by theoretical results on the isolated complex, demonstrating the defining effect of the crystal matrix.
PMCID: PMC3121236  PMID: 21694470
Laue techniques; single-pulse diffraction; quantum-mechanical/molecular-mechanics calculations; QM/MM calculations; time-resolved X-ray crystallography
10.  High-resolution study of (222, 113) three-beam diffraction in Ge 
Good agreement between the high-resolution experimental results for (222, 113) three-beam diffraction in Ge and computer simulations based on the dynamical multiple diffraction theory are presented.
The results of high-resolution analysis of the (222, >113) three-beam diffraction in Ge are presented. For monochromatization and angular collimation of the incident synchrotron beam a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes was used in an attempt to experimentally approach plane-wave incident conditions. Using this setup, for various azimuthal angles the polar angular curves which are very close to theoretical computer simulations for the plane monochromatic wave were measured. The effect of the strong two-beam 222 diffraction was observed for the first time with the maximum reflectivity close to 60% even though the total reflection of the incident beam into a forbidden reflection was not achieved owing to absorption. The structure factor of the 222 reflection in Ge was experimentally determined.
PMCID: PMC3121237  PMID: 21694480
dynamical diffraction; multiple diffraction; synchrotron radiation; plane waves; X-ray optics
11.  Enhanced rigid-bond restraints 
An extension is proposed to the rigid-bond description of atomic thermal motion in crystals.
The rigid-bond model [Hirshfeld (1976 ▶). Acta Cryst. A32, 239–244] states that the mean-square displacements of two atoms are equal in the direction of the bond joining them. This criterion is widely used for verification (as intended by Hirshfeld) and also as a restraint in structure refinement as suggested by Rollett [Crystallographic Computing (1970 ▶), edited by F. R. Ahmed et al., pp. 167–181. Copenhagen: Munksgaard]. By reformulating this condition, so that the relative motion of the two atoms is required to be perpendicular to the bond, the number of restraints that can be applied per anisotropic atom is increased from about one to about three. Application of this condition to 1,3-distances in addition to the 1,2-distances means that on average just over six restraints can be applied to the six anisotropic displacement parameters of each atom. This concept is tested against very high resolution data of a small peptide and employed as a restraint for protein refinement at more modest resolution (e.g. 1.7 Å).
PMCID: PMC3377366
rigid-bond test; refinement restraints; anisotropic displacement parameters
12.  Classifying and assembling two-dimensional X-ray laser diffraction patterns of a single particle to reconstruct the three-dimensional diffraction intensity function: resolution limit due to the quantum noise 
A new algorithm is developed for reconstructing the high-resolution three-dimensional diffraction intensity function of a globular biological macromolecule from many quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The structural resolution is expressed as a function of the incident X-ray intensity and quantities characterizing the target molecule.
A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ∼0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule.
PMCID: PMC3329770  PMID: 22514069
biological macromolecules; classification of two-dimensional diffraction patterns; common intersecting circles; attainable structural resolution
13.  Structure-factor analysis of femtosecond microdiffraction patterns from protein nanocrystals 
A complete set of structure factors has been extracted from hundreds of thousands of femtosecond X-ray diffraction patterns from randomly oriented Photosystem I membrane protein nanocrystals, using the Monte Carlo method of intensity integration. The data, collected at the Linac Coherent Light Source, are compared with conventional single-crystal data collected at a synchrotron source, and the quality of each data set was found to be similar.
A complete set of structure factors has been extracted from hundreds of thousands of femtosecond single-shot X-ray microdiffraction patterns taken from randomly oriented nanocrystals. The method of Monte Carlo integration over crystallite size and orientation was applied to experimental data from Photosystem I nanocrystals. This arrives at structure factors from many partial reflections without prior knowledge of the particle-size distribution. The data were collected at the Linac Coherent Light Source (the first hard-X-ray laser user facility), to which was fitted a hydrated protein nanocrystal injector jet, according to the method of serial crystallography. The data are single ‘still’ diffraction snapshots, each from a different nanocrystal with sizes ranging between 100 nm and 2 µm, so the angular width of Bragg peaks was dominated by crystal-size effects. These results were compared with single-crystal data recorded from large crystals of Photosystem I at the Advanced Light Source and the quality of the data was found to be similar. The implications for improving the efficiency of data collection by allowing the use of very small crystals, for radiation-damage reduction and for time-resolved diffraction studies at room temperature are discussed.
PMCID: PMC3066792  PMID: 21325716
nanocrystals; femtosecond diffraction; free-electron lasers; Monte Carlo methods; protein microdiffraction
14.  Grazing-incidence small-angle X-ray scattering: application to the study of quantum dot lattices 
The modelling of grazing-incidence small-angle X-ray scattering (GISAXS) from three-dimensional quantum dot lattices is described.
The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determination, including lattice type, lattice parameters, the type and degree of disorder in the quantum dot positions and the distributions of the quantum dot sizes. Applications of the developed models are demonstrated using experimentally measured data from several types of quantum dot lattices formed by a self-assembly process.
PMCID: PMC3243409  PMID: 22186289
grazing-incidence small-angle X-ray scattering; GISAXS; quantum dot lattices; self-assembly
15.  A multi-dataset data-collection strategy produces better diffraction data 
Theoretical analysis and experimental validation prove that a multi-dataset data-collection strategy produces better diffraction data. The readiness test is a simple and sensitive method for X-ray data-collection system evaluation and a benchmark.
A multi-dataset (MDS) data-collection strategy is proposed and analyzed for macromolecular crystal diffraction data acquisition. The theoretical analysis indicated that the MDS strategy can reduce the standard deviation (background noise) of diffraction data compared with the commonly used single-dataset strategy for a fixed X-ray dose. In order to validate the hypothesis experimentally, a data-quality evaluation process, termed a readiness test of the X-ray data-collection system, was developed. The anomalous signals of sulfur atoms in zinc-free insulin crystals were used as the probe to differentiate the quality of data collected using different data-collection strategies. The data-collection results using home-laboratory-based rotating-anode X-ray and synchrotron X-ray systems indicate that the diffraction data collected with the MDS strategy contain more accurate anomalous signals from sulfur atoms than the data collected with a regular data-collection strategy. In addition, the MDS strategy offered more advantages with respect to radiation-damage-sensitive crystals and better usage of rotating-anode as well as synchrotron X-rays.
PMCID: PMC3211246  PMID: 22011470
multi-dataset data-collection strategy; readiness test
16.  Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison 
X-ray free-electron lasers are being used to determine the three-dimensional structure of objects from random snapshots. The two apparently very different Bayesian algorithms capable of performing this at ultra-low signal are fundamentally the same.
The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10−2 photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.
PMCID: PMC3171899  PMID: 21844653
X-ray scattering; single-particle structure determination
17.  High-resolution study of dynamical diffraction phenomena accompanying the Renninger (222/113) case of three-beam diffraction in silicon 
The effect of the total reflection of the incident beam into the 222 reflected beam in the Renninger (222/113) case in Si was experimentally observed by using a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes.
X-ray optical schemes capable of producing a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes have been evaluated and utilized to study high-resolution diffraction phenomena in the Renninger (222/113) case of three-beam diffraction in silicon. The effect of the total reflection of the incident beam into the nearly forbidden reflected beam was observed for the first time with the maximum 222 reflectivity at the 70% level. We have demonstrated that the width of the 222 reflection can be varied many times by tuning the azimuthal angle by only a few µrad in the vicinity of the three-beam diffraction region. This effect, predicted theoretically more than 20 years ago, is explained by the enhancement of the 222 scattering amplitude due to the virtual two-stage 000 113 222 process which depends on the azimuthal angle.
PMCID: PMC2891002  PMID: 20555185
dynamical diffraction; multiple diffraction; X-ray optics; plane wave; synchrotron radiation
18.  Exact direct-space asymmetric units for the 230 crystallographic space groups 
A reference table of exact direct-space asymmetric units for the 230 crystallographic space groups is presented, based on a new geometric notation for asymmetric unit conditions.
It is well known that the direct-space asymmetric unit definitions found in the International Tables for Crystallography, Volume A, are inexact at the borders. Face- and edge-specific sub-conditions have to be added to remove parts redundant under symmetry. This paper introduces a concise geometric notation for asymmetric unit conditions. The notation is the foundation for a reference table of exact direct-space asymmetric unit definitions for the 230 crystallographic space-group types. The change-of-basis transformation law for the conditions is derived, which allows the information from the reference table to be used for any space-group setting. We also show how the vertices of an asymmetric unit can easily be computed from the information in the reference table.
PMCID: PMC3082335  PMID: 21487185
asymmetric unit; direct space; space groups
19.  Translation calibration of inverse-kappa goniometers in macromolecular crystallography 
A rapid, easy-to-perform translation calibration procedure has been developed for use with the EMBL/ESRF mini-κ goniometer head and for other inverse-kappa goniometers designed for macromolecular crystallography. Regular calibration ensures the precision of experiments that rely on many degrees of freedom in crystal reorientation.
Precise and convenient crystal reorientation is of experimental importance in macromolecular crystallography (MX). The development of multi-axis goniometers, such as the ESRF/EMBL mini-κ, necessitates the corresponding development of calibration procedures that can be used for the setup, maintenance and troubleshooting of such devices. While traditional multi-axis goniometers require all rotation axes to intersect the unique point of the sample position, recently developed miniaturized instruments for sample reorientation in MX are not as restricted. However, the samples must always be re-centred following a change in orientation. To overcome this inconvenience and allow the use of multi-axis goniometers without the fundamental restriction of having all axes intersecting in the same point, an automatic translation correction protocol has been developed for such instruments. It requires precise information about the direction and location of the rotation axes. To measure and supply this information, a general, easy-to-perform translation calibration (TC) procedure has also been developed. The TC procedure is routinely performed on most MX beamlines at the ESRF and some results are presented for reference.
PMCID: PMC3082334  PMID: 21487180
kappa goniometer; macromolecular crystallography; reorientation; calibration
20.  Time-resolved synchrotron diffraction and theoretical studies of very short-lived photo-induced molecular species 
Excited-state geometries determined by time-resolved synchrotron diffraction are summarized with emphasis on their comparison with a series of theoretical results. The relative merits of monochromatic and polychromatic (Laue) techniques are discussed.
Definitive experimental results on the geometry of fleeting species are at the time of writing still limited to monochromatic data collection, but methods for modifications of the polychromatic Laue data to increase their accuracy and their suitability for pump–probe experiments have been implemented and are reviewed. In the monochromatic experiments summarized, excited-state conversion percentages are small when neat crystals are used, but are higher when photoactive species are embedded in an inert framework in supramolecular crystals. With polychromatic techniques and increasing source brightness, smaller samples down to tenths of a micrometre or less can be used, increasing homogeneity of exposure and the fractional population of the excited species. Experiments described include a series of transition metal complexes and a fully organic example involving excimer formation. In the final section, experimental findings are compared with those from theoretical calculations on the isolated species. Qualitative agreement is generally obtained, but the theoretical results are strongly dependent on the details of the calculation, indicating the need for further systematic analysis.
PMCID: PMC2824528  PMID: 20164641
pump–probe experiments; time-resolved diffraction; excited-state molecular geometries; excimers
21.  Geometric properties of nucleic acids with potential for autobuilding 
Algorithms and geometrical properties are described for the automated building of nucleic acids in experimental electron density.
Medium- to high-resolution X-ray structures of DNA and RNA molecules were investigated to find geometric properties useful for automated model building in crystallographic electron-density maps. We describe a simple method, starting from a list of electron-density ‘blobs’, for identifying backbone phosphates and nucleic acid bases based on properties of the local electron-density distribution. This knowledge should be useful for the automated building of nucleic acid models into electron-density maps. We show that the distances and angles involving C1′ and the P atoms, using the pseudo-torsion angles and that describe the …P—C1′—P—C1′… chain, provide a promising basis for building the nucleic acid polymer. These quantities show reasonably narrow distributions with asymmetry that should allow the direction of the phosphate backbone to be established.
PMCID: PMC3006036  PMID: 21173468
nucleic acids; autobuilding; geometric properties; electron-density distribution
22.  Depth profiling of polymer films with grazing-incidence small-angle X-ray scattering 
A procedure for obtaining depth-specific scattering profiles of laterally defined nanostructure using grazing-incidence small-angle X-ray scattering is described.
A model-free method of reconstructing depth-specific lateral scattering from incident-angle-resolved grazing-incidence small-angle X-ray scattering (GISAXS) data is proposed. The information on the material which is available through variation of the X-ray penetration depth with incident angle is accessed through reference to the reflected branch of the GISAXS process. Reconstruction of the scattering from lateral density fluctuations is achieved by solving the resulting Fredholm integral equation with minimal a priori information about the experimental system. Results from simulated data generated for hypothetical multilayer polymer systems with constant absorption coefficient are used to verify that the method can be applied to cases with large X-ray penetration depths, as typically seen with polymer materials. Experimental tests on a spin-coated thick film of a blend of diblock copolymers demonstrate that the approach is capable of reconstruction of the scattering from a multilayer structure with the identification of lateral scattering profiles as a function of sample depth.
PMCID: PMC2724987  PMID: 19349663
depth profiling; grazing-incidence small-angle X-ray scattering; block copolymers
23.  Time-resolved structural studies of protein reaction dynamics: a smorgasbord of X-ray approaches 
Time-resolved structural studies of proteins have undergone several significant developments during the last decade. Recent developments using time-resolved X-ray methods, such as time-resolved Laue diffraction, low-temperature intermediate trapping, time-resolved wide-angle X-ray scattering and time-resolved X-ray absorption spectroscopy, are reviewed.
Proteins undergo conformational changes during their biological function. As such, a high-resolution structure of a protein’s resting conformation provides a starting point for elucidating its reaction mechanism, but provides no direct information concerning the protein’s conformational dynamics. Several X-ray methods have been developed to elucidate those conformational changes that occur during a protein’s reaction, including time-resolved Laue diffraction and intermediate trapping studies on three-dimensional protein crystals, and time-resolved wide-angle X-ray scattering and X-ray absorption studies on proteins in the solution phase. This review emphasizes the scope and limitations of these complementary experimental approaches when seeking to understand protein conformational dynamics. These methods are illustrated using a limited set of examples including myoglobin and haemoglobin in complex with carbon monoxide, the simple light-driven proton pump bacteriorhodopsin, and the superoxide scavenger superoxide reductase. In conclusion, likely future developments of these methods at synchrotron X-ray sources and the potential impact of emerging X-ray free-electron laser facilities are speculated upon.
PMCID: PMC2824530  PMID: 20164644
time-resolved diffraction; structural biology; protein structural dynamics; Laue diffraction; kinetic crystallography; WAXS; XAS
24.  Five-dimensional crystallography 
Here it is demonstrated how five-dimensional crystallography can be used to determine a comprehensive chemical kinetic mechanism in concert with the atomic structures of transient intermediates that form and decay during the course of the reaction.
A method for determining a comprehensive chemical kinetic mechanism in macromolecular reactions is presented. The method is based on five-dimensional crystallography, where, in addition to space and time, temperature is also taken into consideration and an analysis based on singular value decomposition is applied. First results of such a time-resolved crystallographic study are presented. Temperature-dependent time-resolved X-ray diffraction measurements were conducted on the newly upgraded BioCARS 14-ID-B beamline at the Advanced Photon Source and aimed at elucidating a comprehensive kinetic mechanism of the photoactive yellow protein photocycle. Extensive time series of crystallographic data were collected at two temperatures, 293 K and 303 K. Relaxation times of the reaction extracted from these time series exhibit measurable differences for the two temperatures, hence demonstrating that five-dimensional crystallography is feasible.
PMCID: PMC2824529  PMID: 20164643
time-resolved crystallography; chemical kinetics; protein structure; temperature dependence
25.  The introduction of structure types into the Inorganic Crystal Structure Database ICSD 
The approach used and the progress made in the assignment of structure types to the crystal structures contained in the ICSD database are reported.
Both the approach used and the progress made in the assignment of structure types to the crystal structures contained in the ICSD database are reported. Extending earlier work, an hierarchical set of criteria for the separation of isopointal structures into isoconfigurational structure types is used. It is shown how these criteria, which include the space group (number), Wyckoff sequence and Pearson symbol, c/a ratio, β ranges, ANX formulae and, in certain cases, the necessary elements and forbidden elements, may be used to uniquely identify the representative structure types of the compounds contained in the ICSD database.
PMCID: PMC2525864  PMID: 17703075
Inorganic Crystal Structure Database; ICSD; structure types

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