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1.  Direct observation of solid-state reversed transformation from crystals to quasicrystals in a Mg alloy 
Scientific Reports  2015;5:9816.
Phase transformation of quasicrystals is of interest in various fields of science and technology. Interestingly, we directly observed unexpected solid-state epitaxial nucleation and growth of Zn6Mg3Y icosahedral quasicrystals in a Mg alloy at about 573 K which is about 300 K below the melting point of Zn6Mg3Y, in contrast to formation of quasicrystals through solidification that was usually found in many alloys. Maximizing local packing density of atoms associated with segregation of Y and Zn in Mg adjacent to Mg/Zn3MgY interfaces triggered atomic rearrangement in Mg to form icosahedra coupled epitaxially with surface distorted icosahedra of Zn3MgY, which plays a critical role in the nucleation of icosahedral clusters. A local Zn:Mg:Y ratio close to 6:3:1, corresponding to a valence electron concentration of about 2.15, should have been reached to trigger the formation of quasicrystals at Mg/Zn3MgY interfaces. The solid-state icosahedral ordering in crystals opens a new window for growing quasicrystals and understanding their atomic origin mechanisms. Epitaxial growth of quasicrystals onto crystals can modify the surface/interface structures and properties of crystalline materials.
doi:10.1038/srep09816
PMCID: PMC4464364  PMID: 26066096
2.  High-pressure crystallography of periodic and aperiodic crystals 
IUCrJ  2015;2(Pt 2):218-229.
This article discusses the high-pressure behaviour of molecular crystal structures, energetic materials, phases relevant to the Earth’s interior, materials with a pressure-induced expansion in one or two directions, dealing with high-pressure data from crystals with twinning and pseudosymmetry, pressure-induced phase transitions including an incommensurate phase, and technical developments.
More than five decades have passed since the first single-crystal X-ray diffraction experiments at high pressure were performed. These studies were applied historically to geochemical processes occurring in the Earth and other planets, but high-pressure crystallography has spread across different fields of science including chemistry, physics, biology, materials science and pharmacy. With each passing year, high-pressure studies have become more precise and comprehensive because of the development of instrumentation and software, and the systems investigated have also become more complicated. Starting with crystals of simple minerals and inorganic compounds, the interests of researchers have shifted to complicated metal–organic frameworks, aperiodic crystals and quasicrystals, molecular crystals, and even proteins and viruses. Inspired by contributions to the microsymposium ‘High-Pressure Crystallography of Periodic and Aperiodic Crystals’ presented at the 23rd IUCr Congress and General Assembly, the authors have tried to summarize certain recent results of single-crystal studies of molecular and aperiodic structures under high pressure. While the selected contributions do not cover the whole spectrum of high-pressure research, they demonstrate the broad diversity of novel and fascinating results and may awaken the reader’s interest in this topic.
doi:10.1107/S2052252514025482
PMCID: PMC4392772  PMID: 25866659
high-pressure crystallography; periodic crystals; aperiodic crystals; incommensurate modulation
3.  THE STRUCTURE OF PARAMYOSIN FIBRILS ACCORDING TO X-RAY DIFFRACTION 
From analysis of x-ray diffraction patterns obtained with improved small-angle techniques has been derived the following description for the structure of the fibrils of the fibrous protein, paramyosin, obtained in this case from "white" portions of the adductor muscle of the clam, Venus mercenaria: 1. About 25 significantly different diffraction maxima have been resolved and found accounted for as (hk) reflections of a net whose cell elements are, for the dry material: a = 250 A, b = 720 A (fibril axis identity period), and γ = 90.5° (angle included between a and b axes). For rehydrated material a is larger (ca. 325 A), b is essentially unchanged, and γ is slightly larger. There remains an unresolved discrepancy between the electron-optically derived, cell's a dimension (193 A) and that here reported for dry samples. 2. The h = ±1 row lines are crossed on the diagrams (because γ is not 90°) and thus can be distinguished in spite of natural "rotation" of fibrils (within the massive fibrous specimens) about their commonly oriented axes. The observed reflections are then found to obey a selection rule which indicates that the net cell is non-primitive and contains 5 equivalent locations (nodes) arranged as shown in Fig. 5. The nodal distribution is the same as has been previously photographed electron-optically. 3. Analysis of reflection lengths indicates that the native fibrils are not noticeably ribbon-like, having dimensions normal to the ordered net layers approximating their width across the fibril in the plane of the net layers. Corresponding transverse, interlayer spacings (possibly ca. 100 A) have not been observed, however, and may be hidden in troublesome central scatter. 4. Since paramyosin's wide-angle diffraction is very probably of α-type, supercoiled α-helices must be involved according to current interpretations of α-diagrams. Physicochemical evidence suggests that cables of this type, ca. 1400 A in length, may extend over two cells. Of two possible nodal connections, a favored one is shown in Fig. 5 to join 5 nodes in this way. Considerations of space filling, of transverse distribution of small-angle x-ray scattering, and of nodal significance, suggest that the cable units may be further aggregated into supercables, essentially forming rather solid rods of ca. 100 A diameter. 5. An alternative interpretation of the paramyosin small-angle diffraction, in particular of the observed selection rule, would conclude that large particles are arranged in a helical way, with minimum helix diameter about 150 A (dry). The simplest (genetic) particle connection would have 5 particles in 2 coil turns along 720 A of fibril or helix axis. This view is distinctly different from the arrangement of "rods" in net-like layers as given above, even though the rods are said to be made of supercoils or cables. Reasons are given for preferring the net-of-rods explanation over the particulate-helix model. The helix- vs. true-net ambiguity arises whenever the two types of structure are conceivable, and decision between them is difficult on the basis of the diffraction data alone.
PMCID: PMC2223955  PMID: 13295311
4.  Plasmonic quasicrystals with broadband transmission enhancement 
Scientific Reports  2014;4:5257.
Plasmonic quasicrystals (PlQCs), by integrating the properties of quasicrystals (rotational symmetry and long range ordering but lack translational symmetry) and surface plasmon polariton mediated effects, offer several advantages over plasmonic crystals (PlCs). For example, in PlQCs one could have broadband, polarization independent response. However, large area patterning by electron beam lithography requires precise lattice coordinates as well as a practical way to design the structures for specific spectral response. We demonstrate design and fabrication of large area quasicrystal air hole patterns of π/5 symmetry in metal film in which broadband, polarization and launch angle independent transmission enhancement is observed. We demonstrate bi-grating quasicrystals to show that designable transmission response is possible over visible to near infrared wavelength regions with about 15 times enhancement. These would be useful in many applications like energy harvesting, nonlinear optics and quantum plasmonics.
doi:10.1038/srep05257
PMCID: PMC4052717  PMID: 24918659
5.  Novel hybrid organic/inorganic 2D quasiperiodic PC: from diffraction pattern to vertical light extraction 
Nanoscale Research Letters  2011;6(1):371.
Recently, important efforts have been dedicated to the realization of a fascinating class of new photonic materials or metamaterials, known as photonic quasicrystals (PQCs), in which the lack of the translational symmetry is compensated by rotational symmetries not achievable by the conventional periodic crystals. As ever, more advanced functionality is demanded and one strategy is the introduction of non-linear and/or active functionality in photonic materials. In this view, core/shell nanorods (NRs) are a promising active material for light-emitting applications. In this article a two-dimensional (2D) hybrid a 2D octagonal PQC which consists of air rods in an organic/inorganic nanocomposite is proposed and experimentally demonstrated. The nanocomposite was prepared by incorporating CdSe/CdS core/shell NRs into a polymer matrix. The PQC was realized by electron beam lithography (EBL) technique. Scanning electron microscopy, far field diffraction and spectra measurements are used to characterize the experimental structure. The vertical extraction of the light, by the coupling of the modes guided by the PQC slab to the free radiation via Bragg scattering, consists of a narrow red emissions band at 690 nm with a full width at half-maximum (FWHM) of 21.5 nm. The original characteristics of hybrid materials based on polymers and colloidal NRs, able to combine the unique optical properties of the inorganic moiety with the processability of the host matrix, are extremely appealing in view of their technological impact on the development of new high performing optical devices such as organic light-emitting diodes, ultra-low threshold lasers, and non-linear devices.
PACS: 81.07.Pr Organic-inorganic hybrid nanostructures, 81.16.-c Methods of nanofabrication and processing, 42.70.Qs Photonic band-gap materials.
doi:10.1186/1556-276X-6-371
PMCID: PMC3211462  PMID: 21711884
6.  Diffraction with a coherent X-ray beam: dynamics and imaging 
Techniques for coherent X-ray scattering measurements are detailed. Applications in the study of the dynamics of fluctuations and in lensless high-resolution imaging are described.
Methods for carrying out coherent X-ray scattering experiments are reviewed. The brilliance of the available synchrotron sources, the characteristics of the existing optics, the various ways of obtaining a beam of controlled coherence properties and the detectors used are summarized. Applications in the study of the dynamics of speckle patterns are described. In the case of soft condensed matter, the movement of inclusions like fillers in polymers or colloidal particles can be observed and these can reflect polymer or liquid-crystal fluctuations. In hard condensed-matter problems, like phase transitions, charge-density waves or phasons in quasicrystals, the study of speckle fluctuations provides new time-resolved methods. In the domain of lensless imaging, the coherent beam gives the modulus of the sample Fourier transform. If oversampling conditions are fulfilled, the phase can be obtained and the image in the direct space can be reconstructed. The forthcoming improvements of all these techniques are discussed.
doi:10.1107/S010876730605570X
PMCID: PMC2525861  PMID: 17301470
coherent X-ray beams; dynamics of fluctuations; lensless imaging; small-angle set-ups
7.  A case of structure determination using pseudosymmetry 
When properly applied, pseudosymmetry can be used to improve crystallographic phases through averaging and to facilitate crystal structure determination.
Here, a case is presented of an unusual structure determination which was facilitated by the use of pseudosymmetry. Group A streptococcus uses cysteine protease Mac-1 (also known as IdeS) to evade the host immune system. Native Mac-1 was crystallized in the orthorhombic space group P21212. Surprisingly, crystals of the inactive C94A mutant of Mac-1 displayed monoclinic symmetry with space group P21, despite the use of native orthorhombic Mac-1 microcrystals for seeding. Attempts to solve the structure of the C94A mutant by MAD phasing in the monoclinic space group did not produce an interpretable map. The native Patterson map of the C94A mutant showed two strong peaks along the (1 0 1) diagonal, indicating possible translational pseudosymmetry in space group P21. Interestingly, one-third of the monoclinic reflections obeyed pseudo-orthorhombic P21212 symmetry similar to that of the wild-type crystals and could be indexed and processed in this space group. The pseudo-orthorhombic and monoclinic unit cells were related by the following vector operations: a m = b o − c o, b m = a o and c m = −2c o − b o. The pseudo-orthorhombic subset of data produced good SAD phases, leading to structure determination with one monomer in the asymmetric unit. Subsequently, the structure of the Mac-1 mutant in the monoclinic form was determined by molecular replacement, which showed six molecules forming three translationally related dimers aligned along the (1 0 1) diagonal. Knowing the geometric relationship between the pseudo-orthorhombic and the monoclinic unit cells, all six molecules can be generated in the monoclinic unit cell directly without the use of molecular replacement. The current case provides a successful example of the use of pseudosymmetry as a powerful phase-averaging method for structure determination by anomalous diffraction techniques. In particular, a structure can be solved in a higher pseudosymmetry subcell in which an NCS operator becomes a crystallographic operator. The geometrical relationships between the subcell and parental cell can be used to generate a complete molecular representation of the parental asymmetric unit for refinement.
doi:10.1107/S0907444909039912
PMCID: PMC2789005  PMID: 19966420
pseudosymmetry; structure determination; cysteine proteases; Mac-1
8.  X-RAY DIFFRACTION STUDIES ON FROG MUSCLES 
The Journal of General Physiology  1944;28(2):151-178.
1. X-ray diffraction studies of sartorius muscles of Rana pipiens were made in a new x-ray diffraction camera which permits exposures of 3 to 6 minutes. The object-film distance can be varied from 20 to 80 mm; the muscle inside the camera can be electrically stimulated while contracting isotonically or isometrically, and can be observed by a special device. After exposures up to 30 minutes (approximately 40,830 r) muscles are still alive and responsive. 2. Contrary to the x-ray diffraction pattern of powdered dry muscle, which pattern consists of two rings corresponding to spacings of 4.46 Å.u. and 9.66 Å.u., both moist and dried whole sartorius muscle show signs of orientation in both rings, consisting of two equatorial streaks (wet) or points (dry) and meridional sickles. The moist muscle shows in addition a diffuse water ring. The spacings corresponding to the orientation points and elliptical structure show only slight differences in moist and dried samples. Through statistical computations based on two different series consisting of thirteen moist and twenty-eight dried samples, and nine muscles before and after drying, it was shown that only the divergence in the smaller spacing has some real significance, which indicates that most water of the moist muscle is bound intermolecularly. Upon resoaking of dried muscle the x-ray diffraction pattern of the moist muscle is restored. 3. Stretching of muscle by weights below the breaking point produces an additional well defined diffraction line, corresponding to a spacing of 4.32 Å.u. A similar diffraction line can be produced in frog tendon upon stretching. 4. The influence of heat on the x-ray diffraction pattern of muscle depends upon the maximum temperature and the length of action; 5 minutes at 50° C. markedly reduces the orientation of the sample; 5 minutes' immersion in boiling Ringer's solution destroys the orientation and produces a ring corresponding to a spacing of 5.3 to 5.5 Å.u. in the moist and sharpening of the backbone reflection in the dried specimen. 5. Ultraviolet light brings forth changes in the x-ray diffraction pattern varying with the intensity of the irradiation. Ultimately a disappearance of the equatorial points and of the outside sickles is achieved while the elliptical shape of the outside ring and its diffuseness persist. In addition two salt rings characteristic of NaCl indicate that the irradiated muscles have become permeable to the surrounding medium (Ringer's solution). 6. Both faradic and single shock electrical stimulation were tried on muscles. If shortening of the muscle is prevented either by sufficient weight or by tying the muscle in a frame, no changes in the x-ray diffraction pattern occur; if the muscle is allowed to shorten without weights or by using insufficient weights, then the orientation either disappears completely or partially. When the muscle is stretched while contracted by electrical stimulation the orientation of the x-ray diffraction pattern reappears. 7. A number of salts with uni- and bivalent ions in concentrations corresponding osmotically to 0.73 per cent NaCl and 10 per cent NH4Cl were studied in their effects upon the x-ray diffraction of muscles. Of the salts with univalent ions in the lower concentration only KCl causes a marked decrease of orientation and an increase in the permeability of the fiber membranes. Similar effects on the orientation seem to be produced by CaCl2 while MgCl2 causes rather a more pronounced orientation. At hypertonic salt concentrations the orientation disappears completely and the corresponding salt rings become visible. Besides, NaCNS seems to have a specific effect on the outside ring and LiCl produces a ring at 21.3 Å.u. and a splitting of the outside ring. 8. Strong mineral and lactic acids in concentrations up to 0.005 N have little if any influence upon the x-ray diffraction of muscles. A further increase in acidity to 0.01 N and above destroys the orientation completely, causes sharpening of the backbone reflection, and increased membrane permeability. These changes are irreversible upon neutralization. Also the effects of swelling upon the water ring of fresh muscle become manifest. Weak acids at higher concentrations show an effect similar to that of strong acids. 9. Rigor mortis produces a more or less complete loss of orientation. The muscles show signs of increased permeability. 10. Alkalies destroy the orientation of the x-ray diffraction pattern. The effective concentration is higher than the corresponding amount of acid. 11. Formaldehyde produces only minor changes in the x-ray diffraction patterns of muscles. 12. The effects of alcohol depend primarily upon the concentration applied. Low concentrations (5 per cent) seem to have a passing stimulating effect, at concentrations of 15 per cent, the anesthetizing effect becomes manifest in well defined orientation. The diameter of the water ring is reduced. If 95 per cent alcohol is allowed to act upon muscle for more than 12 minutes, then the orientation disappears completely and the backbone spacing becomes as sharp as in boiled muscle. 13. The effects of chloroform depend upon whether the muscle is allowed to contract or not. Only if the muscle is allowed to contract in chloroform-saturated Ringer's solution is the orientation lost and salt rings appear as well as a ring corresponding to a spacing of 22 Å.u,, which has been observed in other changes in muscles. 14. In muscles allowed to shorten in a caffeine-Ringer's solution the orientation disappears, salt rings become visible as well as a decrease in size of the water ring; a new arc corresponding to a spacing of 4.18 Å.u. was observed in one case.
PMCID: PMC2142657  PMID: 19873411
9.  X-ray diffraction evidence for the existence of 102.0- and 230.0-nm transverse periodicities in striated muscle 
The Journal of Cell Biology  1987;105(3):1311-1318.
Synchrotron radiation techniques have enabled us to record meridional x- ray diffraction patterns from frog sartorius muscle at resolutions ranging from approximately 2,800 to 38 nm (i.e., overlapping with the optical microscope and the region normally accessible with low angle diffraction cameras). These diffraction patterns represent the transform of the low resolution structure of muscle projected on the sarcomere axis and sampled by its repeat. Altering the sarcomere length results in the sampling of different parts of this transform, which induces changes in the positions and the integrated intensities of the diffraction maxima. This effect has been used to determine the transform of the mass projection on the muscle axis in a quasicontinuous fashion. The results reveal the existence of maxima arising from long-range periodicities in the structure. Determination of the zeroes in the transforms has been used to obtain phase information from which electron density maps have been calculated. The x-ray diffraction diagrams and the resulting electron density maps show the existence of a series of mass bands, disposed transversely to the sarcomere axis and distributed at regular intervals. A set of these transverse structures is associated with thin filaments, and their 102.0-nm repeat suggests a close structural relationship with their known molecular components. A second set, spaced by approximately 230.0 nm, is also present; from diffraction theory one has to conclude that this repeat simultaneously exists in thick and thin filament regions.
PMCID: PMC2114824  PMID: 3498727
10.  Experimental and Theoretical Investigation of Macro-Periodic and Micro-Random Nanostructures with Simultaneously Spatial Translational Symmetry and Long-Range Order Breaking 
Scientific Reports  2015;5:7876.
Photonic and plasmonic quasicrystals, comprising well-designed and regularly-arranged patterns but lacking spatial translational symmetry, show sharp diffraction patterns resulting from their long-range order in spatial domain. Here we demonstrate that plasmonic structure, which is macroscopically arranged with spatial periodicity and microscopically constructed by random metal nanostructures, can also exhibit the diffraction effect experimentally, despite both of the translational symmetry and long-range order are broken in spatial domain simultaneously. With strategically pre-formed metal nano-seeds, the tunable macroscopically periodic (macro-periodic) pattern composed from microscopically random (micro-random) nanoplate-based silver structures are fabricated chemically through photon driven growth using simple light source with low photon energy and low optical power density. The geometry of the micro-structure can be further modified through simple thermal annealing. While the random metal nanostructures suppress high-order Floquet spectra of the spatial distribution of refractive indices, the maintained low-order Floquet spectra after the ensemble averaging are responsible for the observed diffraction effect. A theoretical approach has also been established to describe and understand the macro-periodic and micro-random structures with different micro-geometries. The easy fabrication and comprehensive understanding of this metal structure will be beneficial for its application in plasmonics, photonics and optoelectronics.
doi:10.1038/srep07876
PMCID: PMC4297977  PMID: 25597407
11.  Three-dimensional rotation electron diffraction: software RED for automated data collection and data processing 
Journal of Applied Crystallography  2013;46(Pt 6):1863-1873.
Implementation of the RED software package for automated collection and processing of rotation electron diffraction data is described.
Implementation of a computer program package for automated collection and processing of rotation electron diffraction (RED) data is described. The software package contains two computer programs: RED data collection and RED data processing. The RED data collection program controls the transmission electron microscope and the camera. Electron beam tilts at a fine step (0.05–0.20°) are combined with goniometer tilts at a coarse step (2.0–3.0°) around a common tilt axis, which allows a fine relative tilt to be achieved between the electron beam and the crystal in a large tilt range. An electron diffraction (ED) frame is collected at each combination of beam tilt and goniometer tilt. The RED data processing program processes three-dimensional ED data generated by the RED data collection program or by other approaches. It includes shift correction of the ED frames, peak hunting for diffraction spots in individual ED frames and identification of these diffraction spots as reflections in three dimensions. Unit-cell parameters are determined from the positions of reflections in three-dimensional reciprocal space. All reflections are indexed, and finally a list with hkl indices and intensities is output. The data processing program also includes a visualizer to view and analyse three-dimensional reciprocal lattices reconstructed from the ED frames. Details of the implementation are described. Data collection and data processing with the software RED are demonstrated using a calcined zeolite sample, silicalite-1. The structure of the calcined silicalite-1, with 72 unique atoms, could be solved from the RED data by routine direct methods.
doi:10.1107/S0021889813027714
PMCID: PMC3831301  PMID: 24282334
rotation electron diffraction; electron diffraction tomography; three-dimensional electron diffraction; structure analysis; electron diffraction; computer programs
12.  Fractal tiles associated with shift radix systems☆ 
Advances in Mathematics  2011;226(1):139-175.
Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings.
In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials.
We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple tilings and even tilings of the d-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine).
doi:10.1016/j.aim.2010.06.010
PMCID: PMC3778876  PMID: 24068835
Beta expansion; Canonical number system; Shift radix system; Tiling
13.  Precession electron diffraction – a topical review 
IUCrJ  2015;2(Pt 1):126-136.
This topical review highlights progress made recently in the development and application of precession electron diffraction (PED) and its scanning variant for the determination of unknown crystal structures and the mapping of orientations at the nanoscale.
In the 20 years since precession electron diffraction (PED) was introduced, it has grown from a little-known niche technique to one that is seen as a cornerstone of electron crystallography. It is now used primarily in two ways. The first is to determine crystal structures, to identify lattice parameters and symmetry, and ultimately to solve the atomic structure ab initio. The second is, through connection with the microscope scanning system, to map the local orientation of the specimen to investigate crystal texture, rotation and strain at the nanometre scale. This topical review brings the reader up to date, highlighting recent successes using PED and providing some pointers to the future in terms of method development and how the technique can meet some of the needs of the X-ray crystallography community. Complementary electron techniques are also discussed, together with how a synergy of methods may provide the best approach to electron-based structure analysis.
doi:10.1107/S2052252514022283
PMCID: PMC4285886  PMID: 25610633
precession electron diffraction (PED); electron crystallography; electron techniques; electron-based structure analysis
14.  Experimental Evidence of Icosahedral and Decahedral Packing in One-Dimensional Nanostructures 
ACS nano  2011;5(8):6272-6278.
The packing of spheres is a subject that has drawn the attention of mathematicians and philosophers for centuries, and that currently attracts the interest of the scientific community in several fields. At the nanoscale, the packing of atoms affect the chemical and structural properties of the material, and hence, its potential applications. This report describes the experimental formation of five-fold nanostructures by the packing of interpenetrated icosahedral and decahedral units. These nanowires, formed by the reaction of a mixture of metal salts (Au and Ag) in the presence of oleylamine, are obtained when the chemical composition is specifically Ag/Au=3/1. The experimental images of the icosahedral nanowires have a high likelihood with simulated electron micrographs of structures formed by two or three Boerdijk-Coxeter-Bernal helices roped on a single structure, whereas for the decahedral wires, simulations using a model of adjacent decahedra match the experimental structures. To our knowledge, this is the first report of the synthesis of nanowires formed by the packing of structures with five-fold symmetry. These icosahedral nanowire structures remind those of quasicrystals that can only be formed if at least two atomic species are present and in which icosahedral and decahedral packing has been found for bulk crystals.
doi:10.1021/nn202495r
PMCID: PMC3180901  PMID: 21790155
Boerdijk-Coxeter-Bernal helix; nanowires; icosahedra; decahedra; aberration corrected Electron Microscopy
15.  THE STRUCTURE OF ACTIN-RICH FILAMENTS OF MUSCLES ACCORDING TO X-RAY DIFFRACTION 
From analysis of moderate- to small-angle x-ray diffraction patterns, in the light of similar experience with paramyosin, has been derived the following description for the structure of actin-rich filaments in "tinted" portions of the adductor muscle of the clam, Venus mercenaria: 1. Some 11 diffraction maxima, widely streaked along layer lines and occurring at moderate diffraction angles (spacings 7 to 60 A) appear to be accounted for as (hk) reflections of a net whose cell elements are, for dry material: a ≑ 82 A, b = 406 A (filament axis identity period), and γ ≑ 82° (angle between a and b axes). These reflections follow a selection rule which indicates that the net cell is non-primitive and contains 15 equivalent locations (nodes) arranged as shown in Fig. 5. An alternative net has b' = 351 A and 13 nodes per cell. 2. Another interpretation rolls the net into a large-scale helix and places the 15 (or 13) nodes along 7 (or 6) turns of a helical locus projecting 406 (or 351) A along the filament axis. Whether considered to be built of planar-net or helix-net cells, the individual filament contains a single cell width transverse to its axis. Transverse filament dimensions are, therefore, in either case similar (50 to 100 A). 3. Consideration of existing electron-optical, physicochemical, and x-ray diffraction data regarding isolated actin suggests that the net cell is built of rods, each containing in cross-section from one to four actin molecules which run parallel to or twisted about rod axes that extend at 12° to the filament axis along the (21) diagonals of the cell. Depending on monomer shape, 2 to 15 monomers furnish length to reach across two cells, and the actin molecules are built into each rod in such a way as to repeat (or nearly repeat) structure 15 (or 13) times along the double cell length. Further details of intra-rod structure cannot be suggested because of lack of wide-angle diffraction information. 4. The actin system is sensitive to treatment of the muscle with ethanol. Concentrations of 5 per cent or greater abolish the net reflections. Other solvents—water, benzene, ether, pyridine, acetone—do not alter the pattern materially. 5. Two other reflections, occurring at the first and second layer lines of an axial periodicity of about 400 A, do not clearly belong to the actin-net system. They represent either a superstructure built upon the filaments by parts of the actin molecules themselves or by incorporated other molecular species, or they arise from an additional macromolecular component (possibly myosin, or its homologues or fractions) of similar axial periodicity.
PMCID: PMC2223960  PMID: 13295312
16.  Periodic almost-Schrödinger equation for quasicrystals 
Scientific Reports  2015;5:11492.
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrödinger equation in spaces of dimensionality higher than physical space. It enables to get exact results for quasicrystals without expensive non-exact calculations.
doi:10.1038/srep11492
PMCID: PMC4513277  PMID: 26205845
17.  Epitaxial Structure of (001)- and (111)-Oriented Perovskite Ferrate Films Grown by Pulsed-Laser Deposition 
Crystal Growth & Design  2010;10(4):1725-1729.
We report epitaxial growth and structures of SrFeO2.5 (SFO) films on SrTiO3 (STO) (001) and (111) substrates by pulsed-laser deposition. Reflection high-energy electron diffraction intensity oscillations were observed during the initial growth on both substrates, reflecting a layer-by-layer growth mode of the formula unit cell. It was found that the films were stabilized with a monoclinic structure that was derived from the original orthorhombic structure of bulk Brownmillerite. Using an X-ray reciprocal space mapping technique, in-plane domain structures and the orientation relationship were investigated. In addition, the impact of laser spot area on the epitaxial structures was studied. For the films grown on the (001) STO, the orientation relationship was robust against the change of the laser spot area: SFO(001)//STO(001) and SFO(100)//STO(100) for the out-of-plane and the in-plane, respectively, with the [001] axis tilted toward the 4-fold a- and b-axes by ∼1.4°, whereas nearly (111)-oriented films were obtained on the (111) STO, exhibiting a complicated manner of tilting that depended on laser spot area. The observed variation in tilting configurations can be understood in terms of possible atomic arrangements at the SFO/STO interface. These results present a guide to control the heteroepitaxial growth and structure of (111)-oriented noncubic perovskites.
The epitaxial structures of SrFeO2.5 films grown on SrTiO3 (001) and (111) substrates by PLD are reported. A layer-by-layer growth mode was achieved in the initial stage on both substrates. The films were stabilized with a monoclinic structure, where we identified the in-plane domain structures and orientation relationship. Our study presents a guide to control the heteroepitaxy of (111)-oriented noncubic perovskites.
doi:10.1021/cg901355c
PMCID: PMC2851191  PMID: 20383295
18.  Natural quasicrystal with decagonal symmetry 
Scientific Reports  2015;5:9111.
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula.
doi:10.1038/srep09111
PMCID: PMC4357871  PMID: 25765857
19.  Tiling microarray analysis of rice chromosome 10 to identify the transcriptome and relate its expression to chromosomal architecture 
Genome Biology  2005;6(6):R52.
A transcriptome analysis of chromosome 10 of 2 rice subspecies identifies 549 new gene models and gives experimental evidence for around 75% of the previously unsupported predicted genes.
Background
Sequencing and annotation of the genome of rice (Oryza sativa) have generated gene models in numbers that top all other fully sequenced species, with many lacking recognizable sequence homology to known genes. Experimental evaluation of these gene models and identification of new models will facilitate rice genome annotation and the application of this knowledge to other more complex cereal genomes.
Results
We report here an analysis of the chromosome 10 transcriptome of the two major rice subspecies, japonica and indica, using oligonucleotide tiling microarrays. This analysis detected expression of approximately three-quarters of the gene models without previous experimental evidence in both subspecies. Cloning and sequence analysis of the previously unsupported models suggests that the predicted gene structure of nearly half of those models needs improvement. Coupled with comparative gene model mapping, the tiling microarray analysis identified 549 new models for the japonica chromosome, representing an 18% increase in the annotated protein-coding capacity. Furthermore, an asymmetric distribution of genome elements along the chromosome was found that coincides with the cytological definition of the heterochromatin and euchromatin domains. The heterochromatin domain appears to associate with distinct chromosome level transcriptional activities under normal and stress conditions.
Conclusion
These results demonstrated the utility of genome tiling microarray in evaluating annotated rice gene models and in identifying novel transcriptional units. The tiling microarray sanalysis further revealed a chromosome-wide transcription pattern that suggests a role for transposable element-enriched heterochromatin in shaping global transcription in response to environmental changes in rice.
doi:10.1186/gb-2005-6-6-r52
PMCID: PMC1175972  PMID: 15960804
20.  Macromolecular Crystallography for Synthetic Abiological Molecules: Combining xMDFF and PHENIX for Structure Determination of Cyanostar Macrocycles 
Crystal structure determination has long provided insight into structure and bonding of small molecules. When those same small molecules are designed to come together in multi-molecular assemblies, such as in coordination cages, supramolecular architectures and organic-based frameworks, their crystallographic characteristics closely resemble biological macromolecules. This resemblance suggests that bio-macromolecular refinement approaches be used for structure determination of abiological molecular complexes that arise in an aggregate state. Following this suggestion we investigated the crystal structure of a pentagonal macrocycle, cyanostar, by means of biological structure analysis methods and compared results to traditional small molecule methods. Cyanostar presents difficulties seen in supramolecular crystallography including whole molecule disorder and highly flexible solvent molecules sitting in macrocyclic and intermolecule void spaces. We used the force-field assisted refinement method, molecular dynamics flexible fitting algorithm for X-ray crystallography (xMDFF), along with tools from the macromolecular structure determination suite PHENIX. We found that a standard implementation of PHENIX, namely one without xMDFF, either fails to produce a solution by molecular replacement alone or produces an inaccurate structure when using generic geometry restraints, even at a very high diffraction data resolution of 0.84 Å. The problems disappear when taking advantage of xMDFF, which applies an optimized force field to re-align molecular models during phasing by providing accurate restraints. The structure determination for this model system shows excellent agreement with the small-molecule methods. Therefore, the joint xMDFF-PHENIX refinement protocol provides a new strategy that uses macromolecule methods for structure determination of small molecules and their assemblies.
doi:10.1021/jacs.5b04407
PMCID: PMC4504762  PMID: 26121416
21.  Automatic validation of computational models using pseudo-3D spatio-temporal model checking 
BMC Systems Biology  2014;8:124.
Background
Computational models play an increasingly important role in systems biology for generating predictions and in synthetic biology as executable prototypes/designs. For real life (clinical) applications there is a need to scale up and build more complex spatio-temporal multiscale models; these could enable investigating how changes at small scales reflect at large scales and viceversa. Results generated by computational models can be applied to real life applications only if the models have been validated first. Traditional in silico model checking techniques only capture how non-dimensional properties (e.g. concentrations) evolve over time and are suitable for small scale systems (e.g. metabolic pathways). The validation of larger scale systems (e.g. multicellular populations) additionally requires capturing how spatial patterns and their properties change over time, which are not considered by traditional non-spatial approaches.
Results
We developed and implemented a methodology for the automatic validation of computational models with respect to both their spatial and temporal properties. Stochastic biological systems are represented by abstract models which assume a linear structure of time and a pseudo-3D representation of space (2D space plus a density measure). Time series data generated by such models is provided as input to parameterised image processing modules which automatically detect and analyse spatial patterns (e.g. cell) and clusters of such patterns (e.g. cellular population). For capturing how spatial and numeric properties change over time the Probabilistic Bounded Linear Spatial Temporal Logic is introduced. Given a collection of time series data and a formal spatio-temporal specification the model checker Mudi (http://mudi.modelchecking.org) determines probabilistically if the formal specification holds for the computational model or not. Mudi is an approximate probabilistic model checking platform which enables users to choose between frequentist and Bayesian, estimate and statistical hypothesis testing based validation approaches. We illustrate the expressivity and efficiency of our approach based on two biological case studies namely phase variation patterning in bacterial colony growth and the chemotactic aggregation of cells.
Conclusions
The formal methodology implemented in Mudi enables the validation of computational models against spatio-temporal logic properties and is a precursor to the development and validation of more complex multidimensional and multiscale models.
Electronic supplementary material
The online version of this article (doi:10.1186/s12918-014-0124-0) contains supplementary material, which is available to authorized users.
doi:10.1186/s12918-014-0124-0
PMCID: PMC4272535  PMID: 25440773
Stochastic spatial discrete event system (SSpDES); Probabilistic bounded linear spatial temporal logic (PBLSTL); Spatio-temporal; Multidimensional; Model checking; Mudi; Computational model; Model validation; Systems biology; Synthetic biology
22.  ULTRASTRUCTURE OF THE EXOSPORIUM ENVELOPING SPORES OF BACILLUS CEREUS1 
Journal of Bacteriology  1964;88(6):1774-1789.
Gerhardt, Philipp (The University of Michigan, Ann Arbor), and Edgar Ribi. Ultrastructure of the exosporium enveloping spores of Bacillus cereus. J. Bacteriol. 88:1774–1789. 1964.—Structural details in the outer envelope of spores, such as those of Bacillus cereus and B. anthracis, were studied by electron microscopy and by X-ray diffraction analysis. Procedures were developed for isolating homogeneous fragments of the membrane with minimal damage to or germination of the spore proper. Exosporium of B. cereus appeared to embody two main layers. An outer layer was made up of a nap of hairlike projections, irregularly distributed and about 250 A deep; these arose from an intermediate covering, about 60 A in depth and similarly lead-stainable. An inner basal layer had a hexagonally perforate surface pattern of holes, averaging 76 A from center to center, and was made up of four lamellae, which could fragment into crystal-like elements. The intact basal membrane was about 190 A thick and the thinnest elements, 45 A. Microscopic observations of a crystal-like nature of the exosporium basal membrane were confirmed by X-ray diffraction analysis; the pattern of reflection lines in powder diagrams of exosporium fragments or paracrystals, or intact spores, corresponded to a hexagonal, close-packed crystal structure. The unit cell was calculated to have dimensions of 7.6 A along the a axis and 11.9 A along the c axis of the space lattice.
Images
PMCID: PMC277484  PMID: 14240968
23.  Interaction of collagen with the lipids of tendon xanthomata. 
Journal of Clinical Investigation  1978;62(4):836-846.
To determine the physical state of lipids in tendon xanthomata, six specimens surgically removed from three patients with familial hypercholesterolemia were studied by microscopy, calorimetry, and x-ray diffraction. The major constituents of the xanthomata were lipid (33% of dry weight) and collagen (24% of dry weight). The principal lipids were cholesterol ester and cholesterol. Light microscopy and thin-section electron microscopy showed occasional clusters of foam cells separated by masses of extracellular collagen. Polarized light microscopy of fresh, minced tissue showed rare droplets of free cholesterol ester. When heated, the tissue shrank abruptly at approximately equal to 70 degrees C and, consequently, a large amount of cholesterol ester was released. Scanning calorimetry of fresh pieces of xanthoma showed a single, broad, reversible liquid crystalline transition of cholesterol ester with peak temperature from 32 to 38 degrees C. The enthalpy (0971 +/- 0.07 cal/g) was reduced compared with the isolated cholesterol ester from each xanthoma (1.1+/-0.01 cal/g). There was a large irreversible collagen denaturation endotherm (peak temperature = 67 degrees C; enthalpy 9.9 cal/g collagen) that corresponded to the tissue shrinkage noted by microscopy. After the collagen denaturation, the sample displayed double-peaked reversible liquid crystalline transitions of cholesterol ester, of enthalpy 1.18 +/- 0.1 cal/g, that were identical to transitions of isolated cholesterol ester. Fibers dissected fron xanthomata were examined by X-ray diffraction at temperatures below and above the cholesterol ester transition. At 20 degrees C there was a weakly oriented equatorial reflection of Bragg spacing 36A, which corresponded to the smectic phase of cholesterol ester, and a series of oriented collagen reflections. At 42 degrees C the cholesterol ester reflection disappeared. Stretched fibers examined at 10 degrees C showed good orientation of collagen and cholesterol ester reflections, and in addition, meridional spacings which indicated oriented crystallization of cholesterol ester. These studies suggest that a major component of tendon xanthomata is extracellular cholesterol ester which displays altered melting and molecular orientation as a result of an interaction with collagen. At xanthoma temperatures, the cholesterol ester is in a smectic liquid crystalline state, probably layered between collagen fibrils, with the long axis of the cholesterolester molecules perpendicular to the axis of the collagen fiber. Such collagen-cholesterol ester interactions may favor the extracellular deposition of cholesterol ester derived either from intracellular sources or directly from plasma lipoproteins.
Images
PMCID: PMC371836  PMID: 701482
24.  Enabling X-ray free electron laser crystallography for challenging biological systems from a limited number of crystals 
eLife  null;4:e05421.
There is considerable potential for X-ray free electron lasers (XFELs) to enable determination of macromolecular crystal structures that are difficult to solve using current synchrotron sources. Prior XFEL studies often involved the collection of thousands to millions of diffraction images, in part due to limitations of data processing methods. We implemented a data processing system based on classical post-refinement techniques, adapted to specific properties of XFEL diffraction data. When applied to XFEL data from three different proteins collected using various sample delivery systems and XFEL beam parameters, our method improved the quality of the diffraction data as well as the resulting refined atomic models and electron density maps. Moreover, the number of observations for a reflection necessary to assemble an accurate data set could be reduced to a few observations. These developments will help expand the applicability of XFEL crystallography to challenging biological systems, including cases where sample is limited.
DOI: http://dx.doi.org/10.7554/eLife.05421.001
eLife digest
Large biological molecules (or macromolecules) have intricate three-dimensional structures. X-ray crystallography is a technique that is commonly used to determine these structures and involves directing a beam of X-rays at a crystal that was grown from the macromolecule of interest. The macromolecules in the crystal scatter the X-rays to produce a diffraction pattern, and the crystal is rotated to provide further diffraction images. It is then possible to work backwards from these images and elucidate the structure of the macromolecule in three dimensions.
X-ray beams are powerful enough to damage crystals, and scientists are developing new approaches to overcome this problem. One recent development uses ‘X-ray free electron lasers’ to circumvent the damage caused to crystals. However, early applications of this approach required many crystals and thousands to millions of diffraction patterns to be collected—largely because methods to process the diffraction data were far from optimal.
Uervirojnangkoorn et al. have now developed a new data-processing procedure that is specifically designed for diffraction data obtained using X-ray free electron lasers. This method was applied to diffraction data collected from crystals of three different macromolecules (which in this case were three different proteins). For all three, the new method required many fewer diffraction images to determine the structure, and in one case revealed more details about the structure than the existing methods.
This new method is now expected to allow a wider range of macromolecules to be studied using crystallography with X-ray free electron lasers, including cases where very few crystals are available.
DOI: http://dx.doi.org/10.7554/eLife.05421.002
doi:10.7554/eLife.05421
PMCID: PMC4397907  PMID: 25781634
X-ray crystallography; free electron laser; data processing; none
25.  Stacking faults and superstructures in a layered brownmillerite 
Stacking faults in Ca4Fe2Mn0.5Ti0.5O9 have been examined using X-ray diffraction and high-resolution transmission electron microscopy. Electron diffraction revealed two superstructures with ordered stacking sequences.
Single crystals of Ca4Fe2Mn0.5Ti0.5O9 have been synthesized using a flux method. The structural characterization using single-crystal X-ray diffraction revealed the space group Amma and unit-cell dimensions of a = 5.3510 (6), b = 26.669 (3), c = 5.4914 (6) Å. The structure is isotypic with Sr3NdFe3O9 [Barrier et al. (2005 ▸). Chem. Mater. 17, 6619–6623] and exhibits separated brownmillerite-type layers. One-dimensional diffuse scattering shows that the unit cell is doubled along c by alternating the intra-layer order of tetrahedral chains, causing stacking faults along the b direction. A computer simulation was performed, proving that the observed intensity variations along the diffuse scattering rods originates from two different local structures depending on the configuration of the tetrahedral chains. Selected-area electron diffraction experiments exhibit well ordered regions characterized by satellite reflections corresponding to two different superstructures. Both superstructures can be described using the superspace group A21/m(0βγ)0s, with γ = 0.5 and β ≃ 0.27 or β = 0.
doi:10.1107/S0108768111042005
PMCID: PMC3222140  PMID: 22101537
layered brownmillerite; diffuse scattering; stacking faults; modulated structure

Results 1-25 (1003303)