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.
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.
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.
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.
coherent X-ray beams; dynamics of fluctuations; lensless imaging; small-angle set-ups
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
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.
pseudosymmetry; structure determination; cysteine proteases; Mac-1
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.
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.
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.
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.
Boerdijk-Coxeter-Bernal helix; nanowires; icosahedra; decahedra; aberration corrected Electron Microscopy
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.
rotation electron diffraction; electron diffraction tomography; three-dimensional electron diffraction; structure analysis; electron diffraction; computer programs
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.
precession electron diffraction (PED); electron crystallography; electron techniques; electron-based structure analysis
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).
Beta expansion; Canonical number system; Shift radix system; Tiling
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.
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  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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
Precession electron diffraction has seen a fast increase in its adoption as a technique for solving crystallographic structures as well as an alternative to conventional selected-area and converged-beam diffraction methods. One of the key issues of precession is the pivot point alignment, as a stationary apparent beam does not guarantee a fixed pivot point. A large precession tilt angle, along with pre-field and post-field misalignment, induces shift in the image plane. We point out here that the beam should be aligned to the pre-field optic axis to keep the electron illumination stationary during the rocking process. A practical alignment procedure is suggested with the focus placed on minimizing the beam wandering on the specimen, and is demonstrated for a (110)-oriented silicon single crystal and for a carbide phase (~20 nm in size) within a cast cobalt–chromium–molybdenum alloy.
Precession electron diffraction; CoCrMo alloy; M23C6 carbide; Alignment
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.
layered brownmillerite; diffuse scattering; stacking faults; modulated structure
Dark-field scanning transmission electron microscopy was used to perform mass analyses of purified vesicular stomatitis virions, pronase-treated virions, and nucleocapsids, leading to a complete self-consistent account of the molecular composition of vesicular stomatitis virus. The masses obtained were 265.6 +/- 13.3 megadaltons (MDa) for the native virion, 197.5 +/- 8.4 MDa for the pronase-treated virion, and 69.4 +/- 4.9 MDa for the nucleocapsid. The reduction in mass effected by pronase treatment, which corresponds to excision of the external domains (spikes) of G protein, leads to an average of 1,205 molecules of G protein per virion. The nucleocapsid mass, after compensation for the RNA (3.7 MDa) and residual amounts of other proteins, yielded a complement of 1,258 copies of N protein. Calibration of the amounts of M, NS, and L proteins relative to N protein by biochemical quantitation yielded values of 1,826, 466, and 50 molecules, respectively, per virion. Assuming that the remaining virion mass is contributed by lipids in the viral envelope, we obtained a value of 56.1 MDa for its lipid content. In addition, four different electron microscopy procedures were applied to determine the nucleocapsid length, which we conclude to be 3.5 to 3.7 micron. The nucleocapsid comprises a strand of repeating units which have a center-to-center spacing of 3.3 nm as measured along the middle of the strand. We show that these repeating units represent monomers of N protein, each of which is associated with 9 +/- 1 bases of single-stranded RNA. From scanning transmission electron microscopy images of negatively stained nucleocapsids, we inferred that N protein has a wedge-shaped, bilobed structure with dimensions of approximately 9.0 nm (length), approximately 5.0 nm (depth), and approximately 3.3 nm (width, at the midpoint of its long axis). In the coiled configuration of the in situ nucleocapsid, the long axis of N protein is directed radially, and its depth corresponds to the pitch of the nucleocapsid helix.
It has been revealed that in cylindrical nano-confinement, the hydrogen-bonding direction of nylon-12 crystals in the rod could self-assemble to be parallel to the long axis of the rod. The dominant growth direction and hydrogen-bonding direction of the γ-form crystal in the long axis of the rod has been revealed by TEM–SAED and WAXD.
Molecular self-assembly of nylon-12 rods in self-organized nanoporous alumina cylinders with two different diameters (65 and 300 nm) is studied with transmission electron microscopy (TEM) and wide-angle X-ray diffraction (WAXD) in symmetrical reflection mode. In a rod with a 300 nm diameter, the tendency of the hydrogen-bonding direction of a γ-form crystal parallel to the long axis of the rod is not clear because of weak two-dimensional confinement. In a rod with a diameter of 65 nm, the tendency of the hydrogen-bonding direction of a γ-form crystal parallel to the long axis of the rod is more distinct because of strong two-dimensional confinement. For the first time, selected-area electron diffraction (SAED) is applied in a transmission electron microscope to a polymer nanorod in order to determine the hydrogen-bond sheet and lamellar orientations. Results of TEM–SAED and WAXD showed that the crystals within the rod possess the γ-form of nylon-12 and that the b axis (stem axis) of the γ-form crystals is perpendicular to the long axis of the rod. These results revealed that only lamellae with 〈h0l〉 directions are able to grow inside the nanopores and the growth of lamellae with 〈hkl〉 (k ≠ 0) directions is stopped owing to impingements against the cylinder walls. The dominant crystal growth direction of the 65 nm rod in stronger two-dimensional confinement is in between the [−201] and  directions due to the development of a hydrogen-bonded sheet restricted along the long axis of the rod.
molecular self-assembly; nanorods; selected-area electron diffraction; cylindrical confinement
The rather long discussion just given seemed necessary in order to establish certain points before attempting to develop the lattice structure and before working out the identity of the structural unit of the ramie fiber. 1. Certain planes, 6.10, 5.40, 3.98, etc., as given in Table I, run lengthwise of the fiber; that is, they are parallel to the long axis. 2. These planes are in agreement with the assumption that one set, either the 6.10 or the 5.40 is tangential to the fiber and forms concentric cylinders, with the long axis of the fiber as the long axis of the cylinders; the other set, either the 5.40 or the 6.10. cuts the former at right angles and therefore its planes are radial with respect to the fiber, theoretically all of them meeting at the long axis, as indicated in the cross-section of a fiber in Fig. 3. 3. Other planes, 5.15, 3.40, 2.58, etc., as given in Table III, are transverse planes which form right angles with the long axis and therefore with the planes of Table I. 4. All of the planes are composed of reflecting units, probably groups of atoms, located at the intersections of the planes. This being the case, other reflecting planes must occur at other angles to the long axis. This prediction is verified by the lines given in Table IV. 5. The structural units in the wall of the fiber thus form a space lattice, the elementary cell of which is an orthorhombic structure. 6. Comparatively little can be said as yet concerning the structural unit. The unit is very probably composed of a group of atoms which are more or less closely packed together. If the groups were visible they would appear, in a cross-section of a fiber, as closely packed groups of atoms, 6.10 Å.u. from center to center of groups in one direction, and 5.40 Å.u. at right angles to that. In a longitudinal section, however, they would appear less compact and might even lose the appearance of groups in forming long strings of atoms which would extend lengthwise of the fiber. By establishing the positions of the planes in the wall of the fiber, as in Tables I, III, and IV, it would seem that all dimensions of the elementary cell, and the size and character of the structural unit, could be determined. Work along these lines is now in progress.
Studying membrane active peptides or protein fragments within the lipid bilayer environment is particularly challenging in the case of synthetically modified, labeled, artificial, or recently discovered native structures. For such samples the localization and orientation of the molecular species or probe within the lipid bilayer environment is the focus of research prior to an evaluation of their dynamic or mechanistic behavior. X-ray scattering is a powerful method to study peptide/lipid interactions in the fluid, fully hydrated state of a lipid bilayer. For one, the lipid response can be revealed by observing membrane thickening and thinning as well as packing in the membrane plane; at the same time, the distinct positions of peptide moieties within lipid membranes can be elucidated at resolutions of up to several angstroms by applying heavy-atom labeling techniques. In this study, we describe a generally applicable X-ray scattering approach that provides robust and quantitative information about peptide insertion and localization as well as peptide/lipid interaction within highly oriented, hydrated multilamellar membrane stacks. To this end, we have studied an artificial, designed β-helical peptide motif in its homodimeric and hairpin variants adopting different states of oligomerization. These peptide lipid complexes were analyzed by grazing incidence diffraction (GID) to monitor changes in the lateral lipid packing and ordering. In addition, we have applied anomalous reflectivity using synchrotron radiation as well as in-house X-ray reflectivity in combination with iodine-labeling in order to determine the electron density distribution ρ(z) along the membrane normal (z axis), and thereby reveal the hydrophobic mismatch situation as well as the position of certain amino acid side chains within the lipid bilayer. In the case of multiple labeling, the latter technique is not only applicable to demonstrate the peptide’s reconstitution but also to generate evidence about the relative peptide orientation with respect to the lipid bilayer.
Electronic supplementary material
The online version of this article (doi:10.1007/s00249-010-0645-4) contains supplementary material, which is available to authorized users.
Peptide lipid interactions; Membrane active peptides; Model helices; X-ray scattering; Hydrophobic mismatch; Lipid chain correlation
A monoclonal antibody, MF20, which has been shown previously to bind the myosin heavy chain of vertebrate striated muscle, has been proven to bind the light meromyosin (LMM) fragment by solid phase radioimmune assay with alpha-chymotryptic digests of purified myosin. Epitope mapping by electron microscopy of rotary-shadowed, myosin-antibody complexes has localized the antibody binding site to LMM at a point approximately 92 nm from the C-terminus of the myosin heavy chain. Since this epitope in native thick filaments is accessible to monoclonal antibodies, we used this antibody as a high affinity ligand to analyze the packing of LMM along the backbone of the thick filament. By immunofluorescence microscopy, MF20 was shown to bind along the entire A-band of chicken pectoralis myofibrils, although the epitope accessibility was greater near the ends than at the center of the A- bands. Thin-section, transmission electron microscopy of myofibrils decorated with MF20 revealed 50 regularly spaced, cross-striations in each half A-band, with a repeat distance of approximately 13 nm. These were numbered consecutively, 1-50, from the A-band to the last stripe, approximately 68 nm from the filament tips. These same striations could be visualized by negative staining of native thick filaments labeled with MF20. All 50 striations were of a consecutive, uninterrupted repeat which approximated the 14-15-nm axial translation of cross- bridges. Each half M-region contained five MF20 striations (approximately 13 nm apart) with a distance between stripes 1 and 1', on each half of the bare zone, of approximately 18 nm. This is compatible with a packing model with full, antiparallel overlap of the myosin rods in the bare zone region. Differences in the spacings measured with negatively stained myofilaments and thin-sectioned myofibrils have been shown to arise from specimen shrinkage in the fixed and embedded preparations. These observations provide strong support for Huxley's original proposal for myosin packing in thick filaments of vertebrate muscle (Huxley, H. E., 1963, J. Mol. Biol., 7:281-308) and, for the first time, directly demonstrate that the 14-15- nm axial translation of LMM in the thick filament backbone corresponds to the cross-bridge repeat detected with x-ray diffraction of living muscle.