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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
2.  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.
PMCID: PMC4052717  PMID: 24918659
3.  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.
PMCID: PMC2525861  PMID: 17301470
coherent X-ray beams; dynamics of fluctuations; lensless imaging; small-angle set-ups
4.  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
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
6.  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.
PMCID: PMC3831301  PMID: 24282334
rotation electron diffraction; electron diffraction tomography; three-dimensional electron diffraction; structure analysis; electron diffraction; computer programs
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
8.  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).
PMCID: PMC3778876  PMID: 24068835
Beta expansion; Canonical number system; Shift radix system; Tiling
9.  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.
PMCID: PMC3180901  PMID: 21790155
Boerdijk-Coxeter-Bernal helix; nanowires; icosahedra; decahedra; aberration corrected Electron Microscopy
10.  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.
PMCID: PMC2851191  PMID: 20383295
11.  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.
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.
PMCID: PMC1175972  PMID: 15960804
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.
PMCID: PMC277484  PMID: 14240968
13.  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.
PMCID: PMC371836  PMID: 701482
14.  Mass and molecular composition of vesicular stomatitis virus: a scanning transmission electron microscopy analysis. 
Journal of Virology  1985;54(2):598-607.
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.
PMCID: PMC254833  PMID: 2985822
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.
PMCID: PMC2140797  PMID: 19872247
16.  On the alignment for precession electron diffraction 
Ultramicroscopy  2012;117:1-6.
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.
PMCID: PMC3593050  PMID: 22634134
Precession electron diffraction; CoCrMo alloy; M23C6 carbide; Alignment
17.  Axial arrangement of the myosin rod in vertebrate thick filaments: immunoelectron microscopy with a monoclonal antibody to light meromyosin 
The Journal of Cell Biology  1985;101(3):1115-1123.
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.
PMCID: PMC2113698  PMID: 3897243
18.  A look inside epitaxial cobalt-on-fluorite nanoparticles with three-dimensional reciprocal space mapping using GIXD, RHEED and GISAXS 
Journal of Applied Crystallography  2013;46(Pt 4):874-881.
Three-dimensional reciprocal space mapping by X-ray and electron diffraction [namely grazing-incidence X-ray diffraction (GIXD), reflection high-energy electron diffraction (RHEED) and grazing-incidence small-angle X-ray scattering (GISAXS)] was used to explore the internal structure and shape of differently oriented epitaxial Co/CaF2 facetted nanoparticles.
In this work epitaxial growth of cobalt on CaF2(111), (110) and (001) surfaces has been extensively studied. It has been shown by atomic force microscopy that at selected growth conditions stand-alone faceted Co nanoparticles are formed on a fluorite surface. Grazing-incidence X-ray diffraction (GIXD) and reflection high-energy electron diffraction (RHEED) studies have revealed that the particles crystallize in the face-centered cubic lattice structure otherwise non-achievable in bulk cobalt under normal conditions. The particles were found to inherit lattice orientation from the underlying CaF2 layer. Three-dimensional reciprocal space mapping carried out using X-ray and electron diffraction has revealed that there exist long bright 〈111〉 streaks passing through the cobalt Bragg reflections. These streaks are attributed to stacking faults formed in the crystal lattice of larger islands upon coalescence of independently nucleated smaller islands. Distinguished from the stacking fault streaks, crystal truncation rods perpendicular to the {111} and {001} particle facets have been observed. Finally, grazing-incidence small-angle X-ray scattering (GISAXS) has been applied to decouple the shape-related scattering from that induced by the crystal lattice defects. Particle faceting has been verified by modeling the GISAXS patterns. The work demonstrates the importance of three-dimensional reciprocal space mapping in the study of epitaxial nanoparticles.
PMCID: PMC3769055  PMID: 24046491
cobalt-on-fluorite nanoparticles; grazing-incidence X-ray diffraction (GIXD); reflection high-energy electron diffraction (RHEED); grazing-incidence small-angle X-ray scattering (GISAXS); epitaxial growth; three-dimensional reciprocal space mapping
19.  Improving experimental phases for strong reflections prior to density modification 
A genetic algorithm has been developed to optimize the phases of the strongest reflections in SIR/SAD data. This is shown to facilitate density modification and model building in several test cases.
Experimental phasing of diffraction data from macromolecular crystals involves deriving phase probability distributions. These distributions are often bimodal, making their weighted average, the centroid phase, improbable, so that electron-density maps computed using centroid phases are often non-­interpretable. Density modification brings in information about the characteristics of electron density in protein crystals. In successful cases, this allows a choice between the modes in the phase probability distributions, and the maps can cross the borderline between non-interpretable and interpretable. Based on the suggestions by Vekhter [Vekhter (2005 ▶), Acta Cryst. D61, 899–902], the impact of identifying optimized phases for a small number of strong reflections prior to the density-modification process was investigated while using the centroid phase as a starting point for the remaining reflections. A genetic algorithm was developed that optimizes the quality of such phases using the skewness of the density map as a target function. Phases optimized in this way are then used in density modification. In most of the tests, the resulting maps were of higher quality than maps generated from the original centroid phases. In one of the test cases, the new method sufficiently improved a marginal set of experimental SAD phases to enable successful map interpretation. A computer program, SISA, has been developed to apply this method for phase improvement in macromolecular crystallo­graphy.
PMCID: PMC3792643  PMID: 24100322
experimental phasing; density modification; genetic algorithms
20.  Structural Analysis of Peptide-Analogues of Human Zona Pellucida ZP1 Protein with Amyloidogenic Properties: Insights into Mammalian Zona Pellucida Formation 
PLoS ONE  2013;8(9):e73258.
Zona pellucida (ZP) is an extracellular matrix surrounding and protecting mammalian and fish oocytes, which is responsible for sperm binding. Mammalian ZP consists of three to four glycoproteins, called ZP1, ZP2, ZP3, ZP4. These proteins polymerize into long interconnected filaments, through a common structural unit, known as the ZP domain, which consists of two domains, ZP-N and ZP-C. ZP is related in function to silkmoth chorion and in an evolutionary fashion to the teleostean fish chorion, also fibrous structures protecting the oocyte and embryo, that both have been proven to be functional amyloids. Two peptides were predicted as ‘aggregation-prone’ by our prediction tool, AMYLPRED, from the sequence of the human ZP1-N domain. Here, we present results from transmission electron microscopy, X-ray diffraction, Congo red staining and attenuated total reflectance Fourier-transform infrared spectroscopy (ATR FT-IR), of two synthetic peptide-analogues of these predicted ‘aggregation-prone’ parts of the human ZP1-N domain, that we consider crucial for ZP protein polymerization, showing that they both self-assemble into amyloid-like fibrils. Based on our experimental data, we propose that human ZP (hZP) might be considered as a novel, putative, natural protective amyloid, in close analogy to silkmoth and teleostean fish chorions. Experiments are in progress to verify this proposal. We also attempt to provide insights into ZP formation, proposing a possible model for hZP1-N domain polymerization.
PMCID: PMC3772061  PMID: 24069181
1. A close correlation has been obtained between high resolution electron microscopy and low-angle x-ray diffraction studies of the myelin sheath of frog and rat peripheral and central nerves. Extensive studies were performed by application of both techniques to the same specimens, prepared for examination by OsO4 or KMnO4 fixation, and embedding either in methacrylate or in gelatin employing a new procedure. Controlled physical and chemical modifications of the myelin sheath prior to fixation were also investigated. 2. A correspondence was established between the layer spacings observed in electron micrographs and the fundamental radial repeating unit indicated by the low-angle x-ray diffraction patterns. The variations in relative intensities of the low-angle x-ray reflections could be related to the radial density distributions seen in the electron micrographs. 3. An analysis of the preparation procedures revealed that OsO4 fixation introduces a greater shrinkage of the layer spacings and more pronounced changes in the density distribution within the layers than KMnO4 fixation. The effects of methacrylate and gelatin embedding are described, and their relative merits considered in relation to the preservation of myelin structure by OsO4 fixation. 4. The experimental modifications introduced by freezing and thawing of fresh whole nerve are described, particularly the enhancement of the intermediate lines and the dissociation of the layer components in the myelin sheath. A characteristic collapsing of the radial period of the sheath is observed after subjecting fresh nerve trunks to prolonged and intense ultracentrifugation. 5. Controlled extraction of fresh nerve with acetone at 0°C., which preferentially removes cholesterol, produces characteristic, differentiated modifications of the myelin sheath structure. Electron microscopy reveals several types of modifications within a single preparation, including both expanded and collapsed layer systems, and internal rearrangements of the layer components. Alcohol extraction leads to a more extensive structural breakdown, but in certain areas collapsed layer systems can still be observed. The components of the lipide extracts could be identified by means of x-ray diffraction. These modifications emphasize the importance of cholesterol in the myelin structure, and disclose a resistance of the dense osmiophilic lines to lipide solvents. 6. The significance of these structures is discussed in relation to present concepts of the molecular organization of myelin. The available evidence is consistent with the suggestion that the primary site of osmium deposition is at the lipoprotein interfaces and that the light bands probably represent regions occupied by lipide chains. The electron microscope and x-ray diffraction data also indicate the possibility of a regular organization within the plane of the layers, probably involving units of 60 to 80 A. The myelin sheath is regarded as a favourable cell membrane model for detailed analysis by combined application of x-ray diffraction and electron microscopy.
PMCID: PMC2224112  PMID: 13475388
22.  Predicting Human Nucleosome Occupancy from Primary Sequence 
PLoS Computational Biology  2008;4(8):e1000134.
Nucleosomes are the fundamental repeating unit of chromatin and comprise the structural building blocks of the living eukaryotic genome. Micrococcal nuclease (MNase) has long been used to delineate nucleosomal organization. Microarray-based nucleosome mapping experiments in yeast chromatin have revealed regularly-spaced translational phasing of nucleosomes. These data have been used to train computational models of sequence-directed nuclesosome positioning, which have identified ubiquitous strong intrinsic nucleosome positioning signals. Here, we successfully apply this approach to nucleosome positioning experiments from human chromatin. The predictions made by the human-trained and yeast-trained models are strongly correlated, suggesting a shared mechanism for sequence-based determination of nucleosome occupancy. In addition, we observed striking complementarity between classifiers trained on experimental data from weakly versus heavily digested MNase samples. In the former case, the resulting model accurately identifies nucleosome-forming sequences; in the latter, the classifier excels at identifying nucleosome-free regions. Using this model we are able to identify several characteristics of nucleosome-forming and nucleosome-disfavoring sequences. First, by combining results from each classifier applied de novo across the human ENCODE regions, the classifier reveals distinct sequence composition and periodicity features of nucleosome-forming and nucleosome-disfavoring sequences. Short runs of dinucleotide repeat appear as a hallmark of nucleosome-disfavoring sequences, while nucleosome-forming sequences contain short periodic runs of GC base pairs. Second, we show that nucleosome phasing is most frequently predicted flanking nucleosome-free regions. The results suggest that the major mechanism of nucleosome positioning in vivo is boundary-event-driven and affirm the classical statistical positioning theory of nucleosome organization.
Author Summary
Inside the nucleus, DNA is wrapped into a complex molecular structure called chromatin, whose fundamental unit is ∼150 bp of DNA organized around the eight-histone protein complex known as the nucleosome. Understanding the local organization of nucleosomes is critical for understanding how chromatin impacts gene regulation. Here, we describe a computational model that predicts nucleosome placement from DNA sequence. We train the model using data derived from human cell lines, and we apply the model systematically to 1% of the human genome. We show that previously described models trained from yeast data correlate strongly with the human-trained model, suggesting a common mechanism for sequence-based determination of nucleosome occupancy. In addition, we observe a striking complementarity between models trained using data from weakly and strongly digested samples: one type of model recognizes nucleosome-free regions, whereas the other identifies well-positioned nucleosomes. Finally, our analysis of predicted nucleosome positions in the human genome allows us to identify common features of nucleosome-forming and inhibitory sequences. Overall, our results are consistent with the classical statistical positioning theory of nucleosome organization.
PMCID: PMC2515632  PMID: 18725940
23.  Integrated Assessment of Genomic Correlates of Protein Evolutionary Rate 
PLoS Computational Biology  2009;5(6):e1000413.
Rates of evolution differ widely among proteins, but the causes and consequences of such differences remain under debate. With the advent of high-throughput functional genomics, it is now possible to rigorously assess the genomic correlates of protein evolutionary rate. However, dissecting the correlations among evolutionary rate and these genomic features remains a major challenge. Here, we use an integrated probabilistic modeling approach to study genomic correlates of protein evolutionary rate in Saccharomyces cerevisiae. We measure and rank degrees of association between (i) an approximate measure of protein evolutionary rate with high genome coverage, and (ii) a diverse list of protein properties (sequence, structural, functional, network, and phenotypic). We observe, among many statistically significant correlations, that slowly evolving proteins tend to be regulated by more transcription factors, deficient in predicted structural disorder, involved in characteristic biological functions (such as translation), biased in amino acid composition, and are generally more abundant, more essential, and enriched for interaction partners. Many of these results are in agreement with recent studies. In addition, we assess information contribution of different subsets of these protein properties in the task of predicting slowly evolving proteins. We employ a logistic regression model on binned data that is able to account for intercorrelation, non-linearity, and heterogeneity within features. Our model considers features both individually and in natural ensembles (“meta-features”) in order to assess joint information contribution and degree of contribution independence. Meta-features based on protein abundance and amino acid composition make strong, partially independent contributions to the task of predicting slowly evolving proteins; other meta-features make additional minor contributions. The combination of all meta-features yields predictions comparable to those based on paired species comparisons, and approaching the predictive limit of optimal lineage-insensitive features. Our integrated assessment framework can be readily extended to other correlational analyses at the genome scale.
Author Summary
Proteins encoded within a given genome are known to evolve at drastically different rates. Through recent large-scale studies, researchers have measured a wide variety of properties for all proteins in yeast. We are interested to know how these properties relate to one another and to what extent they explain evolutionary rate variation. Protein properties are a heterogeneous mix, a factor which complicates research in this area. For example, some properties (e.g., protein abundance) are numerical, while others (e.g., protein function) are descriptive; protein properties may also suffer from noise and hidden redundancies. We have addressed these issues within a flexible and robust statistical framework. We first ranked a large list of protein properties by the strength of their relationships with evolutionary rate; this confirms many known evolutionary relationships and also highlights several new ones. Similar protein properties were then grouped and applied to predict slowly evolving proteins. Some of these groups were as effective as paired species comparison in making correct predictions, although in both cases a great deal of evolutionary rate variation remained to be explained. Our work has helped to refine the set of protein properties that researchers should consider as they investigate the mechanisms underlying protein evolution.
PMCID: PMC2688033  PMID: 19521505
24.  Helical structure of Bordetella pertussis fimbriae. 
Journal of Bacteriology  1986;167(3):968-974.
The helical structures of Bordetella pertussis fimbriae of serotypes 2 and 6 were determined by optical diffraction analysis of electron micrographs of negatively stained paracrystalline bundles of purified fimbriae. The fimbrial structure is based on an axial repeat of 13 nm that contains five repeating units in two complete turns of a single-start helix. This structure was confirmed by direct measurements of mass per unit length for individual fimbriae performed by dark-field scanning transmission electron microscopy of unstained specimens. These data further established that the helically repeating unit is a monomer of fimbrial protein (Mr congruent to 22,000 for type 2 and Mr congruent to 21,500 for type 6). Radial density profiles calculated from the scanning transmission electron micrographs showed that the fimbria has peak density at its center, i.e., no axial channel, consistent with the results of conventional negative-staining electron microscopy. The radial profile gives an outermost diameter of approximately 7.5 nm, although the peripheral density is, on average, diffuse, allowing sufficient intercalation between adjacent fimbriae to give a center-to-center spacing of approximately 5.5 nm in the paracrystals. Despite serological and biochemical differences between type 2 and type 6 fimbriae, the packing arrangements of their fimbrial subunits are identical. From this observation, we infer that the respective subunits may have in common conserved regions whose packing dictates the helical geometry of the fimbria. It is plausible that a similar mechanism may underlie the phenomenon of phase variations in other systems of bacterial fimbriae.
PMCID: PMC215966  PMID: 2875062
25.  Impact of Network Structure and Cellular Response on Spike Time Correlations 
PLoS Computational Biology  2012;8(3):e1002408.
Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative – or correlated – activity in neural populations, and in the possible impact of such correlations on the neural code. A fundamental theoretical challenge is to understand how the architecture of network connectivity along with the dynamical properties of single cells shape the magnitude and timescale of correlations. We provide a general approach to this problem by extending prior techniques based on linear response theory. We consider networks of general integrate-and-fire cells with arbitrary architecture, and provide explicit expressions for the approximate cross-correlation between constituent cells. These correlations depend strongly on the operating point (input mean and variance) of the neurons, even when connectivity is fixed. Moreover, the approximations admit an expansion in powers of the matrices that describe the network architecture. This expansion can be readily interpreted in terms of paths between different cells. We apply our results to large excitatory-inhibitory networks, and demonstrate first how precise balance – or lack thereof – between the strengths and timescales of excitatory and inhibitory synapses is reflected in the overall correlation structure of the network. We then derive explicit expressions for the average correlation structure in randomly connected networks. These expressions help to identify the important factors that shape coordinated neural activity in such networks.
Author Summary
Is neural activity more than the sum of its individual parts? What is the impact of cooperative, or correlated, spiking among multiple cells? We can start addressing these questions, as rapid advances in experimental techniques allow simultaneous recordings from ever-increasing populations. However, we still lack a general understanding of the origin and consequences of the joint activity that is revealed. The challenge is compounded by the fact that both the intrinsic dynamics of single cells and the correlations among then vary depending on the overall state of the network. Here, we develop a toolbox that addresses this issue. Specifically, we show how linear response theory allows for the expression of correlations explicitly in terms of the underlying network connectivity and known single-cell properties – and that the predictions of this theory accurately match simulations of a touchstone, nonlinear model in computational neuroscience, the general integrate-and-fire cell. Thus, our theory should help unlock the relationship between network architecture, single-cell dynamics, and correlated activity in diverse neural circuits.
PMCID: PMC3310711  PMID: 22457608

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