Patterson Analysis Research Articles

Diffuse X-ray scattering from correlated motions in a protein crystal

Protein dynamics are integral to biological function, yet few techniques are sensitive to collective atomic motions. A long-standing goal of X-ray crystallography has been to combine structural information from Bragg diffraction with dynamic information contained in the diffuse scattering background. However, the origin of macromolecular diffuse scattering has been poorly understood, limiting its applicability. We present a finely sampled diffuse scattering map from triclinic lysozyme with unprecedented accuracy and detail, clearly resolving both the inter- and intramolecular correlations. These correlations are studied theoretically using both all-atom molecular dynamics and simple vibrational models. Although lattice dynamics reproduce most of the diffuse pattern, protein internal dynamics, which include hinge-bending motions, are needed to explain the short-ranged correlations revealed by Patterson analysis. These insights lay the groundwork for animating crystal structures with biochemically relevant motions.

"The Continuous Thread of Revelation": Eudora Welty Reconsidered

"The Continuous Thread of Revelation":Eudora Welty Reconsidered Adrienne Akins Warfield and Sarah Gilbreath Ford In her memoir One Writer's Beginnings, Welty concludes the section on "Learning to See" with the observation that "the events in our lives happen in a sequence in time, but in their significance to ourselves they find their own order, a timetable not necessarily—perhaps not possibly—chronological. The time as we know it subjectively is often the chronology that stories and novels follow: it is the continuous thread of revelation" (914). Deriving its title from Welty's reflections here, the 2019 international conference of the Eudora Welty Society explored current threads of revelation as scholars learn to see Welty's work in new ways. Directed by Harriet Pollack and Julia Eichelberger and sponsored by the College of Charleston's Department of English, School of Humanities and Social Sciences, Southern Studies Program, and Women's and Gender Studies Program, the conference took place from February 21–23, 2019, at the College of Charleston. More than fifty participants presented papers on thirteen different panels. The conference also included several special events. Charleston writers Marcus Amaker, Harlan Greene, Josephine Humphreys, and Michele Moore discussed their work, reflecting on their own beginnings as writers in response to Welty's memoir. Mississippi Department of Archives and History librarians Forrest Galey and Betty Uzman led a roundtable discussion of research methods and resources in the Welty collection in dialogue with Julia Eichelberger and College of Charleston students who have utilized the archives. And a large group of Welty scholars participated in an engaging and unforgettable staged reading of "Moon Lake," adapted and directed by Brenda Currin. Conference participants came from across and outside the United States and were a mix of established and emerging Welty scholars, graduate students new to academia, scholars from adjacent fields, new and retired high school teachers, and emeritus faculty with distinguished careers of pioneering scholarship on Welty's work. The presentations coalesced around the conference's theme of reconsidering Eudora Welty's work, a deliberation occurring at an apt time for Welty studies given several recent publications: [End Page 13] a teaching volume on Welty's work edited by Eichelberger and Mae Miller Claxton, monographs by Pollack, Sally Wolff, and Stephen Fuller, and the publication of the letters between Welty and Ross Macdonald edited by Suzanne Marrs and Tom Nolan. Scholars at the conference were also looking forward to the publication of New Essays on Eudora Welty, Class, and Race, edited by Pollack (a sequel to the 2013 collection Eudora Welty, Whiteness, and Race), as well as the promise of a steady stream of new monographs from the series Critical Perspectives on Eudora Welty just established at the University Press of Mississippi, also under the leadership of Pollack. The recent publications along with the blending of participants from different backgrounds led to productive conversations and, indeed, new revelations about Welty's work. We appreciate the scholars who agreed to expand their conference presentations into essays for this issue; these nine essays reflect the wide range of ideas and approaches presented at the conference. One thread of reconsideration of Welty's work at the conference came from innovative interpretive frameworks that enabled scholars to see her work in novel ways. Four essays in this volume reflect the current literary interest in material culture and read Welty's works using variants of that theoretical lens. Laura Sloan Patterson's essay, "'A lady couldn't expect to travel without a hat': Cultural Capital, Gender, and Sexuality in Welty's Short Fiction," examines hats in several of Welty's stories and in Delta Wedding. By examining "something so seemingly trivial," Patterson finds that a hat is much more than a mere accessory (19). As an artifact of material culture, a hat can communicate a character's identity or sexuality. As hats move from place to place and from character to character, they reflect social norms and divisions. Patterson's analysis of a specific material object thus provides an innovative path toward investigating the power dynamics at play between characters in Welty's work. Monica Carol Miller's essay, "Women!! Make Husband in Own Home!: Welty's Use of...

Investigations into the structure of La3Ni2−xFexO7±δ

The room-temperature (RT) 57Fe Mössbauer spectra of the La3Ni2−xFexO7±δ oxide solid solutions of Ruddlesden-Popper-type (x = 0.05, 0.10) reveal two doublets for Fe3+ ions in octahedral coordination by oxygen. The existence of two inequivalent sites for Fe at RT is at variance with the space groups Fmmm and Cmcm (Amam) which have been reported for La3Ni2O7±δ. This unexpected finding is discussed in connection with Patterson analyses and Rietveld refinements of powder XRD data for x = 0, 0.05, and 0.10. Alternative structural models have been proposed which can explain the spectroscopic findings and which are compatible with the results from X-ray diffraction.

Signal enhancement and Patterson-search phasing for high-spatial-resolution coherent X-ray diffraction imaging of biological objects.

In this decade coherent X-ray diffraction imaging has been demonstrated to reveal internal structures of whole biological cells and organelles. However, the spatial resolution is limited to several tens of nanometers due to the poor scattering power of biological samples. The challenge is to recover correct phase information from experimental diffraction patterns that have a low signal-to-noise ratio and unmeasurable lowest-resolution data. Here, we propose a method to extend spatial resolution by enhancing diffraction signals and by robust phasing. The weak diffraction signals from biological objects are enhanced by interference with strong waves from dispersed colloidal gold particles. The positions of the gold particles determined by Patterson analysis serve as the initial phase, and this dramatically improves reliability and convergence of image reconstruction by iterative phase retrieval. A set of calculations based on current experiments demonstrates that resolution is improved by a factor of two or more.

Patterson analysis for layer profile determination by neutron or X-ray reflectometry. II

A data analysis technique based on the Patterson function is tested with simulated X-ray reflectometry data. In comparison to the case for neutron reflectometry, additional data manipulation is required because the scattering-length density of materials is generally much higher for X-rays than for neutrons. With this extra step duly performed, the technique yields a model layer profile accurate enough for least-squares refinement.

Patterson analysis for layer profile determination by neutron or X-ray reflectometry

The possibility of using Patterson analysis to interpret neutron or X-ray reflectometry data has been critically examined in terms of a hypothetical case study. The technique yields a highly accurate layer profile model provided the data are measured with a beam geometry that gives rise to unit reflectivity atQ= 0 only,i.e.Qc= 0. For those cases where a plateau of unit reflectivity extends out to finiteQ,i.e.Qc> 0, a distorted model is obtained. A strategy to significantly improve this initial estimate of the model is proposed and demonstrated.

Nanosecond Dynamics of Photoexcited Lyotropic Liquid Crystal Structures

Home-based soft X-ray time-resolved diffraction (TR-SXD) experiments with nanosecond time resolution (10 ns) and nanometer spatial resolution were carried out at a tabletop soft X-ray plasma source (2.7-5.9 nm). The investigated system was the lyotropic liquid crystal C(16)E(7)/paraffin/glycerol/formamide/IR 5. Usually, major changes in physical, chemical, and/or optical properties of the sample result from structural changes and shrinking morphology. Here, these effects occur as a consequence of the energy absorption in the sample upon optical laser excitation in the IR regime. The variations observed are integral intensity modulations and displacement in the Bragg diffraction angle. To follow the diffracted integral intensity changes, Patterson analysis was used, and the lattice parameter d variations have been followed by applying the Bragg diffraction law. The experimental intensity modulations occur on the nanosecond time scale, and they are assigned to photoinduced diffusion processes within the liquid crystalline phase. The structural response after photoexcitation is experimentally observed as an increase of the lattice constant by 0.5-1 A and is interpreted as a decrease of order in the liquid crystalline phase. This coincides with a reorientation to a photocreated liquid crystal lattice in the surface plane and with respect to the E-field vector of the laser light. The present studies emphasize the possibility of using TR-SXD techniques for studying the transient mechanical dynamics of nanosystems at the submicrosecond time scale.

Time-Resolved Soft X-ray Diffraction Reveals Transient Structural Distortions of Ternary Liquid Crystals

Home-based soft X-ray time-resolved scattering experiments with nanosecond time resolution (10 ns) and nanometer spatial resolution were carried out at a table top soft X-ray plasma source (2.2–5.2 nm). The investigated system was the lyotropic liquid crystal C16E7/paraffin/glycerol/formamide/IR 5. Usually, major changes in physical, chemical, and/or optical properties of the sample occur as a result of structural changes and shrinking morphology. Here, these effects occur as a consequence of the energy absorption in the sample upon optical laser excitation in the IR regime. The liquid crystal shows changes in the structural response within few hundred nanoseconds showing a time decay of 182 ns. A decrease of the Bragg peak diffracted intensity of 30% and a coherent macroscopic movement of the Bragg reflection are found as a response to the optical pump. The Bragg reflection movement is established to be isotropic and diffusion controlled (1 μs). Structural processes are analyzed in the Patterson analysis framework of the time-varying diffraction peaks revealing that the inter-lamellar distance increases by 2.7 Å resulting in an elongation of the coherently expanding lamella crystallite. The present studies emphasize the possibility of applying TR-SXRD techniques for studying the mechanical dynamics of nanosystems.

BENCHMARKING PATTERSON ANALYSIS IN HELIUM ATOM SCATTERING

The technique of Patterson analysis has proven to be a powerful tool in the deduction of structures, both in 2- and 3-D. Using the standard formulation of the Patterson function, the process has been benchmarked for the Helium Atom Scattering (HAS) experiment. Analytically expanding the Patterson function reveals a straightforward Fourier series, whose coefficients are explicit functions of the surface corrugation and the momentum exchange during scattering. Examples based on this formulation reveal that in surface scattering experiments, the Patterson formulation may not be directly interpreted as a map of the inter-nuclear distances, but as a function of surface corrugation and perpendicular momentum exchange.

Structure analysis of embedded nano-sized particles by precession electron diffraction. η′-precipitate in an Al–Zn–Mg alloy as example

The Vincent-Midgley precession technique has been used to collect three-dimensional electron diffraction intensity data from a dispersion of coherent precipitates in a matrix. In order to suppress severe effects from multiple diffraction via matrix reflections, a fairly large precession (tilt) angle had to be used. This implied a high background from the surrounding matrix, and limited the number of reflections that could be measured from patterns on image plates. The heavily faulted hexagonal η′-precipitates ( a = 0.496 nm , c = 1.405 nm ) with thickness 3–5 nm occur in four equivalent orientations relative to the aluminium matrix; with frequent overlap of reflections. A model of the average structure in the space group P6 3 /mmc with assumed composition Mg 2Zn 5− x Al 2+ x , have been derived by Patterson analysis and intensity comparisons.

Decorated 2D quasicrystals: structure factor for clusters and average Patterson analysis

Covering the two-dimensional Penrose atomic structure with different kite clusters consisting of four, seven and 17 atoms is discussed. These clusters are compared to the well-known 33-atom Gummelt's cluster. The number and concentrations of different atoms decorating the clusters were found. An analytical formula for the structure factor of decorated clusters was derived by a statistical approach.

Structural disorder in the decagonalAl–Co–Ni. I. Patterson analysis of diffuse x-ray scattering data

The three-dimensional (3D) difference Patterson (autocorrelation) function of a disordered quasicrystal (Edagawa phase) has been analyzed. 3D diffuse x-ray diffraction data were collected in situ at 300, 1070, and $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A method, the punch-and-fill technique, has been developed for separating diffuse scattering and Bragg reflections. Its potential and limits are discussed in detail. The different Patterson maps are interpreted in terms of intercluster correlations as a function of temperature. Both at high and low temperatures, the clusters decorate the vertices of the same quasiperiodic covering. At low temperatures, for the disordered part of the structure, short-range intercluster correlations are present, whereas at higher temperatures, medium-range intercluster correlations are formed. This indicates disorder mainly inside clusters at low temperatures, whereas at higher temperatures disorder takes place inside larger superclusters. Qualitatively, the Patterson maps may be interpreted by intercluster correlations mainly inside pentagonal superclusters below $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and inside the larger decagonal superclusters at $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The results of our diffraction study are published in two parts. Part I focuses on the 3D Patterson analysis based on experimental data, Part II reports modeling of structural disorder in decagonal $\mathrm{Al}--\mathrm{Co}--\mathrm{Ni}$.

The sulfur oxygenase reductase from Acidianus ambivalens is an icosatetramer as shown by crystallization and Patterson analysis

The sulfur oxygenase reductase (SOR) is the initial enzyme in the aerobic sulfur metabolism of the thermoacidophilic and chemolithoautotrophic crenarchaeote Acidianus ambivalens. Single colorless polyhedral crystals were obtained under two crystallization conditions from SOR preparations heterologously overproduced in Escherichia coli. They belonged to space-group I4 and diffraction data were collected up to 1.7 Å resolution. Their Patterson symmetry shows additional 4-, 3- and 2-fold non-crystallographic symmetry rotation axes, characteristic of the point group 432. Taking into account the molecular mass of SOR, the crystal unit cell volume, the non-crystallographic symmetry operators and previous electron microscopy studies of the SOR, it was deduced that the quaternary structure of the functionally active enzyme is an icosatetramer with 871 kDa molecular mass.

Statistical approach to multiple-q modulated structures: average Patterson analysis

Using a statistical approach, the average unit cells have been constructed for modulated structures with different types of modulation, from simple sinusoidal to square-wave functions. The obtained unit cells fully describe diffraction intensities of the main reflections and their satellites. A universal distribution, valid for different lengths of the modulation vector, has been found. Average Patterson functions have been constructed and used to distinguish between different types of modulation.

Average Patterson analysis of disordered structures

Average Patterson analysis of disordered structures

Combined pseudo-merohedral twinning, non-crystallographic symmetry and pseudo-translation in a monoclinic crystal form of the gammadelta T-cell ligand T10.

T10 is a non-classical class Ib-like major histocompatibility complex (MHC) cell-surface antigen which binds directly to certain gammadelta T-cell receptors in the absence of any exogenous and endogenous ligands, such as peculiar lipids or glycolipids. The crystal structure at 2.5 A resolution of murine T10 was determined by molecular replacement using data from an almost perfectly twinned monoclinic crystal. The space group is P2(1), with unit-cell parameters a = 78.2, b = 70.0, c = 139.2 A, beta = 106.8 degrees. Self-rotation function analysis and various intensity statistics revealed the presence of pseudo-merohedral twinning, but these tests underestimated the true twin fraction of alpha approximately 0.46. Native Patterson analyses pointed to the presence of pseudo-translation among the four molecules present in the asymmetric unit. Data analysis, structure determination and model refinement are discussed.

Patterson Analysis and Average Unit Cell for Quasicrystals

The average unit cells and the average Patterson functions have been constructed for 1D quasicrystals in statistical approach. A simple formula for the structure factor of decorated Fibonacci chain has been derived. Although the used method operates in the physical space only, its equivalence to the higher-dimensional analysis has been proved. Applications of the analysis to different decorated structures have been also discussed.

Oxygen moment formation and canting inLi2CuO2

The possibilities of oxygen moment formation and canting in the quasi-one-dimensional (quasi-1D) cuprate ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$ are investigated using single-crystal neutron diffraction at 2 K. The observed magnetic intensities could not be explained without the inclusion of a large ordered oxygen moment of $0.11(1){\ensuremath{\mu}}_{B}.$ Least-squares refinement of the magnetic structure of ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$ in combination with a spin-density Patterson analysis shows that the magnetization densities of the Cu and O atoms are highly aspherical, forming quasi-1D ribbons of localized Cu and O moments. Magnetic structure refinements and low-field magnetization measurements both suggest that the magnetic structure of ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$ at 2 K may be canted. A possible model for the canted configuration is proposed.

Characterization of Intermolecular Interactions in a Disordered Solid via a One-Dimensional Patterson Synthesis

We report the application of a one-dimensional Patterson analysis of diffuse X-ray scattering from the 1,8-diiodooctane/urea inclusion compound to obtain information on the intermolecular interacti...

Diffraction analysis of decorated aperiodic structure;: decorated Thue–Morse sequence

As an alternative to the Patterson analysis of quasicrystals and aperiodic structures, the reference lattice approach was applied to describe the diffraction pattern of the decorated Thue–Morse sequence. The Thue–Morse sequence is known as an aperiodic structure with a singular continuous Fourier transform. Such a sequence was decorated by combining every letter in the Thue–Morse sequence with a new expression. By using the reference lattice concept it was possible to find the envelope function, that gives the intensity of peaks in the diffraction patterns for main reflections and their satellites.