scholarly journals On effective and optical resolutions of diffraction data sets

2013 ◽  
Vol 69 (10) ◽  
pp. 1921-1934 ◽  
Author(s):  
Ludmila Urzhumtseva ◽  
Bruno Klaholz ◽  
Alexandre Urzhumtsev
Keyword(s):  
Diffraction Data ◽  
Minimum Distance ◽  
Optical Resolution ◽  
General Interest ◽  
Data Sets ◽  
Accurate Calculation ◽  
Data Set ◽  
X Ray ◽  
X Ray Crystallography ◽  
The Ideal

In macromolecular X-ray crystallography, diffraction data sets are traditionally characterized by the highest resolutiondhighof the reflections that they contain. This measure is sensitive to individual reflections and does not refer to the eventual data incompleteness and anisotropy; it therefore does not describe the data well. A physically relevant and robust measure that provides a universal way to define the `actual' effective resolutiondeffof a data set is introduced. This measure is based on the accurate calculation of the minimum distance between two immobile point scatterers resolved as separate peaks in the Fourier map calculated with a given set of reflections. This measure is applicable to any data set, whether complete or incomplete. It also allows characterizion of the anisotropy of diffraction data sets in whichdeffstrongly depends on the direction. Describing mathematical objects, the effective resolutiondeffcharacterizes the `geometry' of the set of measured reflections and is irrelevant to the diffraction intensities. At the same time, the diffraction intensities reflect the composition of the structure from physical entities: the atoms. The minimum distance for the atoms typical of a given structure is a measure that is different from and complementary todeff; it is also a characteristic that is complementary to conventional measures of the data-set quality. Following the previously introduced terms, this value is called the optical resolution,dopt. The optical resolution as defined here describes the separation of the atomic images in the `ideal' crystallographic Fourier map that would be calculated if the exact phases were known. The effective and optical resolution, as formally introduced in this work, are of general interest, giving a common `ruler' for all kinds of crystallographic diffraction data sets.

EFRESOL: effective resolution of a diffraction data set

2015 ◽  
Vol 48 (2) ◽  
pp. 589-597 ◽  
Author(s):  
Ludmila Urzhumtseva ◽  
Alexandre Urzhumtsev
Keyword(s):  
High Resolution ◽  
Diffraction Data ◽  
Minimum Distance ◽  
Optical Resolution ◽  
Resolving Power ◽  
Data Sets ◽  
Data Set ◽  
Data Resolution ◽  
The Given ◽  
Resolution Data

The resolution of a diffraction data set conveys the details that one expects to distinguish in the Fourier maps calculated with these data. For example, individual atoms in a macromolecular chain cannot be resolved in the maps calculated with 2 Å resolution data sets, while they can be resolved in accurate maps calculated with 1 Å resolution data. However, if a data set is incomplete its high-resolution cutoff becomes less straightforward to interpret. For instance, a Fourier map calculated using a 1 Å resolution data set with many high-resolution reflections missing may rather resemble a map corresponding to 2 Å resolution data. The authors have proposed a method that redefines the traditional notion of data resolution, making it more formal and general. This manuscript presents the corresponding tool, the programEFRESOL. For a data set of an arbitrary completeness, the program calculates its mean, highest and lowest effective resolutions. These values are established through the minimum distance between two point scatterers when their images are still resolved as separate peaks in the Fourier maps calculated with the given data set. Additionally, the program calculates the optical resolution, which is defined as the minimum distance for typical atoms of the structure when they are resolved in a hypothetical synthesis obtained with the given amplitudes and the exact phases if they are known. Both effective and optical resolutions show the `resolving power' of the diffraction data set.

Design of a novel Peltier-based cooling device and its use in neutron diffraction data collection of perdeuterated yeast pyrophosphatase

2010 ◽  
Vol 43 (5) ◽  
pp. 1113-1120 ◽  
Author(s):  
Esko Oksanen ◽  
François Dauvergne ◽  
Adrian Goldman ◽  
Monika Budayova-Spano
Keyword(s):  
Data Collection ◽  
Neutron Diffraction ◽  
Diffraction Data ◽  
Catalytic Mechanism ◽  
Inorganic Pyrophosphatase ◽  
Neutron Diffraction Data ◽  
Cooling Device ◽  
Data Set ◽  
X Ray ◽  
X Ray Crystallography

H atoms play a central role in enzymatic mechanisms, but H-atom positions cannot generally be determined by X-ray crystallography. Neutron crystallography, on the other hand, can be used to determine H-atom positions but it is experimentally very challenging. Yeast inorganic pyrophosphatase (PPase) is an essential enzyme that has been studied extensively by X-ray crystallography, yet the details of the catalytic mechanism remain incompletely understood. The temperature instability of PPase crystals has in the past prevented the collection of a neutron diffraction data set. This paper reports how the crystal growth has been optimized in temperature-controlled conditions. To stabilize the crystals during neutron data collection a Peltier cooling device that minimizes the temperature gradient along the capillary has been developed. This device allowed the collection of a full neutron diffraction data set.

A batch-wise non-linear fitting and analysis tool for treating large X-ray diffraction data sets

2006 ◽  
Vol 39 (2) ◽  
pp. 262-266 ◽  
Author(s):  
R. J. Davies
Keyword(s):  
Diffraction Data ◽  
Operation Mode ◽  
Large Data ◽  
Scattering Data ◽  
Data Sets ◽  
Analysis Tool ◽  
Data Set ◽  
X Ray ◽  
Linear Fitting ◽  
Non Linear

Synchrotron sources offer high-brilliance X-ray beams which are ideal for spatially and time-resolved studies. Large amounts of wide- and small-angle X-ray scattering data can now be generated rapidly, for example, during routine scanning experiments. Consequently, the analysis of the large data sets produced has become a complex and pressing issue. Even relatively simple analyses become difficult when a single data set can contain many thousands of individual diffraction patterns. This article reports on a new software application for the automated analysis of scattering intensity profiles. It is capable of batch-processing thousands of individual data files without user intervention. Diffraction data can be fitted using a combination of background functions and non-linear peak functions. To compliment the batch-wise operation mode, the software includes several specialist algorithms to ensure that the results obtained are reliable. These include peak-tracking, artefact removal, function elimination and spread-estimate fitting. Furthermore, as well as non-linear fitting, the software can calculate integrated intensities and selected orientation parameters.

scholarly journals BraggNet: integrating Bragg peaks using neural networks

2019 ◽  
Vol 52 (4) ◽  
pp. 854-863 ◽  
Author(s):  
Brendan Sullivan ◽  
Rick Archibald ◽  
Jahaun Azadmanesh ◽  
Venu Gopal Vandavasi ◽  
Patricia S. Langan ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Negative Control ◽  
Protein Crystal ◽  
Data Sets ◽  
Data Set ◽  
X Ray ◽  
X Ray Crystallography ◽  
Integrated Intensities ◽  
Neutron Crystallography

Neutron crystallography offers enormous potential to complement structures from X-ray crystallography by clarifying the positions of low-Z elements, namely hydrogen. Macromolecular neutron crystallography, however, remains limited, in part owing to the challenge of integrating peak shapes from pulsed-source experiments. To advance existing software, this article demonstrates the use of machine learning to refine peak locations, predict peak shapes and yield more accurate integrated intensities when applied to whole data sets from a protein crystal. The artificial neural network, based on the U-Net architecture commonly used for image segmentation, is trained using about 100 000 simulated training peaks derived from strong peaks. After 100 training epochs (a round of training over the whole data set broken into smaller batches), training converges and achieves a Dice coefficient of around 65%, in contrast to just 15% for negative control data sets. Integrating whole peak sets using the neural network yields improved intensity statistics compared with other integration methods, including k-nearest neighbours. These results demonstrate, for the first time, that neural networks can learn peak shapes and be used to integrate Bragg peaks. It is expected that integration using neural networks can be further developed to increase the quality of neutron, electron and X-ray crystallography data.

scholarly journals Poisson errors and adaptive rebinning in X-ray powder diffraction data

2018 ◽  
Vol 33 (4) ◽  
pp. 266-269 ◽  
Author(s):  
Marcus H. Mendenhall
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Data Sets ◽  
Powder Diffraction Data ◽  
Data Set ◽  
X Ray ◽  
Short Summary ◽  
Correct Assignment ◽  
Wide Range ◽  
Diffraction Patterns

This work provides a short summary of techniques for formally-correct handling of statistical uncertainties in Poisson-statistics dominated data, with emphasis on X-ray powder diffraction patterns. Correct assignment of uncertainties for low counts is documented. Further, we describe a technique for adaptively rebinning such data sets to provide more uniform statistics across a pattern with a wide range of count rates, from a few (or no) counts in a background bin to on-peak regions with many counts. This permits better plotting of data and analysis of a smaller number of points in a fitting package, without significant degradation of the information content of the data set. Examples of the effect of this on a diffraction data set are given.

scholarly journals Whole-pattern fitting technique in serial femtosecond nanocrystallography

IUCrJ ◽  
2016 ◽  
Vol 3 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Ruben A. Dilanian ◽  
Sophie R. Williams ◽  
Andrew V. Martin ◽  
Victor A. Streltsov ◽  
Harry M. Quiney
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Monte Carlo Integration ◽  
Data Set ◽  
X Ray ◽  
X Ray Crystallography ◽  
Small Crystals ◽  
Crystallite Structure ◽  
Serial Crystallography

Serial femtosecond X-ray crystallography (SFX) has created new opportunities in the field of structural analysis of protein nanocrystals. The intensity and timescale characteristics of the X-ray free-electron laser sources used in SFX experiments necessitate the analysis of a large collection of individual crystals of variable shape and quality to ultimately solve a single, average crystal structure. Ensembles of crystals are commonly encountered in powder diffraction, but serial crystallography is different because each crystal is measured individually and can be orientedviaindexing and merged into a three-dimensional data set, as is done for conventional crystallography data. In this way, serial femtosecond crystallography data lie in between conventional crystallography data and powder diffraction data, sharing features of both. The extremely small sizes of nanocrystals, as well as the possible imperfections of their crystallite structure, significantly affect the diffraction pattern and raise the question of how best to extract accurate structure-factor moduli from serial crystallography data. Here it is demonstrated that whole-pattern fitting techniques established for one-dimensional powder diffraction analysis can be feasibly extended to higher dimensions for the analysis of merged SFX diffraction data. It is shown that for very small crystals, whole-pattern fitting methods are more accurate than Monte Carlo integration methods that are currently used.

Global indicators of X-ray data quality

2001 ◽  
Vol 34 (2) ◽  
pp. 130-135 ◽  
Author(s):  
Manfred S. Weiss
Keyword(s):  
Data Quality ◽  
Diffraction Data ◽  
Optical Resolution ◽  
Data Set ◽  
X Ray ◽  
Global Indicators ◽  
Nominal Resolution

Global indicators of the quality of diffraction data are presented and discussed, and are evaluated in terms of their performance with respect to various tasks. Based on the results obtained, it is suggested that some of the conventional indicators still in use in the crystallographic community should be abandoned, such as the nominal resolutiondminor the mergingRfactorRmerge, and replaced by more objective and more meaningful numbers, such as the effective optical resolutiondeff,optand the redundancy-independent mergingRfactorRr.i.m.. Furthermore, it is recommended that the precision-indicating mergingRfactorRp.i.m.should be reported with every diffraction data set published, because it describes the precision of the averaged measurements, which are the quantities normally used in crystallography as observables.

Determination of depth profiles from X-ray diffraction data

1993 ◽  
Vol 8 (2) ◽  
pp. 122-126 ◽  
Author(s):  
Paul Predecki
Keyword(s):  
Diffraction Data ◽  
Direct Method ◽  
Sample Surface ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Data Set ◽  
X Ray ◽  
Depth Profiles ◽  
A Direct Method

A direct method is described for determining depth profiles (z-profiles) of diffraction data from experimentally determined τ-profiles, where z is the depth beneath the sample surface and τ is the 1/e penetration depth of the X-ray beam. With certain assumptions, the relation between these two profile functions can be expressed in the form of a Laplace transform. The criteria for fitting experimental τ-data to functions which can be utilized by the method are described. The method was applied to two τ-data sets taken from the literature: (1) of residual strain in an A1 thin film and (2) of residual stress in a surface ground A12O3/5vol% TiC composite. For each data set, it was found that the z-profiles obtained were of two types: oscillatory and nonoscillatory. The nonoscillatory profiles appeared to be qualitatively consistent for a given data set. The oscillatory profiles were considered to be not physically realistic. For the data sets considered, the nonoscillatory z-profiles were found to lie consistently above the corresponding τ-profiles, and to approach the τ-profiles at large z, as expected from the relation between the two.

X-Ray Powder Diffraction Study of 2,2′,2″ triamino-triethylamine-Ni(II)-di-thiocyanate by Transmission PSD Diffractometer and Rietveld Techniques

1991 ◽  
Vol 6 (3) ◽  
pp. 166-169
Author(s):  
Britta Lundtoft ◽  
Svend Erik Rasmussen
Keyword(s):  
Diffraction Study ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Internal Standard ◽  
Data Sets ◽  
Powder Diffraction Data ◽  
Data Set ◽  
X Ray ◽  
Lattice Constants ◽  
Deep Blue

AbstractX-Ray powder diffraction data for the compound 2,2′,2″-triamino-triethylamine-Ni(II)-di-thiocyanate were obtained by transmission diffractometric methods at 20°C - 22°C. Two data sets were collected with CuKα1 radiation (λ = 1.54056 Å) one with Si as an internal standard (a = 5.430825 Å) and one without.The deep blue crystals are orthorhombic of space group P212121. Peak positions were corrected by aid of the Si peaks in the first data set. Refinements of lattice constants from indexed reflections yielded the following values: a = 10.8524(18) Å; b = 14.7249(16) Å; c = 8.6511(11) Å; Dx = 1.542 Mg/m3. The second data set was used for a Rietveld refinement. The lattice constants obtained by this method are: a = 10.8451(5) Å; b = 14.7148 Å; c = 8.6447(4) Å.

scholarly journals Resolving indexing ambiguities in X-ray free-electron laser diffraction patterns

2019 ◽  
Vol 75 (2) ◽  
pp. 234-241
Author(s):  
Monarin Uervirojnangkoorn ◽  
Artem Y. Lyubimov ◽  
Qiangjun Zhou ◽  
William I. Weis ◽  
Axel T. Brunger
Keyword(s):  
Diffraction Data ◽  
Free Electron ◽  
Free Electron Laser ◽  
Bravais Lattice ◽  
Data Sets ◽  
Diffraction Image ◽  
Acta Cryst ◽  
Data Set ◽  
X Ray ◽  
Automated Method

Processing X-ray free-electron laser (XFEL) diffraction images poses challenges, as an XFEL pulse is powerful enough to destroy or damage the diffracting volume and thereby yields only one diffraction image per volume. Moreover, the crystal is stationary during the femtosecond pulse, so reflections are generally only partially recorded. Therefore, each XFEL diffraction image must be scaled individually and, ideally, corrected for partiality prior to merging. An additional complication may arise owing to indexing ambiguities when the symmetry of the Bravais lattice is higher than that of the space group, or when the unit-cell dimensions are similar to each other. Here, an automated method is presented that diagnoses these indexing ambiguities based on the Brehm–Diederichs algorithm [Brehm & Diederichs (2014), Acta Cryst. D70, 101–109] and produces a consistent indexing choice for the large majority of diffraction images. This method was applied to an XFEL diffraction data set measured from crystals of the neuronal SNARE–complexin-1–synaptotagmin-1 complex. After correcting the indexing ambiguities, substantial improvements were observed in the merging statistics and the atomic model refinement R values. This method should be a useful addition to the arsenal of tools for the processing of XFEL diffraction data sets.

Sign in / Sign up

Export Citation Format

Share Document