scholarly journals Evaluating crystallographic likelihood functions using numerical quadratures

2020 ◽  
Author(s):  
Petrus H. Zwart ◽  
Elliott D. Perryman
Keyword(s):  
Diffraction Data ◽  
Numerical Quadrature ◽  
Rapid Evaluation ◽  
Relative Ease ◽  
Likelihood Functions ◽  
Non Linear ◽  
Change Of Variable ◽  
Noise Models ◽  
Numerical Quadratures

AbstractIntensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage however is complicated by the ability to efficiently compute these targets functions. Here a numerical quadrature is developed that allows for the rapid evaluation of intensity-based likelihood functions in crystallographic applications. By using a sequence of change of variable transformations, including a non-linear domain compression operation, an accurate, robust, and efficient quadrature is constructed. The approach is flexible and can incorporate different noise models with relative ease.

scholarly journals Evaluating crystallographic likelihood functions using numerical quadratures

2020 ◽  
Vol 76 (8) ◽  
pp. 736-750
Author(s):  
Petrus H. Zwart ◽  
Elliott D. Perryman
Keyword(s):  
Diffraction Data ◽  
Numerical Quadrature ◽  
Rapid Evaluation ◽  
Relative Ease ◽  
Likelihood Functions ◽  
Change Of Variable ◽  
Noise Models ◽  
Numerical Quadratures

Intensity-based likelihood functions in crystallographic applications have the potential to enhance the quality of structures derived from marginal diffraction data. Their usage, however, is complicated by the ability to efficiently compute these target functions. Here, a numerical quadrature is developed that allows the rapid evaluation of intensity-based likelihood functions in crystallographic applications. By using a sequence of change-of-variable transformations, including a nonlinear domain-compression operation, an accurate, robust and efficient quadrature is constructed. The approach is flexible and can incorporate different noise models with relative ease.

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 σ2 R , a reciprocal-space measure of the quality of macromolecular electron-density maps

1999 ◽  
Vol 55 (6) ◽  
pp. 1174-1178 ◽  
Author(s):  
Thomas C. Terwilliger
Keyword(s):  
Standard Deviation ◽  
Ab Initio ◽  
Electron Density ◽  
Reciprocal Space ◽  
Rapid Evaluation ◽  
Reliable Measure ◽  
Similar Measure ◽  
Acta Cryst ◽  
Density Maps

It has previously been shown that the presence of distinct regions of solvent and protein in macromolecular crystals leads to a high value of the standard deviation of local r.m.s. electron density and that this can in turn be used as a reliable measure of the quality of macromolecular electron-density maps [Terwilliger & Berendzen (1999a). Acta Cryst. D55, 501–505]. Here, it is demonstrated that a similar measure, \sigma_{R}^{2}, the variance of the local roughness of the electron density, can be calculated in reciprocal space. The formulation is suitable for rapid evaluation of macromolecular crystallographic phases, for phase improvement and for ab initio phasing procedures.

scholarly journals Protein microcrystallography using synchrotron radiation

IUCrJ ◽  
2017 ◽  
Vol 4 (5) ◽  
pp. 529-539 ◽  
Author(s):  
Masaki Yamamoto ◽  
Kunio Hirata ◽  
Keitaro Yamashita ◽  
Kazuya Hasegawa ◽  
Go Ueno ◽  
...  
Keyword(s):  
Synchrotron Radiation ◽  
Data Collection ◽  
Diffraction Data ◽  
Structure Determination ◽  
Structural Features ◽  
X Ray ◽  
Data Collection Strategy ◽  
Technological Developments ◽  
Novel Method

The progress in X-ray microbeam applications using synchrotron radiation is beneficial to structure determination from macromolecular microcrystals such as smallin mesocrystals. However, the high intensity of microbeams causes severe radiation damage, which worsens both the statistical quality of diffraction data and their resolution, and in the worst cases results in the failure of structure determination. Even in the event of successful structure determination, site-specific damage can lead to the misinterpretation of structural features. In order to overcome this issue, technological developments in sample handling and delivery, data-collection strategy and data processing have been made. For a few crystals with dimensions of the order of 10 µm, an elegant two-step scanning strategy works well. For smaller samples, the development of a novel method to analyze multiple isomorphous microcrystals was motivated by the success of serial femtosecond crystallography with X-ray free-electron lasers. This method overcame the radiation-dose limit in diffraction data collection by using a sufficient number of crystals. Here, important technologies and the future prospects for microcrystallography are discussed.

Communication and Nursing Relationships

2011 ◽  
pp. 25-39
Author(s):  
Kyung Rim Shin ◽  
Dukyoo Jung ◽  
Su Jin Shin
Keyword(s):  
Enriched Environment ◽  
Non Linear ◽  
Basic Features

Communication and relationships are central to nursing. The non-linear quality of communication is discussed and the challenge for nursing to carry quality communication into a technology enriched environment considered. Basic features of communication are laid out.

scholarly journals When protein crystal dehydration helps

2014 ◽  
Vol 70 (a1) ◽  
pp. C337-C337
Author(s):  
Carina Lobley ◽  
Juan Sanchez-Weatherby ◽  
James Sandy ◽  
Marco Mazzorana ◽  
Tobias Krojer ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Crystal Lattice ◽  
Diffraction Data ◽  
Protein Crystal ◽  
Specific Interactions ◽  
Air Stream ◽  
Solvent Molecules

A typical protein crystal contains 30-60% solvent. For a naked crystal, this solvent is distributed between solvent shells, where water and solvent molecules make specific interactions with the crystalline protein, and solvent channels filled with disordered solvent molecules. This internal solvent map of the crystal can be modified by placing the crystal in a dehydrating environment. This may in turn induce changes to the crystal lattice and affect mosaicity, resolution and quality of diffraction data. A dehydrating environment can be generated around a crystal in several ways with various degrees of precision and complexity. In this study we have used the HC1 device (Maatel) to mount crystals an air stream of known relative humidity – a precise yet hassle-free approach to altering crystal hydration. We set out to analyse a range of different crystals to establish usable protocols that will allow one to explore to crystal hydration space, either by preparing samples before synchrotron beamtime or by undertaking the experiments during beamtime. Our results, considered in the light of the literature surrounding crystal dehydration, provide guidance for when dehydration can help diffraction.

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