scholarly journals Rapid chain tracing of polypeptide backbones in electron-density maps

2010 ◽  
Vol 66 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Thomas C. Terwilliger
Keyword(s):  
Electron Density ◽  
High Electron ◽  
Visual Evaluation ◽  
Density Maps ◽  
Density Values ◽  
Speed Up ◽  
Density Map ◽  
Electron Density Map ◽  
And Storage

A method for the rapid tracing of polypeptide backbones has been developed. The method creates an approximate chain tracing that is useful for visual evaluation of whether a structure has been solved and for use in scoring the quality of electron-density maps. The essence of the method is to (i) sample candidate Cαpositions at spacings of approximately 0.6 Å along ridgelines of high electron density, (ii) list all possible nonapeptides that satisfy simple geometric and density criteria using these candidate Cαpositions, (iii) score the nonapeptides and choose the highest scoring ones, and (iv) find the longest chains that can be made by connecting nonamers. An indexing and storage scheme that allows a single calculation of most distances and density values is used to speed up the process. The method was applied to 42 density-modified electron-density maps at resolutions from 1.5 to 3.8 Å. A total of 21 428 residues in these maps were traced in 24 CPU min with an overall r.m.s.d. of 1.61 Å for Cαatoms compared with the known refined structures. The method appears to be suitable for rapid evaluation of electron-density map quality.

A Comparison of Two Algorithms for Electron-Density Map Improvement by Introduction of Atomicity: Skeletonization, and Map Sorting Followed by Refinement

1998 ◽  
Vol 54 (1) ◽  
pp. 81-85 ◽  
Author(s):  
F. M. D. Vellieux
Keyword(s):  
Electron Density ◽  
Initial Density ◽  
Acta Cryst ◽  
Density Maps ◽  
Resolution Electron ◽  
Crystallographic Symmetry ◽  
Density Map ◽  
Ornithine Transcarbamoylase ◽  
Electron Density Map ◽  
Pseudo Atom

A comparison has been made of two methods for electron-density map improvement by the introduction of atomicity, namely the iterative skeletonization procedure of the CCP4 program DM [Cowtan & Main (1993). Acta Cryst. D49, 148–157] and the pseudo-atom introduction followed by the refinement protocol in the program suite DEMON/ANGEL [Vellieux, Hunt, Roy & Read (1995). J. Appl. Cryst. 28, 347–351]. Tests carried out using the 3.0 Å resolution electron density resulting from iterative 12-fold non-crystallographic symmetry averaging and solvent flattening for the Pseudomonas aeruginosa ornithine transcarbamoylase [Villeret, Tricot, Stalon & Dideberg (1995). Proc. Natl Acad. Sci. USA, 92, 10762–10766] indicate that pseudo-atom introduction followed by refinement performs much better than iterative skeletonization: with the former method, a phase improvement of 15.3° is obtained with respect to the initial density modification phases. With iterative skeletonization a phase degradation of 0.4° is obtained. Consequently, the electron-density maps obtained using pseudo-atom phases or pseudo-atom phases combined with density-modification phases are much easier to interpret. These tests also show that for ornithine transcarbamoylase, where 12-fold non-crystallographic symmetry is present in the P1 crystals, G-function coupling leads to the simultaneous decrease of the conventional R factor and of the free R factor, a phenomenon which is not observed when non-crystallographic symmetry is absent from the crystal. The method is far less effective in such a case, and the results obtained suggest that the map sorting followed by refinement stage should be by-passed to obtain interpretable electron-density distributions.

Electron-density maps

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Electron Density ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Unit Cell ◽  
Density Maps ◽  
Wave Cycle ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an electron-density map. The electron-density map is the Fourier transform of the structure factors (with their phases). If the resolution and phases are good enough, the electron-density map may be interpreted in terms of atomic positions. In practice, it may be necessary to alternate between study of the electron-density map and the procedures mentioned in Chapter 10, which may allow improvements to be made to it. Electron-density maps contain a great deal of information, which is not easy to grasp. Considerable technical effort has gone into methods of presenting the electron density to the observer in the clearest possible way. The Fourier transform is calculated as a set of electron-density values at every point of a three-dimensional grid labelled with fractional coordinates x, y, z. These coordinates each go from 0 to 1 in order to cover the whole unit cell. To present the electron density as a smoothly varying function, values have to be calculated at intervals that are much smaller than the nominal resolution of the map. Say, for example, there is a protein unit cell 50 Å on a side, at a routine resolution of 2Å. This means that some of the waves included in the calculation of the electron density go through a complete wave cycle in 2 Å. As a rule of thumb, to represent this properly, the spacing of the points on the grid for calculation must be less than one-third of the resolution. In our example, this spacing might be 0.6 Å. To cover the whole of the 50 Å unit cell, about 80 values of x are needed; and the same number of values of y and z. The electron density therefore needs to be calculated on an array of 80×80×80 points, which is over half a million values. Although our world is three-dimensional, our retinas are two-dimensional, and we are good at looking at pictures and diagrams in two dimensions.

scholarly journals Building brain network in electron density map determined by micro-CT

2014 ◽  
Vol 70 (a1) ◽  
pp. C1752-C1752
Author(s):  
Rino Saiga ◽  
Susumu Takekoshi ◽  
Naoya Nakamura ◽  
Akihisa Takeuchi ◽  
Kentaro Uesugi ◽  
...  
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Model Building ◽  
Three Dimensional ◽  
Brain Network ◽  
X Ray ◽  
Density Maps ◽  
Density Map ◽  
Electron Density Map

In macromolecular crystallography, an electron density distribution is traced to build a model of the target molecule. We applied this method to model building for electron density maps of a brain network. Human cerebral tissue was stained with heavy atoms [1]. The sample was then analyzed at the BL20XU beamline of SPring-8 to obtain a three-dimensional map of X-ray attenuation coefficients representing the electron density distribution. Skeletonized wire models were built by placing and connecting nodes in the map [2], as shown in the figure below. The model-building procedures were similar to those reported for crystallographic analyses of macromolecular structures, while the neuronal network was automatically traced by using a Sobel filter. Neuronal circuits were then analytically resolved from the skeletonized models. We suggest that X-ray microtomography along with model building in the electron density map has potential as a method for understanding three-dimensional microstructures relevant to biological functions.

Automatic procedure for crystal-structure analysis with the heavy-atom technique*

1971 ◽  
Vol 134 (1-2) ◽  
Author(s):  
Vasantha Pattabhi ◽  
K. Venkatesan
Keyword(s):  
Electron Density ◽  
Least Squares Method ◽  
Heavy Atom ◽  
Site Occupancy ◽  
Crystal Structure Analysis ◽  
Density Maps ◽  
Structure Factors ◽  
Subsequent Calculation ◽  
Density Map ◽  
Electron Density Map

AbstractThis paper deals with a possible method of determining molecular structure directly, using x-ray data. The peaks chosen from the electron-density map calculated using the signs obtained from the contribution of the heavy atom are assigned site-occupancy values which depend upon the peak heights. The occupancy parameter is refined by the least-squares method and the peaks for which the value of the occupancy parameters increases are taken as real atoms in the subsequent calculation of structure factors and electron-density maps. The method has been tested in two hypothetical cases and in a real case.

Phase perturbation as a means of electron density map quality evaluation

2008 ◽  
Vol 41 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Olga Kirillova
Keyword(s):  
Electron Density ◽  
Data Sets ◽  
Molecular Replacement ◽  
Data Set ◽  
Density Maps ◽  
Phase Perturbation ◽  
Replacement Solution ◽  
Electron Density Map ◽  
Trial Phase

This paper describes a new means for evaluating the quality of crystallographic electron density maps. It has been found that a better data set possesses greater robustness against perturbations applied to the phases. Thus it allows recognition of a more precise phase set and provides a way to select the best or reject the worst from several noisy data sets derived from the same crystal structure. The results indicate that calculation of the correlations by the procedure described here can be useful in ranking electron density maps in this aspect of quality. The method suggested has potential use for selecting a better molecular replacement solution, as well as for evaluating trial phase sets inab initiophasing procedures.

Phase improvement and extension

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Ab Initio ◽  
Electron Density ◽  
Model Building ◽  
Special Treatment ◽  
Fourier Synthesis ◽  
Density Maps ◽  
Phase Extension ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

The descriptions of the various types of Fourier synthesis (observed, difference, hybrid) and of their properties, given in Chapter 7, suggest that electron density maps are not only a tool for depicting the distribution of the electrons in the target structure, but also a source of information which may be continuously exploited during the phasing process, no matter whether ab initio or non-ab initio methods were used for deriving the initial model. Here, we will describe two important techniques based on the properties of electron density maps. (i) The recursive approach for phase extension and refinement called EDM (electron density modification). Such techniques have dramatically improved the efficiency of phasing procedures, which usually end with a limited percentage of phased reflections and non-negligible phase errors. EDM techniques allow us to extend phase assignment and to improve phase quality. The author is firmly convinced that practical solution of the phase problem for structures with Nasym up to 200 atoms in the asymmetric unit may be jointly ascribed to direct methods and to EDM techniques. (ii) The AMB (automated model building) procedures; these may be considered to be partly EDM techniques and they are used for automatic building of molecular models from electron density maps. Essentially, we will refer to proteins; the procedures used for small to medium-sized molecules have already been described in Section 6.3.5. Two new ab initio phasing approaches, charge flipping and VLD, essentially based on the properties of the Fourier transform, belong to the EDM category, and since they require a special treatment, they will be described later in Chapter 9. Phase extension and refinement may be performed in reciprocal and in direct space. We described the former in Section 6.3.6; here, we are just interested in direct space procedures, the so-called EDM (electron density modification) techniques. Such procedures are based on the following hypothesis: a poor electron density map, ρ, may be modified by a suitable function, f , to obtain a new map, say ρmod, which better approximates the true map: . . . ρmod (r) = f [ρ(r)]. (8.1) . . . If function f is chosen properly, more accurate phases can be obtained by Fourier inversion of ρmod, which may in turn be used to calculate a new electron density map.

Quality of the electron density map

1983 ◽  
Vol 166 (1) ◽  
pp. 80-83
Author(s):  
Abelardo Silva ◽  
Michael G. Rossmann ◽  
Celerino Abad-Zapatero ◽  
R. Huber
Keyword(s):  
Electron Density ◽  
Density Map ◽  
Electron Density Map

A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

2017 ◽  
Vol 24 (5) ◽  
pp. 1024-1038 ◽  
Author(s):  
Yuki Sekiguchi ◽  
Saki Hashimoto ◽  
Amane Kobayashi ◽  
Tomotaka Oroguchi ◽  
Masayoshi Nakasako
Keyword(s):  
Diffraction Pattern ◽  
Electron Density ◽  
Figure Of Merit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Maps ◽  
Diffraction Imaging ◽  
Density Map ◽  
Diffraction Patterns ◽  
Electron Density Map

Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.

Classification and assessment of retrieved electron density maps in coherent X-ray diffraction imaging using multivariate analysis

2016 ◽  
Vol 23 (1) ◽  
pp. 312-323 ◽  
Author(s):  
Yuki Sekiguchi ◽  
Tomotaka Oroguchi ◽  
Masayoshi Nakasako
Keyword(s):  
Diffraction Pattern ◽  
Electron Density ◽  
Phase Retrieval ◽  
Dimensional Space ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Maps ◽  
Diffraction Imaging ◽  
Density Map ◽  
Electron Density Map

Coherent X-ray diffraction imaging (CXDI) is one of the techniques used to visualize structures of non-crystalline particles of micrometer to submicrometer size from materials and biological science. In the structural analysis of CXDI, the electron density map of a sample particle can theoretically be reconstructed from a diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction is difficult because diffraction patterns are affected by Poisson noise and miss data in small-angle regions due to the beam stop and the saturation of detector pixels. In contrast to X-ray protein crystallography, in which the phases of diffracted waves are experimentally estimated, phase retrieval in CXDI relies entirely on the computational procedure driven by the PR algorithms. Thus, objective criteria and methods to assess the accuracy of retrieved electron density maps are necessary in addition to conventional parameters monitoring the convergence of PR calculations. Here, a data analysis scheme, named ASURA, is proposed which selects the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a diffraction pattern. Each electron density map composed ofJpixels is expressed as a point in aJ-dimensional space. Principal component analysis is applied to describe characteristics in the distribution of the maps in theJ-dimensional space. When the distribution is characterized by a small number of principal components, the distribution is classified using thek-means clustering method. The classified maps are evaluated by several parameters to assess the quality of the maps. Using the proposed scheme, structure analysis of a diffraction pattern from a non-crystalline particle is conducted in two stages: estimation of the overall shape and determination of the fine structure inside the support shape. In each stage, the most accurate and probable density maps are objectively selected. The validity of the proposed scheme is examined by application to diffraction data that were obtained from an aggregate of metal particles and a biological specimen at the XFEL facility SACLA using custom-made diffraction apparatus.

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