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.

scholarly journals Evaluation of macromolecular electron-density map quality using the correlation of local r.m.s. density

1999 ◽  
Vol 55 (11) ◽  
pp. 1872-1877 ◽  
Author(s):  
Thomas C. Terwilliger ◽  
Joel Berendzen
Keyword(s):  
Standard Deviation ◽  
Ab Initio ◽  
Electron Density ◽  
Heavy Atom ◽  
Real Space ◽  
Acta Cryst ◽  
Density Maps ◽  
Density Map ◽  
Electron Density Map ◽  
Trial Phase

It has recently been shown that the standard deviation of local r.m.s. electron density is a good indicator of the presence of distinct regions of solvent and protein in macromolecular electron-density maps [Terwilliger & Berendzen (1999). Acta Cryst. D55, 501–505]. Here, it is demonstrated that a complementary measure, the correlation of local r.m.s. density in adjacent regions on the unit cell, is also a good measure of the presence of distinct solvent and protein regions. The correlation of local r.m.s. density is essentially a measure of how contiguous the solvent (and protein) regions are in the electron-density map. This statistic can be calculated in real space or in reciprocal space and has potential uses in evaluation of heavy-atom solutions in the MIR and MAD methods as well as for evaluation of trial phase sets in ab initio phasing procedures.

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.

Application of the maximum entropy method to electron density determination

1985 ◽  
Vol 18 (6) ◽  
pp. 442-445 ◽  
Author(s):  
W. Wei
Keyword(s):  
Maximum Entropy ◽  
Electron Density ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
Resolution Electron ◽  
Density Map ◽  
Electron Density Map ◽  
Principle Of Maximum ◽  
Better Than

The principle of maximum entropy is adopted to derive a procedure for obtaining the electron density distribution in crystals from incomplete X-ray diffraction data. This method was applied to cementite and the result proved to be better than the conventional Fourier inversion in resolution as well as in the absence of ripples. The potential advantages of this method are: (1) the amount of subjective judgment imposed on unavailable data is significantly limited, and (2) the result of this method is consistent with the known information and maximally noncommittal with regard to the unknowns. It is shown that the method is especially well suited to the problem of the determination of a high-resolution electron density map from insufficient experimental data.

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.

scholarly journals HermiteFit: fast-fitting atomic structures into a low-resolution density map using three-dimensional orthogonal Hermite functions

2014 ◽  
Vol 70 (8) ◽  
pp. 2069-2084 ◽  
Author(s):  
Georgy Derevyanko ◽  
Sergei Grudinin
Keyword(s):  
Electron Density ◽  
Cross Correlation ◽  
Three Dimensional ◽  
Hermite Functions ◽  
Low Resolution ◽  
Atomic Structures ◽  
Resolution Electron ◽  
Laplacian Filter ◽  
Density Map ◽  
Electron Density Map

HermiteFit, a novel algorithm for fitting a protein structure into a low-resolution electron-density map, is presented. The algorithm accelerates the rotation of the Fourier image of the electron density by using three-dimensional orthogonal Hermite functions. As part of the new method, an algorithm for the rotation of the density in the Hermite basis and an algorithm for the conversion of the expansion coefficients into the Fourier basis are presented.HermiteFitwas implemented using the cross-correlation or the Laplacian-filtered cross-correlation as the fitting criterion. It is demonstrated that in the Hermite basis the Laplacian filter has a particularly simple form. To assess the quality of density encoding in the Hermite basis, an analytical way of computing the crystallographicRfactor is presented. Finally, the algorithm is validated using two examples and its efficiency is compared with two widely used fitting methods,ADP_EMandcoloresfrom theSituspackage.HermiteFitwill be made available at http://nano-d.inrialpes.fr/software/HermiteFit or upon request from the authors.

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.

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.

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