scholarly journals Brickworxbuilds recurrent RNA and DNA structural motifs into medium- and low-resolution electron-density maps

2015 ◽  
Vol 71 (3) ◽  
pp. 697-705 ◽  
Author(s):  
Grzegorz Chojnowski ◽  
Tomasz Waleń ◽  
Paweł Piątkowski ◽  
Wojciech Potrzebowski ◽  
Janusz M. Bujnicki
Keyword(s):  
Nucleic Acid ◽  
Electron Density ◽  
Three Dimensional ◽  
Real Space ◽  
Density Peaks ◽  
Density Maps ◽  
Resolution Electron ◽  
Fragment Library ◽  
Electron Density Map ◽  
Recurrent Motifs

Brickworxis a computer program that builds crystal structure models of nucleic acid molecules using recurrent motifs including double-stranded helices. In a first step, the program searches for electron-density peaks that may correspond to phosphate groups; it may also take into account phosphate-group positions provided by the user. Subsequently, comparing the three-dimensional patterns of the P atoms with a database of nucleic acid fragments, it finds the matching positions of the double-stranded helical motifs (A-RNA or B-DNA) in the unit cell. If the target structure is RNA, the helical fragments are further extended with recurrent RNA motifs from a fragment library that contains single-stranded segments. Finally, the matched motifs are merged and refined in real space to find the most likely conformations, including a fit of the sequence to the electron-density map. TheBrickworxprogram is available for download and as a web server at http://iimcb.genesilico.pl/brickworx.

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.

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 A moment invariant for evaluating the chirality of three-dimensional objects

2010 ◽  
Vol 8 (54) ◽  
pp. 144-151 ◽  
Author(s):  
Johan Hattne ◽  
Victor S. Lamzin
Keyword(s):  
Electron Density ◽  
Three Dimensional ◽  
Peptide Fragments ◽  
Moment Invariant ◽  
Three Dimensional Objects ◽  
Density Maps ◽  
Wide Range ◽  
Polypeptide Backbone ◽  
Dimensional Object ◽  
Electron Density Map

Chirality is an important feature of three-dimensional objects and a key concept in chemistry, biology and many other disciplines. However, it has been difficult to quantify, largely owing to computational complications. Here we present a general chirality measure, called the chiral invariant (CI), which is applicable to any three-dimensional object containing a large amount of data. The CI distinguishes the hand of the object and quantifies the degree of its handedness. It is invariant to the translation, rotation and scale of the object, and tolerant to a modest amount of noise in the experimental data. The invariant is expressed in terms of moments and can be computed in almost no time. Because of its universality and computational efficiency, the CI is suitable for a wide range of pattern-recognition problems. We demonstrate its applicability to molecular atomic models and their electron density maps. We show that the occurrence of the conformations of the macromolecular polypeptide backbone is related to the value of the CI of the constituting peptide fragments. We also illustrate how the CI can be used to assess the quality of a crystallographic electron density map.

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.

scholarly journals Machine learning to estimate the local quality of protein crystal structures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ikuko Miyaguchi ◽  
Miwa Sato ◽  
Akiko Kashima ◽  
Hiroyuki Nakagawa ◽  
Yuichi Kokabu ◽  
...  
Keyword(s):  
Electron Density ◽  
Protein Structures ◽  
Three Dimensional ◽  
Protein Crystal ◽  
Low Resolution ◽  
X Ray Crystallography ◽  
Density Maps ◽  
Local Quality ◽  
Density Map ◽  
Electron Density Map

AbstractLow-resolution electron density maps can pose a major obstacle in the determination and use of protein structures. Herein, we describe a novel method, called quality assessment based on an electron density map (QAEmap), which evaluates local protein structures determined by X-ray crystallography and could be applied to correct structural errors using low-resolution maps. QAEmap uses a three-dimensional deep convolutional neural network with electron density maps and their corresponding coordinates as input and predicts the correlation between the local structure and putative high-resolution experimental electron density map. This correlation could be used as a metric to modify the structure. Further, we propose that this method may be applied to evaluate ligand binding, which can be difficult to determine at low resolution.

The phase problem and electron-density maps

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Crystal Structure ◽  
Fourier Series ◽  
Diffraction Pattern ◽  
Electron Density ◽  
Bragg Reflection ◽  
Three Dimensional ◽  
Density Maps ◽  
Structure Factors ◽  
Unit Cells ◽  
Phase Angles

In order to obtain an image of the material that has scattered X rays and given a diffraction pattern, which is the aim of these studies, one must perform a three-dimensional Fourier summation. The theorem of Jean Baptiste Joseph Fourier, a French mathematician and physicist, states that a continuous, periodic function can be represented by the summation of cosine and sine terms (Fourier, 1822). Such a set of terms, described as a Fourier series, can be used in diffraction analysis because the electron density in a crystal is a periodic distribution of scattering matter formed by the regular packing of approximately identical unit cells. The Fourier series that is used provides an equation that describes the electron density in the crystal under study. Each atom contains electrons; the higher its atomic number the greater the number of electrons in its nucleus, and therefore the higher its peak in an electrondensity map.We showed in Chapter 5 how a structure factor amplitude, |F (hkl)|, the measurable quantity in the X-ray diffraction pattern, can be determined if the arrangement of atoms in the crystal structure is known (Sommerfeld, 1921). Now we will show how we can calculate the electron density in a crystal structure if data on the structure factors, including their relative phase angles, are available. The Fourier series is described as a “synthesis” when it involves structure amplitudes and relative phases and builds up a picture of the electron density in the crystal. By contrast, a “Fourier analysis” leads to the components that make up this series. The term “relative” is used here because the phase of a Bragg reflection is described relative to that of an imaginary wave diffracted in the same direction at a chosen origin of the unit cell.

Sign in / Sign up

Export Citation Format

Share Document