EDMA: a computer program for topological analysis of discrete electron densities

2012 ◽  
Vol 45 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Lukáš Palatinus ◽  
Siriyara Jagannatha Prathapa ◽  
Sander van Smaalen
Keyword(s):  
Computer Program ◽  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Real Space ◽  
Principal Curvatures ◽  
Electron Densities ◽  
Structure Solution ◽  
Aperiodic Crystals

EDMAis a computer program for topological analysis of discrete electron densities according to Bader's theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins.EDMAcan also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation ofab initioelectron densities obtained in the process of structure solution. A particular feature ofEDMAis that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions.EDMAfirst generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications ofEDMAto model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4or better.

Topological analysis of experimental electron densities

1999 ◽  
Vol 32 (2) ◽  
pp. 210-217 ◽  
Author(s):  
Mohamed Souhassou ◽  
Robert H. Blessing
Keyword(s):  
Amino Acid ◽  
Crystal Structures ◽  
Electron Density ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Electron Densities ◽  
Acid Crystal ◽  
Density Distributions ◽  
Amino Acid Crystal ◽  
Experimental Electron Density

Practical computing algorithms are described for analysing the topology of experimental electron density distributions represented as either three-dimensional grid densities or multipolar pseudoatom superpositions. The algorithms are implemented in the programNEWPROP, results from which are illustrated with applications to twoN-acetyl,C-methylamide blocked amino acid crystal structures.

A topological analysis of the interion interactions of tetraphenylphosphonium squarate

2006 ◽  
Vol 84 (5) ◽  
pp. 804-811 ◽  
Author(s):  
David Wolstenholme ◽  
Manuel AS Aquino ◽  
T Stanley Cameron ◽  
Joseph D Ferrara ◽  
Katherine N Robertson
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Electron Density ◽  
Intermolecular Interactions ◽  
Critical Points ◽  
Topological Analysis ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
Multipole Refinement ◽  
Diverse Interactions

The tetraphenylphosphonium squarate salt crystallizes with a number of diverse interactions, which all have the potential to be classified as hydrogen bonds. The squarate anions are found as dimers linked by O-H···O interactions. The multipole refinement of the tetraphenylphosphonium squarate was performed using the Hansen–Coppens model followed by topological analysis of its intermolecular interactions. A total of 28 interactions were found among the symmetry related molecules, which include a number of C-H···Cπ, C-H···O, and C-H···H-C interactions, along with the O-H···O interaction. With the criteria for hydrogen bonding proposed by Popelier and Koch, it is possible to determine which of these interactions are hydrogen bonds and which are van der Waals interactions. Both linear and exponentially dependent correlations can be seen for the properties of the bond critical points involving the intermolecular interactions that fulfill these criteria. All this leads to a better understanding of the role that hydrogen bonds play in the formation of small organic compounds.Key words: electron density, multiple refinement, hydrogen bonds.

About difference electron densities and their properties

2017 ◽  
Vol 73 (6) ◽  
pp. 460-473 ◽  
Author(s):  
Maria Cristina Burla ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Crystal Structure ◽  
Electron Density ◽  
Probability Distribution Function ◽  
Strong Support ◽  
Joint Probability ◽  
The Other ◽  
Joint Probability Distribution ◽  
Electron Densities ◽  
Structure Solution ◽  
Joint Probability Distribution Function

Difference electron densities do not play a central role in modern phase refinement approaches, essentially because of the explosive success of the EDM (electron-density modification) techniques, mainly based on observed electron-density syntheses. Difference densities however have been recently rediscovered in connection with theVLD(Vive la Difference) approach, because they are a strong support for strengthening EDM approaches and forab initiocrystal structure solution. In this paper the properties of the most documented difference electron densities, here denoted asF−Fp,mF−FpandmF−DFpsyntheses, are studied. In addition, a fourth new difference synthesis, here denoted as {\overline F_q} synthesis, is proposed. It comes from the study of the same joint probability distribution function from which theVLDapproach arose. The properties of the {\overline F_q} syntheses are studied and compared with those of the other three syntheses. The results suggest that the {\overline F_q} difference may be a useful tool for making modern phase refinement procedures more efficient.

scholarly journals How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

2017 ◽  
Vol 50 (4) ◽  
pp. 1200-1207 ◽  
Author(s):  
Jason Porta ◽  
Jeff Lovelace ◽  
Gloria E. O. Borgstahl
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Real Life ◽  
Group Symmetry ◽  
Protein Crystal ◽  
3D Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Aperiodic Crystals ◽  
Periodic Crystal

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and requireqvectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C ofInternational Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal.

FraGen: a computer program for real-space structure solution of extended inorganic frameworks

2012 ◽  
Vol 45 (4) ◽  
pp. 855-861 ◽  
Author(s):  
Yi Li ◽  
Jihong Yu ◽  
Ruren Xu
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
Optimization Method ◽  
Real Space ◽  
Space Structure ◽  
Parallel Tempering ◽  
Global Optimization Method ◽  
Cell Parameters ◽  
Density Maps ◽  
Structure Solution

TheFraGen(framework generator) program has been developed for real-space structure solution. It has been designed especially for the generation of extended inorganic frameworks in a given unit cell.FraGenis based on the parallel tempering global optimization method. Various restraints can be introduced intoFraGen, such as restraints on bonding geometry, relative reflection intensities and three-dimensional density maps. The basic inputs forFraGenare the space group and cell parameters. The number of unique atoms is not a necessary input, since it can be estimated from certain constraints.FraGenalso has the ability to exit unpromising simulation cycles to save computation time for promising ones. Program features, methods and three examples are demonstrated. TheFraGenprogram for the Windows platform is available from the authors upon request.

scholarly journals Numerical computation of critical properties and atomic basins from three-dimensional grid electron densities

2003 ◽  
Vol 36 (1) ◽  
pp. 65-73 ◽  
Author(s):  
C. Katan ◽  
P. Rabiller ◽  
C. Lecomte ◽  
M. Guezo ◽  
V. Oison ◽  
...  
Keyword(s):  
Hydrogen Bonds ◽  
Software Package ◽  
Topological Analysis ◽  
Hessian Matrix ◽  
Three Dimensional ◽  
Chemical Bonds ◽  
Critical Properties ◽  
Electron Densities ◽  
Atomic Properties ◽  
Intermolecular Contacts

InteGriTyis a software package that performs topological analysis following the AIM (atoms in molecules) approach on electron densities given on three-dimensional grids. Tricubic interpolation is used to obtain the density, its gradient and the Hessian matrix at any required position. Critical points and integrated atomic properties have been derived from theoretical densities calculated for the compounds NaCl and TTF–2,5Cl2BQ (tetrathiafulvalene–2,5-dichlorobenzoquinone), thus covering the different kinds of chemical bonds: ionic, covalent, hydrogen bonds and other intermolecular contacts.

Combination of methods used in the structure solution of pyruvate:ferredoxin oxidoreductase from two crystal forms

1999 ◽  
Vol 55 (9) ◽  
pp. 1546-1554 ◽  
Author(s):  
E. Chabrière ◽  
A. Volbeda ◽  
J. C. Fontecilla-Camps ◽  
M. Roth ◽  
M.-H. Charon
Keyword(s):  
Electron Density ◽  
Real Space ◽  
Molecular Replacement ◽  
Crystal Forms ◽  
Isomorphous Replacement ◽  
Resolution Electron ◽  
Structure Solution ◽  
Phase Extension ◽  
Pyruvate:Ferredoxin Oxidoreductase ◽  
Combination Of Methods

The structure of the homodimeric 267 kDa pyruvate:ferredoxin oxidoreductase (PFOR) of Desulfovibrio africanus was solved with data from two crystals forms, both containing two monomers per asymmetric unit. Phases were obtained from multiwavelength anomalous dispersion (MAD), solvent flattening (SF), molecular replacement (MR) using a 5 Å resolution electron-density search model, multiple isomorphous replacement (MIR) and, finally, electron-density averaging (DA) procedures. It is shown how the combination of all these techniques was used to overcome problems arising from incompleteness of MAD data and weak phasing power of MIR data. A real-space refinement (RSR) procedure is described to improve MR solutions and obtain very accurate protein envelopes and non-crystallographic symmetry (NCS) transformations from 5 Å resolution phase information. These were crucial for the phase extension to high resolution by DA methods.

scholarly journals Dealing with Aperiodic Protein Crystal Structures

2014 ◽  
Vol 70 (a1) ◽  
pp. C778-C778
Author(s):  
Gloria Borgstahl
Keyword(s):  
Three Dimensional ◽  
Protein Crystal ◽  
Periodic Lattice ◽  
X Rays ◽  
Future Directions ◽  
Space Group ◽  
3D Space ◽  
Structure Solution ◽  
Quasi Crystals ◽  
Aperiodic Crystals

Protein crystals can be aperiodic. They will diffract X-rays, and are therefore a crystal, but their diffraction is not periodic. This means that their diffraction pattern cannot be simply be indexed by a typical three-dimensional unit cell and space group. Aperiodic crystals include "quasi-crystals" as well as "modulated" crystals. In the latter case, the modulation can be positional or occupational and these modulations can be incommensurate with the normal periodic lattice [1]. An overview of aperiodic protein crystal diffraction will be presented with examples. The discussion will then focus on the characteristics of incommensurately modulated crystals followed by a more detailed discussion of how to solve these crystals. The following details of structure solution will be presented: (1) data collection perils; (2) specialized diffraction data processing in (3+1)D space using a q-vector [2]; (3) how to get an approximation of the structure in 3D space; (4) the assignment of the (3+1)D space group; and the ultimate (5) crystallographic refinement in superspace[3]. Future directions and needs will be discussed.

Determination of the Relative Precision of Atoms in a Macromolecular Structure

1998 ◽  
Vol 54 (3) ◽  
pp. 391-399 ◽  
Author(s):  
Genfa Zhou ◽  
Junfeng Wang ◽  
Eric Blanc ◽  
Michael S. Chapman
Keyword(s):  
Electron Density ◽  
Grid Point ◽  
Real Space ◽  
Positional Error ◽  
Electron Densities ◽  
Isomorphous Replacement ◽  
Temperature Factors ◽  
Improved Methods

Several real-space indices and temperature factors are compared with respect to their correlation with atomic positional error and their ability to indicate atoms and residues with the worst of subtle errors. The best index, r ED, is a correlation coefficient between model and map electron densities, similar to one proposed earlier, but incorporating two improvements. Firstly, resolution is accounted for explicitly by calculating the model electron density by Fourier transformation of resolution-truncated scattering factors. Secondly, the deviation between model and map electron densities is assigned to neighboring atoms according to their contribution to the electron density of each grid point. With maps of various qualities, r ED is the single index with best correlation to atomic error with grouped or individual atoms, and it is the most reliable indicator of poor residues. With poorer omit maps, imprecision of individual atoms is best diagnosed by a combination of low r ED or high B factor. With the improved methods, 60–70% of the least precise atoms can detected in a fully refined structure. Similarly, 40–80% of the least precise atoms of an unrefined model can be detected by comparison with an isomorphous replacement map. This is useful in assessing and improving the quality of a model, but not sufficient to confidently validate all atoms of a structure at sub-atomic resolution.

Envelope skeletonization as a means to determine monomer masks and non-crystallographic symmetry relationships: application in the solution of the structure of fibrinogen fragment D

1999 ◽  
Vol 55 (2) ◽  
pp. 458-463 ◽  
Author(s):  
Glen Spraggon
Keyword(s):  
Three Dimensional ◽  
Real Space ◽  
Reciprocal Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Translation Component ◽  
Rotation Function ◽  
Molecular Envelope

An algorithm is described which utilizes the solvent mask generated by the solvent-flattening technique to calculate a monomer molecular envelope. In the case where non-crystallographic symmetry (NCS) is present in the crystal and self-rotation angles are known from a self-rotation function, the resultant monomer envelopes can be used to search for the translation component of the NCS element by a three-dimensional search in real space. In the absence of self-rotation angles, the monomer envelope may be used to derive the NCS operators by reciprocal-space techniques. Thus, an automatic procedure for averaging directly from the solvent-flattening stage can be implemented. The procedure was instrumental in the structure solution of fibrinogen fragment D, which is presented as an example.

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