scholarly journals High-order analytic translation matrix elements for real-space six-dimensional polar Fourier correlations

2005 ◽  
Vol 38 (5) ◽  
pp. 808-818 ◽  
Author(s):  
David W. Ritchie
Keyword(s):  
Spherical Harmonic ◽  
Three Dimensional ◽  
Data Bank ◽  
Real Space ◽  
High Order ◽  
Molecular Replacement ◽  
Density Maps ◽  
Analytic Expressions ◽  
Docking Proteins ◽  
Structural Homologues

Analytic expressions are presented for calculating translations of high-order three-dimensional expansions of orthonormal real spherical harmonic and Gaussian-type or exponential-type radial basis functions. When used with real spherical harmonic rotation matrices, the resulting translation matrices provide a fully analytic method of calculating six-dimensional real-space rotational–translational correlations. The correlation algorithm is demonstrated by using an exhaustive search to superpose the steric density functions of a pair of similar globular proteins in a matter of seconds on a contemporary personal computer. It is proposed that the techniques described could be used to accelerate the calculation ofe.g.real-space electron density correlations in molecular replacement, docking proteins into electron microscopy density maps, and searching the Protein Data Bank for structural homologues.

scholarly journals Crystallographic models of SARS-CoV-2 3CLpro: in-depth assessment of structure quality and validation

IUCrJ ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 238-256
Author(s):  
Mariusz Jaskolski ◽  
Zbigniew Dauter ◽  
Ivan G. Shabalin ◽  
Miroslaw Gilski ◽  
Dariusz Brzezinski ◽  
...  
Keyword(s):  
Rapid Determination ◽  
Data Bank ◽  
Molecular Replacement ◽  
Structure Quality ◽  
Space Groups ◽  
Important Target ◽  
Density Maps ◽  
Main Protease ◽  
Experimental Approaches

The appearance at the end of 2019 of the new SARS-CoV-2 coronavirus led to an unprecedented response by the structural biology community, resulting in the rapid determination of many hundreds of structures of proteins encoded by the virus. As part of an effort to analyze and, if necessary, remediate these structures as deposited in the Protein Data Bank (PDB), this work presents a detailed analysis of 81 crystal structures of the main protease 3CLpro, an important target for the design of drugs against COVID-19. The structures of the unliganded enzyme and its complexes with a number of inhibitors were determined by multiple research groups using different experimental approaches and conditions; the resulting structures span 13 different polymorphs representing seven space groups. The structures of the enzyme itself, all determined by molecular replacement, are highly similar, with the exception of one polymorph with a different inter-domain orientation. However, a number of complexes with bound inhibitors were found to pose significant problems. Some of these could be traced to faulty definitions of geometrical restraints for ligands and to the general problem of a lack of such information in the PDB depositions. Several problems with ligand definition in the PDB itself were also noted. In several cases extensive corrections to the models were necessary to adhere to the evidence of the electron-density maps. Taken together, this analysis of a large number of structures of a single, medically important protein, all determined within less than a year using modern experimental tools, should be useful in future studies of other systems of high interest to the biomedical community.

SIR2011: a new package for crystal structure determination and refinement

2012 ◽  
Vol 45 (2) ◽  
pp. 357-361 ◽  
Author(s):  
Maria Cristina Burla ◽  
Rocco Caliandro ◽  
Mercedes Camalli ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Diffraction Data ◽  
Protein Structures ◽  
Three Dimensional ◽  
Molecular Geometry ◽  
Electron Diffraction Data ◽  
Medium Size ◽  
Molecular Replacement ◽  
Density Maps ◽  
Difficult Cases

SIR2011, the successor ofSIR2004, is the latest program of theSIRsuite. It can solveab initiocrystal structures of small- and medium-size molecules, as well as protein structures, using X-ray or electron diffraction data. With respect to the predecessor the program has several new abilities:e.g.a new phasing method (VLD) has been implemented, it is able to exploit prior knowledge of the molecular geometryviasimulated annealing techniques, it can use molecular replacement methods for solving proteins, it includes new tools like free lunch and new approaches for electron diffraction data, and it visualizes three-dimensional electron density maps. The graphical interface has been further improved and allows the straightforward use of the program even in difficult cases.

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.

Crystal structure determination and refinementviaSIR2014

2015 ◽  
Vol 48 (1) ◽  
pp. 306-309 ◽  
Author(s):  
Maria Cristina Burla ◽  
Rocco Caliandro ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Corrado Cuocci ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Ab Initio ◽  
Structure Refinement ◽  
Three Dimensional ◽  
Direct Methods ◽  
Molecular Replacement ◽  
Dimensional Electron ◽  
Large Structures ◽  
Density Maps ◽  
Structure Solution

SIR2014is the latest program of theSIRsuite for crystal structure solution of small, medium and large structures. A variety of phasing algorithms have been implemented, bothab initio(standard or modern direct methods, Patterson techniques,Vive la Différence) and non-ab initio(simulated annealing, molecular replacement). The program contains tools for crystal structure refinement and for the study of three-dimensional electron-density mapsviasuitable viewers.

scholarly journals Rapid automated superposition of shapes and macromolecular models using spherical harmonics

2016 ◽  
Vol 49 (3) ◽  
pp. 953-960 ◽  
Author(s):  
Petr V. Konarev ◽  
Maxim V. Petoukhov ◽  
Dmitri I. Svergun
Keyword(s):  
Spherical Harmonics ◽  
Three Dimensional ◽  
Real Space ◽  
Low Resolution ◽  
Three Dimensional Objects ◽  
Heterogeneous Objects ◽  
Density Maps ◽  
Order Of Magnitude ◽  
Protein Nucleic Acid ◽  
Multi Phase

A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented (SUPALM). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models (e.g.of protein–nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented inSUPCOMBby Kozin & Svergun [J. Appl. Cryst.(2001),34, 33–41]. The utility of the new method is demonstrated in a number of test cases and compared with the results ofSUPCOMB. The spherical harmonics algorithm is best suited for low-resolution shape models,e.g. those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.

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.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

Sign in / Sign up

Export Citation Format

Share Document