Mask-Based Approach in Phasing and Restoring of Single-Particle Diffraction Data

The development of experimental techniques, in particular the emergence of the X-ray free-electron lasers, allows one to register the scattering from an isolated particle and, thereby, opens a door to the study of a fine three-dimensional structure of non-crystalline biological objects by X-ray diffraction methods. The possibility to measure non-Bragg reflections makes experimental data mutually dependent and essentially simplifies the structure solution. The sampling of experimental scattering data to a sufficiently fine grid makes the structure determination equivalent to phasing of structure factor magnitudes for a 'virtual' crystal with extremely large solvent content. This makes density modification phasing methods especially powerful supposing the object envelope is known. At the same time, such methods may be sensitive to the accuracy of the predefined envelope and completeness of experimental data and may suffer from non-uniqueness of the solution of the phase problem. The mask-based approach is a preliminary phasing method that performs random search for connected object envelopes possessing of the structure factor magnitudes close to the values observed in X-ray experiment. The alignment and averaging of the phase sets corresponding to selected putative envelopes produce an approximate solution of the phase problem. Beside the estimation of unknown phase values this approach allows one to estimate the values of structure factor magnitudes lost in the experiment, e.g. those corresponding to beam-stop shade zone or to oversaturated reflections.

Download Full-text

The biological crystallography without crystals

Математическая биология и биоинформатика ◽

10.17537/2017.12.55 ◽

2017 ◽

Vol 12 (1) ◽

pp. 55-72 ◽

Cited By ~ 3

Author(s):

В.Ю. Лунин ◽

V.Y. Lunin

Keyword(s):

Three Dimensional ◽

Scattering Data ◽

Dimensional Structure ◽

Biological Macromolecules ◽

X Ray Diffraction ◽

X Ray ◽

Biological Objects ◽

Standard Problem ◽

Problems And Solutions

The main obstacle to the determination of the atomic structure of a biological macromolecule by X-ray structural analysis is the need to obtain a crystal of the object under study. This need is due to the complexity of the experimental registration of scattering from a separate molecule. However, it is not always possible to get crystals of biological objects. The development of experimental techniques, in particular the emergence of the X-ray free-electron lasers, allows to approach the practical solution of the problem of registration of the scattering from an isolated particle and thereby to obtain information about the three-dimensional structure of non-crystalline biological objects by X-ray diffraction methods. Sampling of experimental scattering data makes the task of the structure determination of a single particle equivalent to the standard problem of biological crystallography, which allows to extend the biological crystallography techniques to the study of isolated biological particles (individual cells, organelles, molecular machines and, in the future, biological macromolecules). This article is devoted to the state of the art in this area, problems and solutions.

Download Full-text

Elucidation of zeolite microstructure by synchrotron X-ray diffuse scattering

Journal of Applied Crystallography ◽

10.1107/s0021889803028048 ◽

2004 ◽

Vol 37 (2) ◽

pp. 187-192 ◽

Cited By ~ 18

Author(s):

B. J. Campbell ◽

T. R. Welberry ◽

R. W. Broach ◽

Hawoong Hong ◽

A. K. Cheetham

Keyword(s):

Diffuse Scattering ◽

Three Dimensional ◽

Scattering Data ◽

Dimensional Structure ◽

Columnar Defect ◽

Mosaic Pattern ◽

X Ray ◽

Framework Materials ◽

Columnar Defects ◽

Ccd Detector

Single-crystal diffuse scattering measurements can now rapidly probe the three-dimensional structure of subtle defects in microporous framework materials. Diffuse scattering data from natural mordenite crystals are shown to exhibit a complex distribution of weak features which have been mapped out using a synchrotron X-ray source and a CCD detector. Comparison with computer-simulated diffuse scattering patterns yields a detailed three-dimensional columnar defect structure and reveals that roughly one third of the mordenite's columnar defects cooperate to form a block-mosaic pattern of {110} stacking faults.

Download Full-text

Geometric Constraints for the Phase Problem in X-Ray Crystallography

10.29007/p2pj ◽

2018 ◽

Author(s):

Corinna Heldt ◽

Alexander Bockmayr

Keyword(s):

Electron Density Distribution ◽

Fourier Coefficients ◽

Three Dimensional ◽

Geometric Constraints ◽

Dimensional Structure ◽

Biological Macromolecules ◽

Phase Problem ◽

X Ray ◽

X Ray Crystallography

X-ray crystallography is one of the main methods to establish the three-dimensional structure of biological macromolecules. In an X-ray experiment, one can measure only the magnitudes of the complex Fourier coefficients of the electron density distribution under study, but not their phases. The problem of recovering the lost phases is called the phase problem. Building on earlier work by Lunin/Urzhumtsev/Bockmayr, we extend their constraint-based approach to the phase problem by adding further 0-1 linear programming constraints. These constraints describe geometric properties of proteins and increase the quality of the solutions. The approach has been implemented using SCIP and CPLEX, first computational results are presented here.

Download Full-text

Revealing gross three-dimensional structure in the SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100127712 ◽

1987 ◽

Vol 45 ◽

pp. 656-657

Author(s):

Sterling P. Newberry

Keyword(s):

Freeze Drying ◽

Three Dimensional ◽

Dimensional Structure ◽

Small Object ◽

Final Solution ◽

Dimensional Representation ◽

X Ray ◽

Three Dimensional Representation ◽

Freeze Dried ◽

Critical Point Drying

The beautiful three dimensional representation of small object surfaces by the SEM leads one to search for ways to open up the sample and look inside. Could this be the answer to a better microscopy for gross biological 3-D structure? We know from X-Ray microscope images that Freeze Drying and Critical Point Drying give promise of adequately preserving gross structure. Can we slice such preparations open for SEM inspection? In general these preparations crush more readily than they slice. Russell and Dagihlian got around the problem by “deembedding” a section before imaging. This some what defeats the advantages of direct dry preparation, thus we are reluctant to accept it as the final solution to our problem. Alternatively, consider fig 1 wherein a freeze dried onion root has a window cut in its surface by a micromanipulator during observation in the SEM.

Download Full-text

The three-dimensional structure of interleukin-1β

Biochemical Society Transactions ◽

10.1042/bst0160949 ◽

1988 ◽

Vol 16 (6) ◽

pp. 949-953 ◽

Cited By ~ 5

Author(s):

JOHN P. PRIESTLE ◽

HANS-PETER SCHÄR ◽

MARKUS G. GRÜTTER

Keyword(s):

Polypeptide Chain ◽

Three Dimensional ◽

Interleukin 1Β ◽

Dimensional Structure ◽

X Ray ◽

Three Dimensional Structure ◽

R Factor ◽

The Core ◽

Internal Sequence ◽

Network Of Hydrogen Bonds

Summary The three-dimensional structure of human recombinant interleukin-1β has been determined at 0.24 nm resolution by X-ray crystallographic techniques. The partially refined model has a crystallographic R-factor of just under 19%. The structure is composed of 12 β-strands forming a complex network of hydrogen bonds. The core of the structure can best be described as a tetrahedron whose edges are each formed by two antiparallel β-strands. The interior of this structure is filled with hydrophobic side-chains. There is a 3-fold repeat in the folding of the polypeptide chain. Although this folding pattern suggests gene triplication, no significant internal sequence homology between topologically corresponding residues exists. The folding topology of interleukin-1β is very similar to that described by A. D. McLachlan [(1979) J. Mol. Biol. 133, 557–563] for soybean trypsin inhibitor.

Download Full-text

Crystallization and preliminary X-ray analysis of the major peanut allergen Ara h 1 core region

Acta Crystallographica Section F Structural Biology and Crystallization Communications ◽

10.1107/s1744309110029040 ◽

2010 ◽

Vol 66 (9) ◽

pp. 1071-1073 ◽

Cited By ~ 9

Author(s):

Cerrone Cabanos ◽

Hiroyuki Urabe ◽

Taro Masuda ◽

Mary Rose Tandang-Silvas ◽

Shigeru Utsumi ◽

...

Keyword(s):

Sodium Citrate ◽

Three Dimensional ◽

Core Region ◽

Dimensional Structure ◽

Monoclinic Space Group ◽

X Ray ◽

Cell Parameters ◽

Peg 400 ◽

Ara H 1 ◽

Peanut Allergens

Peanuts contain some of the most potent food allergens known to date. Ara h 1 is one of the three major peanut allergens. As a first step towards three-dimensional structure elucidation, recombinant Ara h 1 core region was cloned, expressed inEscherichia coliand purified to homogeneity. Crystals were obtained using 0.1 Msodium citrate pH 5.6, 0.1 MNaCl, 15% PEG 400 as precipitant. The crystals diffracted to 2.25 Å resolution using synchrotron radiation and belonged to the monoclinic space groupC2, with unit-cell parametersa= 156.521,b= 88.991,c= 158.971 Å, β = 107.144°. Data were collected at the BL-38B1 station of SPring-8 (Hyogo, Japan).

Download Full-text

Determination of the Three-dimensional Structure of Dislocations by Synchrotron White X-ray Topography Combined with a Topo-tomographic Technique

Materia Japan ◽

10.2320/materia.46.823 ◽

2007 ◽

Vol 46 (12) ◽

pp. 823-823

Author(s):

Seiji Kawado ◽

Toshinori Taishi ◽

Satoshi Iida ◽

Yoshifumi Suzuki ◽

Yoshinori Chikaura ◽

...

Keyword(s):

Three Dimensional ◽

Dimensional Structure ◽

X Ray ◽

Three Dimensional Structure ◽

Tomographic Technique

Download Full-text

The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data. II. The Dependence of the Accuracy of the Solution on the Sampling Step of Experimental Data

Математическая биология и биоинформатика ◽

10.17537/2015.10.508 ◽

2015 ◽

Vol 10 (2) ◽

pp. 508-525 ◽

Cited By ~ 3

Author(s):

Н.Л. Лунина ◽

N.L. Lunina

Keyword(s):

Experimental Data ◽

Particle Image ◽

Expected Improvement ◽

Problem Solution ◽

Phase Problem ◽

X Ray Diffraction ◽

Sampling Step ◽

X Ray ◽

X Ray Crystallography ◽

Grid Points

Advances in the methodology of the X-ray diffraction experiments leads to a possibility to register the rays scattered by large isolated biological particles (viruses and individual cells) but not only by crystalline samples. The experiment with an isolated particle provides researchers with the intensities of the scattered rays for the continuous spectrum of scattering vectors. Such experiment gives much more experimental data than an experiment with a crystalline sample where the information is limited to a set of Bragg reflections. This opens up additional opportunities in solving underlying problem of X-ray crystallography, namely, calculating phase values for the scattered waves needed to restore the structure of the object under study. In practice, the original continuous diffraction pattern is sampled, reduced to the values at grid points in the space of scattering vectors (in the reciprocal space). The sampling step determines the amount of the information involved in solving the phase problem and the complexity of the necessary calculations. In this paper, we investigate the effect of the sampling step on the accuracy of the phase problem solution obtained by the method proposed earlier by the authors. It is shown that an expected improvement of the accuracy of the solution with the reducing the sampling step continues even after crossing the Nyquist limit defined as the inverse of the double size of the object under study.

Download Full-text