Particle shape reconstruction by small-angle scattering: Integration of group theory and maximum entropy to multipole expansion method

1998 ◽  
Vol 109 (23) ◽  
pp. 10148-10158 ◽  
Author(s):  
Francesco Spinozzi ◽  
Flavio Carsughi ◽  
Paolo Mariani
Keyword(s):  
Group Theory ◽  
Maximum Entropy ◽  
Small Angle ◽  
Particle Shape ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Shape Reconstruction ◽  
Small Angle Scattering ◽  
Angle Scattering ◽  
Multipole Expansion Method

Rapid and accurate calculation of small-angle scattering profiles using the golden ratio

2013 ◽  
Vol 46 (4) ◽  
pp. 1171-1177 ◽  
Author(s):  
Max C. Watson ◽  
Joseph E. Curtis
Keyword(s):  
Small Angle ◽  
Golden Ratio ◽  
Expansion Method ◽  
Multipole Expansion ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Approximation Technique ◽  
Scattering Intensity ◽  
Angle Scattering ◽  
Multipole Expansion Method

Calculating the scattering intensity of anN-atom system is a numerically exhaustingO(N2) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensityI(q) at a given wavevectorq, the rotationally averaged intensityI(q) is computed by evaluatingI(q) in several scattering directions. The orientations of theqvectors are taken from a quasi-uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub-linearly inNwhen the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small-angle scattering data.

Information retrieval from X-ray small-angle scattering with polychromatic (`white') synchrotron radiation

1983 ◽  
Vol 16 (1) ◽  
pp. 42-46 ◽  
Author(s):  
O. Glatter ◽  
P. Laggner
Keyword(s):  
Synchrotron Radiation ◽  
Small Angle ◽  
Particle Shape ◽  
Structural Information ◽  
Small Angle Scattering ◽  
Radius Of Gyration ◽  
X Ray ◽  
Angle Scattering ◽  
Slit Length ◽  
Hinge Bending

The possibilities of obtaining structural information from X-ray small-angle scattering experiments with `white' polychromatic synchrotron radiation using line collimation are investigated by numerical simulation. Theoretical scattering curves of geometrical models were smeared with the appropriate wavelength distributions and slit-length functions, afflicted by statistical noise, and then evaluated by identical methods as normally used for experimental data, as described previously [program ITP; Glatter (1977). J. Appl. Cryst. 10, 415–421]. It is shown that even for a wavelength distribution of 50% half width, the information content is not limited to the parameters derived from the central part of the scattering curves, i.e. the radius of gyration and the zero-angle intensity, but also allows qualitative information on particle shape via the distance distribution function p(r). By a `hinge-bending model' consisting of two cylinders linked together at different angles it is demonstrated that changes in the radius of gyration amounting to less than 5% can be detected and quantified, and the qualitative changes in particle shape be reproduced.

scholarly journals DAMMIF, a program for rapidab-initioshape determination in small-angle scattering

2009 ◽  
Vol 42 (2) ◽  
pp. 342-346 ◽  
Author(s):  
Daniel Franke ◽  
Dmitri I. Svergun
Keyword(s):  
Small Angle ◽  
Particle Shape ◽  
Small Angle Scattering ◽  
Binary Form ◽  
Scattering Data ◽  
Search Volume ◽  
Angle Scattering ◽  
Shape Determination ◽  
Equivalent Conditions

DAMMIF, a revised implementation of theab-initioshape-determination programDAMMINfor small-angle scattering data, is presented. The program was fully rewritten, and its algorithm was optimized for speed of execution and modified to avoid limitations due to the finite search volume. Symmetry and anisometry constraints can be imposed on the particle shape, similar toDAMMIN. In equivalent conditions,DAMMIFis 25–40 times faster thanDAMMINon a single CPU. The possibility to utilize multiple CPUs is added toDAMMIF. The application is available in binary form for major platforms.

scholarly journals Neither Sphere nor Cube - Analyzing the Particle Shape Using Small-Angle Scattering and the Superball Model

2021 ◽  
Author(s):  
Dominique Dresen ◽  
Asmaa Qdemat ◽  
Dominika Zákutná ◽  
Erik Wetterskog ◽  
Emmanuel Kentzinger ◽  
...  
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Particle Shape ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Monodisperse Nanoparticles ◽  
Statistical Relevance ◽  
Angle Scattering ◽  
Microscopy Data ◽  
User Friendly

<div>Accurate characterization of the nanocrystal shape with high statistical relevance is essential for exploiting the strongly shape-dependent properties of cuboidal nanoparticles towards applications. <br></div><div>This work presents the development of a new small-angle scattering form factor based on the superball geometry. The superball quantifies the characteristic rounding of corners and edges of cuboidalnanoparticles with a single parameter. Applied to small-angle scattering data of sufficiently monodisperse nanoparticles, the superball form factor enables differentiation between the effects of extended<br></div>particle size distribution and irregular particle shape. The quantitative application of the superball form factor is validated against microscopy data for a series of monodisperse nanoparticles and implemented into the user-friendly, open source software Sasview.

Neither Sphere nor Cube—Analyzing the Particle Shape Using Small-Angle Scattering and the Superball Model

2021 ◽  
Author(s):  
Dominique Dresen ◽  
Asma Qdemat ◽  
Seda Ulusoy ◽  
Flore Mees ◽  
Dominika Zákutná ◽  
...  
Keyword(s):  
Small Angle ◽  
Particle Shape ◽  
Small Angle Scattering ◽  
Angle Scattering

scholarly journals Resolution ofab initioshapes determined from small-angle scattering

IUCrJ ◽  
2016 ◽  
Vol 3 (6) ◽  
pp. 440-447 ◽  
Author(s):  
Anne T. Tuukkanen ◽  
Gerard J. Kleywegt ◽  
Dmitri I. Svergun
Keyword(s):  
Ab Initio ◽  
Small Angle ◽  
Three Dimensional ◽  
Simulated Data ◽  
Shape Reconstruction ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Structural Method ◽  
X Rays ◽  
Angle Scattering

Spatial resolution is an important characteristic of structural models, and the authors of structures determined by X-ray crystallography or electron cryo-microscopy always provide the resolution upon publication and deposition. Small-angle scattering of X-rays or neutrons (SAS) has recently become a mainstream structural method providing the overall three-dimensional structures of proteins, nucleic acids and complexes in solution. However, no quantitative resolution measure is available for SAS-derived models, which significantly hampers their validation and further use. Here, a method is derived for resolution assessment forab initioshape reconstruction from scattering data. The inherent variability of theab initioshapes is utilized and it is demonstrated how their average Fourier shell correlation function is related to the model resolution. The method is validated against simulated data for proteins with known high-resolution structures and its efficiency is demonstrated in applications to experimental data. It is proposed that henceforth the resolution be reported in publications and depositions ofab initioSAS models.

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