Scatter: software for the analysis of nano- and mesoscale small-angle scattering

2010 ◽  
Vol 43 (3) ◽  
pp. 639-646 ◽  
Author(s):  
S. Förster ◽  
L. Apostol ◽  
W. Bras
Keyword(s):  
Small Angle ◽  
Calculated Data ◽  
Form Factors ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Mathematical Treatment ◽  
Mesoscale Structures ◽  
Structure Factors ◽  
Angle Scattering

Scatteris a new software for analysis, modeling and fitting of one- and two-dimensional small-angle scattering data of non-ordered, partially ordered or fully ordered nano- and mesoscale structures. The calculations are based on closed analytical expressions for the scattering intensity, enabling efficient evaluation of form factors and structure factors. The software allows one to sequentially fit large series of scattering curves and scattering patterns automatically. It provides further tools for data loading, beam centering, calibration, zooming, binning, lattice identification, calculation of density profiles and size distributions, and visualization of real-space structures. Presentations of experimental and calculated data can be saved as is for presentations or exported for further graphical or mathematical treatment.

scholarly journals Analysis of small-angle scattering data using model fitting and Bayesian regularization

2018 ◽  
Vol 51 (4) ◽  
pp. 1151-1161 ◽  
Author(s):  
Andreas Haahr Larsen ◽  
Lise Arleth ◽  
Steen Hansen
Keyword(s):  
Prior Knowledge ◽  
Small Angle ◽  
Regularization Method ◽  
Prior Information ◽  
Form Factors ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Parameters ◽  
Bayesian Regularization ◽  
Angle Scattering

The structure of macromolecules can be studied by small-angle scattering (SAS), but as this is an ill-posed problem, prior knowledge about the sample must be included in the analysis. Regularization methods are used for this purpose, as already implemented in indirect Fourier transformation and bead-modeling-based analysis of SAS data, but not yet in the analysis of SAS data with analytical form factors. To fill this gap, a Bayesian regularization method was implemented, where the prior information was quantified as probability distributions for the model parameters and included via a functional S. The quantity Q = χ2 + αS was then minimized and the value of the regularization parameter α determined by probability maximization. The method was tested on small-angle X-ray scattering data from a sample of nanodiscs and a sample of micelles. The parameters refined with the Bayesian regularization method were closer to the prior values as compared with conventional χ2 minimization. Moreover, the errors on the refined parameters were generally smaller, owing to the inclusion of prior information. The Bayesian method stabilized the refined values of the fitted model upon addition of noise and can thus be used to retrieve information from data with low signal-to-noise ratio without risk of overfitting. Finally, the method provides a measure for the information content in data, N g, which represents the effective number of retrievable parameters, taking into account the imposed prior knowledge as well as the noise level in data.

Assessment of structure factors for analysis of small-angle scattering data from desired or undesired aggregates

2020 ◽  
Vol 53 (4) ◽  
pp. 991-1005
Author(s):  
Andreas Haahr Larsen ◽  
Jan Skov Pedersen ◽  
Lise Arleth
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Protein Structures ◽  
Simulated Data ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Spherical Cluster ◽  
Structure Factors ◽  
Angle Scattering ◽  
Aggregation Processes

Aggregation processes are central features of many systems ranging from colloids and polymers to inorganic nanoparticles and biological systems. Some aggregated structures are controlled and desirable, e.g. in the design of size-controlled clustered nanoparticles or some protein-based drugs. In other cases, the aggregates are undesirable, e.g. protein aggregation involved in neurodegenerative diseases or in vitro studies of single protein structures. In either case, experimental and analytical tools are needed to cast light on the aggregation processes. Aggregation processes can be studied with small-angle scattering, but analytical descriptions of the aggregates are needed for detailed structural analysis. This paper presents a list of useful small-angle scattering structure factors, including a novel structure factor for a spherical cluster with local correlations between the constituent particles. Several of the structure factors were renormalized to get correct limit values in both the high-q and low-q limit, where q is the modulus of the scattering vector. The structure factors were critically evaluated against simulated data. Structure factors describing fractal aggregates provided approximate descriptions of the simulated data for all tested structures, from linear to globular aggregates. The addition of a correlation hole for the constituent particles in the fractal structure factors significantly improved the fits in all cases. Linear aggregates were best described by a linear structure factor and globular aggregates by the newly derived spherical cluster structure factor. As a central point, it is shown that the structure factors could be used to take aggregation contributions into account for samples of monomeric protein containing a minor fraction of aggregated protein. After applying structure factors in the analysis, the correct structure and oligomeric state of the protein were determined. Thus, by careful use of the presented structure factors, important structural information can be retrieved from small-angle scattering data, both when aggregates are desired and when they are undesired.

Real space functions from experimental small angle scattering data

2011 ◽  
Vol 13 (13) ◽  
pp. 5872 ◽  
Author(s):  
Gerhard Fritz-Popovski ◽  
Alexander Bergmann ◽  
Otto Glatter
Keyword(s):  
Small Angle ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

An iterative method to extract the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data

2014 ◽  
Vol 47 (2) ◽  
pp. 712-718 ◽  
Author(s):  
D. Sen ◽  
Avik Das ◽  
S. Mazumder
Keyword(s):  
Iterative Method ◽  
Size Distribution ◽  
Small Angle ◽  
Real Space ◽  
Colloidal Dispersions ◽  
Small Angle Scattering ◽  
Spherical Particles ◽  
Scattering Data ◽  
X Ray Scattering ◽  
Angle Scattering

In this article, an iterative method for estimating the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data is presented. It utilizes the iterative addition of relevant contributions to an instantaneous size distribution, as obtained from the fractional difference between the experimental data and the simulated profile. An inverse relation between scattering vector and real space is assumed. This method does not demand the consideration of any basis function set together with an imposed constraint such as a Lagrange multiplier, nor does it depend on the Titchmarsh transform. It is demonstrated that the method works quite well in extracting several forms of distribution. The robustness of the present method is examined through the successful retrieval of several forms of distribution, namely monomodal, bimodal, trimodal, triangular and bitriangular distributions. Finally, the method has also been employed to extract the particle size distribution from experimental small-angle X-ray scattering data obtained from colloidal dispersions of silica.

Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures

2015 ◽  
Vol 48 (1) ◽  
pp. 44-51 ◽  
Author(s):  
Gerhard Fritz-Popovski
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Two Dimensional ◽  
Spruce Wood ◽  
Angle Scattering ◽  
Nanostructured Silica ◽  
Internal Architecture

The new two-dimensional indirect Fourier transformation converts small-angle scattering patterns obtained by means of area detectors into two-dimensional real-space functions. These functions contain identical information to the scattering patterns, but many parameters related to the microstructure can be obtained directly from them. The size and shape of the microstructures are mainly reflected in the contours of the real-space functions. Their height can be used to get information on the internal architecture of the microstructures. The principles are demonstrated on nanostructured silica biotemplated by spruce wood.

Two-dimensional indirect Fourier transformation for evaluation of small-angle scattering data of oriented samples

2013 ◽  
Vol 46 (5) ◽  
pp. 1447-1454 ◽  
Author(s):  
Gerhard Fritz-Popovski
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Real Space ◽  
Small Angle Scattering ◽  
Basis Functions ◽  
Scattering Data ◽  
Normal Wood ◽  
Two Dimensional ◽  
Model Free ◽  
Angle Scattering

An extension of the indirect Fourier transformation method for two-dimensional small-angle scattering patterns is presented. This allows for a model-free investigation of real-space functions of oriented structures. The real-space function is built from two-dimensional basis functions. The Fourier transformed basis functions are approximated to the scattering pattern. The solution to this problem in reciprocal space can be used to compute the corresponding real-space functions. These real-space functions contain information on size, shape, internal structure and orientation of the structures studied. Information on structures that are oriented in different distinct directions can be partly separated. The applicability of the technique is demonstrated on simulated data of oriented cuboids and on two experimental data sets based on the nanostructure of spruce normal wood.

Update for BayesApp: a web site for analysis of small-angle scattering data

2014 ◽  
Vol 47 (4) ◽  
pp. 1469-1471 ◽  
Author(s):  
Steen Hansen
Keyword(s):  
Maximum Entropy ◽  
Bayesian Methods ◽  
Small Angle ◽  
Web Site ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Structure Factors ◽  
Angle Scattering ◽  
Ellipsoid Of Revolution ◽  
The Web

An update for BayesApp, a web site for analysis of small-angle scattering data, is presented. The indirect transformation of the scattering data now includes an option for a maximum-entropy constraint in addition to the conventional smoothness constraint. The maximum-entropy constraint uses an ellipsoid of revolution as a prior, and the dimensions of the ellipsoid as well as the overall noise level of the experimental data are estimated using Bayesian methods. Furthermore, a correction for slit smearing has been added. The web site also includes options for calculation of the scattering intensity from simple models as well as the estimation of structure factors for polydisperse spheres and nonspherical objects of axial ratios between 0.4 and 2.5.

scholarly journals 2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update

2017 ◽  
Vol 73 (9) ◽  
pp. 710-728 ◽  
Author(s):  
Jill Trewhella ◽  
Anthony P. Duff ◽  
Dominique Durand ◽  
Frank Gabel ◽  
J. Mitchell Guss ◽  
...  
Keyword(s):  
Small Angle ◽  
Task Force ◽  
Data Bank ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Quality Data ◽  
Angle Scattering ◽  
Publication Guidelines ◽  
Guidelines And Recommendations

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.

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