Analysis Of Small-angle Scattering Data Research Articles

The human factor: results of a small-angle scattering data analysis round robin

A round-robin study has been carried out to estimate the impact of the human element in small-angle scattering data analysis. Four corrected datasets were provided to participants ready for analysis. All datasets were measured on samples containing spherical scatterers, with two datasets in dilute dispersions and two from powders. Most of the 46 participants correctly identified the number of populations in the dilute dispersions, with half of the population mean entries within 1.5% and half of the population width entries within 40%. Due to the added complexity of the structure factor, far fewer people submitted answers on the powder datasets. For those that did, half of the entries for the means and widths were within 44 and 86%, respectively. This round-robin experiment highlights several causes for the discrepancies, for which solutions are proposed.

Desmearing small-angle scattering data by central moment expansions

This article proposes a robust method for desmearing 1D small-angle scattering (SAS) intensity profiles. Using the central-moment-expansion technique, smearing in SAS intensity profiles is achieved in a model-free manner, eliminating the need for presumptive input during the desmearing. This innovative approach enables data analysis of SAS data without the resolution being convoluted with the structural model, thereby facilitating faster implementation and performance of fitting functions directly from the scattering models.

Ambiguities in and completeness of SAS data analysis of membrane proteins: the case of the sensory rhodopsin II-transducer complex.

Membrane proteins (MPs) play vital roles in the function of cells and are also major drug targets. Structural information on proteins is vital for understanding their mechanism of function and is critical for the development of drugs. However, obtaining high-resolution structures of membrane proteins, in particular, under native conditions is still a great challenge. In such cases, the low-resolution methods small-angle X-ray and neutron scattering (SAXS and SANS) might provide valuable structural information. However, in some cases small-angle scattering (SAS) provides ambiguous ab initio structural information if complementary measurements are not performed and/or a priori information on the protein is not taken into account. Understanding the nature of the limitations may help to overcome these problems. One of the main problems of SAS data analysis of solubilized membrane proteins is the contribution of the detergent belt surrounding the MP. Here, a comprehensive analysis of how the detergent belt contributes to the SAS data of a membrane-protein complex of sensory rhodopsin II with its cognate transducer from Natronomonas pharaonis (NpSRII-NpHtrII) was performed. The influence of the polydispersity of NpSRII-NpHtrII oligomerization is the second problem that is addressed here. It is shown that inhomogeneity in the scattering length density of the detergent belt surrounding a membrane part of the complex and oligomerization polydispersity significantly impacts on SAXS and SANS profiles, and therefore on 3D ab initio structures. It is described how both problems can be taken into account to improve the quality of SAS data treatment. Since SAS data for MPs are usually obtained from solubilized proteins, and their detergent belt and, to a certain extent, oligomerization polydispersity are sufficiently common phenomena, the approaches proposed in this work might be used in SAS studies of different MPs.

Small-angle X-ray and neutron scattering

Small-angle scattering (SAS) is a technique that is able to probe the structural organization of matter and quantify its response to changes in external conditions. X-ray and neutron scattering profiles measured from bulk materials or materials deposited at surfaces arise from nanostructural inhomogeneities of electron or nuclear density. The analysis of SAS data from coherent scattering events provides information about the length scale distributions of material components. Samples for SAS studies may be prepared in situ or under near-native conditions and the measurements performed at various temperatures, pressures, flows, shears or stresses, and in a time-resolved fashion. In this Primer, we provide an overview of SAS, summarizing the types of instrument used, approaches for data collection and calibration, available data analysis methods, structural information that can be obtained using the method, and data depositories, standards and formats. Recent applications of SAS in structural biology and the soft-matter and hard-matter sciences are also discussed.

Searching for an Efficient Solution Reconstruction Algorithm in the Analysis of Small-Angle Scattering Data from Silicasol Solution

Searching for an Efficient Solution Reconstruction Algorithm in the Analysis of Small-Angle Scattering Data from Silicasol Solution

Application of neural networks for small-angle scattering data analysis

Application of neural networks for small-angle scattering data analysis

Small Angle Scattering Data Analysis Assisted by Machine Learning Methods

ABSTRACTSmall angle scattering (SAS) is a widely used technique for characterizing structures of wide ranges of materials. For such wide ranges of applications of SAS, there exist a large number of ways to model the scattering data. While such analysis models are often available from various suites of SAS data analysis software packages, selecting the right model to start with poses a big challenge for beginners to SAS data analysis. Here, we present machine learning (ML) methods that can assist users by suggesting scattering models for data analysis. A series of one-dimensional scattering curves have been generated by using different models to train the algorithms. The performance of the ML method is studied for various types of ML algorithms, resolution of the dataset, and the number of the dataset. The degree of similarities among selected scattering models is presented in terms of the confusion matrix. The scattering model suggestions with prediction scores provide a list of scattering models that are likely to succeed. Therefore, if implemented with extensive libraries of scattering models, this method can speed up the data analysis workflow by reducing search spaces for appropriate scattering models.

Global small-angle scattering data analysis of inverted hexagonal phases.

A global analysis model has been developed for randomly oriented, fully hydrated, inverted hexagonal (HII) phases formed by many amphiphiles in aqueous solution, including membrane lipids. The model is based on a structure factor for hexagonally packed rods and a compositional model for the scattering length density, enabling also the analysis of positionally weakly correlated HII phases. Bayesian probability theory was used for optimization of the adjustable parameters, which allows parameter correlations to be retrieved in much more detail than standard analysis techniques and thereby enables a realistic error analysis. The model was applied to different phosphatidylethanolamines, including previously unreported HII data for diC14:0 and diC16:1 phosphatid-yl-ethanolamine. The extracted structural features include intrinsic lipid curvature, hydrocarbon chain length and area per lipid at the position of the neutral plane.

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

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.

Ambiguities and completeness of SAS data analysis: investigations of apoferritin by SAXS/SANS EID and SEC-SAXS methods

The method of small angle scattering (SAS) is widely used in the field of biophysical research of proteins in aqueous solutions. Obtaining low-resolution structure of proteins is still a highly valuable method despite the advances in high-resolution methods such as X-ray diffraction, cryo-EM etc. SAS offers the unique possibility to obtain structural information under conditions close to those of functional assays, i.e. in solution, without different additives, in the mg/mL concentration range. SAS method has a long history, but there are still many uncertainties related to data treatment. We compared 1D SAS profiles of apoferritin obtained by X-ray diffraction (XRD) and SAS methods. It is shown that SAS curves for X-ray diffraction crystallographic structure of apoferritin differ more significantly than it might be expected due to the resolution of the SAS instrument. Extrapolation to infinite dilution (EID) method does not sufficiently exclude dimerization and oligomerization effects and therefore could not guarantee total absence of dimers account in the final SAS curve. In this study, we show that EID SAXS, EID SANS and SEC-SAXS methods give complementary results and when they are used all together, it allows obtaining the most accurate results and high confidence from SAS data analysis of proteins.

Extension of the sasCIF format and its applications for data processing and deposition.

Recent advances in small-angle scattering (SAS) experimental facilities and data analysis methods have prompted a dramatic increase in the number of users and of projects conducted, causing an upsurge in the number of objects studied, experimental data available and structural models generated. To organize the data and models and make them accessible to the community, the Task Forces on SAS and hybrid methods for the International Union of Crystallography and the Worldwide Protein Data Bank envisage developing a federated approach to SAS data and model archiving. Within the framework of this approach, the existing databases may exchange information and provide independent but synchronized entries to users. At present, ways of exchanging information between the various SAS databases are not established, leading to possible duplication and incompatibility of entries, and limiting the opportunities for data-driven research for SAS users. In this work, a solution is developed to resolve these issues and provide a universal exchange format for the community, based on the use of the widely adopted crystallographic information framework (CIF). The previous version of the sasCIF format, implemented as an extension of the core CIF dictionary, has been available since 2000 to facilitate SAS data exchange between laboratories. The sasCIF format has now been extended to describe comprehensively the necessary experimental information, results and models, including relevant metadata for SAS data analysis and for deposition into a database. Processing tools for these files (sasCIFtools) have been developed, and these are available both as standalone open-source programs and integrated into the SAS Biological Data Bank, allowing the export and import of data entries as sasCIF files. Software modules to save the relevant information directly from beamline data-processing pipelines in sasCIF format are also developed. This update of sasCIF and the relevant tools are an important step in the standardization of the way SAS data are presented and exchanged, to make the results easily accessible to users and to promote further the application of SAS in the structural biology community.

SASfit: a tool for small-angle scattering data analysis using a library of analytical expressions.

SASfit is one of the mature programs for small-angle scattering data analysis and has been available for many years. This article describes the basic data processing and analysis workflow along with recent developments in the SASfit program package (version 0.94.6). They include (i) advanced algorithms for reduction of oversampled data sets, (ii) improved confidence assessment in the optimized model parameters and (iii) a flexible plug-in system for custom user-provided models. A scattering function of a mass fractal model of branched polymers in solution is provided as an example for implementing a plug-in. The new SASfit release is available for major platforms such as Windows, Linux and MacOS. To facilitate usage, it includes comprehensive indexed documentation as well as a web-based wiki for peer collaboration and online videos demonstrating basic usage. The use of SASfit is illustrated by interpretation of the small-angle X-ray scattering curves of monomodal gold nanoparticles (NIST reference material 8011) and bimodal silica nanoparticles (EU reference material ERM-FD-102).

Small-angle scattering gives direct structural information about a membrane protein inside a lipid environment

Monomeric bacteriorhodopsin (bR) reconstituted into POPC/POPG-containing nanodiscs was investigated by combined small-angle neutron and X-ray scattering. A novel hybrid approach to small-angle scattering data analysis was developed. In combination, these provided direct structural insight into membrane-protein localization in the nanodisc and into the protein-lipid interactions. It was found that bR is laterally decentred in the plane of the disc and is slightly tilted in the phospholipid bilayer. The thickness of the bilayer is reduced in response to the incorporation of bR. The observed tilt of bR is in good accordance with previously performed theoretical predictions and computer simulations based on the bR crystal structure. The result is a significant and essential step on the way to developing a general small-angle scattering-based method for determining the low-resolution structures of membrane proteins in physiologically relevant environments.

The Small Angle Scattering Toolbox

Small Angle Scattering (SAS) is a technique used to investigate structure and dynamics of macromolecules in solution. Proteins in buffer conditions close to their physiological environment, are subject to Xray or Neutron scattering experiments. The resulting one-dimensional scattering curves are directly related to their three-dimensional structure. The SAS technique is routinely used to determining the low resolution shape of protein and map specific large scale conformation changes in protein structures.We present a recently developed computational platform for SAS data analysis and model construction/refinement.The Small Angle Scattering Toolbox (SASTBX) has tools four major modules: (1) Raw data reduction; (2) theoretical scattering profile calculation based on PDB structures; (3) Pair distance distribution function (PDDF) estimation; and (4) 3D model construction and structure refinement.The toolbox can be utilized to read raw scattering images obtained from the detector to generate an intensity profile. The basic analyses, such as Guiner and Kratky plots can be carried out in real time to assess the sample and data quality while collecting data. The PDDF estimation is a fully automated procedure, linked with a database a known PDDF's allowing for a rough initial classification of the shape of the protein. Model data can be calculated on the basis of a spherical harmonics expansions. Initial structures can be further refined with normal mode movements or rigid-body motions.The sastbx is built on the open source Computational Crystallography Toolbox (CCTBX). The toolbox is implemented by using Python/C++ hybrid approach: the computing intensive jobs are handled in C++, and the python allows easy integration between other components. The source code will be distributed as open source project.

ATSAS 2.1 – towards automated and web-supported small-angle scattering data analysis

Small-angle scattering (SAS) is frequently employed for screening large numbers of samples and for studying these samples under different conditions, including space- and time-resolved analysis. These measurements produce immense amounts of data, especially on modern high-flux and high-brilliance sources (e.g. third-generation synchrotrons). In biological SAS, like high-throughput macromolecular crystallography, large-scale analysis of proteins and macromolecular complexes is also emerging. Automation of data analysis becomes an indispensable prerequisite for adequate evaluation of high-throughput SAS experiments. Here a prototype of an automated data-analysis system for isotropic solution scattering based on the further development of the programs belonging to the package ATSAS 2.1 is reported. This system allows the major analysis tasks starting from the raw data processing and, for monodisperse systems, finishing with a three-dimensional model, to be performed automatically. Convenient web interfaces for the online use of individual ATSAS programs are also provided.

Small-angle scattering from spherical particles on randomly oriented interfaces

Abstract Small-angle scattering (SAS) has long been used to study nucleation and growth of particles in solid or liquid matrices. In some special cases, nucleation of particles occurs on interfaces, e.g., grain boundaries in crystalline solids or membranes in a solvent. Clearly, the position of the particles is constrained in this case to a narrow region close to the interface, which leads to correlations between the particles. In the present paper, we derive simple expressions for the analysis of SAS data from particles located on planar interfaces, and compare the analytical approximations with computer simulations.

Ligand-Induced Conformational Changes in Tissue Transglutaminase: Monte Carlo Analysis of Small-Angle Scattering Data

Small-angle neutron and x-ray scattering experiments have been performed on type 2 tissular transglutaminase to characterize the conformational changes that bring about Ca 2+ activation and guanosine triphosphate (GTP) inhibition. The native and a proteolyzed form of the enzyme, in the presence and in the absence of the two effectors, were considered. To describe the shape of transglutaminase in the different conformations, a Monte Carlo method for calculating small-angle neutron scattering profiles was developed by taking into account the computer-designed structure of the native transglutaminase, the results of the Guinier analysis, and the essential role played by the solvent-exposed peptide loop for the conformational changes of the protein after activation. Although the range of the neutron scattering data is rather limited, by using the Monte Carlo analysis, and because the structure of the native protein is available, the distribution of the protein conformations after ligand interaction was obtained. Calcium activation promotes a rotation of the C-terminal with respect to the N-terminal domain around the solvent-exposed peptide loop that connects the two regions. The ψ angle between the longest axes of the two pairs of domains is found to be above 50°, larger than the ψ value of 35° calculated for the native transglutaminase. On the other hand, the addition of GTP makes possible conformations characterized by ψ angles lower than 34°. These results are in good agreement with the proposed enzyme activity regulation: in the presence of GTP, the catalytic site is shielded by the more compact protein structure, while the conformational changes induced by Ca 2+ make the active site accessible to the substrate.

Restoring Three-Dimensional Structure of Biopolymers from Solution Scattering

The methods of small-angle scattering data analysis, developed to study the three-dimensional structure of biological macromolecules in solution, are reviewed. The direct methods include low-resolution shape determination in the homogeneous approximation and multiphase structure search by simultaneous fitting of the contrast-variation data sets from multicomponent particles. Approaches using crystallographic data involve evaluation of the solution scattering from the atomic coordinates, taking into account the solvation shell and relative positioning of subunits (domains) with known structure in complex particles. Practical applications of these methods to study biological macromolecules in solution are described.

Analysis of Small-Angle Scattering Data from Spherical Particles by both the Indirect Transform Method and the Maximum-Entropy Method

In this paper extensive comparison studies of the indirect transform method (ITM) and the maximum-entropy method (MEM) were made for recovering the size distribution of spherical particles. Simulated small-angle scattering (SAS) data with different noise levels for various size distributions are tested. It is found that both the MEM and ITM are capable of accurately recovering the original size distributions for various types of size distributions from simulated SAS data with a 1% noise level. When the noise level of the simulated SAS data is increased to 6%, the size distributions recovered by both the ITM and MEM begin to have many noisy oscillations. It is also found that the MEM is more vulnerable to termination effects, i.e. when low-Q or high-Q data are not available. On the other hand, even for cases with limited-Q-range data the ITM can still accurately recover the original size distribution. This was clearly shown in the analysis of the measured small-angle X-ray scattering data, with a limited Q range, from a β-quenched zircaloy-4 specimen.

The Analysis of Small-Angle Scattering Data from Polydisperse Rodlike Particles by Indirect Transform and Maximum-Entropy Methods

Both the indirect transform and maximum-entropy methods are developed for analyzing small-angle scattering data from polydisperse rodlike particles to recover the original length distribution. Simulated small-angle scattering data are used to test the ability of these two methods. Both methods are found to be able to recover accurately the original length distribution of the rodlike particles when the full Q-range scattering data are available. However, the maximum-entropy method is not able to recover the original length distribution as accurately as the indirect transform method when the very low Q scattering data are not available. The indirect transform method is successfully applied to the analysis of experimental small-angle scattering data from diheptanoylphosphatidylcholine rodlike micelles. The recovered length distribution of these rodlike micelles agrees well with that predicted by the `ladder' thermodynamic model for rodlike micellar systems. This study shows that the indirect transform method described in this paper can be successfully used in the analysis of the small-angle scattering data from polydisperse rodlike particles to recover their length distribution. To use the maximum-entropy method for analyzing the small-angle scattering data from polydisperse rodlike particles, scattering data down to the very low Q limit must be measured in order to recover the length distribution accurately.