Small-angle Scattering Data Research Articles

Quantitative selection of sample structures in small-angle scattering using Bayesian methods.

Small-angle scattering (SAS) is a key experimental technique for analyzing nanoscale structures in various materials. In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting. This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models. The performance of the method is assessed through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that this proposed analysis approach yields highly accurate and interpretable results. The ability of the method to analyze a range of mixing ratios and particle size ratios for mixed components is also discussed, along with its precision in model evaluation by the degree of fitting. The proposed method effectively facilitates quantitative analysis of nanoscale sample structures in SAS, which has traditionally been challenging, and is expected to contribute significantly to advancements in a wide range of fields.

SEB: a computational tool for symbolic derivation of the small-angle scattering from complex composite structures.

Analysis of small-angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time-consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub-units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub-units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data.

Spatial Model of the Organization of Chromatin in the Nucleus of a Biological Cell According to Small-Angle Scattering Data

Small-angle neutron and X-ray scattering data for HeLa nuclei with the normal and suppressed transcription activities are reported. Small-angle neutron scattering data demonstrate the presence of a bifractal structure inside a nucleus. The logarithmic fractal structure is observed in the range from the size of the nucleus to several hundreds of nanometer, whereas the volume fractal structure exists at smaller scales down to a nucleosome structure. Small-angle X-ray scattering data show that the presence of the volume fractal structure correlates with the transcription activity of a cell. In view of the successful description of chromatin by the fractal globule model (Hi–C method data), a scenario for the formation of the bifractal structure inside the nucleus has been proposed. A system of transport channels (logarithmic fractal) is located inside close-packed chromatin, whereas active chromatin is localized near transport channels or inside them and forms volume fractal structures due to the transcription activity. Thus, the logarithmic fractal structure ensures the uniform distribution of voids at various scales, which is potentially necessary for the transcription and transport of substances inside the nucleus, whereas the volume fractal structure is due to the transcription activity of the cell.

Spatial Model of the Organization of Chromatin in the Nucleus of a Biological Cell According to Small-Angle Scattering Data

Spatial Model of the Organization of Chromatin in the Nucleus of a Biological Cell According to Small-Angle Scattering Data

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.

2023 update of template tables for reporting biomolecular structural modelling of small-angle scattering data.

In 2017, guidelines were published for reporting structural modelling of small-angle scattering (SAS) data from biomolecules in solution that exemplified best-practice documentation of experiments and analysis. Since then, there has been significant progress in SAS data and model archiving, and the IUCr journal editors announced that the IUCr biology journals will require the deposition of SAS data used in biomolecular structure solution into a public archive, as well asadherence to the 2017 reporting guidelines. In this context, the reporting template tables accompanying the 2017 publication guidelines have been reviewed with a focus on making them both easier to use and more general. With input from the SAS community via the IUCr Commission on SAS and attendees of the triennial 2022 SAS meeting (SAS2022, Campinas, Brazil), an updated reporting template table has been developed that includes standard descriptions for proteins, glycosylated proteins, DNA and RNA, with some reorganization of the data to improve readability and interpretation. In addition, a specialized template has been developed for reporting SAS contrast-variation (SAS-cv) data and models that incorporates the additional reporting requirements from the 2017 guidelines for these more complicated experiments. To demonstrate their utility, examples of reporting with these new templates are provided for a SAS study of a DNA-protein complex and a SAS-cv experiment on a protein complex. The examples demonstrate how the tabulated information promotes transparent reporting that, in combination with the recommended figures and additional information best presented in the main text, enables the reader of the work to readily draw their own conclusions regarding the quality of the data and the validity of the models presented.

Scrutinizing the protein hydration shell from MD simulations against SAXS/SANS data from a worldwide round robin benchmark.

The hydration shell of proteins plays key roles in protein stability, folding, recognition, and enzyme activity. However, it remained unclear whether the hydration shell predicted by explicit-solvent molecular dynamics (MD) simulations matches experimental conditions, while accurate experimental probes of the hydration shell structure remained limited. Small-angle scattering (SAS) in solution using X-rays (SAXS) or neutrons (SANS) in principle provides information on the hydration shell, since both the radius of gyration (Rg) and the zero-angle scattering (I0) depend on the hydration shell contrast relative to bulk solvent. Using MD simulations and explicit-solvent SAXS/SANS calculations, we computed Rg and I0 for five different proteins and a set of 18 different combinations of protein force fields and water models, and we validated the simulation results against consensus data from a recent worldwide round robin benchmark (Trewhella, Vachette et al., doi:10.1107/S2059798322009184). Overall, we find remarkable agreement between MD simulations and consensus SAS data; however the agreement is force field dependent. Certain force field/water model combinations underestimate the hydration layer contrast significantly, while water models with increased dispersion interactions may, for some proteins, overestimate the hydration layer contrast. Our study shows that explicit-solvent SAS calculation and consensus SAS data provide a novel route for scrutinizing the hydration layer of proteins.

Phone2SAS: 3D scanning by smartphone aids the realization of small-angle scattering.

Small-angle scattering (SAS) is a powerful tool for the detailed structural analysis of objects at the nanometer scale. In contrast to techniques such as electron microscopy, SAS data are presented as reciprocal space information, which hinders the intuitive interpretation of SAS data. This study presents a workflow: (1) creating objects, (2) 3D scanning, (3) the representation of the object as point clouds on a laptop, (4) computation of a distance distribution function, and (5) computation of SAS, executed via the computer program Phone2SAS. This enables us to realize SAS and perform the interactive modeling of SAS of the object of interest. Because 3D scanning is easily accessible through smartphones, this workflow driven by Phone2SAS contributes to the widespread use of SAS. The application of Phone2SAS for the structural assignment of SAS to Y-shaped antibodies is reported in this study.

Visualizing and accessing correlated SAXS data sets with Similarity Maps and Simple Scattering web resources.

Constructing a comprehensive understanding of macromolecular behavior from a set of correlated small angle scattering (SAS) data is aided by tools that analyze all scattering curves together. SAS experiments on biological systems can be performed on specimens that are more easily prepared, modified, and formatted relative to those of most other techniques. An X-ray SAS measurement (SAXS) can be performed in less than a milli-second in-line with treatment steps such as purification or exposure to modifiers. These capabilities are valuable since biological macromolecules (proteins, polynucleotides, lipids, and carbohydrates) change conformation or assembly under specific conditions that often define their biological role. Furthermore, mutation or post-translational modification change their behavior and provides an avenue to tailor their mechanics. Here, we describe tools to combine multiple correlated SAS measurements for analysis and review their application to biological systems. The SAXS Similarity Map (SSM) compares a set of scattering curves and quantifies the similarity between them for display as a color on a grid. Visualizing an entire correlated data set with SSMs helps identify patterns that reveal biological functions. The SSM analysis is available as a web-based tool at https://sibyls.als.lbl.gov/saxs-similarity/. To make data available and promote tool development, we have also deployed a repository of correlated SAS data sets called Simple Scattering (available at https://simplescattering.com). The correlated data sets used to demonstrate the SSM are available on the Simple Scattering website. We expect increased utilization of correlated SAS measurements to characterize the tightly controlled mechanistic properties of biological systems and fine-tune engineered macromolecules for nanotechnology-based applications.

VOLDIS: A Direct Search for the Size Distribution of Nanoparticles from Small-Angle Scattering Data and Stability of the Solution

The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for several solutions with different degrees of smoothness of the distribution contour, are considered. Methods for evaluating the stability of both the whole distribution contour and its individual parts are discussed. The work of the program is illustrated by examples of the analysis of polydisperse spherical particles in silicasol solutions.

Simplified Polydispersion Analysis of Small-Angle Scattering Data

With polydisperse inhomogeneities, the analysis of small-angle scattering (SAS) data is possible by fitting the experimental data to theoretical models. Despite scientific software being available for this task, many scientists in different fields prefer other techniques for their investigations. With the simplified polydispersion analysis (SPA) presented here, it is possible to analyse the SAS data in a much simpler way. A straightforward interpolation of SAS data using any commercial software, requiring no advanced computational skills, allows the determination of the size distribution function (SDF) of the polydisperse inhomogeneities. Here, this innovative approach was tested against simulated SAS data of spherical inhomogeneities, as well as experimental data with excellent results. The results reported here offer new opportunities for many scientists to use the SAS technique to investigate polydisperse systems.

Simulation systems of: "A Round Robin Approach Provides a Detailed Assessment of Biomolecular Small-Angle Scattering Data Reproducibility and Yields Consensus Curves for Benchmarking"

Simulation systems of: "A Round Robin Approach Provides a Detailed Assessment of Biomolecular Small-Angle Scattering Data Reproducibility and Yields Consensus Curves for Benchmarking"

Describing small-angle scattering profiles by a limited set of intensities.

Small-angle scattering (SAS) probes the size and shape of particles at low resolution through the analysis of the scattering of X-rays or neutrons passing through a solution of particles. One approach to extracting structural information from SAS data is the indirect Fourier transform (IFT). The IFT approach parameterizes the real-space pair distribution function [P(r)] of a particle using a set of basis functions, which simultaneously determines the scattering profile [I(q)] using corresponding reciprocal-space basis functions. This article presents an extension of an IFT algorithm proposed by Moore [J.Appl. Cryst. (1980), 13, 168-175] which used a trigonometric series to describe the basis functions, where the real-space and reciprocal-space basis functions are Fourier mates. An equation is presented relating the Moore coefficients to the intensities of the SAS profile at specific positions, as well as a series of new equations that describe the size and shape parameters of a particle from this distinct set of intensity values. An analytical real-space regularizer is derived to smooth the P(r) curve and ameliorate systematic deviations caused by series termination. Regularization is commonly used in IFT methods though not described in Moore's original approach, which is particularly susceptible to such effects. The algorithm is provided as a script, denss.f it_data.py, as part of the DENSS software package for SAS, which includes both command line and interactive graphical interfaces. Results of the program using experimental data show that it is as accurate as, and often more accurate than, existing tools.

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.

Vesicle Viewer: Online visualization and analysis of small-angle scattering from lipid vesicles

Small-angle X-ray and neutron scattering are among the most powerful experimental techniques for investigating the structure of biological membranes. Much of the critical information contained in small-angle scattering (SAS) data is not easily accessible to researchers who have limited time to analyze results by hand or to nonexperts who may lack the necessary scientific background to process such data. Easy-to-use data visualization software can allow them to take full advantage of their SAS data and maximize the use of limited resources. To this end, we developed an internet-based application called Vesicle Viewer to visualize and analyze SAS data from unilamellar lipid bilayer vesicles. Vesicle Viewer utilizes a modified scattering density profile (SDP) analysis called EZ-SDP in which key bilayer structural parameters, such as area per lipid and bilayer thickness, are easily and robustly determined. Notably, we introduce a bilayer model that is able to describe an asymmetric bilayer, whether it be chemically or isotopically asymmetric. The application primarily uses Django, a Python package specialized for the development of robust web applications. In addition, several other libraries are used to support the more technical aspects of the project; notable examples are Matplotlib (for graphs) and NumPy (for calculations). By eliminating the barrier of downloading and installing software, this web-based application will allow scientists to analyze their own vesicle scattering data using their preferred operating system. The web-based application can be found at https://vesicleviewer.dmarquardt.ca/.

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

Molecular model of a sensor of two-component signaling system

Two-component systems (TCS) are widespread signaling systems present in all domains of life. TCS typically consist of a signal receptor/transducer and a response regulator. The receptors (histidine kinases, chemoreceptors and photoreceptors) are often embedded in the membrane and have a similar modular structure. Chemoreceptors were shown to function in highly ordered arrays, with trimers of dimers being the smallest functional unit. However, much less is known about photoreceptors. Here, we use small-angle scattering (SAS) to show that detergent-solubilized sensory rhodopsin II in complex with its cognate transducer forms dimers at low salt concentration, which associate into trimers of dimers at higher buffer molarities. We then fit an atomistic model of the whole complex into the SAS data. The obtained results suggest that the trimer of dimers is "tripod"-shaped and that the contacts between the dimers occur only through their cytoplasmic regions, whereas the transmembrane regions remain unconnected.

MATSAS: a small-angle scattering computing tool for porous systems.

MATSAS is a script-based MATLAB program for analysis of X-ray and neutron small-angle scattering (SAS) data obtained from various facilities. The program has primarily been developed for sedimentary rock samples but is equally applicable to other porous media. MATSAS imports raw SAS data from .xls(x) or .csv files, combines small-angle and very small angle scattering data, subtracts the sample background, and displays the processed scattering curves in log-log plots. MATSAS uses the polydisperse spherical (PDSP) model to obtain structural information on the scatterers (scattering objects); for a porous system, the results include specific surface area (SSA), porosity (Φ), and differential and logarithmic differential pore area/volume distributions. In addition, pore and surface fractal dimensions (D p and D s, respectively) are obtained from the scattering profiles. The program package allows simultaneous and rapid analysis of a batch of samples, and the results are then exported to .xlsx and .csv files with separate spreadsheets for individual samples. MATSAS is the first SAS program that delivers a full suite of pore characterizations for sedimentary rocks. MATSAS is an open-source package and is freely available at GitHub (https://github.com/matsas-software/MATSAS).

Assessment and Correction of Small-Angle Scattering Data for Combination with other Experimental Data and with Molecular Simulations

Small-angle X-ray and neutron scattering (SAXS and SANS) can probe the structure of biomolecular complexes in solution. These include disordered proteins and self-assembled protein-lipid complexes, such as high- and low-density lipoproteins and nanodiscs. By combining SAXS or SANS with other experimental data and/or molecular dynamics (MD) simulations, a higher level of spatial and temporal detail can be obtained. The accuracy of the results, however, rely on correctly balancing the information from the different sources of data.