X-ray small-angle scattering in the study of the structure of disordered nanosystems

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Abstract

Small-angle scattering (SAS) of X-rays and neutrons is a method for studying the nanostructure of condensed systems with resolutions ranging from fractions to hundreds of nanometers. Its capabilities have significantly expanded in recent decades thanks to the emergence of bright synchrotron radiation sources and laboratory setups with microfocus sources. The increase in computational power of available computers has been accompanied by the development of new algorithms and data analysis techniques, making SAS one of the most effective methods for studying nanostructured materials. After a brief overview of the basic principles of SAS, this paper presents the most prominent examples of such analysis with isotropic dispersive nanosystems: modeling the structure of biological macromolecules in solution, determining size distributions of inhomogeneities in polydisperse systems, and studying multicomponent systems of nanoparticles of various natures. The SAS method does not require special sample preparation and allows for studying objects under conditions close to natural, which is particularly demanded in the development of nature-like technologies.

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About the authors

V. V. Volkov

Shubnikov Institute of Crystallography of Kurchatov Complex of Crystallography and Photonics of NRC “Kurchatov Institute”

Author for correspondence.
Email: vvo@crys.ras.ru
Russian Federation, Moscow

P. V. Konarev

Shubnikov Institute of Crystallography of Kurchatov Complex of Crystallography and Photonics of NRC “Kurchatov Institute”

Email: vvo@crys.ras.ru
Russian Federation, Moscow

M. V. Petoukhov

Shubnikov Institute of Crystallography of Kurchatov Complex of Crystallography and Photonics of NRC “Kurchatov Institute”

Email: vvo@crys.ras.ru
Russian Federation, Moscow

V. E. Asadchikov

Shubnikov Institute of Crystallography of Kurchatov Complex of Crystallography and Photonics of NRC “Kurchatov Institute”

Email: vvo@crys.ras.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. MURR intensity from the model of the three-component system of AOT-water micelles in isooctane

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3. Fig. 2. Model of the cross-section of AOT-water micelles. Density ρ is represented in units of electrons/Å3. Rhs is the sticky potential radius (hard sticky potential radius). dh - thickness of the layer occupied by sulfate groups of surfactants

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4. Fig. 3. MURR intensities of the solution of AOT-water micelles in isooctane at different temperatures (a), b - found volume distribution by particle radii (b)

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5. Fig. 4. MURR intensities from liposome mixture solutions of 10% DOPS + 90% DOPC with different lipid/protein M1 molar ratios (a). White lines are theoretical intensities corresponding to models of lipid bilayer density profiles (panel b). The density peak ρ in the region z ~ 2.3 nm relative to the center of the lipid bilayer corresponds to adsorbed molecules of matrix protein M1

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6. Fig. 5. Analysis of the structure of bacterial virus T7: a - X-ray MUR data (upper panel; solid curve - experiment, dotted - model scattering), b - contours of the reduced density of the phage particle [20], c, d - structure of the whole particle and phage procapsid, respectively, according to the cryo-EM data [21], found 25 years later

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7. Fig. 6. Balloon models of immunoglobulin M (IgM) and rheumatoid factor IgM-RF macromolecules found by MUR data from solutions. The circles show the regions occupied by Fab fragments. It can be seen that these regions are less symmetrical in the IgM-RF molecule

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8. Fig. 7. Example of refinement of the crystal domain structure of the enzyme pyruvate decarboxylase by molecular tectonics [32]: a - scattering data: broken line - experiment, black - theoretical scattering from the MUR model (c), dotted line - scattering from the crystal model (b)

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9. Fig. 8. Chromatographic profile (C - relative concentration) of aldolase solution, frame acquisition interval ~1 s, in the inset - spectrum of singular numbers of the measurement matrix, two significant components are visible (a); evolution of the values of the first two singular numbers with the growth of included frames (1, 2 - direct calculation run) and with the growth of excluded frames (3, 4 - reverse run), vertical lines indicate the time moments of change in the number of components (b); concentration profiles of the components yield calculated by factor analysis: 1 - octamers, 2 - hexamers, 3 - total contour (c); found scattering intensity profiles from components (d) (same designations)

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10. Fig. 9. Ball structure of the 50S ribosome particle according to MURN data [38] (a), crystal model found later [39] (b). The lighter balls in model a denote the RNA phase, the darker ones the regions occupied by proteins

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