A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering

In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transfer q, together with a computationally efficient way of inferring their radii of gyration R G. Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shape ab initio. In this work, a low-angle approximation of the scattering intensity I(q) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative and ab initio reconstruction tools available in the literature. However, it can be considered as an extension of the Guinier approximation and used to generate initial estimates for the aforementioned iterative techniques, which usually rely on R G and D max for initialization. This formulation also demonstrates that nonlinearity in the Guinier plot can arise from anisotropy in the scattering particles. Beyond ideal ellipsoids of revolution, it is shown that this approximation can be used to estimate the size and shape of molecules in solution, in both computational and experimental scenarios. The limits of the approach are discussed and the impact of a particle's anisotropy in the Guinier estimate of R G is assessed.

Small-angle scattering: the Guinier technique underestimates the size of hard globular particles due to the structure-factor effect

The straightforward calculation of small-angle scattering intensity by hard spheres at different concentrations is performed. For the same system of hard spheres, the scattering intensities were found both using the product of the form factor and the structure factor {based on the work of Kinning & Thomas [Macromolecules, (1984),17, 1712–1718]} and using the correlation function {based on the work of Kruglov [J. Appl. Cryst.(2005),38, 716–720] and Hansen [J. Appl. Cryst.(2011),44, 265–271;J. Appl. Cryst.(2012),45, 381–388]}. All three intensities are in agreement at every concentration. The values of the radii of gyration found from the Guinier plot are shown to be noticeably underestimated compared to the true radius of gyration of a single sphere. Presented are the calculated correction factors that should be applied to the experimentally found radius of gyration of spheres. Also, the concentration effects are shown to have an even greater impact on the radius of gyration of prolate particles that is found from the Guinier plot.

The structural characterisation of HWCVD-deposited nanocrystalline silicon films

Nanocrystalline silicon (nc-Si) films were deposited by hot-wire chemical vapour deposition (HWCVD) in the presence of varying H2 concentrations and their structural and interfacial character investigated by X-ray diffraction, small-angle X-ray scattering (SAXS) and Raman spectroscopy. The crystalline fraction was around 30–50% and the nc-Si crystallite size was in the range 20–35 nm. The SAXS results were analysed by Guinier plot, scaling factor, and correlation distance. The nc-Si grains displayed a mass fractal appearance, and the interfacial inhomogeneity distance was ~2 nm.

High-Pressure Solution X-ray Scattering of Protein Using a Hydrostatic Cell with Diamond Windows

A hydrostatic high-pressure cell (maximum pressure 700 MPa) with synthetic diamond windows is applied to measure small-angle X-ray scattering of a protein at high pressure. Use of the present cell allows an accurate solvent background correction, providing quantitative analyses. The performance of the present cell for X-ray scattering is shown by using lysozyme as a sample solution. From the Guinier plot, values of the radius of gyration of lysozyme are evaluated to be 15.31 ± 0.09 Å at 1 atm (0.10 MPa) and 14.80 ± 0.15 Å at 400 MPa.