Solution X-ray Scattering Form Factors of Supramolecular Self-Assembled Structures

Abstract

In this paper, the analysis of several involved models, relevant for evaluating solution X-ray scattering form factors of supramolecular self-assembled structures, is presented. Different geometrical models are discussed, and the scattering form factors of several layers of those shapes are evaluated. The thickness and the electron density of each layer are parameters in those models. The models include Gaussian electron density profiles and/or uniform electron density profiles at each layer. Various forms of cuboid, layered, spherical, cylindrical, and helical structures are carefully treated. The orientation-averaged scattering intensities of those form factors are calculated. Similar classes of form factors are examined and compared, and their fit to scattering data of lipid bilayers, capsids of the Simian virus 40 virus-like particle and microtubule is discussed. A more detailed model of discrete helices composed of uniform spheres was derived and compared to solution X-ray scattering data of microtubules. Our analyses show that when high-resolution data are available the more detailed models with Gaussian electron density profiles or helical structures composed of spheres should be used to better capture all the elements in the scattering curves. The models presented in this paper may also be applied, with minor corrections, for the analysis of solution neutron scattering data.

Effect of capsid confinement on the chromatin organization of the SV40 minichromosome

“…The methodology followed for measuring the diffraction of viral particles has been previously described (42,43) and is detailed in SI sec.1c .…”

“…To model the SV40 samples, a form factor of multiple concentric spherical shells with smoothly varying electron density (ED) profiles, represented by hyperbolic tangent functions: was fit to the data, as described (42,43). Δ ρ ( r ) indicates the radial ED contrast with respect to the solvent (buffer).…”

“…Δ ρ N = 0 and corresponds to the solvent ED contrast. To numerically solve arbitrary ED profiles, the form factor of the smooth ED profiles, Δ ρ ( r ) were calculated by discretizing the profiles and transforming them to a sum of Heaviside step functions that can be analytically solved (42,43). …”

Investigating Macromolecular Complexes in Solution by Small Angle X-Ray Scattering

“…Also, advanced modeling approaches can be found in specialized articles in the literature (Székely et al, 2010).…”

Spline-based parallel nonlinear optimization of function sequences

“…According to Székely et al [48], using the Gaussian electron density profile, the model for the form factor is defined by:…”