Gaussian deconvolution: a useful method for a form-free modeling of scattering data from mono- and multilayered planar systems

Abstract

A new method for analysis of scattering data from lamellar bilayer systems is presented. The method employs a form‐free description of the cross‐section structure of the bilayer and the fit is performed directly to the scattering data, introducing also a structure factor when required. The cross‐section structure (electron density profile in the case of X‐ray scattering) is described by a set of Gaussian functions and the technique is termed Gaussian deconvolution. The coefficients of the Gaussians are optimized using a constrained least‐squares routine that induces smoothness of the electron density profile. The optimization is coupled with the point‐of‐inflection method for determining the optimal weight of the smoothness. With the new approach, it is possible to optimize simultaneously the form factor, structure factor and several other parameters in the model. The applicability of this method is demonstrated by using it in a study of a multilamellar system composed of lecithin bilayers, where the form factor and structure factor are obtained simultaneously, and the obtained results provided new insight into this very well known system.

Effect of Oxidation on the Structure of Human Low- and High-Density Lipoproteins

“…In this work, we investigate the structure of LDL and HDL particles using the SAXS technique and present to our knowledge a new approach for analysis of these data. This approach was originally developed by Oliveira and co-workers to model experimental curves of scattering intensity and obtain electron density profiles of lamellar systems (28). The model was adapted to systems with spherical symmetry so that it could be used for LDL and HDL SAXS data.…”

Effect of iron oxide loading on magnetoferritin structure in solution as revealed by SAXS and SANS

“…Such aggregation alone cannot explain the observed smearing of the curves, hence, it points to the increasing polydispersity with increasing amount of magnetic material in magnetoferritin. The size and structure polydispersity together with the absence of strictly defined scattering formfactor of the macromolecules prevent the easy determination and separation of the structurefactor which would correspond to the average effective interactions of the basic structural units (here, magnetoferritin macromolecules) in the solutions like in the case of homogeneous or 8 multilayered structures [31,32]. Instead, the structures formed resemble more the partly aggregated particles in aqueous dispersions of magnetite nanoparticles coated with surfactant shells [33].…”

Estudo de interações entre membranas lipídicas por experimentos de SAXS: o efeito da composição

“…Os parâmetros que caracterizam a estrutura lamelar podem ser obtidos por meio da técnica de espalhamento de raios-x a baixos ângulos (SAXS) e a análise do espalhamento difuso, que fornece informações sobre as flutuações térmicas (Nallet; Laversanne; Roux, 1992;Oliveira et al, 2012;Gerbelli et al, 2013).…”

“…Um modelo um pouco mais elaborado é proposto por Oliveira et al (2012), onde o perfil de contraste de densidade eletrônica é formado por somas de gaussianas, como ilustra a Figura 2.9. Neste caso, foram utilizadas gaussianas para descrever as variações do contraste de densidade eletrônica ao longo da membrana.…”

“…Os ajustes foram efetuados utilizando o método de mínimos quadrados e convergem para curvas muito próximas das obtidas experimentalmente. (Oliveira et al, 2012) Utilizando essa relação se pode determinar a periodicidade lamelar de cada uma das amostras. É possível verificar que na medida em que se aumenta a pressão, ou seja, quando se olha as curvas de baixo para cima, se observa que os valores de q dos picos de primeira ordem aumentam.…”