Small Angle X-Ray Scattering Data Analysis and Theoretical Modelling for the Size and Shape Characterization of Drug Delivery Systems Based on Vitamin E TPGS Micelles

Characterization of Surfactant Spheroidal Micelle Structure for Pharmaceutical Applications: A Novel Analytical Framework

“…Nowadays, even challenging samples, difficult to obtain in large amounts, can be examined within minutes. (ii) Novel methods for data analysis [4] and related software tools have become available to facilitate the interpretation of scattering patterns from biological systems. Most of the available software allows us to calculate theoretical scattering SAXS curves from macromolecular models to be compared with the experimental data, generate the Pair Distribution Function (PDF) from the measured SAXS intensities, and determine size/shape models of the investigated scattering samples.…”

“…In the case of dodecyl phosphocholine micelles, using various core-shell models consisting of a hydrophobic core and a shell representing hydrated polar headgroups, it was shown that a spherical model incorporating a core-shell mixed region used to describe non-ideal interfaces could account for the changes in the size and shape of the scattering profiles [11]. These non-ideal core-shell and shell-solvent interfaces were also implemented in our work [4], where we convolved the theoretical PDF profiles with a gaussian function. Clearly, a further fitting parameter was introduced in the modeling [4,11], making the model equivalent, in terms of total number of parameters, to that obtainable assuming spheroidal micelles, i.e., non-perfect spherical micelles but prolate/oblate ellipsoids with the polar axis longer/shorter with respect to the equatorial axis.…”

“…In this framework, we have recently investigated by SAXS the structure and functionality of a D-α-tocopherol polyethylene glycol 1000 succinate (VitE-TPGS) system of micelles, without and with an addition of a Poorly Soluble Compound (PSC), assuming a spherical-shaped hydrophobic inner core and an outer hydrated hydrophilic shell [4]. A simple two-dimensional/two-components theoretical model was developed to describe the SAXS data and related Pair Distribution Function (PDF), collected from the VitE-TPGS micelles with and without the PSC Eltrombopag.…”

“…These non-ideal core-shell and shell-solvent interfaces were also implemented in our work [4], where we convolved the theoretical PDF profiles with a gaussian function. Clearly, a further fitting parameter was introduced in the modeling [4,11], making the model equivalent, in terms of total number of parameters, to that obtainable assuming spheroidal micelles, i.e., non-perfect spherical micelles but prolate/oblate ellipsoids with the polar axis longer/shorter with respect to the equatorial axis. In other words, the obtained results on the core/shell sizes, their electron density contrasts, and the actual shape of the micelles, as already underlined, are clearly model-dependent.…”

“…In the following: (i) we discuss how to graphically estimate-from the PDF first derivative-the core and shell sizes of the micelle under study; (ii) we derive analytical equations useful both for determining the core-shell and shell-buffer electron density contrasts, starting from the core and shell sizes derived graphically; (iii) we apply the new proposed graphical-analytical approach, whose mathematical details are reported in Appendix A, to micelles formed by different surfactants that have been previously characterized, namely PS20 [12], DPC and SDS [13], and VitE-TPGS with and without a PSC [4]. This comparison with literature data helped us validate the new graphicalanalytical method and demonstrate its potentiality compared to the conventional approach based on the current SAXS/PDF simulation software [5][6][7][8][9][10].…”