# Global Small-Angle Scattering Data Analysis of Inverted Hexagonal Phases

## TL;DR

This paper presents a comprehensive global analysis model for inverted hexagonal phases in amphiphilic systems, utilizing Bayesian optimization to accurately determine structural parameters and analyze weakly correlated phases.

## Contribution

The study introduces a novel global analysis model combining a structure factor and compositional SLD model, enhanced by Bayesian parameter optimization, for detailed analysis of inverted hexagonal phases.

## Key findings

- Successfully applied the model to various phosphatidylethanolamines.
- Extracted key structural features like lipid curvature and chain length.
- Provided new data for previously unreported H$_ ext{II}$ phases.

## Abstract

We have developed a global analysis model for randomly oriented, fully hydrated inverted hexagonal (H$_\text{II}$) phases formed by many amphiphiles in aqueous solution, including membrane lipids. The model is based on a structure factor for hexagonally packed rods and a compositional model for the scattering length density (SLD) enabling also the analysis of positionally weakly correlated H$_\text{II}$ phases. For optimization of the adjustable parameters we used Bayesian probability theory, which allows to retrieve parameter correlations in much more detail than standard analysis techniques, and thereby enables a realistic error analysis. The model was applied to different phosphatidylethanolamines including previously not reported H$_\text{II}$ data for diC14:0 and diC16:1 phosphatidylethanolamine. The extracted structural features include intrinsic lipid curvature, hydrocarbon chain length and area per lipid at the position of the neutral plane.