Estimating the Anisotropy of Protein Structures from SAXS

TL;DR

This paper introduces a new low-angle approximation method for SAXS data to estimate the size and anisotropy of protein structures, extending the classic Guinier approach beyond spherical particles.

Contribution

It develops an approximation for ellipsoids of revolution to extract size and shape information from SAXS data, applicable to real molecules beyond idealized models.

Findings

The approximation accurately estimates size and anisotropy for ellipsoids.

It can infer molecular shape in computational and experimental SAXS data.

The approach reveals how anisotropy affects Guinier estimates of $R_G$.

Abstract

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 $q$, 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 \textit{ab initio}.\\ In this work we develop a low angle approximation of the scattering intensity $I(q)$ for ellipsoids of revolution and show how to extract size and anisotropy information from the parameters of that approximation. Beyond ideal ellipsoids of revolution, we show that this approximation can be used to infer the size and shape of molecules in solution, both in computational and experimental scenarios. We discuss the limits of our approach and study the impact of a particle's anisotropy in the Guinier estimate of $R_G$.