标题： 从SAXS估算蛋白质结构的各向异性 显示英文标题

标题： Estimating the Anisotropy of Protein Structures from SAXS

摘要： 在小角X射线散射（SAXS）领域，估算溶液中粒子的大小通常等同于Guinier图。 这项图表背后的近似方法由Guinier于1939年开发，为低散射角$q$的粒子散射行为提供了一种简单而准确的表征，并且提供了一种计算效率高的方法来推断它们的回转半径$R_G$。 此外，这种近似方法不仅适用于球形散射体，因此在SAXS领域被广泛使用。 然而，当需要估算更多的粒子特性时，例如散射体形状的各向异性，没有类似的或扩展的近似方法可用。 现有的用于表征散射体形状的工具要么依赖于对散射体几何结构的先验知识，要么依赖于迭代过程来推断粒子形状\textit{从头计算}。 \\ 在这项工作中，我们开发了旋转椭球体的低角度散射强度$I(q)$的近似方法，并展示了如何从该近似的参数中提取尺寸和各向异性信息。 除了理想的旋转椭球体之外，我们还表明，该近似方法可以用于推断溶液中分子的尺寸和形状，无论是计算还是实验场景。 我们讨论了我们方法的局限性，并研究了粒子各向异性对Guinier估计值$R_G$的影响。 显示英文摘要

摘要： 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 $R_G$.