Two-dimensional structure from random multiparticle X-ray scattering images using cross-correlations

Abstract

Knowledge of the structure of biological macromolecules, especially in their native environment, is crucial because of the close structure-function relationship. X-ray small-angle scattering is used to determine the shape of particles in solution, but the achievable resolution is limited owing to averaging over particle orientations. In 1977, Kam proposed to obtain additional structural information from the cross-correlation of the scattering intensities. Here we develop the method in two dimensions, and give a procedure by which the single-particle diffraction pattern is extracted in a model-independent way from the correlations. We demonstrate its application to a large set of synchrotron X-ray scattering images on ensembles of identical, randomly oriented particles of 350 or 200 nm in size. The obtained 15 nm resolution in the reconstructed shape is independent of the number of scatterers. The results are discussed in view of proposed 'snapshot' scattering by molecules in the liquid phase at X-ray free-electron lasers.

Algorithm for Reconstruction of 3D Images of Nanorice Particles from Diffraction Patterns of Two Particles in Independent Random Orientations with an X-ray Laser

“…These arguments are equally applicable to pair correlation as to the two-point triple correlations defined by Kam [3]. Although Pedrini [15] and Kurta et al [16] have proposed methods involving a three-point triple correlation function, the two-point triple correlation functions introduced by Kam [14] are easier to measure when photon counts are weak, as pixels with just two non-zero pixels make contributions. If the probability of a high resolution pixel is non-zero is 10 −2 [12], the probability that two of them are non-zero is 10 −4 .…”

Science Opportunities at the SwissFEL X-ray Laser

“…7b is the 2D diffraction image of the single particle reconstructed following the cross-correlation based protocol, described in detail in ref. [29]. 7.…”

Comparison Study of Different Approaches to Classification of Diffraction Images of Biological Particles Obtained in Coherent X-Ray Diffractive Imaging Experiments

“…Хотя изображения нескольких частиц не подходят для восстановления структуры в экспериментах CXDI, такие изображения позволяют определить параметры структуры изучаемых частиц на основе метода XCCA [45,46,47,48].…”