Autocovariance structures for radial averages in small-angle X-ray scattering experiments


Correspondence to: F. Jay Breidt, Department of Statistics, Colorado State University, 201 Statistics Colorado State University, Fort Collins, CO 80523 USA


Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging, that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This article reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.