Fluctuation X-ray scattering for systems of particles obeying arbitrary orientational distributions: from theory to applications

In the field of single-particle imaging (SPI) randomness manifests itself in the distribution of rotation states of several instances of the particle to be imaged. The technique of fluctuation X-ray scattering (FXS) seeks to merge the concept of statistical moments with SPI and use randomness to its advantage. It can be understood as natural extension to the study of the averaged diffraction pattern ⟨I⟩, which is a common analysis method in Small- and Wide-angle X-ray scattering (SAXS/WAXS). Specifically, FXS aims to characterize the structural information that averages of the form ⟨I⟩, ⟨I²⟩, . . . contain and therefore quite literally seeks structure in randomness. Despite its development in the late 1970s and early 1980s, applications of FXS have only recently become possible with the emergence of X-ray free-electron lasers (XFEL). Interestingly XFELs themselves rely on the use of fluctuations as they produce highly intense and coherent X-ray pulses via the process of self-amplified spontaneous emission (SASE), i.e. the amplification of X-ray noise. Their introduction made it possible to carry out “diffraction before destruction” experiments on individual bio-particles, which have been theorized before. These measurements allow to record diffraction patterns from random orientation states of the studied particles. Alongside of F XS this lead to the development of the previously mentioned single-particle imaging (SPI) technique, which holds the prospect of providing high resolution structure recovery. FXS shares this prospect with SPI, but it also allows for single-particle reconstructions from multi-particle scattering. This makes FXS especially interesting for the study of particles in solution. It can also be used in a forward modeling approach to understand dynamical changes in optically exited particles, as has been recently demonstrated. This thesis pursues three goals. Firstly it aims to provide a generalized theoretical description of fluctuation X-ray scattering. The second goal is, to report on the development of a software suite for single-particle structure recovery from FXS data and its applications to experimental datasets. Finally, it describes an extension to the theoretical concepts of FXS, that allows the treatment of systems of particles following arbitrary nonuniform rotational probability distributions. The latter is relevant in the analysis of optically excited particles which are known to follow nonuniform distributions, as well as in studies of molecular alignment.