Computation of fluctuation scattering profiles via three-dimensional Zernike polynomials

Ultrashort X-ray pulses from free-electron laser X-ray sources make it feasible to conduct small- and wide-angle scattering experiments on biomolecular samples in solution at sub-picosecond timescales. During these so-called fluctuation scattering experiments, the absence of rotational averaging, typically induced by Brownian motion in classic solution-scattering experiments, increases the information content of the data. In order to perform shape reconstruction or structure refinement from such data, it is essential to compute the theoretical profiles from three-dimensional models. Based on the three-dimensional Zernike polynomial expansion models, a fast method to compute the theoretical fluctuation scattering profiles has been derived. The theoretical profiles have been validated against simulated results obtained from 300 000 scattering patterns for several representative biomolecular species.