Nowadays, advanced technologies have made it possible to observe and record biomedical, chemical, and physical phenomena at the molecular level. However, relating data items collected from the particle level into a natural context is still a challenge both theoretically and practically. As mentioned in this paper, under appropriate chemical conditions, a small-angle x-ray scattering (SAXS) can find the distribution of distances between every pair of points in a biomolecular complex. The authors’ focus is on the relationship between the shape of a biomolecular complex composed of a number of rigid parts and the data obtained from SAXS experiments.

In this preliminary work, the authors propose a model using spherical-Bessel functions to relate the data collected by SAXS to the underlying structure, and viewing rigid-body motion as a sequence of transformations. The model requires calculating integrals of products of these spherical-Bessel functions, which presents a challenge computationally. To overcome the challenge, the authors suggest a recursive computational scheme through deriving a sequence of mathematical equations, and claim their computational approach should be applicable for solving problems of interest in structural biology.

This conference paper presents preliminary theoretical work with advanced mathematics. People who work in bioinformatics, computational biology, and health informatics may want to keep an eye on the results of their planned future work on computer implementation and applications.