An Algorithm to Calculate the Diffraction Patterns of X-rays and Neutrons From Simulations of Open and Closed Chemical Surfaces

Small-angle scattering (SAS), either with X-rays (SAXS) or neutrons (SANS), is an experimental structural characterization technique for rapid analysis of biological macromolecules in solution. Because the macromolecules do not need to be crystallized, they can be analyzed at different pH and concentration values, thus yielding their general shape, size, and structure-function relationships. Theoretical scattering profiles can be obtained using the Debye scattering equation. It is a weighted, analytical Fourier transform of the radial distribution function of the atoms in the macromolecule. In addition, this equation is weighted by the scattering length of the particles being considered. The Debye scattering equation is helpful because it allows the modeling of complex objects by summing small spherical volumes. It requires as input only the atomic Cartesian coordinates to generate intensities as a function of the magnitude of the moment transfer vector. In this study, we developed, implemented, and validated an algorithm for calculating the diffraction patterns of X-rays and neutrons using the Debye scattering equation. The proposed algorithm is general and can be applied to any biochemical system. In addition, we have also developed an alternative approach to calculate diffraction profiles from electron and neutron distributions. We have benchmarked the new implementations for atomistic trajectories of lipid membranes and vesicles taking advantage of functionalities available in the SuAVE software [1,2], developed in our research group (www.biomatsite.net/suave-software).

1. Santos, Pontes, Lins, Coutinho, Soares. 2020. SuAVE: A Tool for Analyzing Curvature-Dependent Properties in Chemical Interfaces. JCIM, 60, 473-484.
DOI: 10.1021/acs.jcim.9b00569
2. Santos, Coutinho, Soares. 2022. Surface Assessment Grid Evaluation (SuAVE) for Every Surface Curvature and Cavity Shape. JCIM, 62, 4690–4701.
DOI: 10.1021/acs.jcim.2c00673