Efficient Analysis of Small-Angle Scattering Curves for Large Biomolecular Assemblies Using Monte Carlo Methods

Structure elicitation from small angle scattering (i.e. SAXS, SANS) curves of large biomolecular assemblies is notoriously challenging. This is because the simulation of high-resolution features in the structure of large macromolecular assemblies, such as de-novo protein assemblies, is computationally demanding when it needs to cover a broad range of length scales. Conventional methods such as the numerical solution to the Debye equation or the use of Spherical Harmonics do not scale well as the size of the assembly increases, which limits their application to small structures (e.g. individual proteins). In this work, we explore the effectiveness of a Monte Carlo method to simulate and fit scattering curves for large biomolecular assemblies spanning over ranges covering atomic and molecular detail as well as the large scale (100’s of nm) features that describe the shape of assemblies integrating complex building blocks. The method uses Monte Carlo sampling to first estimate the pairwise distribution of scattering points, by randomly selecting pairs of points, calculating the distance between them, weighing them by the local scattering length density (SLD), and statistically accounting for the prevalence of pair-distances. The resulting pair-distance distribution is then quickly transformed into the simulated and experimentally accessible scattering intensity using Fourier Inversion. Due to its excellent speed and scalability, we can combine it with a fitting algorithm to extract structural features from real small angle scattering curves in biomolecular assemblies that were otherwise intractable for interpretation. We first demonstrate the effectiveness of this tool with experimental data from tile-like proteins that assemble in 1D tube-like macromolecular structures, where we extract information on the size distribution of the diameters of the tubes and confirm the results by comparing quantitatively with electron microscopy images. We also obtain experimental data on 2D sheet-like protein assemblies and use our method to quantify information on structural features such as the separation distance between protein building blocks. We finally describe the open-source implementation of the computational tools and anticipate widespread usage given their relevance to studies in biological systems, computation speed, accessibility, and accuracy.