Efficient analysis of small-angle scattering curves for large biomolecular assemblies using Monte Carlo methods

Abstract

Structure elucidation from small-angle scattering 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 approximation 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). This work explores 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 (e.g. spacing and orientation of proteins in an assembly) as well as large-scale (hundreds of nanometres) features. Owing to its speed and scalability, it can be combined with a fitting algorithm to extract structural features from experimental small-angle scattering curves in biomolecular assemblies that are otherwise intractable for interpretation. This work first demonstrates the effectiveness of the tool using experimental small-angle X-ray scattering (SAXS) data from tile-like proteins that assemble into 1D tube-like macromolecular structures. Here, the diameter distribution of tubes is extracted from SAXS fits, and this is quantitatively compared with distributions from electron microscopy. SAXS data are also obtained from 2D sheet-like protein assemblies, and the proposed method is used to quantify structural features such as the separation distance between protein building blocks and the flexing of the sheet. An open-source implementation of the methodology is provided for use in a broad range of biological systems involving multi-scale scattering analysis.