A new algorithm for the reconstruction of protein molecular envelopes from X-ray solution scattering data

Abstract

At sufficiently low resolution, the scattering density within the volume occupied by a well folded protein molecule appears relatively flat. By enforcing this condition, three-dimensional protein molecular envelopes may be reconstructed using information obtained from X-ray solution scattering profiles. A practical approach for solving the low-resolution structures of protein molecules from solution scattering data involves modelling the protein shape using a set of volume-filling points (`beads') and transforming the scattering data to a more convenient target, the pair distance distribution function, P(r). Using algorithms described here, the beads interact via a modified Lennard–Jones potential and their positions are adjusted and confined until they fit the expected protein volume and agreement with P(r) is obtained. This methodology allows the protein volume to be modelled by an arbitrary, user-defined number of beads, enabling the rapid reconstruction of protein structures of widely varying sizes. Tests carried out with a variety of synthetic and experimental data sets show that this approach gives efficient and reliable determinations of protein molecular envelopes.