Computer modeling of solution X-ray scattering intensity for biomacromolecules

Abstract

Increasing amounts of scattering data are obtained from high-throughput Solution X-ray scattering (SXS) experiments, including small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). There is a great demand of computational methods that can retrieve useful structural information or build structure model from these data. We have proposed substantial improvements to current methods that model the scattering profiles from protein structure at both atomistic scale and coarse-grained (CG) scale. In addition, our coarse-grained approach can be conveniently applied to structure optimization based on target scattering intensity.

Firstly, a fast Fourier transform (FFT) based orientational average method is proposed to improve the computational efficiency of modeling scattering profiles using an atomistic protein structure representation, especially in case of considering explicit hydration water molecules. Comparing with the popular spherical average method, our method will become more efficient for systems with more than 3000 atoms. Moreover, the computational time of our FFT-based method remains nearly unchanged as the system size increases, making it suitable for very large protein complexes.

CG representations are also widely used to improve the computational efficiency of theoretical scattering intensity computation. Given the importance of accuracy for CG approaches, we have proposed the electron density matching (EDM) method to parameterize the CG form factors. Comparing with the CG form factors used in literature, our EDM-derived ones result in better agreement to atomistic scattering intensities. Furthermore, the resulting CG xxform factors are shown to reproduce the experimental scattering profiles well by including the contribution of hydration layer and the correction of protein excluded volume.

Finally, in order to perform structure modeling with our EDM-derived CG form factors, we have proposed an implicit hydration term to take account the contribution of the hydration layer scattering. This term is only related to the surface accessible solvent area (SASA) of protein atoms, making our formulation to evaluate scattering intensity analytically differentiable to the protein coordinates. The implicit hydration term is fitted to best reproduce the overall scattering intensity computed using explicit hydration water molecules. It is shown that the conjugate gradient structure optimization based on the target scattering intensity can produce final molecular structures very close to the known target structure.