Implicit Hydration Modelling in Small-Angle X-Ray Scattering for Protein Structure Determination

Abstract

Small angle X-ray scattering (SAXS) data are being increasingly used in structure modeling of biomacromolecular systems such as proteins. While some great progresses have been made in modelling theoretical scattering intensity from a given structure, what is still challenging is the molecular structure optimization based on experimental intensity data. To address this issue, we propose a new method to evaluate the theoretical scattering intensity of an input protein structure by accounting for hydration in an accurate, but efficient fashion. The method is designed specifically for performing efficient structure optimizations. In our approach, form factors of protein atoms or coarse-grained beads are modified by incorporating an implicit hydration term scaled by their solvent accessible surface areas to represent the hydration-layer scattering. A key advantage of the approach is the availability of analytical derivatives of the scattering intensity with respect to the protein coordinates, making our method very suitable for performing structure modelling using gradient-based optimization schemes. Another technical advance is that the implicit hydration term is parameterized by fitting the theoretical scattering intensities computed from all-atom protein models with explicit hydration water molecules for a high resolution non-redundant protein structure dataset. We show that the obtained implicit hydration term is of good accuracy and applicable to both atomistic and coarse-grained structure representations. By using a pseudo energy function containing a SAXS-fitting score and a structure-restraint term, together with the conjugate gradient method to perform structure optimization, we can obtain final structures very close to the known target structures for four benchmark protein molecules. Taken together, this newly developed implicit hydration approach for SAXS-intensity evaluation is capable of accurate SAXS computing, thereby can be of great usage in the structure modelling based on experimental SAXS profiles.