Fitting high-resolution electron density maps from atomic models to solution scattering data

Abstract

Solution scattering techniques, such as small and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for a free fitting parameter commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated which uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization results in a significant improvement of the calculated scattering profiles compared to the leading software. The algorithm is computationally efficient, showing more than tenfold reduction in execution time compared to the leading software. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package ( https://github.com/tdgrant1/denss ). In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms utilizing SWAXS data while decreasing the risk of overfitting. Statement of Significance: Accurate calculation of small and wide-angle scattering (SWAXS) profiles from atomic models is useful for studying the solution state and conformational dynamics of biological macromolecules in solution. Here we present a new approach to calculating SWAXS profiles from atomic models using high resolution real space density maps. This approach includes novel calculations of solvent contributions that remove a significant fitting parameter. The algorithm is tested on multiple high quality experimental SWAXS datasets, showing improved accuracy compared to leading software. The algorithm is computationally efficient and robust to overfitting, paving the way for increasing the accuracy and resolution of modeling algorithms utilizing experimental SWAXS data.