Benchmarking predictive methods for small-angle X-ray scattering from atomic coordinates of proteins using maximum likelihood consensus data

Stimulated by informal conversations at the XVII International Small Angle Scattering (SAS) conference (Traverse City, 2017), an international team of experts undertook a round-robin exercise to produce a large dataset from proteins under standard solution conditions. These data were used to generate consensus SAS profiles for xylose isomerase, urate oxidase, xylanase, lysozyme and ribonuclease A. Here, we apply a new protocol using maximum likelihood with a larger number of the contributed datasets to generate improved consensus profiles. We investigate the fits of these profiles to predicted profiles from atomic coordinates that incorporate different models to account for the contribution to the scattering of water molecules of hydration surrounding proteins in solution. Programs using an implicit, shell-type hydration layer generally optimize fits to experimental data with the aid of two parameters that adjust the volume of the bulk solvent excluded by the protein and the contrast of the hydration layer. For these models, we found the error-weighted residual differences between the model and the experiment generally reflected the subsidiary maxima and minima in the consensus profiles that are determined by the size of the protein plus the hydration layer. By comparison, all-atom solute and solvent molecular dynamics (MD) simulations are without the benefit of adjustable parameters and, nonetheless, they yielded at least equally good fits with residual differences that are less reflective of the structure in the consensus profile. Further, where MD simulations accounted for the precise solvent composition of the experiment, specifically the inclusion of ions, the modelled radius of gyration values were significantly closer to the experiment. The power of adjustable parameters to mask real differences between a model and the structure present in solution is demonstrated by the results for the conformationally dynamic ribonuclease A and calculations with pseudo-experimental data. This study shows that, while methods invoking an implicit hydration layer have the unequivocal advantage of speed, care is needed to understand the influence of the adjustable parameters. All-atom solute and solvent MD simulations are slower but are less susceptible to false positives, and can account for thermal fluctuations in atomic positions, and more accurately represent the water molecules of hydration that contribute to the scattering profile.