Bayesian Refinement of Accelerated Molecular Dynamics Simulations for Interpreting SAXS Experiments

Small angle X-ray scattering (SAXS) is an experimental method that is useful for capturing the full ensemble of flexible biomolecules, but it typically results in low-dimensional data that is difficult to interpret without additional structural knowledge. In principle, this information may be provided by molecular dynamics (MD) simulation, but conventional MD trajectories rarely represent the complete ensemble. Accelerated MD (aMD) was developed to overcome these sampling inadequacies by introducing a bias to the underlying energy landscape, which distorts the observed ensemble as a result. Here, we present a method for fitting aMD simulations with experimental SAXS data to accurately model the relative populations of representative solution states. Scattering states are first identified from MD trajectories, and then their populations are re-weighted against empirical data through a Bayesian Monte Carlo approach. Resistance to ensemble over-fitting is achieved by iteratively considering increasing subsets of scattering states and by reducing experimental data to the Shannon sampling limit. We apply this technique to several ubiquitin trimers and find that aMD models converge upon agreement with the observed SAXS profiles up to an order of magnitude faster than conventional simulations.