Using Small-Angle Scattering Data and Parametric Machine Learning to Optimize Force Field Parameters for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered regions (IDRs) play important roles in many aspects of normal cell physiology, such as signal transduction and transcription, as well as pathological states, including Alzheimer's, Parkinson's, and Huntington's disease. Unlike their globular counterparts that are defined by a few structures and free energy minima, IDP/IDR comprise a large ensemble of rapidly interconverting structures and a corresponding free energy landscape characterized by multiple minima. This aspect has precluded the use of structural biological techniques, such as X-ray crystallography and nuclear magnetic resonance (NMR) for resolving their structures. Instead, low-resolution techniques, such as small-angle X-ray or neutron scattering (SAXS/SANS), have become a mainstay in characterizing coarse features of the ensemble of structures. These are typically complemented with NMR data if possible or computational techniques, such as atomistic molecular dynamics, to further resolve the underlying ensemble of structures. However, over the past 10-15 years, it has become evident that the classical, pairwise-additive force fields that have enjoyed a high degree of success for globular proteins have been somewhat limited in modeling IDP/IDR structures that agree with experiment. There has thus been a significant effort to rehabilitate these models to obtain better agreement with experiment, typically done by optimizing parameters in a piecewise fashion. In this work, we take a different approach by optimizing a set of force field parameters simultaneously, using machine learning to adapt force field parameters to experimental SAXS scattering profiles. We demonstrate our approach in modeling three biologically IDP ensembles based on experimental SAXS profiles and show that our optimization approach significantly improve force field parameters that generate ensembles in better agreement with experiment.