Reweighting Ensembles of Backmapped Configurations for Protein Sidechains and Water

Multiscale modeling requires the linking of models at different levels of detail, with the goal of gaining accelerations from lower fidelity models while recovering fine details from higher resolution models. Ideally, tight communication and seamless switching between models at different resolutions is possible. This is particularly important in molecular simulations of soft matter, where there is a tight coupling between molecular-level details and mesoscale structures. While multiscale modeling of soft matter has become a critical component in exploring the structure and reorganization of mesoscopic domains, backmapping from coarse-grained to fine-grained, or atomistic, representations presents a challenge, despite recent advances through machine learning. A major hurdle, especially for machine learning strategies, is that most backmappings can only approximately recover the atomistic ensemble of interest. This can be corrected, however, through the process of reweighting, where careful assignment of weights to samples drawn from one ensemble allows for the calculation of properties in another ensemble. For both protein sidechains and water, we present backmapping models based on conditional normalizing flows and geometric algebra attention. Critical for reweighting, our trained models provide not only configurations, but the probabilities associated with their generation. We also demonstrate, however, that reweighting is extremely challenging despite state-of-the-art performance on recently developed metrics and generation of configurations with low energies in atomistic protein force fields. Through detailed analysis of configurational weights, we demonstrate that machine-learned backmappings must not only generate configurations with reasonable energies, but also correctly assign relative probabilities under the generative model. These considerations are of fundamental importance when developing generative models at atomistic resolution for any system.