Unified bottom-up coarse-graining through active subspace learning

Classical molecular dynamics (MD) simulations offer atomistic-scale insight into dynamics, such as protein folding, which are challenging to probe experimentally. To address limitations in achievable timescales of all-atom MD, bottom-up coarse-graining (CG) techniques can be used, where lower-resolution CG models are derived from atomistic information via statistical mechanical principles. However, most approaches treat CG mapping and parametrization as independent problems despite their inherent coupling. We present a unified methodology, called Active Subspace Coarse-Graining (ASCG), for deriving CG mappings and associated potentials of mean force. By identifying directions in atomistic configurational space that maximally describe gradients of the potential energy, we obtain a CG mapping projection describing collective motions and, with that projection, derive corresponding CG forces and equations of motion. For tested biomolecules, the ASCG method recapitulates atomistic distributions while reducing degrees of freedom by over 90% and can be integrated with timesteps up to an order of magnitude larger than conventional CG methods. Overall, ASCG is an interpretable, unified bottom-up CG methodology, and we anticipate its use for long timescale simulations of molecular systems.