Next generation of ultra-coarse-graining: Self-consistent inference of critical internal states

Bottom-up coarse-graining systematically expands the length and effective timescales accessible to molecular dynamics simulations, but the information loss during coarse-graining can prevent an accurate incorporation of the multistate phenomena common in complex biomolecular dynamics. The Ultra-Coarse-Graining (UCG) method projects the influence of discrete "quantum-like" extended degrees of freedom, "internal states," onto the coarse-grained (CG) mapped molecules, significantly extending the expressiveness of the CG model. The previous rapid-local-equilibrium (RLE) approximation in UCG depends on user-defined collective variables (CVs, e.g., local density) and does not incorporate correlations between internal states within and between CG molecules. We present Self-Consistent UCG (SC-UCG), an integrated methodology that utilizes the underlying UCG interactions directly for internal state designation, without designing collective variables in the CG ensemble. For simulations, the internal state probabilities are self-consistently determined via graph message-passing in simulation time. We also enhance the RLE Hamiltonian with the Bethe approximation plus AI-based inference to allow explicit internal state correlations between UCG beads. For forcefield training, we develop Multilayer Internal State Consistency, a machine-learning-based method derived from the relative entropy minimization principle that does not require iterative sampling of the intermediate forcefields. We then apply SC-UCG to a model tetramer system with a second-order symmetry-breaking phase transition from the supercritical racemic fluid into subcritical D-rich and L-rich fluids. We show that SC-UCG can capture collective switching events of internal UCG states in the subcritical region, and it exhibits temperature transferability by recapitulating the phase transition, even if trained from a single-temperature dataset.