Entropy-based methods for formulating bottom-up ultra-coarse-grained models.

Bottom-up coarse-grained (CG) modeling is an effective means of bypassing the limited spatiotemporal scales of conventional atomistic molecular dynamics while retaining essential information from the atomistic model. A central challenge in CG modeling is the trade-off between accuracy and efficiency, as the inclusion of often pivotal many-body interaction terms in the CG force-field renders simulation markedly slower than simple pairwise models. The Ultra Coarse-Graining (UCG) method incorporates many-body terms through discrete internal state variables that modulate the CG force-field according to, e.g., changes in local environment when substantial chemical heterogeneities exist. However, assigning optimal internal states systematically from atomistic simulation data, as well as the practical application of bottom-up UCG theory to biomolecular systems, remain open problems. We develop two synergistic methods to aid in the development of UCG models that can capture inhomogeneities in atomistic systems such as those induced by phase coexistence. The first method establishes the systematic construction of UCG force-fields from a relative entropy minimization principle, while the second method utilizes machine-learning to obtain optimal local order parameters for enhanced model efficiency and transferability. We apply these methods to a methanol liquid-vapor interface and the ripple phase of a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine lipid bilayer and demonstrate that UCG modeling alone recapitulates aspects of phase coexistence that are otherwise not observed in CG modeling.