Systematic Parameterization of Flory-Huggins Models from Molecular Dynamics Simulations for Ternary Lipid Mixtures

Ternary lipid mixtures with saturated and unsaturated lipids and cholesterol serve as widely used model systems to study coexisting liquid-ordered (L_o) and liquid-disordered (L_d) domains in biomembranes. Despite advances in both experiments and simulations, a computationally efficient systematic approach to extract effective pairwise lipid-lipid and lipid-cholesterol interactions from molecular dynamics (MD) simulations for mesoscale models remains limited. Moreover, parametrizing Flory-Huggins (FH) or lattice Monte Carlo (MC) models becomes especially challenging for multicomponent systems due to the size and complexity of the pairwise interaction matrix. To address this, we aim to bridge molecular-level interactions and continuum mean-field models by implementing a multiscale framework that integrates coarse-grained (CG-MD) and all-atom (AA-MD) simulations with FH theory and lattice MC models. Pairwise interaction energies (w_ij) are extracted from radial distribution functions using the reversible work theorem and formulated into FH interaction parameters (χ_ij). We apply this multiscale framework to determine phase count and analyze tie-line and bistable phase behavior of (L_d/L_o) domains for ternary lipid mixtures, specifically using the FH model. The extracted χ_ij values from MD reproduce domain formation in both MC and FH models. Comparisons across AA-MD, CG-MD, MC, and FH frameworks reveal both quantitative differences and similarities, as well as conserved trends in phase separation behavior. This study establishes a systematic approach to parametrize mesoscale models for multicomponent lipid membranes directly from MD simulations. Furthermore, our approach can serve as a tool for system-specific mesoscale biomembrane modeling studies that embed molecular-level detail and bridge top-down and bottom-up perspectives for future studies.