A Dynamical Density Functional Theory Framework for Non-Equilibrium Phase Dynamics in Biomolecular Condensates

Biomolecular condensates, membrane-less organelles that arise from liquid-liquid phase separation (LLPS) of proteins and nucleic acids, play vital roles in cellular organization and regulation. Computational modeling is crucial for uncovering the molecular mechanisms behind LLPS; however, the fluctuations across a wide range of spatial scales and the inherently non-equilibrium nature of these systems make capturing their long-timescale dynamics particularly challenging. Here, we present a continuum dynamical density functional theory (DDFT) framework that captures the non-equilibrium dynamics of LLPS by integrating a physics-based statistical mechanical theory with key experimentally-derived parameters. Our model couples DDFT with a continuum free energy functional, incorporating two-body correlations between monomers and surface tension effects to determine binodal densities under phase coexistence. By solving the DDFT equations, we describe the time evolution of phase-separated domains, capturing key long-timescale processes such as droplet maturation, coalescence, and interface relaxation, phenomena that are difficult to probe using atomistic or mesoscale coarse-grained simulations. This implementation integrates experimental phase equilibrium data with molecular-scale descriptors, such as amino acid properties, to construct a quantitative link between molecular interactions and macroscopic phase behavior. However, the approach is generalizable, providing a foundation for self-contained molecular-to-continuum modeling bridge platforms.