Abstract
The assembly, number density, and size distribution of biomolecular condensates are central to their biological functions, but the nucleation kinetics that precede growth and coalescence remain difficult to characterise experimentally and in simulations. In this work, we develop a theoretical framework to apply the critical cluster equivalence principle (CEP), which builds on the thermodynamic equivalence between stable clusters in confined systems and critical clusters in open systems, to multicomponent liquids undergoing phase separation into solvent-and solute-rich phases. We first test the proposed approach in a symmetric Lennard-Jones mixture, where nucleation rates agree with large-scale Yasuoka–Matsumoto simulations and the predicted critical cluster sizes match independent seeding results. We then use the validated approach to investigate a homopolymeric chainsolvent system, introducing concepts intrinsic to biomolecular condensates such as chain rigidity and connectivity. Here, the CEP predicts the coexistence composition and interfacial tension for both the forward nucleation of dense condensates and the reverse formation of dilute voids, indicating that the curvature dependence is consistent in both directions, thereby uncovering a forward/reverse relationship that has primarily been studied for single-component droplets and bubbles, now demonstrated for a compositionally mixed liquid phase separation. Overall, the CEP-based workflow employs smaller systems and shorter simulations than conventional nucleation methods. These findings indicate a comprehensive methodology for quantitatively examining biomolecular condensate nucleation in explicit solvent.