Liquid-liquid phase separation in a minimal explicit-solvent lattice model mimicking protein solutions

Biomolecular condensates play an essential role in cellular processes, and recent studies have focused on understanding their assembly and rational design principles. In this work, we have employed an explicit-solvent minimal statistical mechanical model based on the lattice-gas Hamiltonian with quenched disorder-which mimics crowders-to investigate how protein-solvent and protein-crowder interactions influence condensate phase behavior and morphology. The computed phase diagrams reveal rich behavior, including upper critical solution temperature, closed-loop, and reentrant type, under varying protein-solvent interactions in both equilibrium and out-of-equilibrium conditions. We elucidated the origin of the observed solvent-induced alterations of phase behavior and examined the role of protein-crowder interactions in modulating the morphology and stability of the condensate. We further extended this model to binary protein mixtures, where we studied the phase behavior in the presence and absence of quenched disorder. Without disorder, the system exhibits diverse phase-separated morphologies-partially wetted, fully wetted, segregative, and associative-with phase boundaries delicately sensitive to protein-solvent interactions. The presence of quenched disorder (or crowders) expands the range of accessible morphologies through the intricate interplay between protein-protein, protein-solvent, and protein-crowder interactions. Overall, this work underscores that protein-solvent and protein-crowder interactions, together with protein-protein interactions, can act as key regulatory parameters for modulating the morphology of the condensate. These insights may guide future computational and experimental studies of liquid-liquid phase separation in biomolecular systems aimed at designing stimuli-responsive condensates.