Speed-quality tradeoff in a physical model of molecular sorting

Abstract

Eukaryotic cells rely on membrane-mediated processes to compartmentalize biomolecules, counteracting diffusion-driven homogenization. These processes involve the selective sorting and packing of molecules into lipid vesicles, which are then dispatched to appropriate intracellular destinations. Previous works introduced an abstract statistical physics framework for studying this molecular distillation process, where the membrane was treated as static and the focus was on molecular aggregation and extraction. Here, we extend this framework to explicitly incorporate dynamic membrane behavior, including bending, curvature generation, and changes in membrane size due to vesicle fusion and fission events. Sorting domains drive membrane curvature, leading to vesicle formation, detachment, and a molecular distillation process that alters membrane size. Using mesoscopic modeling and numerical tools, we investigate the resulting interplay between membrane mechanics and molecular sorting. We determine a well-defined parameter region where vesicle fission and efficient molecular sorting occur, controlled by membrane rigidity, spontaneous curvature, and pressure difference across the membrane. We further identify a trade-off between speed and quality of molecular distillation: parameters that accelerate vesicle formation tend to reduce the quality of distillation, and vice versa. We propose maximization of the rate of negative entropy production as a natural criterion to optimally balance these competing effects. In this context, optimal parameters emerge naturally from the coupled dynamics of molecular aggregation and membrane mechanics, suggesting a possible strategy for cellular sorting systems to strike an efficient balance between rapid vesicle formation and high sorting quality.