Membrane vesicles embedded with multiple curved proteins subjected to osmotic pressure

Biological membranes with distinct mechanics are crucial for many important biological processes (e.g., endocytosis, metabolism and intercellular trafficking) that require specific cell or organelle membrane shape for successful implementation of relevant cellular functions. In biological systems, the membrane morphology would be simultaneously modulated by curvature-sensing proteins and osmotic pressure. However, the underlying mechanical interplay among these two biophysical factors and the membrane mechanics remains largely unclear during membrane deformation. To address this issue, using dynamic triangulation Monte Carlo simulations of membrane vesicles embedded with multiple curved proteins under osmotic pressure, we investigate the stochastic dynamics and thermal equilibrium configurations of the vesicle system. This stochastic method captures a range of microscopic stochastic behaviors, including membrane fluctuations, protein motion, and vesicle shrinkage. A comparative study reveals the cooperative effects of osmotic pressure and curved proteins on vesicle morphology, dependent on membrane mechanics. In elastic membranes, osmotic pressure alone induces concave shapes, while curved proteins create rough quasi-spherical structures; their combination synergistically forms highly folded, low volume-to-area ratio morphologies. In fluid membranes, osmotic pressure inhibits tubular structures driven by curved proteins due to increased membrane tension. Diverse dynamic and equilibrium configurations are identified as functions of solution concentration, protein curvature, and membrane mechanics, consistent with prior literature. These findings provide a mechanical understanding of how osmotic pressure and curvature-sensing proteins jointly regulate vesicle deformation.