Tubulation of membrane sheets by curvature-inducing proteins

The endoplasmic reticulum (ER) is a highly dynamic organelle that undergoes continuous remodeling between tubular and sheet-like structures, driven by curvature-inducing proteins and membrane mechanics. Understanding the physical principles underlying ER shape transitions is crucial for elucidating its role in cellular homeostasis and disease. In this study, we use a mesoscopic model of membrane-protein interactions to investigate how intrinsic curvature, protein concentration, and membrane stiffening collectively regulate ER tubulation. Our results demonstrate that the critical concentration for tubulation depends nonlinearly on intrinsic curvature due to a competition between adsorption and remodeling ability. Additionally, increased membrane stiffness upon protein adsorption enhances tubulation efficiency at lower intrinsic curvatures and changes tubule geometry at higher intrinsic curvatures. Phase diagrams are constructed to map the conditions necessary for membrane remodeling, revealing critical protein concentration thresholds for ER transformation. These findings provide a quantitative framework for ER shape regulation, offering insights into how different curvature-inducing proteins coordinate ER morphogenesis.