Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Abstract

Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. The formation of plasma membrane tubes can be due to localized forces acting on the membrane or by curvature-induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.1Significance StatementCylindrical tubes are ubiquitous on cellular membranes and many studies have focused on how forces can give rise to tubes. How do curvature-inducing proteins, in the absence of forces, form cylindrical tubes on lipid bilayers? The answer to this question relies on minimizing the bending energy of the membrane to accommodate two different principal curvatures such that a cylindrical shape is an energy minimizer. Here, we build on previous works to develop such a model and show that the formation of an elongated cylindrical tube is accompanied by a snapthrough transition in the bending energy. Furthermore, we identify how this transition depends on different membrane properties, providing a landscape for comparing with different experimental observations. These findings have implications for our understanding how tubes forms in different cellular processes including trafficking, mitochondrial inner membrane cristae formation, and T-tubule formation in myocytes.

Cristae formation is a mechanical buckling event controlled by the inner mitochondrial membrane lipidome

“…To understand the interaction between CL, which contributes to net membrane spontaneous curvature, and ATP synthase oligomers, whose induced curvature is localized specifically at cristae ridges, we employed a continuum modeling framework based on previous efforts to model membrane tubule formation (Mahapatra & Rangamani, 2023). We modeled the simplest CM structure—tubules—as axisymmetric tubes that bud from a flat membrane (Fig 5A).…”

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

“…To understand the interaction between CL, which contributes to net membrane spontaneous curvature, and ATP synthase oligomers, whose induced curvature is localized specifically at cristae ridges, we employed continuum modeling framework based on previous efforts to model membrane tubule formation 73,103–105 . We modeled the simplest CM structure — cristae tubules — as axisymmetric tubes that bud from a flat membrane (Figure 5A).…”

“…via CL-encoded membrane spontaneous) was increased for a fixed value of anisotropic curvature (Figure 5Cii) for the different values of bending moduli (see also Figure S5 for additional simulations). This sudden change in length is characterized by a snapthrough transition, where a small amount of thermodynamic work done on the system, by changing either material properties or curvatures induced, results in a change in the minimal energy state of the system where a tube-like shape is a low energy configuration 103,104,108,109 . We observed that the curvature values at which this transition occurs was modulated by the presence of a collar force at the tubular neck, suggesting that mechanics could underlie the functional interactions observed between Mic60p at the CJ and PL saturation (Figure S2C, Figure S5).…”

Formation of membrane invaginations by curvature-inducing peripheral proteins: free energy profiles, kinetics, and membrane-mediated effects

“…Mathijs et al considered a Ginzburg-Landau-type free energy for the protein coat and discussed the stability of the cylindrical tubes covered with proteins [19]. Mahapatra and Rangamani developed a theoretical model to estimate the free energy of membrane tubulation due to bound BAR-domain proteins with anisotropic curvature, and showed the snapthrough characteristics in the dome-to-cylinder transitions [20] Here we offer a fresh take on this problem, using a mesoscopic dynamical membrane model [21]. We had previously shown this model to reproduce realistic kinetics attributed to membrane fluctuations [22,23] as well as lateral diffusion of membrane-bound peripheral proteins [24].…”

“…Mathijs et al considered a Ginzburg-Landau-type free energy for the protein coat and discussed the stability of the cylindrical tubes covered with proteins [19]. Mahapatra and Rangamani developed a theoretical model to estimate the free energy of membrane tubulation due to bound BAR-domain proteins with anisotropic curvature, and showed the snap-through characteristics in the dome-to-cylinder transitions [20]. While these studies are quite illuminating, they usually ignore membrane-protein interplay in a dynamical setup, and thus, provide limited information on the kinetics of the tubulation process.…”