Endocytic vesicle scission by lipid phase boundary forces

Abstract

Endocytosis in budding yeast is thought to occur in several phases. First, the membrane invaginates and then elongates into a tube. A vesicle forms at the end of the tube, eventually pinching off to form a "free" vesicle. Experiments show that actin polymerization is an active participant in the endocytic process, along with a number of membrane-associated proteins. Here we investigate the possible roles of these components in driving vesiculation by constructing a quantitative model of the process beginning at the stage where the membrane invagination has elongated into a tube encased in a sheath of membrane-associated protein. This protein sheath brings about the scission step where the vesicle separates from the tube. When the protein sheath is dynamin, it is commonly assumed that scission is brought about by the constriction of the sheath. Here, we show that an alternative scenario can work as well: The protein sheath acts as a "filter" to effect a phase separation of lipid species. The resulting line tension tends to minimize the interface between the tube region and the vesicle region. Interestingly, large vesicle size can further facilitate the reduction of the interfacial diameter down to a few nanometers, small enough so that thermal fluctuations can fuse the membrane and pinch off the vesicle. To deform the membrane into the tubular vesicle shape, the membrane elastic resistance forces must be balanced by some additional forces that we show can be generated by actin polymerization and/or myosin I. These active forces are shown to be important in successful scission processes as well.

Fig. 1.

Schematic picture of the theoretical model for endocytosis. (Inset) The actin filaments exert protrusive surface stresses on the bud and tubule. The tubule coat proteins create a lipid phase boundary between the bud and the tubule. The clathrin adaptor proteins may add to the bending modulus and spontaneous curvature of the bud region.

Fig. 2.

The decrease in the diameter of the interfacial line as the surface area of the bud increases for large interfacial line tension λ = 60 pN. The series of equilibrium membrane shapes is obtained by means of the variational method with the constraints that the mechanical forces applied to the membrane surface by the actin filaments is constant. The membrane parameters are as follows: bending rigidities κ₁ = 50 k_BT, κ₂ = 100 k_BT; the Gaussian bending rigidities κ_G⁽¹⁾ = κ_G⁽²⁾; the surface tensions σ₁ = 5 × 10⁻⁵ N/m, σ₂ = 1 × 10⁻⁴ N/m; the active force ƒ = 1.0 pN, α = 2π/3; the osmotic pressure P₀ = 0. The surface areas of the buds are as follows: 1,668 nm² (a); 2,980 nm² (b); 4,760 nm² (c); and 8,415 nm² (d). The corresponding diameters of the interfacial line are as follows: 16.00 nm (a); 8.94 nm (b); 6.14 nm (c); and 4.71 nm (d). The natural length cutoff in this model is the width of the membrane, ≈5 nm. Therefore, the actual distance between the two inner leaflets at the interface for d is negative, i.e., the bud is already pinched off. The line is fit to the computed points (♦). Note that as the surface area of the bud region approaches zero, the diameter of the interface does as well. Because the surface area of the bud region is very small, the bending energy per area dominates the line tension; consequently, increasing the interfacial line dominates bending the membrane surface. Conversely, when the surface area of the bud is very large, the bending energy per area is dominated by the line tension, and the interface will shrink, making the membrane bend more. Therefore, the peak in the plot corresponds to the point where the bending energy per area is comparable to the line tension. We restrict ourselves to line tensions that dominate, corresponding to the case where the interfacial diameter decreases as the bud size increases.

Fig. 3.

The decrease in the diameter of the interfacial line upon increasing the surface area of the bud for small interfacial line tension λ = 30 pN, using the same parameters as in Fig. 2. The surface areas of the buds are as follows: 3,371 nm² (a); 4,952 nm² (b); and 13,235 nm² (c). The corresponding diameters of the interfacial line are as follows: 30.9 nm (a); 26.6 nm (b); and 20.55 nm (c). Using the same cutoff length of 5 nm as in Fig. 2, the actual distances between the two inner leaflets at the interface for a, b, and c are 25.92, 21.61, and 15.55 nm, respectively. Line is fit to the computed points (●).

Fig. 4.

The phase diagram (line tension, λ, vs. surface active force, ƒ) for the successful scission of the bud for a given set of the membrane mechanical forces. Large line tension and large active forces are needed for successful scission of the vesicle. The membrane mechanical constants are κ₁ = 50 k_BT, κ₂ = 100 k_BT; κ_G⁽¹⁾ = κ_G⁽²⁾; σ₁ = 5 × 10⁻⁵ N/m, σ₂ = 1 × 10⁻⁴ N/m; ƒ = 1.0 pN, α = 2π/3; P₀ = 0, and α = 2π/3. The criteria for successful scission of the bud is when the actual distance between the two inner leaflets at the interface is less than zero for the surface area of the bud <2 × 10⁴ nm².