The hydrophobic insertion mechanism of membrane curvature generation by proteins

Abstract

A wide spectrum of intracellular processes is dependent on the ability of cells to dynamically regulate membrane shape. Membrane bending by proteins is necessary for the generation of intracellular transport carriers and for the maintenance of otherwise intrinsically unstable regions of high membrane curvature in cell organelles. Understanding the mechanisms by which proteins curve membranes is therefore of primary importance. Here we suggest, for the first time to our knowledge, a quantitative mechanism of lipid membrane bending by hydrophobic or amphipathic rodlike inclusions which simulate amphipathic alpha-helices-structures shown to sculpt membranes. Considering the lipid monolayer matrix as an anisotropic elastic material, we compute the intramembrane stresses and strains generated by the embedded inclusions, determine the resulting membrane shapes, and the accumulated elastic energy. We characterize the ability of an inclusion to bend membranes by an effective spontaneous curvature, and show that shallow rodlike inclusions are more effective in membrane shaping than are lipids having a high propensity for curvature. Our computations provide experimentally testable predictions on the protein amounts needed to generate intracellular membrane shapes for various insertion depths and membrane thicknesses. We also predict that the ability of N-BAR domains to produce membrane tubules in vivo can be ascribed solely to insertion of their amphipathic helices.

FIGURE 1

Schematic representation of lipid monolayer bending (lipid molecules shown in light shading) by insertion of a cylindrical inclusion (shown in dark shading), where L is the half-distance between the inclusions, h is the monolayer thickness, and r is the inclusion radius. (a) The monolayer is flat before the inclusion insertion; (b) the monolayer bends as a result of inclusion insertion.

FIGURE 2

Different cases of monolayer coupling within a bilayer. (a) Laterally uncoupled monolayers. The inclusions (rectangles) are inserted only into a small fragment of a large membrane. The two monolayers of the fragment can independently exchange lipids with the monolayers of the surrounding membrane which plays a role of lipid reservoir (the exchange is indicated by the arrows). (b) Laterally coupled monolayers. The inclusions are inserted across the whole area of a closed membrane. The effects of slow trans-monolayer flip-flop of lipids are neglected.

FIGURE 3

Qualitative essence of the mechanism of membrane bending by small cylindrical inclusions. The case of laterally coupled monolayers. (a) A shallow inclusion insertion expands the upper layer of the membrane (left). Partial relaxation of the generated stresses results in positive curvature (J > 0) (right). (b) Deeper insertion produces an expansion of the upper monolayer (left), which due to the lateral coupling generates stresses in the lower monolayer leading to positive membrane curvature (right). (c) Insertion in the bilayer midplane generates symmetrically distributed stresses, causing an overall membrane expansion but no curvature. (d) Insertion into the lower monolayer expands the lower part of the membrane, hence generating negative curvature (J < 0).

FIGURE 4

Qualitative essence of the mechanism of membrane bending by small cylindrical inclusions. The case of laterally uncoupled monolayers. (a) A shallow inclusion insertion expands the upper part of the upper monolayer (left), which generates a positive curvature of the upper monolayer leading to positive curvature of the whole membrane (J > 0) (right). (b) Deeper insertion produces a bare expansion of the upper monolayer, which, due to the monolayer uncoupling, does not generate curvature. (c) Insertions in the lower portion of the upper monolayer (left) induces negative membrane curvature (J < 0).

FIGURE 5

A typical conformation of a membrane with cylindrical inclusions (dark blue). (a) The case of laterally uncoupled monolayers (where the second monolayer is not considered to influence the ability to bend). The membrane shape corresponds to the preferred shape of the upper monolayer containing the inclusions as if the lower monolayer (depicted in gray) would not resist bending and just fit the upper one. (b) The case of laterally uncoupled monolayers. The membrane shape is determined by the interplay of the tendency of the upper monolayer to adopt the conformation presented in panel a and the resistance of the lower monolayer to bend. (c) The case of laterally coupled monolayers. The shear strain (dimensionless) in the monolayers is represented as a logarithmic color scale.

FIGURE 6

Monolayer spontaneous curvature plotted as a function of the inclusion area fraction for a 0.8-nm depth of insertion.

FIGURE 7

Spontaneous curvature for an inclusion plotted as a function of the position of the center of the inclusion for (a) uncoupled, and (b) coupled monolayers. Cartoons of the bilayer are shown for different insertion depths.

FIGURE 8

Sensitivity of the effective spontaneous curvature of the inclusion, ς_inc, to the monolayer thickness. (a) ς_inc as a function of the position of the center of the inclusion for different values of the monolayer thicknesses h, where h can be 1.8, 2.0, or 2.2 nm. (b) ς_inc as a function of the monolayer thickness h for the insertion depth of 0.8 nm.

FIGURE 9

Energetic penalty per unit length of the inclusion plotted as a function of the depth of the insertion for coupled monolayers.

FIGURE 10

The range of α-helix area fractions required to form cylindrical membrane tubes of diameter 35–50 nm, plotted as a function of the position of the center of the inclusion, for uncoupled (red) and coupled (gray) monolayers. The maximal possible area fractions of α-helices for endophilin and amphiphysin are represented by straight lines.

FIGURE 11

The effective spontaneous curvature of inclusion as a function of the position of the center of the inclusion in the case of coupled monolayers (a) without any lateral stress profile and (b) with a lateral stress profile accounting for a monolayer spontaneous curvature in the initial state

FIGURE 12

The energy penalty of the inclusion insertion per inclusion unit length as a function of the position of the center of the inclusion in the case of coupled monolayers without any lateral stress profile and with a lateral stress profile accounting for a monolayer spontaneous curvature in the initial state

FIGURE 13

Sensitivity of the effective spontaneous curvature of the inclusion, ς_inc, to the specific value of the transverse shear modulus λ_xzxz.

FIGURE 14

Sensitivity of the effective spontaneous curvature to (a) the monolayer thickness and (b) the transverse shear modulus for the case of coupled monolayers.

FIGURE 15

Sensitivity of the energy penalty of the inclusion insertion per inclusion unit length in the case of coupled monolayers to (a) the monolayer thickness h and (b) the transverse shear modulus λ_xzxz.

FIGURE 16

Sensitivity of the effective spontaneous curvature to the inclusion radius for the cases of (a) uncoupled monolayers, and (b) coupled monolayers.