Field theoretic study of bilayer membrane fusion: II. Mechanism of a stalk-hole complex

Abstract

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first article of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with lipid architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few k(B)T over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway. We emphasize that any mechanism, such as this alternative one, which affects, even modestly, the line tension of a hole in a membrane, affects greatly the ability of that membrane to undergo fusion.

FIGURE 1

Density profiles of bilayers pierced by an isolated hole are shown for three different hole radii: R/R_g = 1, 2, and 5, with R_g the radius of gyration of all polymers. Only the majority component is shown at each point. Solvent segments are white. Hydrophilic and hydrophobic segments of the amphiphile are shaded dark and light, respectively. The tension is zero and f = 0.33.

FIGURE 2

(a) Free energy of a hole in an isolated bilayer as a function of R/R_g at zero tension for various amphiphile architectures, f. From top to bottom the values of f are 0.29, 0.31, 0.33, and 0.35. (b) Same as above, but at fixed f = 0.35 and various tensions γ/γ₀. From top to bottom, γ/γ₀ varies from 0.0 to 0.6 in increments of 0.1.

FIGURE 3

Parameterization of the elongated stalk. The shading schematically shows location of the hydrophobic segments in the plane of symmetry between fusing bilayers. The arc radius R corresponds to the radial distance to the outer hydrophilic/hydrophobic interface in the plane of symmetry. Values of the fractional arc angle α, defined in the range [0, 1], are given at the top of each stalk configuration. Note that α = 0 corresponds to the original stalk, whereas α = 1 corresponds to a family of structures reminiscent of the IMI (see also Fig. 4).

FIGURE 4

Density profile of an inverted micellar intermediate (IMI). The amphiphiles are characterized by f = 0.3. The radius of the IMI, in units of the radius of gyration, R/R_g is 3.4. Grayscale as in Fig. 1. The tension is zero.

FIGURE 5

(a) Free energy of an IMI as a function of R/R_g at zero tension for various amphiphile architectures, f. (b) Free energy of an IMI with f = 0.31 and for various tensions γ/γ₀. From top to bottom, γ/γ₀ varies from 0.0 to 0.4 in increments of 0.1. The minima on these curves correspond to metastable IMI structures.

FIGURE 6

Parameterization of the stalk-hole complex. The shading schematically shows location of the hydrophobic segments in the plane of symmetry between fusing bilayers. The arc radius R corresponds to the radial distance to the hydrophilic/hydrophobic interface of the hemifusion intermediate in the plane of symmetry. Projection of the edge of a hole in one of the membranes is shown with dashed line. The radius of this hole is R – δ. The other membrane does not have a hole. The hydrophobic thickness of the bilayer is δ. Values of the fractional arc angle α, defined in the range [0, 1], are given at the top of each stalk configuration.

FIGURE 7

Four free energy landscapes (in units of k_BT) of the fusion process, plotted as a function of the radius, R (in units of R_g) and circumference fraction α. The architecture of the amphiphiles and the value of the tension γ/γ₀ are given. The dotted line shows a ridge of possible transition states, separating two valleys. The region close to the α = 0 line corresponds to a barely elongated stalk intermediate (see Eq. 5). The other valley, close to α = 1 states, corresponds to a hole almost completely surrounded by an elongated stalk. The saddle point on the ridge, denoted by an open dot, corresponds to the optimal (lowest free energy) transition state. The energy of the defect, F_d has been set to zero here.

FIGURE 8

Plot of α*, which corresponds to the optimal transition state in the stalk-hole mechanism, as a function of architecture of the amphiphiles and the tension of the membrane.

FIGURE 9

Line tensions of an elongated linear stalk, λ_ES, of a bare hole in a membrane, λ_H, and of a hole that forms next to an elongated stalk, λ_SH as a function of architecture, f. All line tensions are in units of k_BT/R_g.

FIGURE 10

Free energy barriers measured relative to the initial metastable stalk, in units of k_BT, in (a) the new stalk-hole complex mechanism, and (b) the standard hemifusion mechanism.

FIGURE 11

(a) Difference between the free energy barrier in the standard mechanism and that in the new mechanism, in units of k_BT, as a function of architecture, f₀, and tension. The defect free energy is here taken to be zero. (b) Same as in a, except that the defect free energy is taken to be 4 k_BT.

FIGURE 12

Difference in free energy, in units of k_BT, between the stalk-hole transition state and fusion pore of the same radius.