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. 2001 Jun 19;98(13):7235-40.
doi: 10.1073/pnas.121191898. Epub 2001 Jun 12.

A quantitative model for membrane fusion based on low-energy intermediates

P I Kuzmin  1 , J Zimmerberg, Y A Chizmadzhev, F S Cohen
Affiliations

A quantitative model for membrane fusion based on low-energy intermediates

P I Kuzmin et al. Proc Natl Acad Sci U S A. .

Abstract

The energetics of a fusion pathway is considered, starting from the contact site where two apposed membranes each locally protrude (as "nipples") toward each other. The equilibrium distance between the tips of the two nipples is determined by a balance of physical forces: repulsion caused by hydration and attraction generated by fusion proteins. The energy to create the initial stalk, caused by bending of cis monolayer leaflets, is much less when the stalk forms between nipples rather than parallel flat membranes. The stalk cannot, however, expand by bending deformations alone, because this would necessitate the creation of a hydrophobic void of prohibitively high energy. But small movements of the lipids out of the plane of their monolayers allow transformation of the stalk into a modified stalk. This intermediate, not previously considered, is a low-energy structure that can reconfigure into a fusion pore via an additional intermediate, the prepore. The lipids of this latter structure are oriented as in a fusion pore, but the bilayer is locally compressed. All membrane rearrangements occur in a discrete local region without creation of an extended hemifusion diaphragm. Importantly, all steps of the proposed pathway are energetically feasible.

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Figures

Figure 1
Figure 1
Illustrations of the intermediate structures of membrane fusion: nipples (N), stalk (S), modified stalk (m-S), and prepore (p-P). The three-dimensional structures are obtained by rotating the illustrated cross sections around the symmetry axis of the system (i.e., the vertical dashed line). The bold solid lines are drawn along the polar head groups of the lipid molecules. The thin solid lines are the neutral surfaces of the bilayer. The dividing surface of m-S, used to calculate the tilt energy, is through the head group region and just on the bilayer side of the thick bold lines. The gray ellipses illustrate the lipid cross-section area along the dividing surface, at, and perpendicular to the molecule axis, a0. The dotted lines are the neutral surfaces of the monolayers. Variables are described in the text.
Figure 2
Figure 2
Equipotentials of the surface of free energy W(rf, l) of two nipples with hydrophobic patches as a function of their separation, l, and radii, rf, of the hydrophobic patches. The contours are 10 kT apart. The circle denotes a saddle-like point; the lowest energy pathway from nipples to stalks is to pass over it, yielding a total energy for transition of 37 kT. Arrows point in the direction of decreases in energy. A three-dimensional representation is shown in the Inset. The trajectory of stalk formation is from the Lower Left to Upper Right (l = 0). The parameters used for calculation are: Rn = 8 nm, P0 = 109 N/m2, ξh = 0.25 nm, Wp − Wn = 400 kT, Lp = 5 nm.
Figure 3
Figure 3
Free energy of a stalk as a function of its outer radius, rp, in the equatorial plane. Wc (planar) and Wc are the free energies of bending cis monolayers into stalks from planar membranes and nipples, respectively. Wf is the free energy of the hydrophobic void that would result if trans monolayers did not approach each other. Ws is the free energy of the modified stalk. The parameters of calculation were: Rn = 8 nm, B = 10 kT, σ0 = 27 erg/cm2, kA = 100 erg/cm2, h = 2 nm, rh = 0.6 nm, l0 = 0.8 nm.
Figure 4
Figure 4
Free energy of a modified stalk, a prepore, and a fusion pore. Lipids rearrange from a modified stalk to the prepore at the intersection point, r*. The prepore spontaneously converts to a conducting fusion pore. Parameters are: Rn = 8 nm, KA = 100 erg/cm2, B = 10 kT, h = 2 nm, rh = 0.6 nm, rw = 0.4 nm, l0 = 0.8 nm.
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