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* Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Faculty of Sciences, Holon Institute of Technology, Holon, Israel; and Section on Membrane Biology, Laboratory of Cellular and Molecular Biophysics, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
Correspondence: Address reprint requests and inquiries to Michael M. Kozlov, E-mail: michk{at}post.tau.ac.il.
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ABSTRACT |
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INTRODUCTION |
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,2). Currently, it is largely accepted that merger of protein-free lipid bilayers as well as fusion between viral and cell membranes, intracellular and developmental membrane fusion reactions proceed according to a universal scenario called the fusion-through-hemifusion pathway (3,4). Within this model, fusion begins with formation of a minimal lipidic bridge between the contacting monolayers of the apposing membranes referred to as the fusion stalk. Further expansion of the fusion stalk into a hemifusion diaphragm and its decay into a growing fusion pore completes the fusion process (1).
Recently, an extensive analysis of the energies of the fusion intermediates was performed aimed at revealing the rate-limiting step of the fusion reaction (see for review Chernomordik and Kozlov (1)). It was shown that for lipid compositions typical for an average biological membrane, the stalk energy is only slightly larger than 40kT (where kT is the product of the Boltzmann constant and the absolute temperature), and can be overcome in the biologically relevant timescale (5). In most cases, the fusion stages downstream the stalk formation and, especially, the fusion pore growth are more energy consuming (1).
Despite its current recognition and successful applications, the fusion-through-hemifusion model leaves open important questions about the structures and energies of lipid intermediates preceding the fusion stalk formation and a possibility that these intermediates limit the rate of the whole fusion reaction. Indeed, to form a stalk, the membranes have to establish, at least locally, a dehydrated contact allowing them to perturb the continuity of their surfaces and merge, without exposure of the hydrophobic moieties of lipids to the aqueous surrounding. Such membrane contact requires overcoming the resistance of the powerful short-range repulsion forces referred to as the hydration forces (6). Straightforward estimations based on the representation of the prestalk intermediates as conventional wave-like membrane bulges approaching each other and creating extended dehydrated contacts predict the energies of hundreds of kT. Such intermediates are unfeasible and, hence, a more delicate structure must emerge on the way from two separated flat membranes to the fusion stalk.
Point-like protrusion
Here we suggest an energetically feasible structure of prestalk intermediate, which will be referred to as the point-like protrusion (PLP), and is illustrated in Fig. 1.
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Below, we analyze the overall energy of the PLP (Fig. 1) using the elastic tilt-splay model for the membrane deformations (8) and the hydration force model for the intermembrane repulsion (6). The results below have to be considered as semiquantitative.
Model
We consider a point-like protrusion formed on one membrane, while the second membrane remains flat (Fig. 1). The PLP configuration is determined by the tip angle 
, the distance dw between the flat parts of the two membranes and the requirement that no empty void forms inside the structure. The PLP monolayers undergo deformations of splay of the lipid hydrocarbon chains and tilt of the chains with respect to the monolayer surface (Fig. 1). Because we are using the essentially continuous description of a system consisting of discrete lipid molecules, the meaning of a point-like membrane contact (Fig. 1) is that of a contact with an area smaller than the area per lipid molecule a 
1 nm2.
Elastic energy
The elastic theory of the tilt and splay deformations was presented in Hamm and Kozlov (8) and applied to calculation of the energy of fusion intermediates (7). In brief, the tilt-splay energy per unit area of lipid monolayer is given by
 | (1) |
and tilt 
are related to the unit vector 
of the average direction of the hydrocarbon chains and the unit vector 
normal to the monolayer surface by 
(
being the two-dimensional divergence operator at the monolayer surface) and 
and 
are the monolayer splay (bending) and tilt elastic moduli, respectively, while Js is the monolayer spontaneous curvature (spontaneous splay). The total elastic energy is given by integration of Eq. 1 over the surfaces of the two monolayers constituting the PLP.
Energy of hydration repulsion
To calculate the hydration repulsion energy of PLP formation, we have to account for the discreteness of distribution, on the membrane surface, of the effective centers generating hydration of the lipid-water interface. The characteristic distance between the hydration centers has to be of the order of dimension of a lipid polar head 
* 
1 nm. Hence, the discreteness effects should be irrelevant and can be neglected if extended membrane contacts of tens of nanometers and larger are produced by smooth membrane bulges. At the same time, these effects must become significant for the point-like membrane contacts considered in this work, which are of the order of the discreteness length.
The energy of hydration repulsion per unit area of the monolayer surface is given in Rand and Parsegian (6)
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= 0.2 nm are, respectively, the upper boundary for the measured values of the hydration pressure and the decay length of the hydration interaction (6). The total hydration energy is obtained by integration of Eq. 2 over the PLP surface facing the flat membrane. We assume that the point of contact between PLP and the flat membrane is in the middle between the adjacent hydration centers, which reduces the overall hydration energy. Therefore, the area of diameter * around the PLP tip is not included in the integration.
To find the optimal conformation of the PLP, we calculate the sum of its elastic and hydration energies and minimize it, numerically, with respect to the PLP shape and distribution along the PLP surface of the tilt and splay of the hydrocarbon chains of the two PLP monolayers. Full details of the numerical technique we use for the energy calculation are presented in Kozlovsky and Kozlov (7).
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RESULTS |
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* influence the probability of the PLP formation.
The PLP energy dependence on the tip angle , which determines the PLP sharpness, is presented in Fig. 2. We found that the change of from almost zero (smooth bulge) to 45° decreases the energy by nearly an order of magnitude (the angle range between 0° and 20° is not shown). Requirement of small tilt implied by the model (Eq. 1) does not allow us to extend the results beyond = 45° but, as indicated by Fig. 2, the energy continues to decrease with growing sharpness.
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*, and depends weakly on the monolayer spontaneous curvature Js (Fig. 3 b). The PLP energy depends on dw stronger, and on Js weaker than the energy of the stalk (red line). The PLP energy is smaller than that of the stalk for the experimentally relevant values of Js 
–0.1 nm–1 and dw 
3 nm provided that the distance between the hydration centers has a feasible value of * 1 nm.
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CONCLUSION |
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Altogether we showed that for the relevant lipid compositions of membrane monolayers, the overall energy of PLP is lower than that of the fusion stalk, which may exceed the values presented in Fig. 3 due to contribution of the saddle-splay elasticity (9). Consequently, PLP does not limit the rate of hemifusion and the lipid dependency of hemifusion is determined by the stalk and the hemifusion diaphragm. Moreover, a point-like dehydrated contact between PLP and the target membrane facilitates stalk formation. Summarizing, PLP is a feasible prestalk intermediate completing the model pathway of fusion reaction. Experiments and/or molecular dynamics simulations are needed to confirm formation of PLP at the very initial steps of membrane fusion.
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ACKNOWLEDGEMENTS |
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Submitted on December 19, 2006; accepted for publication January 22, 2007.
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REFERENCES |
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2. Jahn, R., and T. C. Sudhof. 1999. Membrane fusion and exocytosis. Annu. Rev. Biochem. 68:863–911.[CrossRef][Medline]
3. Chernomordik, L. V., J. Zimmerberg, and M. M. Kozlov. 2006. Membranes of the world unite! J. Cell Biol. 175:201–207.
4. Lee, J., and B. R. Lentz. 1998. Secretory and viral fusion may share mechanistic events with fusion between curved lipid bilayers. Proc. Natl. Acad. Sci. USA. 95:9274–9279.
5. Kuzmin, P. I., J. Zimmerberg, Y. A. Chizmadzhev, and F. S. Cohen. 2001. A quantitative model for membrane fusion based on low-energy intermediates. Proc. Natl. Acad. Sci. USA. 98:7235–7240.
6. Rand, R. P., and V. A. Parsegian. 1989. Hydration forces between phospholipid bilayers. Biochim. Biophys. Acta. 988:351–376.
7. Kozlovsky, Y., and M. Kozlov. 2002. Stalk model of membrane fusion: solution of energy crisis. Biophys. J. 88:882–895.
8. Hamm, M., and M. Kozlov. 1998. Tilt model of inverted amphiphilic mesophases. Eur. Phys. J. B. 6:519–528.[CrossRef]
9. Kozlovsky, Y., A. Efrat, D. P. Siegel, and M. M. Kozlov. 2004. Stalk phase formation: effects of dehydration and saddle splay modulus. Biophys. J. 87:2508–2521.
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