Fourth-order curvature energy model for the stability of bicontinuous inverted cubic phases in amphiphile-water systems.

The bicontinuous inverted cubic (Q(II)) phases of amphiphiles in water have many practical applications. It is necessary to understand the stability of these phases as a function of composition and ambient conditions in order to make the best use of them. Moreover, many biomembrane lipids and some biomembrane lipid extracts form Q(II) phases. The stability of Q(II) phases in a given lipid composition is closely related to the susceptibility of that composition to membrane fusion: changes in composition that stabilize Q(II) phases usually increase the rate of membrane fusion. However, the factors determining Q(II) phase stability are not fully understood. Previously, an expression was derived for the curvature free energy of Q(II) phases with respect to that of the lamellar (L(alpha)) phase using a model for the curvature energy with terms up to fourth order in curvature as formulated by Mitov. Here this model is extended to account for the effects of water content on Q(II) phase stability. It is shown that the observed L(alpha)/Q(II) phase-transition temperature, transition enthalpy, and transition kinetics are all sensitive to water content. The same observables also become sensitive to small noncurvature energy contributions to the total free-energy difference between the Q(II) and L(alpha) phases, especially the unbinding energy in the L(alpha) phase. These predictions rationalize earlier observations of Q(II) phase formation in N-monomethylated dioleoylphosphatidylethanolamine that otherwise appear to be inconsistent. The model also provides a fundamental explanation of the hysteresis typically observed in transitions between the L(alpha) and Q(II) phases. It is an accurate model of Q(II) phase stability when the ratio of the volume fraction of the lipid in the Q(II) phase unit cell is < or = 0.5.

The Gaussian curvature elastic energy of intermediates in membrane fusion.

The Gaussian curvature elastic energy contribution to the energy of membrane fusion intermediates has usually been neglected because the Gaussian curvature elastic modulus, kappa, was unknown. It is now possible to measure kappa for phospholipids that form bicontinuous inverted cubic (Q(II)) phases. Here, it is shown that one can estimate kappa for lipids that do not form Q(II) phases by studying the phase behavior of lipid mixtures. The method is used to estimate kappa for several lipid compositions in excess water. The values of kappa are used to compute the curvature elastic energies of stalks and catenoidal fusion pores according to recent models. The Gaussian curvature elastic contribution is positive and similar in magnitude to the bending energy contribution: it increases the total curvature energy of all the fusion intermediates by 100 units of k(B)T or more. It is important to note that this contribution makes the predicted intermediate energies compatible with observed lipid phase behavior in excess water. An order-of-magnitude fusion rate equation is used to estimate whether the predicted stalk energies are consistent with the observed rates of stalk-mediated processes in pure lipid systems. The current theory predicts a stalk energy that is slightly too large, by approximately 30 k(B)T, to rationalize the observed rates of stalk-mediated processes in phosphatidylethanolamine or N-monomethylated dioleoylphosphatidylethanolamine systems. Despite this discrepancy, the results show that models of fusion intermediate energy are accurate enough to make semiquantitative predictions about how proteins mediate biomembrane fusion. The same rate model shows that for proteins to drive biomembrane fusion at observed rates, they have to perform mediating functions corresponding to a reduction in the energy of a purely lipidic stalk by several tens of k(B)T. By binding particular peptide sequences to the monolayer surface, proteins could lower fusion intermediate energies by altering the elastic constants of the patches of lipid monolayer that form the stalk. Here, it is shown that if peptide binding changes kappa or some other combinations of local elastic constants by only tens of percents, the stalk energy and the energy of catenoidal fusion pores would decrease by tens of k(B)T relative to the pure lipid value. This is comparable to the required mediating effect. The curvature energies of stalks and catenoidal fusion pores have almost the same dependence on monolayer elastic constants as the curvature energies of the rhombohedral and Q(II) phases; respectively. The effects of isolated fusion-relevant peptides on the energies of these intermediates can be determined by studying the effects of the peptides on the stability of rhombohedral and Q(II) phases.

Cubic phases in phosphatidylcholine-cholesterol mixtures: cholesterol as membrane "fusogen".

X-ray diffraction reveals that mixtures of some unsaturated phosphatidylcholines (PCs) with cholesterol (Chol) readily form inverted bicontinuous cubic phases that are stable under physiological conditions. This effect was studied in most detail for dioleoyl PC/Chol mixtures with molar ratios of 1:1 and 3:7. Facile formation of Im3m and Pn3m phases with lattice constants of 30-50 nm and 25-30 nm, respectively, took place in phosphate-buffered saline, in sucrose solution, and in water near the temperature of the Lalpha-HII transition of the mixtures, as well as during cooling of the HII phase. Once formed, the cubic phases displayed an ability to supercool and replace the initial Lalpha phase over a broad range of physiological temperatures. Conversion into stable cubic phases was also observed for mixtures of Chol with dilinoleoyl PC but not for mixtures with palmitoyl-linoleoyl PC or palmitoyl-oleoyl PC, for which only transient cubic traces were recorded at elevated temperatures. A saturated, branched-chain PC, diphytanoyl PC, also displayed a cubic phase in mixture with Chol. Unlike the PEs, the membrane PCs are intrinsically nonfusogenic lipids: in excess water they only form lamellar phases and not any of the inverted phases on their own. Thus, the finding that Chol induces cubic phases in mixtures with unsaturated PCs may have important implications for its role in fusion. In ternary mixtures, saturated PCs and sphingomyelin are known to separate into liquid-ordered domains along with Chol. Our results thus suggest that unsaturated PCs, which are excluded from these domains, could form fusogenic domains with Chol. Such a dual role of Chol may explain the seemingly paradoxical ability of cell membranes to simultaneously form rigid, low-curvature raft-like patches while still being able to undergo facile membrane fusion.

Determining the ratio of the Gaussian curvature and bending elastic moduli of phospholipids from Q(II) phase unit cell dimensions.

A method is presented for measuring M, the ratio of the Gaussian (saddle splay) elastic modulus to the bending elastic modulus of a lipid monolayer. The ratio M is determined from measurements of the equilibrium bicontinuous inverted cubic (Q(II)) phase unit cell size in excess water as a function of temperature. The analysis includes the effect of a curvature elastic term that is second-order in the Gaussian curvature, K. Preliminary results using data on DOPE-Me validate the method. The fitted value of M is within 8% of the value estimated in an earlier treatment. The method can be used to measure changes in M due to addition of exogenous lipids and peptides to a host lipid system. The Gaussian elastic modulus has a substantial effect on the stability of fusion intermediates (stalks, hemifusion diaphragms, and fusion pores). Studying the effects of peptides and different lipids on M via this method may yield insights into how fusion protein moieties stabilize intermediates in membrane fusion in vivo. The contribution of the K2 curvature elastic term to the free energy of Q(II) phase and fusion pores explains some features of fusion pore stability and dynamics, and some peculiar observations concerning the mechanism of L(alpha)/Q(II) phase transitions.

Stalk phase formation: effects of dehydration and saddle splay modulus.

One of the earliest lipid intermediates forming in the course of membrane fusion is the lipid stalk. Although many aspects of the stalk hypothesis were elaborated theoretically and confirmed by experiments it remained unresolved whether stalk formation is always an energy consuming process or if there are conditions where the stalks are energetically favorable and form spontaneously resulting in an equilibrium stalk phase. Motivated by a recent breakthrough experiments we analyze the physical factors determining the spontaneous stalk formation. We show that this process can be driven by interplay between two factors: the elastic energy of lipid monolayers including a contribution of the saddle splay deformation and the energy of hydration repulsion acting between apposing membranes. We analyze the dependence of stalk formation on the saddle splay (Gaussian) modulus of the lipid monolayers and estimate the values of this modulus based on the experimentally established phase boundary between the lamellar and the stalk phases. We suggest that fusion proteins can induce stalk formation just by bringing the membranes into close contact, and accumulating, at least locally, a sufficiently large energy of the hydration repulsion.