In this paper the Helfrich ansatz for bending an amphiphilic monolayer is re-expressed in terms of the deviations in curvature away from a preferred value. Using this expression and a simple model of the response of amphiphiles to interfacial bending, it is demonstrated that there are strict limits to the value of the ratio of the Gaussian curvature modulus to the mean curvature modulus (κG/κ). We have made an estimate of κG/κ from measurements of the swelling behavior in water of inverse bicontinuous cubic mesophases in a system composed of 1-monoolein, dioleoylphosphatidylcholine, and dioleoylphosphatidylethanolamine. The estimate, −0.75 ± 0.08, is in agreement with the limits set by our model of −1 < κG/κ < 0. This determination is the first to be made on an inverse bicontinuous cubic phase which is sufficiently swollen to be in a regime where first-order curvature elastic energetics should be sufficient to describe the state of the mesophase and hence provide a reliable estimate of κG/κ.

Inverse bicontinuous cubic lyotropic phases are a complex solution to the dilemma faced by all self-assembled water-amphiphile systems: how to satisfy the incompatible requirements for uniform interfacial curvature and uniform molecular packing. The solution reached in this case is for the water-amphiphile interfaces to deform hyperbolically onto triply periodic minimal surfaces. We have previously suggested that although the molecular packing in these structures is rather uniform the relative phase behavior of the gyroid, double diamond, and primitive inverse bicontinuous cubic phases can be understood in terms of subtle differences in packing frustration. In this work, we have calculated the packing frustration for these cubics under the constraint that their interfaces have constant mean curvature. We find that the relative packing stress does indeed differ between phases. The gyroid cubic has the least packing stress, and at low water volume fraction, the primitive cubic has the greatest packing stress. However, at very high water volume fraction, the double diamond cubic becomes the structure with the greatest packing stress. We have tested the model in two ways. For a system with a double diamond cubic phase in excess water, the addition of a hydrophobe may release packing frustration and preferentially stabilize the primitive cubic, since this has previously been shown to have lower curvature elastic energy. We have confirmed this prediction by adding the long chain alkane tricosane to 1-monoolein in excess water. The model also predicts that if one were able to hydrate the double diamond cubic to high water volume fractions, one should destabilize the phase with respect to the primitive cubic. We have found that such highly swollen metastable bicontinuous cubic phases can be formed within onion vesicles. Data from monoelaidin in excess water display a well-defined transition, with the primitive cubic appearing above a water volume fraction of 0.75. Both of these results lend support to the proposition that differences in the packing frustration between inverse bicontinuous cubic phases play a pivotal role in their relative phase stability.

The bending elasticity of the monoglyceride 1-monoolein (MO) in water has been measured in the inverse hexagonal (HII) phase at 37 °C. At this temperature, fully hydrated MO is normally in an inverse bicontinuous cubic phase based on Schwarz's D surface, . The addition of either of the C23 chainlength hydrocarbons, tricosane or 9-cis-tricosene, at mole fractions with respect to MO in excess of 0.05, induces a phase transition into the HII phase. This transition is understood to occur because packing stresses in the hydrophobic regions of the HII phase are reduced to levels where this phase is at a lower free energy than the phase. We have used X-ray diffraction on gravimetrically prepared samples and samples subjected to an osmotic stress to determine the bending energy of MO in this phase. The evidence suggests that 9-cis-tricosene can relieve almost all of the packing stress in the HII phase. In this case, we find that the spontaneous radius of curvature at the pivotal surface, R 0, is −20.0 ± 0.3 Å, and the monolayer bending rigidity, κ, is (1.2 ± 0.1) × 10-20 J. Comparing these energetics with those of the phase indicates that the packing stress for an excess water, HII phase at 37 °C in the absence of 9-cis-tricosene would constitute at least 50% of the total equilibrium free energy. With tricosane, the packing stress cannot be completely relieved because tricosane melts at 47.6 °C in the bulk. The results from geometric measurements on this system suggest that when the packing stress is not fully relieved in the HII phase, the polar/apolar interface is deformed away from being cylindrical. Treating the interface as if it were cylindrical leads to a nonphysical location of the pivotal surface that is in disagreement with all previous measurements, a 35% increase in the magnitude of R 0, and a 4-fold increase in the calculated bending rigidity.

The influence of thylakoid lipids on the association kinetics and thermal stability of the major light-harvesting complex of photosytem II (LHCII) has been studied in vitro. The apoprotein, light-harvesting chlorophyll a/b-binding protein (Lhcb1), can be refolded and complexed with pigments in detergent solution even in the absence of lipids. Two thylakoid lipids, phosphatidyl glycerol and digalactosyl diacylglycerol, are known to interact specifically with LHCII in vivo. Here we show that both of these lipids, as well as monogalactosyl diacylglycerol, stabilize reconstituted LHCII toward thermal denaturation. Two slow kinetic phases are connected with the establishment of energy transfer between chlorophyll b and chlorophyll a and, thus, are thought to reflect the formation of the pigment-protein complex with tightly coupled chlorophylls. The lipids studied here all have the same effect on the rate of complex assembly in vitro and slow these two kinetic phases by the same degree. Both kinetic phases also slow when reactant concentrations are decreased, suggesting that the corresponding reaction step(s) involve(s) pigment binding.