A statistical mechanical model of the lipid bilayer above its phase transition.

A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules above their phase transition is presented. A molecular field approximation developed in previous work by Marcelja is extended by setting the molecular field at each depth in the bilayer in proportion to the average chain order at that depth. The free energy of the hydrocarbon/water interface and that due to the interaction of the polar headgroups is included in the evaluation of the statistical weights of the chain conformations. The model gives good agreement with several independent experimental results. It resolves the dilemma posed by the experimental evidence that there is (i) a considerable variation in order parameter along the lipid chain, but (ii) no collective tilt in the more ordered region of the chain. The model gives an explanation of how the lipid chains pack under these two constraints. The order parameter profile down the chain does not correspond to the profile across the bilayer.

Lateral tensions and pressures in membranes and lipid monolayers.

The effects of lateral tension on the properties of membranes are often explained in comparison with analogous experiments on monolayers, which yield more detailed data. To calculate the effects of changes in tension on the composition of, or incorporation of amphiphiles into membranes we examine (i) the fidelity of the monolayer analogy, (ii) the range of possible tensions in a membrane, and the way in which tensions arise and (iii) the equilibrium partitioning of amphiphiles between aqueous solution and a bilayer under tension. We argue that, at the same areas per molecule, a monolayer at an n-alkane/water interface is a closer analogy of the lipid bilayer than a monolayer at an air/water interface. Next, we show from a thermodynamic argument that changes in membrane tension can affect the absorption of very large amphiphiles such as proteins, but that physiological tensions are unlikely to affect the absorption of lipids or drugs. Finally we consider the possibility that the measured bulk tension in a complicated membrane such as that of the erythrocyte may be larger than the local tension in the fluid mosaic portions, and suggest a model which explains the ability of the erythrocyte membrane to withstand much higher tensions than other biological membranes and lipid bilayers.

A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model.

A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure.

A mean-field model of the alkane-saturated lipid bilayer above its phase transition. II. Results and comparison with experiment.

Equilibrium properties of a model lipid bilayer saturated with an n-alkane are presented. The model exhibits a cut-off in absorption as the chain length of the alkane increases which is similar to that observed with black lipid films. The reasons for this cut-off are explored in detail. The model provides qualitative agreement with the experimental enthalpies of transfer of the various alkanes from bulk pure liquid to the bilayer, and with results of electrical compression experiments on black films. Distributions of alkane across the bilayer for different volume fractions in the membrane are presented. For small volume fractions of alkane, its distribution is fairly even across the bilayer and the alkane chains line up essentially parallel to the lipid chains. For larger volume fractions, the alkane distribution is strongly peaked in the center of the membrane. The alkane chains in the outer regions of the membrane line up essentially parallel to the lipid chains, while those in the center are almost completely disordered. The model suggests that the chains (both lipid and alkane) are in an essentially liquid state with no well defined interface between opposing monolayers. It gives a possible explanation for the discrepancy between the experimental free energy of thinning of some lipid membranes formed from the longer chain length alkanes and the theoretical values estimated from Lifshitz's theory.

The adsorption of nonpolar molecules into lipid bilayer membranes.

Thermodynamic considerations show that the adsorption of nonpolar molecules into lipid bilayer membranes should depend upon the curvature of the membranes. Estimations of the differences in adsorption of a small n-alkane between a planar phospholipid bilayer and liposomal vesicles have been attempted. For spherical multilamellar liposomes exposed to saturated solutions of alkane in water the adsorption is calculated to be 17-65% of the value for the planar bilayer, depending on the assumptions in the model.

Thickness fluctuations in black lipid membranes.

Because a black lipid membrane is compressible, there will be spontaneous fluctuations in its thickness. Qualitative arguments are given that the preferred configuration of the membranes is flat and that thickness fluctuations are smaller in amplitude than the differences in mean thickness observed using different hydrocarbon solvents. Fluctuations with short characteristic lengths will not be large as a result of the large amounts of oil-water contact these would entail. Quantitative analysis based on an extension of the treatment for soap films, predicts that the root mean square (rms) amplitude for fluctuations of wavelength longer than approximately 10 nm is negligible for glyceryl monooleate membranes with squalene (less than 3%) but may be approximately 20% with n-decane. rms fluctuations of 20% would lead to a discrepancy between the rms thickness of the core and the mean reciprocal thickness of only 6%.