Some models for lipid bilayer and biomembrane phase transitions

Effects of small nonpolar molecules on membrane compressibility and permeability. A theoretical study of the effects of anesthetic gases

We explore from a theoretical perspective the effects of small nonpolar molecules, such as anesthetic gases, on membrane compressibility and permeability. As a model system we expand a previously proposed generalization of Nagle's model for biomembrane phase transitions. In this model anesthetic gases alter membrane compressibility, causing profound changes in membrane permeability. Anesthetics either increase or decrease membrane permeability, depending on whether the membrane lipid is originally in the solid or melted state, or in a two-phase region. These changes are reversed by high pressure, in agreement with experimental results. Anesthetic-induced changes in compressibility are predicted to inhibit fusion of phospholipid vesicles to each other and to planar bilayers, and thus might be expected to inhibit the fusion of presynaptic vesicles with the presynaptic nerve membrane. This work provides a detailed molecular theory for many of the effects of anesthetic gases on both synapse and axon, and provides a coherent framework for understanding diverse experimental results.

A theoretical model of the temperature- and pressure-induced phase transition of phospholipid bilayers

A statistical thermodynamic model of phospholipid bilayers is developed. In the model, a new concept of a closely packed system is applied, i.e., a system of hard cylinders of equal radii, the radius being a function of the average number of gauche rotations in a hydrocarbon chain. Using this concept of a closely packed system, reasonable values are obtained for the change in specific volume at the order-disorder transition of lecithin bilayers. In addition to interactions between the lipid matrix and water molecules, between the head groups, themselves and between hydrocarbon chains, as well as the intramolecular energy associated with chain conformation, the Hamiltonian of the membrane also includes the energy of the pressure field. Thus, the phase transition of phospholipid membranes induced not only by temperature but also by hydrostatic pressure is described by this model simultaneously. In accordance with the experimental results, a linear relationship is obtained between the phase transition temperature and phase transition pressure. The other calculated phase transition properties of lecithin homologues, e.g., changes in enthalpy, surface area, thickness and gauche number per chain are in agreement with the available experimental data. The ratio of kink to interstitial conduction of bilayers is also estimated.

Interactions of small nonpolar molecules with biological membranes: an exactly solvable model

An exactly solvable model of the interaction of small nonpolar molecules with biological membranes is developed. This model, which is based upon a "decreased dimer model" extension of Nagle's membrane model, is demonstrated to qualitatively reproduce many of the changes in the order-disorder phase transition seen when biological membranes are exposed to anesthetic gases. The decorated dimer model is itself interesting because it provides an example of an exactly solvable monomer-dimer model in which phase transitions can occur in the presence of monomers.

A statistical mechanical treatment of fatty acyl chain order in phospholipid bilayers and correlation with experimental data. B. Dipalmitoyl-3-sn-phosphatidylcholine

In order to help bridge the conceptual gap between experimental data on chains of phospholipid molecules and their microscopic organization, a theoretical model has proposed in a preceding paper. The intentions associated with the new theory were to describe a model able to reproduce accurately the experimental data. This capability is essential to monitor some of the mechanisms behind the physical data. The results presented here show first that, provided a suitable fitting of the phenomenological parameters entailed in the model, the theory indeed gives good agreement with experimental data (2H-NMR, neutron scattering, calorimetry) obtained for a dipalmitoyl-3-sn-phosphatidylcholine bilayer. This property of the model is then specifically used to describe the nature of the perturbing effects of local anaesthetics and cholesterol on the organization of the acyl chains and to correlate these effects with the experimental data. Finally the theoretical model is used to supplement experimental data by describing the acyl chain organization in terms of the most probable spectrum of chain conformations. Predictions are made about the one-, two- and three-dimensional mean spatial characteristics of the acyl chains.

A theory of the effects of head-group structure and chain unsaturation on the chain melting transition of phospholipid dispersions

We have developed statistical mechanical descriptions of the effects of head-group structure and acyl chain unsaturation on the chain melting phase transition of aqueous dispersions of bilayers containing glycerophosphocholines and glycerophosphoethanolamines. The theoretical framework is an extension of the model of Jacobs et al. [Jacobs, R. E., Hudson, B. S., & Andersen, H. C. (1975) Proc. Natl. Acad. Sci. U.S.A. 72, 3993]. There are several systematic trends in the experimental transition data for various types of phospholipids. Assumptions about the physical origins of these trends were incorporated into statistical mechanical models, which were used to calculate transition temperatures and enthalpies. The extent to which the calculated results of a model reproduce the experimental trends is taken as a measure of the validity of the assumptions on which the model is based. We found that the gross differences among the transition temperatures of phospholipids with two saturated chains, two trans-unsaturated chains, two cis-unsaturated chains, and one cis-unsaturated and one saturated chain can all be explained in terms of the effect of the double bonds on molecular shape and the subsequent effect of shape on the ability of molecules to pack together into a low-energy state at high density. The dependence of transition temperature on the location of the double bond in cis-unsaturated molecules can be understood on the same basis. The differences between the transition temperatures of glycerophosphocholines and glycerophosphoethanolamines with the same hydrocarbon chains can be explained in terms of a larger intermolecular attraction (or smaller repulsion) for the latter than for the former. These differences depend on the presence or absence of unsaturation in the hydrocarbon chains in a way that is consistent with the postulate that hydrogen bonding between glycerophosphoethanolamines is responsible for the differences.

A theoretical description of phase diagrams for nonideal lipid mixtures

A theoretical description of phase diagrams for nonideal lipid mixtures is presented. The phase diagrams in this model are constructed by a quasi-chemical approach for the calculations of enthalpies of the regular solutions and by van der Waals attractive energy of lipids which described the degree of nonideality in the solid and fluid phases. The results of theoretical calculations of phase diagrams for dimyristoyl phsophatidylcholine/dipalmitoyl phosphatidylcholine dimyristoyl phosphatidylcholine/distearoyl phosphatidylcholine, and dipalmitoyl phosphatidylcholine/distearoyl phosphatidylcholine mixtures are in good agreement with experimental data.

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.

A theory of the electric field-induced phase transition of phospholipid bilayers

Improving the statistical mechanical model of Jacobs et al. (Jacobs, R.E., Hudson, B. and Andersen, H.C. (1975) Proc. Natl. Acad. Sci. U.S. 72, 3993--3997) we have constructed a model which describes not only the temperature but also the external field dependence of the membrane structure of phospholipid bilayers. In addition to the interactions between head groups, between hydrocarbon chains, and the internal conformational energy of the chains (which were considered in Jacobs' model), our model includes the energy of deformation and the field energy as well. By the aid of this model we can explain the phenomenon of dielectric breakdown, the non-linearity of current-voltage characteristics, and the mechanism of membrane elasticity. The free energy of the membrane, the average number of the gauche conformations in the hydrocarbon interior and at the membrane surface, gauche distribution along the chain, the membrane thickness, area and volume are calculated at different temperatures and voltages. The calculation also gives the temperature dependence of Young's modulus and that of the linear thermal expansion coefficient.

Estimation of molecular averages and equilibrium fluctuations in lipid bilayer systems from the excess heat capacity function

It is demonstrated that the bilayer partition function can be numerically obtained from scanning calorimetric data without assuming a particular model for the gel-liquid crystalline transition. From this partition function, the enthalpy, entropy and volume changes accompanying the transition can be calculated. In the limit of very large systems, the method of the grand partition function allows calculation of cluster model distribution functions from which average sizes of gel and liquid-crystal clusters, cluster densities and equilibrium fluctuations are obtained. These results indicate that the main transition in phospholipid bilayers proceeds through the formation of clusters and that these clusters are not static domains but highly fluctuating entities. These fluctuations in cluster size are approximately equal to the average cluster size and give rise to localized density and volume fluctuations. The magnitude of these fluctuations is affected by the radius of curvature of the bilayer and by the addition of small molecular weight compounds to the system.

Theory of lipid monolayer and bilayer phase transitions: effect of headgroup interactions

Headgroup and soft core interactions are added to a lipid monolayer-bilayer model and the surface pressure-area phase diagrams are calculated. The results show that quite small headgroup interactions can have biologically significant effects on the transition temperature and the phase diagram. In particular, the difference in transition temperatures of lecithins and phosphatidyl ethanolamines is easy to reproduce in the model. The phosphatidic acid systems seem to require weak transient hydrogen bonding which is also conjectured to play a role in most of the lipid systems. By a simple surface free energy argument it is shown that monolayers under a surface pressure of 50 dynes/cm should behave as bilayers, in agreement with experiment. Although the headgroup interactions are biologically very significant, in fundamental studies of the main phase transition in lipids they are secondary in importance to the hydrocarbon chain interactions (including the excluded volume interaction, the rotational isomerism, and the attractive van der Waals interaction).

A theoretical model for lipid monolayer phase transitions

We present a theoretical model for the liquid-expanded to liquid-condensed phase transition observed in many phospholipid monolayer films. The total two-dimensional pressure in the model is the sum of the hydrocarbon chain pressure and the surface pressure. The hydrocarbon chain pressure is calculated in an exteded version of a model published earlier. The surface pressure results from a lowering of the surface tension in the monolayer over that of pure water, thus producing a force on a Langmuir float. When these two contributions are added, pi/A isotherms are obtained which have slope discontinuities very similar to those observed experimentally. The results indicate that a successful model for lipid phase behavior must consider the interactions between head groups and water as well as cooperative hydrocarbon chain melting.