The permeability and the effect of acyl-chain length for phospholipid bilayers containing cholesterol: theory and experiment.

The model of Cruzeiro-Hansson et al. (Biochim. Biophys. Acta (1989) 979, 166-1176) for lipid-cholesterol bilayers at low cholesterol concentrations is used to predict the thermodynamic properties and the passive ion permeability of lipid bilayers as a function of acyl-chain length and cholesterol concentration. Numerical simulations based on the Monte Carlo method are used to determine the equilibrium state of the system near the main gel-fluid phase transition. The permeability is calculated using an ansatz which relates the passive permeability to the amount of interfaces formed in the bilayer when cholesterol is present. The model predicts at low cholesterol contents an increase in the membrane permeability in the transition region both for increasing cholesterol concentration and for decreasing chain length at a given value of the reduced temperature. This is in contrast to the case of lipid bilayers containing high cholesterol concentrations where the cholesterol strongly suppresses the permeability. Experimental results for the Na+ permeability of C15PC and DPPC (C16PC) bilayers containing cholesterol are presented which confirm the theoretical predictions at low cholesterol concentrations.

Phase diagrams for impure lipid systems. Application to lipid/anaesthetic mixtures.

A physical model is presented to describe theoretically the temperature-dependent interactions of lipid bilayers with small molecules such as anaesthetics. Based on an earlier model, a triangular lattice in which each site is occupied by a single lipid chain is constructed and the small (anaesthetic) molecules are assumed to occupy interstitial sites in the centre of each lattice triangle. The phase characteristics of such lipid/anaesthetic mixtures are described in terms of the interaction parameters between lipid-lipid, lipid-anaesthetic and anaesthetic-anaesthetic molecules. Depending on the chemical nature of the interacting species the following three models are formulated: Model I. An interstitial model in which the only perturbation is in the head-group region of the bilayer and direct interactions between neighbouring anaesthetic molecules are taken into account. Model II. Here, only hydrophobic interactions between anaesthetics and lipids are considered. Model III. Both van der Waals' and coulombic interactions are taken into account. Phase diagrams for the three models are obtained by numerical calculation over a wide range of interaction parameters. It is shown that in all three models, lateral phase separation takes place due to the presence of anaesthetics. The heat of transition, however, is found to be virtually independent of the anaesthetic concentration.

A microscopic model for lipid/protein bilayers with critical mixing.

A statistical mechanical lattice model is proposed to describe the phase diagram of phospholipid bilayers with small transmembrane proteins or polypeptides. The model is based on the extended Pink-Green-Chapman model (Zhang et al. (1992) Phys. Rev. A 45, 7560-7567) for pure lipid bilayers which undergo a first-order gel-fluid phase transition. The interaction between the lipid bilayer and the protein or polypeptide is modelled using the concept of hydrophobic matching. The phase diagram has been derived by computer-simulation techniques which fully account for thermal density fluctuations and which operate on the level of the free-energy thereby permitting an accurate identification of the phase boundaries. The calculations predict a closed loop of gel-fluid coexistence with a lower critical mixing point. Specific-heat traces across the phase diagram are also presented. The theoretical results for the phase diagram, the specific-heat function, and the transition enthalpy are related to recent experimental measurements on phospholipid bilayers mixed with synthetic transmembrane amphiphilic polypeptides or with gramicidin A.

A model of hydrogen bond formation in phosphatidylethanolamine bilayers.

We have modelled hydrogen bond formation in phospholipid bilayers formed, in excess water, from lipids with phosphatidylethanolamine (PE) headgroups. The hydrogen bonds are formed between the NH3+ group and either of the PO2- or the (sn2 chain) C=O groups. We used a model that represented the conformational states accessible to a PE headgroup by 17 states and modelled lipid dipole-dipole interactions using a non-local electrostatics theory to include the effects of hydrogen bonding in the aqueous medium. We used Monte-Carlo simulation to calculate equilibrium thermodynamic properties of bilayers in the fluid (T = 340 K) or gel (T = 300 K) phases of the bilayer. We defined Eh to be the difference in free energy between a hydrogen bond formed between a pair of lipid groups, and the energy of hydrogen bonds formed between water and those two groups, and we required its average value, [Eh], to be approximately -0.3kcal/mol (approximately -0.2 X 10(-13) erg) as reported by T.-B. Shin, R. Leventis, J.R. Silvius, Biochemistry 30 (1991) 7491. We found: (i) Eh = -0.9 X 10(-13) erg gave [Eh] = -0.21 X 10(-13) erg (gel phase) and [Eh] = -0.19 X 10(-13) erg (fluid phase). (ii) The relative number of C=O groups on the sn2 chain calculated to take part in interlipid hydrogen bonding in the fluid phase compared to the gel is 1.06 which compares well with the experimental ratio of approximately 1.25 (R.N.A.H. Lewis, R.N. McElhaney, Biophys. J. 64 (1993) 1081). The ratio of such groups taking part in interlipid hydrogen bonding compared to water hydrogen bonding in each phase was calculated to lie between 0.16 and 0.17. (iii) We calculated the distribution of positions of the headgroup moieties, P, O, CH2(alpha), CH2(beta) and N, and found that, in both phases, the O lay furthest from the hydrocarbon chain layer (average approximately 5.3A) with the PO2 and NH3 groups lying at approximately 5A. This results in the P-N dipole lying nearly parallel to the bilayer plane in both phases. The thickness of the headgroup layer underwent essentially no change on going from the gel to the fluid phase. The 2H NMR quadrupole splittings for the alpha and beta CH2 groups were 4.9 and 5.7kHz (fluid phase) and 7.1 and 7.3 kHz (gel phase), respectively, on the assumption of sufficiently rapid rotation around the z-axis. (iv) In both phases, the location of the NH3+ group exhibited a strong peak around 5.2 A into the aqueous medium, with much smaller peaks around 2.6 and 7.8 A, the two CH2 groups exhibited narrower, double-peaked distributions and the O and the PO2 each exhibited a narrow single peak. (v) PE headgroups, in a homogeneous gel phase, exhibited dipolar orientational long-range order in the plane of the bilayer. The distribution of orientation angles exhibited a full width at half height of between approximately 40 degrees and approximately 50 degrees. In a fluid phase no such order was observed. (vi) The number of hydrogen bonds did not differ substantially between the fluid and gel phases. This model is unlikely to display any significant effect of hydrogen bonding upon the "main" hydrocarbon chain melting phase transition at Tm, except, possibly, a broadening of any hysteresis, compared to the case of PC bilayers where interlipid hydrogen bonding is absent.

Lateral diffusion of gramicidin S, M-13 coat protein and glycophorin in bilayers of saturated phospholipids. Mean field and Monte Carlo studies.

We have developed a general model that relates the lateral diffusion coefficient of one isolated large intrinsic molecule (mol. wt. greater than or approximately 1000) in a phosphatidylcholine bilayer to the static lipid hydrocarbon chain order. We have studied how protein lateral diffusion can depend upon protein-lipid interactions but have not investigated possible non-specific contributions from gel-state lattice defects. The model has been used in Monte Carlo simulations or in mean-field approximations to study the lateral diffusion coefficients of Gramicidin S, the M-13 coat protein and glycophorin in dimyristoyl- and dipalmitoylphosphatidylcholine (DMPC and DPPC) bilayers as functions of temperature. Our calculated lateral diffusion coefficients for Gramicidin S and the M-13 coat protein are in good agreement with what has been observed and suggest that Gramicidin S is in a dimeric form in DMPC bilayers. In the case of glycophorin we find that the 'ice breaker' effect can be understood as a consequence of perturbation of the lipid polar region around the protein. In order to understand this effect is necessary that the protein hydrophilic section perturb the polar regions of at least approx. 24 lipid molecules, in good agreement with the numbers of 29-30 measured using 31P-NMR. Because of lipid-lipid interactions this effect extends itself out to four or five lipid layers away from the protein so that the hydrocarbon chains of between approx. 74 and approx. 108 lipid molecules are more disordered in the gel phase, so contributing less to the transition enthalpy, in agreement with the numbers of 80-100 deduced from differential scanning calorimetry (DSC). An understanding of the abrupt change in the diffusion coefficient at a temperature below the main bilayer transition temperature requires an additional mechanism. We propose that this change may be a consequence of a 'coupling-uncoupling' transition involving the protein hydrophilic section and the lipid polar regions, which may be triggered by the lipid bilayer pretransition. Our calculation of the average number of gauche bonds per lipid chain as a function of temperature and distance away from an isolated polypeptide or integral protein shows the extent of statically disordered lipid around such molecules. The range of this disorder depends upon temperature, particularly near the main transition.

Phase equilibria in the phosphatidylcholine-cholesterol system.

A thermodynamic and a microscopic interaction model are proposed to describe the phase equilibria in the phosphatidylcholine-cholesterol system. The model calculations allow for a solid phase with conformationally ordered acyl chains and liquid phases with conformationally ordered as well as disordered chains. The resulting phase diagram is in excellent agreement with the experimental phase diagram for dipalmitoylphosphatidylcholine bilayers with cholesterol as determined by a recent NMR and calorimetry study. It is thus demonstrated that the phase behaviour of phosphatidylcholine-cholesterol mixtures can be rationalized using only a few basic assumptions: (i) Cholesterol interacts favourably with phosphatidylcholine chains in an extended conformation, (ii) the main transition of pure phosphatidylcholine bilayers takes place in terms of translational variables as well acyl-chain conformational variables, and (iii) cholesterol disturbs the translational order in the crystalline (gel) state of phosphatidylcholine. These results suggest that the occurrence of specific phosphatidylcholine-cholesterol complexes is not implied by the experimental thermodynamic data.

A general model for the interaction of foreign molecules with lipid membranes: drugs and anaesthetics.

A general microscopic interaction model is proposed to describe the changes in the physical properties of phospholipid bilayer membranes due to foreign molecules which, to different degrees, partition between the membrane phases and the aqueous environment. The model is a multi-state lattice model for the main phase transition of lipid bilayers and the foreign molecules are assumed to intercalate as interstitials in the lattice. By varying the model parameters, the diversity in the thermodynamic properties of the model is explored using computer-simulation techniques which faithfully take account of the thermal fluctuations. The calculations are performed in both the canonical and the grand canonical ensembles corresponding to the cases where the concentration of foreign molecules in the membrane is either fixed or varies as the external conditions are changed. A classification of the diverse thermal behaviour, specifically with regard to the phase diagram, the specific heat, the density fluctuations, and the partition coefficient, is suggested with a view to rationalizing a large body of experimental measurements of the effects of different foreign molecules on membrane properties. The range of foreign molecules considered includes compounds as diverse as volatile general anaesthetics like halothane, cocaine-derived local anaesthetics like procaine, calcium-channel blocking drugs like verapamil, antidepressants like chlorpromazine, and anti-cancer agents like adriamycin.

The effects of density fluctuations on the partitioning of foreign molecules into lipid bilayers: application to anaesthetics and insecticides.

An extensive computer-simulation study is performed on a simple but general molecular model recently proposed (Jørgensen et al. (1991) Biochem. Biophys. Acta 1062, 277-238) to describe foreign molecules interacting with lipid bilayers. The model is a multi-state lattice model of the main bilayer transition in which the foreign molecules are assumed to intercalate at interstitial lattice positions. Specific as well as non-specific interactions between the foreign molecules and the lipid acyl chains are considered. Particular attention is paid to the fluctuating properties of the membrane and how the presence of the foreign molecules modulates these fluctuations in the transition region. By means of computer-stimulation techniques, a detailed account is given of the macroscopic as well as microscopic consequences of the fluctuations. The macroscopic consequences of the fluctuations are seen in the thermal anomalies of the specific heat and the passive trans-membrane permeability. Microscopically, the fluctuations manifest themselves in lipid-domain formation in the transition region which implies an effective dynamic membrane heterogeneity. Within the model it is found that certain anaesthetics and insecticides which are characterised by specific interactions with the lipids have a strong effect on the heterogeneity of the membrane inducing regions of locally very high concentration of the foreign molecules. This leads to a broadening of the specific heat peak and a maximum in the membrane/water partition coefficient. These results are in accordance with available experimental data for volatile general anaesthetics like halothane, local anaesthetics like cocain derivatives, and insecticides like lindane.

Phase equilibria and local structure in binary lipid bilayers.

A molecular interaction model is used to describe the phase diagram of two-component phospholipid bilayer membranes of saturated phospholipids, DCnPC, with different acyl-chain lengths, n = 12,14,18,20. The interaction between acyl chains of different length is formulated in terms of a hydrophobic mismatch which permits the series of binary phase diagrams to be calculated in terms of a single 'universal' interaction parameter. The properties of the model are calculated by computer-simulation techniques which not only permit determination of the specific-heat function and the phase diagram but also reveal the local structure of the mixture in the different parts of the phase diagram. The local structure is described pictorially and characterized quantitatively in terms of a correlation function. It is shown that the non-ideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively increasing local ordering as the chain-length difference is increased. A pronounced local structure is found to persist deep inside the fluid phase of the mixture. The local structure is discussed in relation to the features observed in the specific-heat function, for which theoretical data, as well as experimental data obtained from differential-scanning calorimetry are presented.

Model of a sub-main transition in phospholipid bilayers.

A recently discovered submain phase transition in multi-lamellar bilayers of long-chain saturated diacyl phosphatidylcholines (Jørgensen, K. (1995) Biochim. Biophys. Acta 1240, 111-114) is discussed in terms of a theoretical molecular interaction model using computer simulation techniques. The model interprets the transition to be due to a decoupling of the acyl-chain melting from the melting of the pseudo-two-dimensional crystalline lattice of the P beta' phase. A two-stage melting process is predicted by the calculations suggesting that the sub-main transition involves a lattice melting whereas the acyl-chain melting takes place at a higher temperature at the main transition. The calculated heat contents of the two transitions as well as the chain-length dependence compare favorably with experimental data for multi-lamellar phosphatidylcholine lipid bilayers.

Theoretical analysis of protein organization in lipid membranes.

The fundamental physical principles of the lateral organization of trans-membrane proteins and peptides as well as peripheral membrane proteins and enzymes are considered from the point of view of the lipid-bilayer membrane, its structure, dynamics, and cooperative phenomena. Based on a variety of theoretical considerations and model calculations, the nature of lipid-protein interactions is considered both for a single protein and an assembly of proteins that can lead to aggregation and protein crystallization in the plane of the membrane. Phenomena discussed include lipid sorting and selectivity at protein surfaces, protein-lipid phase equilibria, lipid-mediated protein-protein interactions, wetting and capillary condensation as means of protein organization, mechanisms of two-dimensional protein crystallization, as well as non-equilibrium organization of active proteins in membranes. The theoretical findings are compared with a variety of experimental data.

Anesthetics affect membrane heterogeneity.

A computer-simulation study is performed on a simple but general molecular model of the interaction of general and local anesthetics with lipid membranes. In the neighborhood of the gel-to-fluid membrane phase transition it is found that anesthetics have a strong effect on the heterogeneity of the membrane-inducing regions of locally high anesthetics concentration. This leads to a broadening of the specific heat peak and a maximum in the membrane/water partition coefficient. These results are in accordance with available experimental data for volatile general anesthetics like halothane and local anesthetics like cocaine derivatives.

The computer as a laboratory for the physical chemistry of membranes.

A mini-review is given of some recent advances in the use of computer-simulation approaches to the study of physico-chemical properties of lipid bilayers and biological membranes. The simulations are based on microscopic molecular interaction models as well as random-surface models of fluid membranes. Particular emphasis is put on those properties that are controlled by the many-particle character of the lamellar membrane, i.e. correlations and fluctuations in density, composition and large-scale conformational structure. It is discussed how dynamic membrane heterogeneity arises and how it is affected by various molecular species interacting with membranes, such as cholesterol, drugs, insecticides, as well as polypeptides and integral membrane proteins. The influence of bending rigidity and osmotic-pressure gradients on large-scale membrane conformation and topology is described.

The effect of anaesthetics on the dynamic heterogeneity of lipid membranes.

The influence of membrane-perturbing drugs such as anaesthetics on the lipid membrane properties is analyzed theoretically on the basis of a general microscopic interaction model of the gel-to-fluid chain melting transition of one-component phospholipid membranes and phospholipid membranes with a low content of cholesterol. Monte Carlo computer simulation of the model shows that the gel-to-fluid transition of the lipid membrane, manifested in the formation of dynamically coexisting domains of gel and fluid lipids, is strongly influenced by the presence of anaesthetics. Macroscopically the effect of anaesthetics on the membrane properties is seen in a depression of the transition temperature and a smearing of thermodynamic response functions like the specific heat. Microscopically the calculations reveal that anaesthetics have a high affinity to the fluctuating domain interfaces that are dominated by kink-like lipid-chain conformations. This leads to formation of more interfaces and to a locally high concentration of anaesthetics in the interfacial regions, which is much larger than the global concentration in the membrane. Important membrane components like cholesterol, which also has been shown to be interfacially active, are found to decrease the absorption of anaesthetics and to squeeze out anaesthetics from the interfaces. The results of the general model study of anaesthetics-membrane interactions are discussed in relation to both general anaesthetics, like halothane, and local anaesthetics like cocaine-derivatives.

Effect of incompressibility on lateral instabilities of polymer brushes in a poor solvent.

We report a theoretical investigation of the lateral instability of grafted polymer layers in a poor solvent. Within self-consistent mean-field theory, we carry out a linear stability analysis at the random phase approximation level, for which an explicit incompressibility condition is enforced. Our analysis predicts a stability diagram in which regions of stable and unstable polymer brush profiles are located. Compared with analysis where incompressibility is not taken into account, our results suggest that lateral stability is enhanced.

Erythrocyte shape simulation by numerical optimization.

In a recent paper we examined the morphology of erythrocytes in terms of the mean mean curvature (MMC) of their cell membranes. A computer simulation of these shapes based on the different geometries showed that the MMC increased from the sphero-stomatocyte to the spheroechinocyte via the discocyte. In this work we extend this analysis by using a numerical optimization method based on importance sampling and the principle of adiabatic cooling. The erythrocyte membrane is treated as a single closed fluid lamina exhibiting viscoelastic characteristics. The energy function of the lamina includes the following terms: (i) Curvature-elastic energy terms which depend on both local and global curvature. (ii) A term describing the compression elasticity of the lamina. (iii) A term which depends on the volume of the cell and which is related to the osmotic pressure across the membrane. In the simulation the cell is assumed to have axial symmetry and it can therefore be described by a finite set of conic sections. So far we have been able to obtain an energy minimum corresponding to a discocyte shape using a sphere as the initial configuration. Our results therefore imply that the well-known sequence of erythrocyte shapes could solely be governed by the above mentioned properties of an ideal fluid forming a closed singly connected lamina.

Universal behavior of membranes with sterols.

Lanosterol is the biosynthetic precursor of cholesterol and ergosterol, sterols that predominate in the membranes of mammals and lower eukaryotes, respectively. These three sterols are structurally quite similar, yet their relative effects on membranes have been shown to differ. Here we study the effects of cholesterol, lanosterol, and ergosterol on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine lipid bilayers at room temperature. Micropipette aspiration is used to determine membrane material properties (area compressibility modulus), and information about lipid chain order (first moments) is obtained from deuterium nuclear magnetic resonance. We compare these results, along with data for membrane-bending rigidity, to explore the relationship between membrane hydrophobic thickness and elastic properties. Together, such diverse approaches demonstrate that membrane properties are affected to different degrees by these structurally distinct sterols, yet nonetheless exhibit universal behavior.

Softening of lipid bilayers.

The softening of wet lipid bilayer membranes during their gel-to-fluid first-order phase transition is studied by computer simulation of a family of two-dimensional microscopic interaction models. The models include a variable number, q, of lipid chain conformational states, where 2 less than or equal to q less than or equal to 10. Results are presented as functions of q and temperature for a number of bulk properties, such as internal energy, specific heat, and lateral compressibility. A quantitative account is given of the statistics of the lipid clusters which are found to form in the neighborhood of the transition. The occurrence of these clusters is related to the softening and the strong thermal density fluctuations which dominate the specific heat and the lateral compressibility for the high-q models. The cluster distributions and the fluctuations behave in a manner reminiscent of critical phenomena and percolation. The findings of long-lived metastable states and extremely slow relaxational behavior in the transition region are shown to be caused by the presence of intermediate lipid chain conformational states which kinetically stabilize the cluster distribution and the effective phase coexistence. This has as its macroscopic consequence that the first-order transition appears as a "continuous" transition, as invariably observed in all experiments on uncharged lecithin bilayer membranes. The results also suggest an explanation of the non-horizontal isotherms of lipid monolayers. Possible implications of lipid bilayer softening and enhanced passive permeability for the functioning of biological membranes are discussed.

Interbilayer transfer of phospholipid-anchored macromolecules via monomer diffusion.

A series of conjugates has been prepared by linking various hydrophilic macromolecules [poly-(ethylene glycols), polylysine, aminodextrans, or apotransferrin] to synthetic phosphatidylethanolamines via linker moieties incorporating a fluorescent bimane group. Using a fluorescence energy transfer-based assay, the rate of transfer of these species between phospholipid vesicles has been monitored as a function of the nature and size of the coupled macromolecule and of the acyl chain composition of the lipid anchor. Conjugates in which the phospholipid anchor is linked to a small hydrophilic terminal residue (e.g., ethanolamine or ethylenediamine) transfer between large unilamellar vesicles of egg phosphatidylcholine with half-times ranging from tens of minutes (for dimyristoyl lipid conjugates) to a few tens of hours (for dipalmitoyl and 1-palmitoyl-2-oleoyl lipid conjugates), in agreement with previous results for unlabeled phospholipids. Conjugation of these same lipid anchors to larger hydrophilic molecules markedly accelerates their rates of intermembrane transfer, by factors ranging from 5-7-fold (for conjugates with apotransferrin and aminodextrans of molecular weight 10,000-70,000) to over 25-fold [for conjugates with poly(ethylene glycol)-5000]. In all cases the observed transfer appears to reflect the diffusion of lipid monomers through the aqueous phase. Our results suggest that substantial intermembrane transfer can occur, on a time scale of several hours or less, for hydrophilic macromolecules conjugated to diacyl(/alkyl) lipids with 14- to 18-carbon chains unless portions of the conjugate other than the lipid anchor also interact strongly with the membrane.