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 (J?rgensen 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.     

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.     

Calculation of intermolecular interaction strengths in the P beta' phase in lipid bilayers. Implications for theoretical models.

The existence of the P beta' phase in certain lipid bilayers is evidence that molecular interactions between lipids are capable of producing unusual large-scale structures at or near biological conditions. The problem of identifying the specific intermolecular interactions responsible for the structures requires construction of theoretical models capable of clear predictions of the observable consequences of postulated intermolecular interactions. To this end we have carried out a twofold modeling effort aimed at understanding the ripple phase. First, we have performed detailed numerical calculations of potential energies of interaction between pairs and triplets of lipid molecules having different chain tilt angles and relative vertical alignments. The calculations support the notion that chain tilting in the gel phase is a result of successive 3-5-A displacements of neighboring molecules perpendicular to the bilayer plane rather than long-range cooperative chain tilting. Secondly, we have used these results as a guide to formulate a new lattice model for lipid bilayer condensed phases. The new model is less complex than our earlier model and it includes interactions which are, based on the energy calculations, more likely to be responsible for the ripple phase. In a certain limit the model maps onto the chiral clock model, a model of much interest in condensed matter theory. In this limit the model exhibits a chain-tilted ordered phase followed by (as temperature increases) a modulated phase followed by a disordered phase. Within this limit we discuss the properties of the model and compare structures of the modulated phase exhibited by the model with experimental data for the P beta' phase in lipid bilayers.     

Cardiolipin and phosphatidylethanolamine role in dibucaine interaction with the mitochondrial membrane

Mitochondrial membranes are pointed out as the site of cardiotoxic action of local anaesthetics. Its three main phospholipids components are phosphatidylcholine, phosphatidylethanolamine and cardiolipin. Cardiolipins, in eukaryotes, are only found in mitochondria and are essential for the maintenance of its integrity and dynamics. Fluorescence and nuclear magnetic resonance spectroscopy were used to study the interactions of a local anaesthetics, Dibucaine (DBC), with different mitochondrial membrane models constituted by combinations of its three main lipid components in which cardiolipin was a natural extract (CL_mix). Both CL_mix presence/absence and its percentage in the model membranes were evaluated. Fluorescence spectroscopy showed that DBC lowered the transition temperature of all membrane models understudy. DBC partition showed to be dependent of CL_mix presence and phosphatidylethanolamine:CL ratio. Furthermore, the maximum emission wavelength (λ_max) exhibited a notorious decreased with increasing phospholipid to DBC ratio, in all the membrane models containing CL_mix. Nevertheless, it remained approximately the same in the membrane without CL_mix. This indicates a differential membrane localization of the anaesthetics, dependent on the membrane models used. NMR results showed that DBC interaction and location in the membrane models is mainly influenced by CL_mix presence, and DBC can significant alter lipid systems properties e.g. percentage and type of lipid phase present. Taken all together it was shown that DBC interaction and location are largely dependent on the membrane model system. Furthermore, DBC is able to produce significant changes in the lipidic systems which might help to explain its high toxicity.     

Statistical thermodynamics of association colloids. IV. Inhomogeneous membrane systems

A previously developed self-consistent field theory to describe the equilibrium properties of lipid-like membranes is extended to allow the presence of inhomogeneities parallel to the membrane. Conformations of lipid molecules and foreign ('guest') molecules in the membrane are obtained by step-weighted random walk generation of the chains on a lattice, where the theory is made two-dimensional to account for the parallel inhomogeneities. No pre-assigned positions of the head groups, or other parts of the molecules, are introduced. Nearest neighbor interactions are accounted for through Flory-Huggins type interaction parameters. The theory is applied to the incorporation of trans-membrane molecules and conditions for channel formation are discussed. Lateral phase separation in membranes consisting of non-mixing lipids is also considered. Water only slightly enriches the boundary between the two lipid regions. The aliphatic chains are very well able to smoothly cover inhomogeneities in the bilayer. No indications of instability of the membrane due to the induced inhomogeneities are found.     

A self-consistent chain model for the phase transitions in lipid bilayer membranes

We presented a mechanical model of a lipid bilayer membrane. The internal conformations of a polar head group and double hydrocarbon chains in a lipid molecule were described on the basis of the isomeric bond-rotation scheme. The thermodynamic properties of the lipid membranes were represented by a density matrix that described the rotational isomeric states of the head groups and chains. The parameters that determined the density matrix were obtained in the presence of the intermolecular interactions, which depend on the conformation of the molecules. The interchain interaction was given by the Kihara potential, which depends on the shape of the chains. The Coulomb interaction between the polar head groups and the lateral pressure were considered. The calculation was made for the three lipid molecules corresponding to DMPC, DPPC, and DSPC. The model agreed well with the following experimental results: the temperature, the latent heat of the gel-to-liquid crystalline phase transition, the temperature dependencies of (a) the intermolecular distance, (b) the number of gauche bonds in a hydrocarbon chain, (c) the order parameter for the bond orientation, (d) the volume of the membrane, (e) the thermal expansion coefficients, and (f) the birefringence.     

Theory of lipid polymorphism: application to phosphatidylethanolamine and phosphatidylserine

We introduce a microscopic model of a lipid with a charged headgroup and flexible hydrophobic tails, a neutral solvent, and counter ions. Short-ranged interactions between hydrophilic and hydrophobic moieties are included as are the Coulomb interactions between charges. Further, we include a short-ranged interaction between charges and neutral solvent, which mimics the short-ranged, thermally averaged interaction between charges and water dipoles. We show that the model of the uncharged lipid displays the usual lyotropic phases as a function of the relative volume fraction of the headgroup. Choosing model parameters appropriate to dioleoylphosphatidylethanolamine in water, we obtain phase behavior that agrees well with experiment. Finally we choose a solvent concentration and temperature at which the uncharged lipid exhibits an inverted hexagonal phase and turn on the headgroup charge. The lipid system makes a transition from the inverted hexagonal to the lamellar phase, which is related to the increased waters of hydration correlated with the increased headgroup charge via the charge-solvent interaction. The polymorphism displayed upon variation of pH mimics that of the behavior of phosphatidylserine.     

MRS study of the interaction of dihydropyridines with lipid molecules in phosphatidylcholine vesicles

Dihydropyridines (DHPs), synthetic molecules used as antihypertensive agents, bind to plasma membrane receptors following diffusion through the hydrophobic phase. In this study, MRS technique has been used to clarify the interactions of the dihydrophyridines Nifedipine and Lacidipine within the lipid bilayer. 1D and 2D 1H MRS at high field have been employed to examine the behavior of unilamellar dimyristoyl-phosphatidylcholine liposomes when the two drugs have been inserted in the bilayer. In particular, the study represents an innovative application of 2D 1H NOESY technique to clarify different mechanisms of interactions of small molecules inside model membranes. On the other hand, 31P measurements have been performed in multilamellar dimyristoyl-phosphatidylcholine lipsomes to detect alterations of lipid polymorphic phases. The experiments show that the two dihydropyridines interact with the lipids by different modalities. Lacidipine undergoes a very strong interaction with lipids, possibly inducing a phase segregation of lipid molecules into the bilayer, while self-association seems to be the prevalent interaction of Nifedipine inside the bilayer.     

Computer simulation studies on the significance of lipid polar head charge

Ripple phase modelling was achievable by taking into consideration the dipole structure of the polar heads of model membrane molecules. Computer simulations enabled the selective analysis of a model membrane. Considering only the hydrophobic part of the lipid membrane, the gel-fluid transition stage can be obtained in such a simulation. Assuming an additional degree of freedom, the entire molecule can move along the normal to the membrane surface projected from two C-C bonds. The amounts of shifted lipids were 17% and 33% at temperatures of 300 K (gel) and 330 K (fluid), respectively. Taking into account only polar head interactions in media of different ionic strength I, dielectric constant epsilon, and an effective charge and temperature, we could observe the same behaviour of the examined system independently of the values of I and ( when the charge was reduced to q/2. The amount of shifted heads at 300 K decreases sharply with the reduced charge value, with an accompanying increase in the number of "standing" polar heads. Summing up, it can be stated that hydrocarbon lipid chains exhibit a greater tendency to displacement in the fluid state than in the gel state. However, the polar heads behave in the opposite way: there are more displaced heads at 300 K than at 330 K. Thus, the overall analysis of the interactions between the molecules of the model membrane should enable us to find model parameters suitable for studying the lipid membrane at a wide range of temperatures. Finally, an electrostatic profile close to the membrane surface could be estimated in different membrane states. This should be useful in membrane-biologically active compound interaction analysis.     

Lipid-cholesterol interactions in the P beta' phase. Application of a statistical mechanical model.

We describe a statistical mechanical model for lipid-cholesterol mixtures in the P beta' (ripple) phase of lipid bilayers. The model is a simple extension of an earlier model for the ripple phase in pure lipid bilayers. The extension consists of adding a degree of freedom to allow for the occupation of underlying lattice sites by cholesterol molecules, and adding a lipid-cholesterol interaction term to the model Hamiltonian. The interaction term was constructed based on numerical calculations of lipid-cholesterol energies for several different packing juxtapositions of the two molecules. Other than the lipid-cholesterol interactions, the extended model uses the same parameter set as the earlier model, so that comparison of the properties of the extended model with experimental data serves as a test of the validity of the original model. Properties of the model were calculated using the Monte Carlo method. Results are displayed as snapshots of the ripple configurations at different cholesterol concentrations. The spacing of the ripples increases with increasing cholesterol concentration and the rate of increase compares very well with experimental data. The success of this model supports the conclusion drawn earlier that frustration arising from anisotropic packing interactions is responsible for the ripple phase in lipid bilayers. In the extended model these packing interactions are responsible for the selective partitioning of cholesterol in the regions between the ripples.     

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

Summary 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).     

Helix-helix interactions in lipid bilayers.

Using a continuum model, we calculated the electrostatic interaction free energy between two alpha-helices in three environments: the aqueous phase, a low dielectric alkane phase, and a simple representation of a lipid bilayer. As was found in previous work, helix-helix interactions in the aqueous phase are quite weak, because of solvent screening, and slightly repulsive, because of desolvation effects that accompany helix assembly. In contrast, the interactions can be quite strong in a hypothetical alkane phase because desolvation effects are essentially nonexistent and because helix-helix interactions are not well screened. In this type of environment, the antiparallel helix orientation is strongly favored over the parallel orientation. In previous work we found that the free energy penalty associated with burying helix termini in a bilayer is quite high, which is why the termini tend to protrude into the solvent. Under these conditions the electrostatic interaction is strongly screened by solvent; indeed, it is sufficient for the termini to protrude a few angstroms from the two surfaces of the bilayer for their interaction to diminish almost completely. The effect is consistent with the classical model of the helix dipole in which the dipole moment is represented by point charges located at either terminus. Our results suggest, in agreement with previous models, that there is no significant nonspecific driving force for helix aggregation and, hence, that membrane protein folding must be driven by specific interactions such as close packing and salt-bridge and hydrogen bond formation.     

Influence of local and neutral anaesthetics on the polymorphic phase preferences of egg yolk phosphatidylethanolamine

(1) The polymorphic phase preferences of egg phosphatidylethanolamine have been examined in the presence of normal alcohols and alkanes of varying chain length, as well as charged amine anaesthetics. (2) It is shown that the charged anaesthetics, ethanol and butanol can stabilize a bilayer arrangement for egg phosphatidylethanolamine. In contrast, longer chain ($\text{C}\text{?6}$) normal alcohols and alkanes induce the hexagonal (H_II) phase. (3) The relative potency of local anaesthetics in vitro (chlorpromazine, dibucaine, tetracaine and procaine) is mirrored by their relative ability to stabilize bilayer structure for hydrated egg phosphatidylethanolamine. Further, the aqueous concentrations of anaesthetic required to affect phospholipid polymorphism is sensitive to the lipid composition. For example, the inclusion of 20 mol% egg phosphatidylserine in egg phosphatidylethanolamine dispersions can reduce the aqueous concentrations of dibucaine required to induce appreciable bilayer stabilization effects from 5.0 mM to 0.5 mM. (4) It is suggested that the ability of amphipatic molecules such as anaesthetics to influence phosphatidylethanolamine polymorphism arises from their molecular shape. The possibility that anaesthetic molecules may exert their effects by virtue of this shape property is raised.     

Magnetic resonance studies on the binding of etomidate to lipid bilayers

Physicochemical studies on the binding of etomidate, a fast acting anaesthetic, with lipid bilayers have been carried out. ESR spin labeling studies indicate that the gel to liquid crystalline phase transition of dipalmitoyl phosphatidyl choline (DPPC) vesicles retains its cooperative nature on incorporation of the anaesthetic. For a 5:1 lipid to drug molar ratio, the phase transition occurs at an unusually lower temperature than those observed with other drug-DPPC systems. Results of 13C NMR and 1H NOE experiments suggest that the drug molecules reside in the close proximity of the terminal of hydrocarbon chains of the lipid molecules. 31P NMR and Electron Microscopic experiments indicate that the presence of etomidate alters the normal lamellar structure of DPPC vesicles into hexagonal (HII) type. Based on these observations, a model for drug-lipid binding has been proposed.     

A theoretical model for the association of amphiphilic transmembrane peptides in lipid bilayers

A theoretical model is proposed for the association of trans-bilayer peptides in lipid bilayers. The model is based on a lattice model for the pure lipid bilayer, which accounts accurately for the most important conformational states of the lipids and their mutual interactions and statistics. Within the lattice formulation the bilayer is formed by two independent monolayers, each represented by a triangular lattice, on which sites the lipid chains are arrayed. The peptides are represented by regular objects, with no internal flexibility, and with a projected area on the bilayer plane corresponding to a hexagon with seven lattice sites. In addition, it is assumed that each peptide surface at the interface with the lipid chains is partially hydrophilic, and therefore interacts with the surrounding lipid matrix via selective anisotropic forces. The peptides would therefore assemble in order to shield their hydrophilic residues from the hydrophobic surroundings. The model describes the self-association of peptides in lipid bilayers via lateral and rotational diffusion, anisotropic lipid-peptide interactions, and peptide-peptide interactions involving the peptide hydrophilic regions. The intent of this model study is to analyse the conditions under which the association of trans-bilayer and partially hydrophilic peptides (or their dispersion in the lipid matrix) is lipid-mediated, and to what extent it is induced by direct interactions between the hydrophilic regions of the peptides. The model properties are calculated by a Monte Carlo computer simulation technique within the canonical ensemble. The results from the model study indicate that direct interactions between the hydrophilic regions of the peptides are necessary to induce peptide association in the lipid bilayer in the fluid phase. Furthermore, peptides within each aggregate are oriented in such a way as to shield their hydrophilic regions from the hydrophobic environment. The average number of peptides present in the aggregates formed depends on the degree of mismatch between the peptide hydrophobic length and the lipid bilayer hydrophobic thickness: The lower the degree of mismatch is the higher this number is. Received: 30 December 1996 / Accepted: 9 May 1997     

Model analysis of surfactant--polymer interaction as cooperative ligand binding to linear lattice

An improved model of the cooperative binding of monomeric ligands to a linear lattice is proposed for the analysis of surfactant association on the polymer. The interaction between bound ligands across an unoccupied site as well as the steric hindrance effect in consecutive bindings is taken into account here. Typical results of the model calculations are represented, and several least squares fittings of the binding isotherms of the ionic surfactant-polyelectrolyte systems are attempted. The characteristic binding behavior in those systems is interpretable by the feasible model of the interactions between surfactant molecules. The advantages and limitations of the analysis using this model also are discussed.     

Interfacial tension of phosphatidylcholine-phosphatidylserine system in bilayer lipid membrane

The effect of pH of electrolyte solution on the interfacial tension of lipid membrane formed of phosphatidylcholine (PC, lecithin)–phosphatidylserine (PS) system was studied. In this article, three models describing the H⁺ and OH⁻ ions adsorption in the bilayer lipid surface are presented. In Model I and Model II, the surface is continuous with uniformly distributed functional groups constituting the centres of H⁺ and OH⁻ ions adsorption while in the other the surface is built of lipid molecules, free or with attached H⁺ and OH⁻ ions. In these models contribution of the individual lipid molecule forms to interfacial tension of the bilayer were assumed to be additive. In Model III the adsorption of the H⁺ and OH⁻ ions at the PC–PS bilayer surface was described in terms of the Gibbs isotherm. Theoretical equations are derived to describe this dependence in the whole pH range.     

A Monte Carlo study of the self-assembly of bacteriorhodopsin

Bacteriorhodopsin (BR) and specific lipid molecules self-assemble into a quasi two-dimensional lattice structure known as the purple membrane (PM). In the PM, BR molecules exist in a trimeric form with lipid molecules present in the space enclosed by each trimeric unit and in the inter-trimer space. These trimeric units, which have a roughly circular cross-section, are arranged in hexagonal patterns with long-ranged crystalline order. In this work, we investigate the self-assembly of BR in the PM via Monte Carlo simulations of a two-dimensional model of the membrane and proteins. The protein molecules are modeled as 120 degrees sectors of a circle and the lipid molecules enter into the model through effective protein-protein interactions. The sectors cannot overlap with each other, and in addition to this excluded volume interaction there are site-site attractive interactions between specific points of the proteins to mimic interactions between helices on the proteins and lipid-induced interactions. At low values of the attractive well depth, the proteins are found in the monomeric form at all concentrations. At moderate and high values of the attractive well depth, trimers are formed as the concentration increases, and with a further increase in concentration the trimers organize into a hexagonal lattice. The interactions between the proteins and those induced by the intra-trimer lipids play an equally important role in the formation of trimers and the lattice. The lipids in the inter-trimer space cause the trimers to orient in a specific direction in the hexagonal crystal lattice.