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.     

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 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.     

Phase-State Dependent Current Fluctuations in Pure Lipid Membranes

Current fluctuations in pure lipid membranes have been shown to occur under the influence of transmembrane electric fields (electroporation) as well as a result from structural rearrangements of the lipid bilayer during phase transition (soft perforation). We demonstrate that the ion permeability during lipid phase transition exhibits the same qualitative temperature dependence as the macroscopic heat capacity of a D15PC/DOPC vesicle suspension. Microscopic current fluctuations show distinct characteristics for each individual phase state. Although current fluctuations in the fluid phase show spikelike behavior of short timescales (∼2 ms) with a narrow amplitude distribution, the current fluctuations during lipid phase transition appear in distinct steps with timescales of ∼20 ms. We propose a theoretical explanation for the origin of timescales and permeability based on a linear relationship between lipid membrane susceptibilities and relaxation times near the phase transition.     

Structural determinants of purple membrane assembly

The purple membrane is a two-dimensional crystalline lattice formed by bacteriorhodopsin and lipid molecules in the cytoplasmic membrane of Halobacterium salinarum. High-resolution structural studies, in conjunction with detailed knowledge of the lipid composition, make the purple membrane one of the best models for elucidating the forces that are responsible for the assembly and stability of integral membrane protein complexes. In this review, recent mutational efforts to identify the structural features of bacteriorhodopsin that determine its assembly in the purple membrane are discussed in the context of structural, calorimetric and reconstitution studies. Quantitative evidence is presented that interactions between transmembrane helices of neighboring bacteriorhodopsin molecules contribute to purple membrane assembly. However, other specific interactions, particularly between bacteriorhodopsin and lipid molecules, may provide the major driving force for assembly. Elucidating the molecular basis of protein-protein and protein-lipid interactions in the purple membrane may provide insights into the formation of integral membrane protein complexes in other systems.     

Dipalmitoylphosphatidylcholine membranes modified with carotenoid pigment lutein: Experiment versus Monte Carlo simulation study of the membrane organization

Organization of bilayer lipid membrane formed with dipalmitoylphosphatidylcholine and containing a xanthophyll pigment lutein was studied by both the Monte Carlo simulation and UV-Vis absorption spectroscopy. The simulations were based on ten-state Pink model. The proposed model consisted of two monolayers represented by a two-dimensional triangular lattice with vacancies. The orientation and aggregation state of lutein, obtained from the analysis of the spectroscopic measurements, were used to calibrate intermolecular interactions in the model. In accordance with the experimental data, the model allows two orientations of lutein molecules: one spanning the membrane and the other parallel to its plane. The influence of the intermolecular interactions on the main phase transition as well as on the aggregation of lutein molecules is discussed. The analysis of the model enables us to learn about molecular mechanisms that govern the effects of lutein on the membrane properties as well as the effects of the lipid matrix on lutein organization in the membrane. A concept is discussed according to which increasing domination of parallel lutein orientation, observed at high temperatures, can protect the membrane against penetration by water molecules and reactive oxygen species and against loss of the membrane compactness, especially in the regions of oxidized acyl chains.     

Dynamics of lipid domain formation: Fluctuation analysis

Scanning-fluctuation correlation spectroscopy was used to detect subresolution organizational fluctuations in the lipid liquid-crystalline phase for single lipid model systems. We used the fluorescent probe Laurdan which is sensitive to the amount of water in the membrane to show that there is a spatial heterogeneity on the scale of few pixels (the size of the pixel is 50 nm). We calculated the pixel variance of the GP function and we found that the variance has a peak at the phase transition for 3 different samples made of pure lipids. The pixel variance has an abrupt change at the phase transition of the membrane and then it slowly decreases at higher temperature. The relatively large variance of the GP indicates that the liquid phase of the membrane is quite heterogeneous even several degrees higher than the phase transition temperature. We interpreted this result as evidence of an underlying microscale structure of the membrane in which water is not uniformly distributed at the micron scale. Imaging of these microstructures shows that the pixels with different GP tend to concentrate in specific domains in the membrane. In the case of single lipid membrane, the statistical and fluctuation analysis of the GP data shows that even such simple lipid systems are capable of generating and maintaining stable structural and organizational heterogeneities.     

Means of optimizing light energy conversion in the primary stages of photosynthesis. II. Optimization of the structure of an uniform photosynthetic unit lattice

The possibility of optimization of the structure of a model photosynthetic unit lattice is analysed. The efficiency of the photosynthetic unit operation is evaluated from the time of excitation energy trapping by reaction centers. The calculations assume a F?rster inductive resonance mechanism for energy transfer within light--harvesting antenna and pairwise dipolar interactions. We use the probability matrix method which is adapted to excitation trapping time (but not to excitation jumps number) calculation. It is shown that the specific anisotropy of the distances between antenna molecules (which is in principle possible due to the diskshaped form of chlorophyll molecules) in combination with the optimal spatial arrangement of reaction centers as "well regulated clusters" allows to decrease the time of excitation energy trapping by over an order of magnitude. The requirements for optimization of the structure of a macroscopic photosynthetic unit lattice and the consequences following from them for the in vivo systems are formulated.     

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 model for the lipid pretransition: coupling of ripple formation with the chain-melting transition

Below the thermotropic chain-melting transition, lipid membrane c(P) traces display a transition of low enthalpy called the lipid pretransition. It is linked to the formation of periodic membrane ripples. In the literature, these two transitions are usually regarded as independent events. Here, we present a model that is based on the assumption that both pretransition and main transition are caused by the same physical effect, namely chain melting. The splitting of the melting process into two peaks is found to be a consequence of the coupling of structural changes and chain-melting events. On the basis of this concept, we performed Monte Carlo simulations using two coupled monolayer lattices. In this calculation, ripples are considered to be one-dimensional defects of fluid lipid molecules. Because lipids change their area by approximately 24% upon melting, line defects are the only ones that are topologically possible in a triangular lattice. The formation of a fluid line defect on one monolayer leads to a local bending of the membrane. Geometric constraints result in the formation of periodic patterns of gel and fluid domains. This model, for the first time, is able to predict heat capacity profiles, which are comparable to the experimental c(P) traces that we obtained using calorimetry. The basic assumptions are in agreement with a large number of experimental observations.     

Lipid-protein interactions of integral membrane proteins: a comparative simulation study

The interactions between membrane proteins and their lipid bilayer environment play important roles in the stability and function of such proteins. Extended (15-20 ns) molecular dynamics simulations have been used to explore the interactions of two membrane proteins with phosphatidylcholine bilayers. One protein (KcsA) is an alpha-helix bundle and embedded in a palmitoyl oleoyl phosphatidylcholine bilayer; the other (OmpA) is a beta-barrel outer-membrane protein and is in a dimyristoyl phosphatidylcholine bilayer. The simulations enable analysis in detail of a number of aspects of lipid-protein interactions. In particular, the interactions of aromatic amphipathic side chains (i.e., Trp, Tyr) with lipid headgroups, and "snorkeling" interactions of basic side chains (i.e., Lys, Arg) with phosphate groups are explored. Analysis of the number of contacts and of H-bonds reveal fluctuations on an approximately 1- to 5-ns timescale. There are two clear bands of interacting residues on the surface of KcsA, whereas there are three such bands on OmpA. A large number of Arg-phosphate interactions are seen for KcsA; for OmpA, the number of basic-phosphate interactions is smaller and shows more marked fluctuations with respect to time. Both classes of interaction occur in clearly defined interfacial regions of width approximately 1 nm. Analysis of lateral diffusion of lipid molecules reveals that "boundary" lipid molecules diffuse at about half the rate of bulk lipid. Overall, these simulations present a dynamic picture of lipid-protein interactions: there are a number of more specific interactions but even these fluctuate on an approximately 1- to 5-ns timescale.     

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.     

Tuning Membrane Thickness Fluctuations in Model Lipid Bilayers

Membrane thickness fluctuations have been associated with a variety of critical membrane phenomena, such as cellular exchange, pore formation, and protein binding, which are intimately related to cell functionality and effective pharmaceuticals. Therefore, understanding how these fluctuations are controlled can remarkably impact medical applications involving selective macromolecule binding and efficient cellular drug intake. Interestingly, previous reports on single-component bilayers show almost identical thickness fluctuation patterns for all investigated lipid tail-lengths, with similar temperature-independent membrane thickness fluctuation amplitude in the fluid phase and a rapid suppression of fluctuations upon transition to the gel phase. Presumably, in vivo functions require a tunability of these parameters, suggesting that more complex model systems are necessary. In this study, we explore lipid tail-length mismatch as a regulator for membrane fluctuations. Unilamellar vesicles of an equimolar mixture of dimyristoylphosphatidylcholine and distearoylphosphatidylcholine molecules, with different tail-lengths and melting transition temperatures, are used as a model system for this next level of complexity. Indeed, this binary system exhibits a significant response of membrane dynamics to thermal variations. The system also suggests a decoupling of the amplitude and the relaxation time of the membrane thickness fluctuations, implying a potential for independent control of these two key parameters.     

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.     

The Temperature Dependence of Lipid Membrane Permeability, its Quantized Nature, and the Influence of Anesthetics

We investigate the permeability of lipid membranes for fluorescence dyes and ions. We find that permeability reaches a maximum close to the chain melting transition of the membranes. Close to transitions, fluctuations in area and compressibility are high, leading to an increased likelihood of spontaneous lipid pore formation. Fluorescence correlation spectroscopy reveals the permeability for rhodamine dyes across 100-nm vesicles. Using fluorescence correlation spectroscopy, we find that the permeability of vesicle membranes for fluorescence dyes is within error proportional to the excess heat capacity. To estimate defect size we measure the conductance of solvent-free planar lipid bilayer. Microscopically, we show that permeation events appear as quantized current events very similar to those reported for channel proteins. Further, we demonstrate that anesthetics lead to a change in membrane permeability that can be predicted from their effect on heat capacity profiles. Depending on temperature, the permeability can be enhanced or reduced. We demonstrate that anesthetics decrease channel conductance and ultimately lead to blocking of the lipid pores in experiments performed at or above the chain melting transition. Our data suggest that the macroscopic increase in permeability close to transitions and microscopic lipid ion channel formation are the same physical process.     

The influence of proteins and peptides on the phase properties of lipids

This paper reviews model membrane studies on the modulation of the macroscopic structure of lipids by lipid-protein interactions, with particular emphasis on the gramicidin molecule. This hydrophobic peptide has three main effects on lipid polymorphism: (1) in lysophosphatidylcholine it triggers a micellar to bilayer transition, (2) in phosphatidylethanolamine it lowers the bilayer to hexagonal H_II phase transition temperature and (3) in phosphatidylcholine and other bilayer preferring lipids it is able to induce the formation of an H_II phase. From experiments in which the gramicidin molecule was chemically modified it can be concluded that the tryptophan residues play a determining role in the peptide-induced changes in polymorphism. The experimental data lead to the proposal that gramicidin molecules have a tendency to self-associate, possibly mediated by tryptophan-tryptophan interactions and organize into tubular structures such as found in the H_II phase.     

The lipid/protein interface as xenobiotic target site. Kinetic analysis of tadpole narcosis

High-resolution X-ray diffraction structures of integral membrane proteins have revealed various binding modes of lipids, but current spectroscopic studies still use uniform macroscopic binding constants to describe lipid binding. The Adair approach employing microscopic lipid-binding constants has previously been taken to explain the enhancement of agonist binding to the nicotinic acetylcholine receptor by general anaesthetics in terms of the competitive displacement of essential lipid activator molecules [Walcher S, Altschuh J & Sandermann H (2001) J. Biol. Chem.276, 42191-42195]. This approach was extended to tadpole narcosis induced by alcohols. A single class, or two different classes of lipid activator binding sites, are considered. Microscopic lipid and inhibitor binding constants are derived and allow a close fit to dose-response curves of tadpole narcosis on the basis of a preferential displacement of more loosely bound essential lipid activator molecules. This study illustrates the potential of the Adair approach to resolve protein-bound lipid populations.