Microscopic Interaction Model Research Articles

Stationary states of a two-state defect quadratically coupled to a few bosonic modes

A fully quantistic microscopic two-phonon interaction model between an active centre and localized modes of an irradiated insulating material is introduced. Its exact diagonalization is accomplished with the help of a suitable unitary operator. Explicit expressions for the eigenvalues and eigenvectors are reported. The possible relevance of such a model in the context of the material science area is briefly pointed out.

Molecular sorting of lipids by bacteriorhodopsin in dilauroylphosphatidylcholine/distearoylphosphatidylcholine lipid bilayers

A combined experimental and theoretical study is performed on binary dilauroylphosphatidylcholine/distearoylphosphatidylcholine (DLPC/DSPC) lipid bilayer membranes incorporating bacteriorhodopsin (BR). The system is designed to investigate the possibility that BR, via a hydrophobic matching principle related to the difference in lipid bilayer hydrophobic thickness and protein hydrophobic length, can perform molecular sorting of the lipids at the lipid-protein interface, leading to lipid specificity/selectivity that is controlled solely by physical factors. The study takes advantage of the strongly nonideal mixing behavior of the DLPC/DSPC mixture and the fact that the average lipid acyl-chain length is strongly dependent on temperature, particularly in the main phase transition region. The experiments are based on fluorescence energy transfer techniques using specifically designed lipid analogs that can probe the lipid-protein interface. The theoretical calculations exploit a microscopic molecular interaction model that embodies the hydrophobic matching as a key parameter. At low temperatures, in the gel-gel coexistence region, experimental and theoretical data consistently indicate that BR is associated with the short-chain lipid DLPC. At moderate temperatures, in the fluid-gel coexistence region, BR remains in the fluid phase, which is mainly composed of short-chain lipid DLPC, but is enriched at the interface between the fluid and gel domains. At high temperatures, in the fluid phase, BR stays in the mixed lipid phase, and the theoretical data suggest a preference of the protein for the long-chain DSPC molecules at the expense of the short-chain DLPC molecules. The combined results of the experiments and the calculations provide evidence that a molecular sorting principle is active because of hydrophobic matching and that BR exhibits physical lipid selectivity. The results are discussed in the general context of membrane organization and compartmentalization and in terms of nanometer-scale lipid-domain formation.

Phase separation dynamics and lateral organization of two-component lipid membranes

The non-equilibrium dynamic ordering process of coexisting phases has been studied for two-component lipid bilayers composed of saturated di-acyl phospholipids with different acyl chain lengths, such as DC14PC-DC18PC and DC12PC-DC18PC. By means of a microscopic interaction model and computer-simulation techniques the non-equilibrium properties of these two mixtures have been determined with particular attention paid to the effects of the non-equilibrium ordering process on membrane heterogeneity in terms of local and global lateral membrane organization. The results reveal that a sudden temperature change that takes the lipid mixture from the fluid one-phase region into the gel-fluid phase-coexistence region leads to the formation of a large number of small lipid domains which slowly are growing in time. The growth of the lipid domains, which is limited by long-range diffusion of the lipid molecules within the two-dimensional membrane plane, gives rise to the existence of a highly heterogeneous percolative-like structure with a network of interfacial regions that have properties different from those of the phase-separated gel and fluid bulk phases. The results, which are discussed in relation to recent experimental observations interpreted in terms of a percolative-like membrane structure within the two phase region (Almeida, P.F.F., Vaz, W.L.C., and T.E. Thompson. 1992. Biochemistry 31:7198-7210), suggest that non-equilibrium effects may influence lipid domain formation and membrane organization on various length and time scales. Such effects might be of importance in relation to membrane processes that require molecular mobility of the membrane components in restricted geometrical environments of the compartmentalized lipid membrane.

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.

Calorimetric and theoretical studies of the effects of lindane on lipid bilayers of different acyl chain length

The effects of the insecticide lindane on the phase transition in multilamellar bilayers of saturated diacylphosphatidylcholines of different acyl chain length (DC 14PC, DC 16PC, and DC 18PC) have been studied by means of differential scanning calorimetry (DSC), as well as computer-simulation calculations on a molecular interaction model. The calorimetric data show that increasing concentrations of lindane lower the transition temperature and lead to a broadening of the specific heat in a systematic way depending on the lipid acyl chain length. Kinetic effects in the observed calorimetric traces indicate that the incorporation of lindane into multilamellar lipid bilayers is slow, but faster for the shorter lipid species. Large unilamellar vesicles do not show such kinetic effects. The transition enthalpy is for all three lipid species found to be independent of the lindane concentration which implies that the entropy of mixing is vanishingly small. This lends support to a microscopic molecular interaction model which assigns the absorbed lindane molecules to interstitial sites in the bilayer. Computer-simulation calculations on this model, which assumes a specific interaction between lindane and certain excited acyl chain configurations, lead to predictions of the lipid-water partition coefficient in qualitative agreement with experimental measurements (Antunes-Madeira and Madeira (1985) Biochim. Biophys. Acta 820, 165–172). The partition coefficient has a peak near the phase transition which is a consequence of enhanced interfacial adsorption of lindane at lipid-domain interfaces.

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.

Electrostatics at the Water-Hydrocarbon Interface / Elektrostatische Einflüsse an der Grenzfläche Wasser-Kohlenwasserstoff

A molecular dynamics study of a columnar aqueous sodium octanoate micelle in the high-concentration hexagonal phase is discussed. The simulation is based on a microscopic interaction model which includes the electronic surfactant polarization. First, the approximations underlying this model are outlined. Then the results are discussed with emphasis on analyzing the electrostatics of the ionic charge density and polarization at the water-hydrocarbon interface.

Evidence for electron-phonon coupling in vibrational spectrum of Bi 2Sr 2CaCu 2O 8 single crystal

The detailed investigation of the phonon line shape in the spectrum of ϵ ″( ω) extracted from the reflectivity spectrum of Bi 2Sr 2CaCu 2O 8 single crystal is reported. A model approximation of the ϵ ″( ω) spectrum in the frequency region of apex oxygen axial vibration reveals the resonance interaction between this vibration and one-particle excitation spectrum. The results are interpreted within the microscopic model of electron-phonon interaction based on the assumption about phonon modulated hybridization between the electronic band states of the copper-oxygen planes and a narrow band connected with apex oxygen atoms.

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.

Relationships between lipid membrane area, hydrophobic thickness, and acyl-chain orientational order. The effects of cholesterol

A microscopic interaction model for a fully hydrated lipid bilayer membrane containing cholesterol is used to calculate, as a function of temperature and composition, the membrane area, the membrane hydrophobic thickness, and the average acyl-chain orientational order parameter, S. The order parameter, S, is related to the first moment, M1, of the quadrupolar magnetic resonance spectrum which can be measured for lipids with perdeuterated chains. On the basis of these model calculations as well as recent experimental measurements of M1 using magnetic resonance and of membrane area using micromechanical measurements, a discussion of the possible relationships between membrane area, hydrophobic thickness, and moments of nuclear magnetic resonance spectra is presented. It is pointed out that S under certain circumstances may be useful for estimating the hydrophobic membrane thickness. This is particularly advantageous for multicomponent membranes where structural data are difficult to obtain by using diffraction techniques. The usefulness of the suggested relationships is demonstrated for cholesterol-containing bilayers.

Computer Simulation of Interfacial Fluctuation Phenomena

Monte Carlo computer-simulation techniques applied to a microscopic interaction model of the gel-to-fluid chain-melting phase transition in pseudo-two-dimensional lipid membranes (mono- and bilayers) have shown that the density fluctuations at the transition induce formation of pseudo-one-dimensional fluctuating interfaces between lipid clusters in the membrane plane leading to dynamically heterogeneous membrane states. The characteristics of the fluctuations and the scaling properties of the clusters show that the membrane exhibits pseudo-critical behavior. In thermodynamic equilibrium, the interfacial area has a dramatic temperature dependence with an anomaly at the transition temperature. This anomaly is related to similar anomalies in response functions and in the transmembrane permeability. The interfacial area may be modulated by appropriate "impurities", e.g., by interfacially active molecules such as cholesterol or interstitial small molecules such as general anaesthetics. The properties of the interfacial area provide a means for understanding aspects of the functioning of certain interfacially active membrane-bound enzymes, such as phospholipase A2.

Theory of thermal anomalies in the specific heat of lipid bilayers containing cholesterol

A theoretical explanation of the experimentally observed characteristic thermal anomalies in the specific heat of lipid bilayers containing cholesterol is provided in terms of the phase equilibria in the phosphatidylcholine-cholesterol system. The phase equilibria are calculated via a microscopic interaction model that takes proper account of both the conformational and the crystalline degrees of freedom of the lipid acyl chains. It is shown that the characteristic double-peaked specific heat, with a narrow and a broad component, is a natural consequence of the topology of the phase diagram. Some results for the enthalpy of the mixed system are also reported. It is suggested that there is no need for invoking special mechanisms such as lipid-cholesterol complexing or formation of special interfacial regions in the bilayer in order to explain the specific-heat anomalies.

Decoupling of crystalline and conformational degrees of freedom in lipid monolayers

A theoretical study is performed on a microscopic interaction model which describes the transitions between liquid and solid phases of lipid monolayers spread on air/water interfaces. The model accounts for condensation in terms of acyl-chain conformational degrees of freedom as well as in terms of variables which describe the orientations of crystalline domains in the solid. The phase behavior of the model as a function of temperature and lateral pressure is explored using mean-field theory and computer-simulation techniques. Attention is paid to the particular interplay between the two types of condensation processes and effects on the phase behavior due to decoupling of crystalline and conformational order parameters. In the case of decoupling, the model predicts that the high-pressure solid-conformationally ordered phase is separated from the low-pressure liquid-conformationally disordered phase by a liquid-conformationally ordered phase. This prediction is consistent with synchrotron x-ray experiments which show that the chain-ordering transition and the crystallization process need not take place at the same lateral pressure. A characterization is provided of the nonequilibrium effects and pattern-formation processes observed along the isotherms in the phase diagram spanned by lateral pressure and area. A description is given of the kinetics of the nonequilibrium phase transitions and the concomitant heterogeneous microstructure of the monolayer. This leads to an explanation of the peculiarities of the experimentally observed isotherms of lipid monolayer phase behavior. It is pointed out that cholesterol, which promotes lipid-chain conformational order, has a unique capacity of acting as a ‘crystal breaker’ in the solid monolayer phases and therefore provides a molecular mechanism for decoupling crystalline and conformational order in lipid monolayers containing cholesterol. The phase diagram of mixed cholesterol–lipid monolayers is derived and discussed in relation to monolayer experiments.

Lateral density fluctuations in the chain-melting phase transition of lipid monolayers

A detailed statistical mechanical study has been carried out on a microscopic interaction model of lipid monolayers on the air—water interface. The model is Pink's ten-state model which accounts for the internal conformational states of the lipid acyl chains and their statistics and mutual interactions. Particular attention is paid to the chain-melting phase transition of saturated lecithin monolayers (e.g., DPPC) and the microscopic phenomena which accompany this phase transition. By means of computer-simulation techniques we have calculated the equilibrium and nonequilibrium isotherms and obtained quantitative measures of the lateral density fluctuations in the transition region in terms of the size distribution of lipid domains and the average coherence length of the conformational order of the acyl chains. Indications of the presence of a critical point are obtained. The results are compared with experimental observations of DPPC lipid monolayer phase behavior with special emphasis on an understanding of the origin of the nonhorizontal experimental isotherms.

Computer simulation of temperature-dependent growth of fractal and compact domains in diluted Ising models.

A version of the two-dimensional site-diluted spin-(1/2 Ising model is proposed as a microscopic interaction model which governs solidification and growth processes controlled by vacancy diffusion. The Ising Hamiltonian describes a solid-fluid phase transition and it permits a thermodynamic temperature to be defined. The dynamics of the model are taken to involve (i) solid-fluid conversion and (ii) diffusion of vacancies in the fluid phase. By means of Monte Carlo computer-simulation techniques the solidification and growth processes following rapid thermal quenches below the transition temperature are studied as functions of temperature, time, and concentration. At zero temperature and high dilution, the growing solid is found to have a fractal morphology and the effective fractal exponent D varies with concentration and ratio of time scales of the two dynamical processes. The mechanism responsible for forming the fractal solid is shown to be a buildup of a locally high vacancy concentration in the active growth zone. The growth-probability measure of the fractals is analyzed in terms of multifractality by calculating the f(\ensuremath{\alpha}) spectrum. It is shown that the basic ideas of relating probability measures of static fractal objects to the growth-probability distribution during formation of the fractal apply to the present model. The f(\ensuremath{\alpha}) spectrum is found to be in the universality class of diffusion-limited aggregation. At finite temperatures, the fractal solid domains become metastable and a crossover to compact equilibrium solidification is observed as a function of both temperature and time. At low temperatures in the metastable fractal growth regime, the time dependence of the particle content of the domains is found to obey the scaling law, N(t)\ensuremath{\sim}${t}^{D/(2d\mathrm{\ensuremath{-}}D\mathrm{\ensuremath{-}}1)}$. At higher temperatures where the growth is stable and leads to compact domains, the time dependence of N(t) can be described by a simple hyperbolic function. The various results of the theoretical model study are related to fractal and compact growth patterns observed in experimental studies of impure lipid monolayer films at air-water interfaces.

Intrinsic molecules in lipid membranes change the lipid-domain interfacial area: cholesterol at domain interfaces

A theoretical analysis of the effects of intrinsic molecules on the lateral density fluctuations in lipid bilayer membranes is carried out by means of computer simulations on a microscopic interaction model of the gel-to-fluid chain-melting phase transition. The inhomogeneous equilibrium structures of gel and fluid domains, which in previous work (Cruzerio-Hansson, L. and Mouritsen, O.G. (1988) Biochim. Biophys. Acta 944, 63–72) were shown to characterize the transition region of pure lipid membranes, are here shown to be enhanced by intrinsic molecules such as cholesterol. Cholesterol is found to increase the interfacial area and to accumulate in the interfaces. The interfacial area, the average cluster size, the lateral compressibility, and the membrane area are calculated as functions of temperature and cholesterol concentration. It is shown that the enhancement by cholesterol of the lateral density fluctuations and the lipid-domain interfacial area is most pronounced away from the transition temperature. The implications of the results are discussed in relation to passive ion permeability and function of interfacially active enzymes such as phospholipase.

Passive ion permeability of lipid membranes modelled via lipid-domain interfacial area

A microscopic interaction model of the gel-to-fluid chain-melting phase transition of fully hydrated lipid bilayer membranes is used as a basis for modelling the temperature dependence of passive transmembrane permeability of small ions, e.g. Na +. Computer simulation of the model shows that the phase transition is accompanied by strong lateral density fluctuations which manifest themselves in the formation of inhomogeneous equilibrium structures of coexisting gel and fluid domains. The interfaces of these domains are found to be dominated by intermediate lipid-chain conformations. The interfacial area is shown to have a pronounced peak at the phase transition. By imposing a simple model for ion diffusion through membranes which assigns a high relative permeation rate to the domain interfaces, the interfacial area is then identified as a membrane property which has the proper temperature variation to account for the peculiar experimental observation of a strongly enhanced passive ion permeability at the phase transition. The excellent agreement with the experimental data for Na +-permeation, taken together with recent experimental results for the phase transition kinetics, provides new insight into the microphysical mechanism of reversibel electric breakdown. This insight indicates that there is no need for aqueous pore-formation to explain the experimental observation of a dramatic increase in ion conductance subsequent to electric pulses.

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 disturbes the translational order in the crystalline (gel) state of phosphatidylcholine. These results suggest that the occurrence of specific phosphatidylcholien-cholesterol complexes is not implied by the experimental thermodynamic data.

The effects of acyl chain ordering and crystallization on the main phase transition of wet lipid bilayers

The main gel-fluid phase transition of wet lipid bilayers is examined in terms of a microscopic interaction model which incorporates both trans-gauche isomerism of the lipid acyl chains and crystal orientation variables for the lipid molecules. The model gives two scenarios for the phase behavior of wet lipid bilayers in terms of temperature: (i) chain melting occurs at a higher temperature than crystallization, or (ii) chain melting and crystallization occur at the same temperature. Experimental data for lipid bilayers is consistent with the second scenario. In this case, computer simulation is used to investigate the non-equilibrium behaviour of the model. The numerical data is intepreted in terms of interfacial melting on heating and grain formation on cooling through the main phase transition. Interfacial melting is a non-equilibrium process in which the grains of a polycrystalline bilayer melt inwards from the boundaries. The prediction of interfacial melting in wet lipid bilayers is examined in relation to data from both equilibrium and nonequilibrium measurements, to corresponding phase behavior in monolayers, and to previous theoretical work.

Acyl chain ordering and crystallization in lipid monolayers

The condensed phases of phospholipid monolayers on an air/water interface are described by means of a microscopic interaction model which incorporates intra-chain flexibility as well as crystal orientation variables. The phase transitions and microstructures are studied as functions of lateral pressure. The model predicts, in accordance with recent synchrotron X-ray experiments, that the chain-ordering transition and the crystallization of the monolayer need not take place at the same lateral pressure.