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.     

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.     

Lipid chains and cholesterol in model membranes: a Monte Carlo Study

The Monte Carlo method has been employed to study the equilibrium properties of a planar array of hydrocarbon chains interacting with a cholesterol molecule. The chains are arranged to model one monolayer of a lipid bilayer and within this monolayer are allowed to move laterally and change conformations by gauche rotations. In the simulation cell there are 90 lipid chains and a single cholesterol molecule. Periodic boundary conditions are imposed upon the cell. The primary results of the calculations are order parameter profiles for the C-C bonds. These are calculated for (i) all chains, (ii) the 6 chains which are nearest neighbors to the cholesterol, and (iii) the 12 chains which are next-nearest neighbors to the cholesterol. Calculations are carried out for C-14, C-16, and C-18 chains. The results show that cholesterol strongly affects the upper portions of the chains, leaving them less able to change conformations. For C-16 and C-18 chains, the chain termini of the cholesterol neighbors are more disordered than the bulk chain termini. The magnitude of the effect depends strongly on the chain length. The results suggest that the changes in the lipid phase transition caused by cholesterol are a consequence of each cholesterol hindering the rotameric freedom of five to seven lipid chains.     

Lateral organization in lipid-cholesterol mixed bilayers

Interactions between lipid and cholesterol molecules in membranes play an important role in the structural and functional properties of cell membranes. Although structural properties of lipid-cholesterol mixtures have been extensively studied, an understanding of the role of cholesterol in the lateral organization of bilayers has been elusive. In this article, we propose a simple yet powerful model, based on self-consistent mean-field theory and molecular dynamics simulations, for lipid bilayers containing cholesterol. Properties predicted by our model are shown to be in excellent agreement with experimental data. Our model predicts that cholesterol induces structural changes in the bilayer through the formation of regions of ordered lipids surrounding each cholesterol molecule. We find that the "smooth" and "rough" sides of cholesterol play crucial roles in formation and distribution of the ordered regions. Our model is predictive in that input parameters are obtained from independent atomistic molecular dynamics simulations. The model and method are general enough to describe other heterogeneous lipid bilayers, including lipid rafts.     

A simple theoretical model for the effects of cholesterol and polypeptides on lipid membranes

A simple theoretical model for the effects of impurities on biomembranes is proposed. The model accounts for the cholesterol-induced decrease of membrane phase transition temperature, membrane condensation above the gel to liquid crystalline phase transition, and increase in lateral compressibility. The model also predicts that addition of molecules such as cholesterol and polypeptides to membranes results in unmasking of a continuous phase transition. This results in a second broad peak in the calorimetric curves for melting of lipid-cholesterol mixtures, and the appearance of a second melting transition in membranes modified by the incorporation of polypeptides. The theory assumes that the membrane may be adequately described by a kink model, and that impurities are randomly distributed in the membrane. The difference in size and shape of impurity molecules, compared to membrane lipids, results in a spatial disordering in the membrane which in turn causes increased chain disorder and membrane condensation, as well as a decrease in the cooperativity of melting. The second transition results from a second expansion of the condensed, partially disordered membrane, which takes place over a several degree temperature range. This transition, although unmasked by boundary effects of non-lipid molecules, does not correspond to melting of a boundary annulus or phase separation.     

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.     

Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.     

Monte Carlo studies of a model for lipid-gramicidin A bilayers.

This paper presents results of Monte Carlo simulations of a full bilayer of 200 lipid chains and one gramicidin A dimer. Simulations are described for systems with lipid chains of 14, 16, and 18 carbons, respectively. Using accepted potential functions to calculate interactions between all non-hydrogen atoms a Monte Carlo configuration sampling is generated from which order parameter profiles are calculated and specific configurations are displayed. Results are compared with experimental data for lipid-gramicidin bilayers.     

A simple model of the hydrophobic effect for molecular simulation of interfacial phenomena

A coarse-grained model for simulation of interfacial phenomena in aqueous systems has been developed. The model captures the hydrophobic effect by only considering the structure and cohesiveness of water. Monte Carlo (MC) simulations of water-oil mixtures show that low concentrations of oil are solvated with little perturbation of the hydrogen bonding network structure of the water, while high concentrations of oil are excluded altogether. Analysis of the water structure in the simulations indicates that the water molecules maintain close to four coordination in the presence of solutes and the distribution of bond angles is not markedly affected by the presence of solutes. MC simulations of an alkane oligomer in water and a poly(ethylene oxide) (PEO) oligomer in water indicate that the chains are quite flexible and also do not perturb the network structure of the water phase.     

Monte Carlo studies of lipid chains and gramicidin A in a model membrane

The Monte Carlo method has been used to simulate the equilibrium properties of a planar array of 94 saturated lipid chains and one monomer of Gramicidin A. Chains are free to move laterally in the layer plane and to change conformation via gauche rotations and long axis rotations in a continuum. All non-hydrogen atoms on chains and on the Gramicidin A monomer interact via 6-12 potentials, and periodic boundary conditions are imposed. Calculated results consist of order parameter profiles for C-14 and C-16 chains. Profiles are calculated for chains which are neighbors to the Gramicidin A molecule and for chains which are not neighbors to the peptide. The main conclusion is that the average conformations of the chains neighboring the Gramicidin A monomer are very similar to those of the bulk chains.     

Investigation of domain formation in sphingomyelin/cholesterol/POPC mixtures by fluorescence resonance energy transfer and Monte Carlo simulations

We have recently proposed a phase diagram for mixtures of porcine brain sphingomyelin (BSM), cholesterol (Chol), and 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) on the basis of kinetics of carboxyfluorescein efflux induced by the amphipathic peptide delta-lysin. Although that study indicated the existence of domains, phase separations in the micrometer scale have not been observed by fluorescence microscopy in BSM/Chol/POPC mixtures, though they have for some other sphingomyelins (SM). Here we examine the same BSM/Chol/POPC system by a combination of fluorescence resonance energy transfer (FRET) and Monte Carlo simulations. The results clearly demonstrate that domains are formed in this system. Comparison of the FRET experimental data with the computer simulations allows the estimate of lipid-lipid interaction Gibbs energies between SM/Chol, SM/POPC, and Chol/POPC. The latter two interactions are weakly repulsive, but the interaction between SM and Chol is favorable. Furthermore, those three unlike lipid interaction parameters between the three possible lipid pairs are sufficient for the existence of a closed loop in the ternary phase diagram, without the need to involve multibody interactions. The calculations also indicate that the largest POPC domains contain several thousand lipids, corresponding to linear sizes of the order of a few hundred nanometers.     

Direct measurement of phase coexistence in DPPC/cholesterol vesicles using Raman spectroscopy

The phase behavior of bilayers of binary mixtures of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and cholesterol has been studied using Raman spectroscopy. It is observed that the shape of the cholesterol vibrational spectrum in lipid-cholesterol binary mixtures does not vary significantly with either the cholesterol concentration or the temperature. This permits determination of the lipid vibrational signatures of the liquid-disordered (l(d)), solid-ordered (s(o)) and liquid-ordered (l(o)) phases. Within the phase coexistence region, the measured spectra are described very well by a linear combination of the different spectral components, which permits a quantitative analysis of the phase diagram. In contrast to earlier findings, our experiments provide no indication of a phase boundary at low cholesterol concentration. The upper boundary of the phase coexistence region is found at approximately 27 and approximately 22 mol% for l(d)-l(o) and s(o)-l(o) coexistence region, respectively. Within these phase coexistence regions, the partitioning of cholesterol between the cholesterol-poor and the cholesterol-rich phases is in close agreement with the lever rule.     

Evidence for a regular distribution of cholesterol in phospholipid bilayers from diphenylhexatriene fluorescence.

Cholesterol/dimyristoylphosphatidylcholine (DMPC) multilamellar vesicles were studied by steady-state fluorescence using diphenylhexatriene (DPH) as a probe. A series of dips were found in the plot of DPH fluorescence intensity versus cholesterol concentration at certain specific cholesterol concentrations. This observation indicates that there are dominant domains in which cholesterol molecules are regularly distributed on a hexagonal superlattice in the acyl chain matrix of DMPC at critical cholesterol concentrations. These concentrations can be predicted by an equation or a mathematical series, except the one at 33 mol %. These dips of DPH fluorescence intensity are temperature dependent. The excellent agreement between experimental data and calculated values as well as similar previous findings of dips and/or kinks in the excimer-over-monomer fluorescence in pyrenephosphatidylcholine/phospholipid mixtures confirm our conclusion about lateral organizations of cholesterol and acyl lipid chains in cholesterol/phospholipid multilamellar vesicles. The regular distribution model at critical concentration is consistent with the phase diagram of cholesterol/DMPC. Using the model of regular distribution, the physical origin of the liquid-disordered (Ld) phase, liquid-ordered phase (Lo), and coexistence of liquid-disordered phase and Lo phase (Lo + Ld) is discussed on the molecular level.     

Melting of individual lipid components in binary lipid mixtures studied by FTIR spectroscopy, DSC and Monte Carlo simulations

Monte Carlo (MC) simulations, Differential Scanning Calorimetry (DSC) and Fourier Transform InfraRed (FTIR) spectroscopy were used to study the melting behavior of individual lipid components in two-component membranes made of DMPC and DSPC. We employed Monte Carlo simulations based on parameters obtained from DSC profiles to simulate the melting of the different lipids as a function of temperature. The simulations show good agreement with the FTIR data recorded for deuterated and non-deuterated lipids, which demonstrates that the information on the differential melting of the individual components is already contained in the calorimetric profiles. In mixtures, both lipids melt over a wide temperature range. As expected, the lipid melting events of the lipid with the lower melting temperature occur on average at lower temperatures. The simulations also yield information on the lateral distribution of the lipids that is neither directly contained in the DSC nor in the FTIR data. In the phase coexistence region, liquid disordered domains are typically richer in the lower-melting-temperature lipid species.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Effect of membrane characteristics on phase separation and domain formation in cholesterol-lipid mixtures

We examine, using an analytical mean-field model, the distribution of cholesterol in a lipid bilayer. The model accounts for the perturbation of lipid packing induced by the embedded cholesterol, in a manner similar to that of transmembrane proteins. We find that the membrane-induced interactions between embedded cholesterol molecules vary as a function of the cholesterol content. Thus, the effective lipid-cholesterol interaction is concentration-dependent. Moreover, it transitions from repulsive to attractive to repulsive as the cholesterol content increases. As the concentration of cholesterol in the bilayer exceeds a critical value, phase separation occurs. The coexistence between cholesterol-rich and cholesterol-poor domains is universal for any bilayer parameters, although the composition of the cholesterol-rich phase varies as a function of the lipid properties. Although we do not assume specific cholesterol-lipid interactions or the formation of a lipid-cholesterol cluster, we find that the composition of the cholesterol-rich domains is constant, independent of the cholesterol content in the bilayer.     

Chemical activity of cholesterol in membranes

Measurements are reported for the rate constants for the release of cholesterol (and dihydrocholesterol) to beta-cyclodextrin from mixtures with phospholipids in homogeneous monolayers at constant pressure at the air-water interface. In each mixture, it is found that the release rate shows a sharp decrease as the cholesterol concentration in the monolayer decreases through a composition corresponding to the stoichiometry of a cholesterol-phospholipid complex. The stoichiometry of the complex was established previously by the position of a sharp cusp in the thermodynamic phase diagram of each mixture and also by a minimum in average molecular area versus composition measurements. A theoretical model used earlier to account for the phase diagrams predicts the chemical potential and chemical activity of cholesterol in these mixtures. The calculated chemical activity also shows a sharp change at the complex stoichiometry in homogeneous monolayers. The similarities in change of observed release rate and calculated chemical activity are expected from reaction rate theory where the release rate is proportional to the cholesterol chemical activity. The chemical activity of cholesterol as determined by complex formation between some phospholipids and cholesterol in the plasma membrane of cells may serve a regulatory function with respect to intracellular cholesterol transport and biosynthesis.     

Integral equation theories for predicting water structure around molecules

Water plays a crucial role in the structure and function of proteins and other biological macromolecules; thus, theories of aqueous solvation for these molecules are of great importance. However, water is a complex solvent whose properties are still not completely understood. Statistical mechanical integral equation theories predict the density distribution of water molecules around a solute so that all particles are fully represented and thus potentially both molecular and macroscopic properties are included. Here we discuss how several theoretical tools we have developed have been integrated into an integral equation theory designed for globular macromolecular solutes such as proteins. Our approach predicts the three-dimensional spatial and orientational distribution of water molecules around a solute. Beginning with a three-dimensional Ornstein-Zernike equation, a separation is made between a reference part dependent only on the spatial distribution of solvent and a perturbation part dependent also on the orientational distribution of solvent. The spatial part is treated at a molecular level by a modified hypernetted chain closure whereas the orientational part is treated as a Boltzmann prefactor using a quasi-continuum theory we developed for solvation of simple ions. A potential energy function for water molecules is also needed and the sticky dipole models of water, such as our recently developed soft-sticky dipole (SSD) model, are ideal for the proposed separation. Moreover, SSD water is as good as or better than three point models typically used for simulations of biological macromolecules in structural, dielectric and dynamics properties and yet is seven times faster in Monte Carlo and four times faster in molecular dynamics simulations. Since our integral equation theory accurately predicts results from Monte Carlo simulations for solvation of a variety of test cases from a single water or ion to ice-like clusters and ion pairs, the application of this theory to biological macromolecules is promising.