Monte Carlo simulation of lipid mixtures: finding phase separation.

The nonideal mixing of phosphatidylserine (PS) and phosphatidylcholine (PC) binary lipid mixtures was studied by computer simulation based on a model wherein the excess energy of mixing is divided between an electrostatic term and one adjustable term delta Em that includes all other nonideal interactions. The lateral distribution of the lipids and the energy of the mixtures were obtained by using Kawasaki relaxation in a canonical ensemble. The Gibbs free energies were calculated by Kirkwood's coupling parameter method. The simulation results are strongly dependent on simulation size for sizes smaller than about 1000 lipids. Nonideal interaction between lipids can result in large scale separation of lipid phases of different composition at reasonable delta Em values as well as clustering of like lipids. In plots of total Gibbs free energy of mixing versus PS mole fraction in PS/PC, the boundaries of the two phase region could be accurately determined. The electrostatic interaction influences cluster size and shape, and also the composition of phases in the two-phase region.     

Binding of cationic surfactants to DNA, protein and DNA-protein mixtures

Extent of binding (gamma 2(1)) of cationic surfactants cetyltrimethyl ammonium bromide (CTAB), myristyltrimethyl ammonium bromide (MTAB) and dodecyl trimethyl ammonium bromide (DTAB) to calf-thymus DNA, bovine serum albumin (BSA) and to their binary mixture respectively have been measured as function of bulk concentration of the surfactant by using equilibrium dialysis technique. Binding of CTAB has been studied at different pH, ionic strength (mu), temperature and biopolymer composition and with native and denatured states of the biopolymers. The chain-length of different long chain amines plays a significant role in the extent of binding under identical solution condition. The binding ratios for CTAB to collagen, gelatin, DNA-collagen and DNA-gelatin mixtures respectively have also been determined. The conformational structures of different biopolymers are observed to play significant role in macromolecular interactions between protein and DNA in the presence of CTAB. From the experimental values of the maximum binding ratio (gamma 2m) at the saturation level for each individual biopolymer, ideal values (gamma 2m)id have been theoretically calculated for binary mixtures of biopolymers using additivity rule. The protein-DNA-CTAB interaction in mixture has been explained in terms of the deviation (delta) of (gamma 2m) from (gamma 2m)id in the presence of a surfactant in bulk. The binding of surfactants to biopolymers and to their binary mixtures are compared more precisely in terms of the Gibbs' free energy decrease (-delta G degree) for the saturation of the binding sites in the biopolymers or biopolymer mixtures with the change of the bulk surfactant activity from zero to unity in the rational mole fraction scale.     

Non-ideal phase behaviour of binary mixtures of triglycerides with mono- and diglycerides

Non-ideal miscibility in the liquid phase of mono- or diglycerides with triglycerides has been described in terms of thermodynamic excess functions. To this end the heat of mixing and the solubility temperatures of several ideal and non-ideal binary glyceride mixtures have been measured. The non-ideal phase behaviour of glyceride systems reported in the literature has been satisfactorily predicted, which indicates that the excess functions are generally applicable to mixtures of mono- or diglycerides with triglycerides.     

Molecular simulation of volume of mixing,Helmholtz free energy of mixing and entropy of mixing in bulk fluid mixtures

We describe a kinetic Monte Carlo molecular simulation procedure to calculate the Helmholtz free energy, the entropy and the chemical potentials of all components in a bulk fluid mixture. This allows us to derive the excess properties (volume, free energy and entropy) resulting from the mixing of homogeneous fluids of pure components at constant temperature and pressure. We have chosen neon–xenon mixtures to illustrate our method because of the large difference in collision diameter and well-depth of the interaction energy. When xenon is predominant in the mixture, the volume of mixing is larger. The excess entropy of mixing correlates with the volume of mixing, since a positive excess volume enables more configurations (more possible molecular distributions). The excess thermodynamic quantities as functions of the total density were found to be insensitive to temperature. To investigate the effects of the molecular parameters, we also studied argon–nitrogen and argon–krypton mixtures. The effect of the difference in molecular parameters is in the order: argon–nitrogen < argon–krypton < neon–xenon. A large difference in the well-depth of the interaction energies results in an increase in the excess thermodynamic variables, which is in agreement with the literature McDonald IR. NpT-ensemble Monte Carlo calculations for binary liquid mixtures. Mol Phys. 1972;23(1):41–58; Singer JVL, Singer K. Monte Carlo calculation of thermodynamic properties of binary mixtures of Lennard-Jones (12-6) liquids. Mol Phys. 1972;24(2):357–390.     

Nonideal mixing of phosphatidylserine and phosphatidylcholine in the fluid lamellar phase.

The mixing of phosphatidylserine (PS) and phosphatidylcholine (PC) in fluid bilayer model membranes was studied by measuring binding of aqueous Ca2+ ions. The measured [Ca2+]aq was used to derive the activity coefficient for PS, gamma PS, in the lipid mixture. For (16:0, 18:1) PS in binary mixtures with either (16:0, 18:1)PC, (14:1, 14:1)PC, or (18:1, 18:1)PC, gamma PS > 1; i.e., mixing is nonideal, with PS and PC clustered rather than randomly distributed, despite the electrostatic repulsion between PS headgroups. To understand better this mixing behavior, Monte Carlo simulations of the PS/PC distributions were performed, using Kawasaki relaxation. The excess energy was divided into an electrostatic term Uel and one adjustable term including all other nonideal energy contributions, delta Em. Uel was calculated using a discrete charge theory. Kirkwood's coupling parameter method was used to calculate the excess free energy of mixing, delta GEmix, hence In gamma PS,calc. The values of In gamma PS,calc were equalized by adjusting delta Em in order to find the simulated PS/PC distribution that corresponded to the experimental results. We were thus able to compare the smeared charge calculation of [Ca2+]surf with a calculation ("masked evaluation method") that recognized clustering of the negatively charged PS: clustering was found to have a modest effect on [Ca2+]surf, relative to the smeared charge model. Even though both PS and PC tend to cluster, the long-range nature of the electrostatic repulsion reduces the extent of PS clustering at low PS mole fraction compared to PC clustering at an equivalent low PC mole fraction.     

Self-aggregation of trehalose in the mixed solvents of 1,3-dimethylimidazolium ionic liquid and water

Abstract

Conformational variations of solvated trehaloses in binary mixtures of 1,3-dialkylimidazolium ([dmim]Cl) ionic liquids and trehalose as well as ternary mixtures of trehalose, [dmim]Cl and water have been studied by molecular dynamics (MD) simulations with and without polarisable force fields. The interaction energy between anion Cl^? and water is stronger than that between water itself in the [dmim]Cl-water mixtures. Isolated water clusters were found in the binary [dmim]Cl-water mixtures with 60.0 and 75.0% mole fraction of water, but a continuous water network appears when the concentration of the mixture increases to 99.9%. In the case of binary mixtures of trehalose and [dmim]Cl, both non-polarisable and polarisable models demonstrated that the pyranose rings of trehalose displayed chair conformations. MD simulations with polarisation model could sample larger conformation space than that with non-polarisable model. A self-aggregation behaviour of trehalose was found in the ternary trehalose-[dmim]Cl-water mixtures, which can be rationalised by the stronger non-bonded interaction energy between trehalose molecules and anion Cl^? than that between trehalose molecules and water.     

Modelling the phase equilibria in two-component membranes of phospholipids with different acyl-chain lengths

A phenomenological model is proposed to describe the membrane phase equilibria in binary mixtures of saturated phospholipids with different acyl-chain lengths. The model is formulated in terms of thermodynamic and thermomechanic properties of the pure lipid bilayers, specifically the chain-melting transition temperature and enthalpy, the hydrophobic bilayer thickness, and the lateral area compressibility modulus. The model is studied using a regular solution theory made up of a set of interaction parameters which directly identify that part of the lipid-lipid interaction which is due to hydrophobic mismatch of saturated chains of different lengths. It is then found that there is effectively a single universal interaction parameter which, in the full composition range, describes the phase equilibria in mixtures of DMPC/DPPC, DPPC/DSPC, DMPC/DSPC, and DLPC/DSPC, in excellent agreement with experimental measurements. The model is used to predict the variation with temperature and composition of the specific heat, as well as of the average membrane thickness and area in each of the phases. Given the value of the universal interaction parameter, the model is then used to predict the phase diagrams of binary mixtures of phospholipids with different polar head groups, e.g., DPPC/DPPE, DMPC/DPPE and DMPE/DSPC. By comparison with experimental results for these mixtures, it is shown that difference in acyl-chain lengths gives the major contribution to deviation from ideal mixing. Application of the model to mixtures with non-saturated lipids is also discussed.     

Thermodynamics of phosphatidylcholine-cholesterol mixed model membranes in the liquid crystalline state studied by the orientational order parameter.

It is shown that good estimates of the activity of cholesterol in phosphatidylcholine-cholesterol mixed model membranes are obtained by examining the orientational order parameter S of cholestane spin probe (CSL) that is obtained from electron spin resonance by spectral simulation. By introducing thermodynamic stability conditions of liquid mixtures, the variation of activity (or S) as a function of cholesterol mole fraction is utilized to predict the concentration at which the phase separation occurs. These results for DMPC and cholesterol binary mixtures agree very well with those of Tempo-partitioning experiments. The comparison of activity coefficients and the phase boundary in DMPC/cholesterol mixtures with those of POPC/cholesterol mixtures suggests that acyl chain unsaturation leads to poorer mixing of cholesterol in phosphatidylcholine model membranes at higher temperatures (i.e., greater than 35 degrees C). In ternary solutions of DMPC, POPC, and cholesterol, it is found that cholesterol shows less deviation from ideality than in either of the two binary mixtures, and this implies that the phase separation occurs at higher cholesterol concentration than in either of the two binary mixtures. The present analysis suggests that there may not be a critical point in DMPC/cholesterol mixtures, even though phase separation does occur.     

Solubilization and binding of DNA-CTAB complex with SDS in aqueous media

Extent of binding (gamma 2(1)) of sodium dodecyl sulphate (SDS) to the binary complex formed between calfthymus DNA and cetyltrimethylammonium bromide (CTAB) has been measured in mole per mole of nucleotide in the complex as function of concentration of SDS by using equilibrium dialysis technique at different temperatures and pH. Binding of SDS to thermally denatured DNA-CTAB complex has also been studied. The most interesting aspect to be noted in this experiment is that the water insoluble DNA-CTAB binary complex gets solubilized in the ternary mixture in presence of SDS but when DNA is thermally denatured, the ternary system DNA-CTAB-SDS remains insoluble. Significant change in the extent of binding has been noted with the variation of the relative composition of DNA and CTAB in their binary mixture. The data of binding of SDS to DNA-CTAB complex are compared more precisely in terms of the standard Gibbs' free energy decrease (-delta G degree) for the saturation of the binding sites in the complex with the change of SDS activity from zero to unity in the rational mole fraction scale.     

Micellization of fatty acyl-CoA mixtures and its relevance to the fatty acyl selectivity of acyltransferases

The critical micelle concentrations (CMCs) of palmitoyl-CoA/stearoyl-CoA and palmitoyl-CoA/oleoyl-CoA mixtures in 0.050 M KPi, pH 7.4, a buffer used in enzymatic studies, were determined by fluorescence. Mixed micelle solution theory, analogous to the thermodynamic treatment of vapor pressure, was applied to calculate monomer and micelle compositions. The behavior of the palmitoyl-CoA/stearoyl-CoA mixture is ideal, while the palmitoyl-CoA/oleoyl-CoA mixture, although not exhibiting ideal behavior, can be fitted reasonably well by nonideal theory. In both mixtures, selective micellization takes place and, unlike the case of pure fatty acyl-CoAs, above the CMC of the mixtures the concentration of molecules free in solution is strongly dependent upon total concentration. The information derived from the present physical studies becomes important in enzymatic studies with membrane-bound acyltransferases, where selectivity toward various fatty acyl donors, presented as binary mixtures, is frequently observed.     

Simulation of Surface Excess Concentrations for a Binary Hydrocarbon Mixture on Graphite

We perform Molecular Dynamics simulations of thin hydrocarbon films adsorbed on the basal plane of graphite to determine structural and thermodynamic properties. Specifically we study the behaviour of liquid benzene/n-heptane mixtures. The intra adsorbate and the adsorbate-substrate interactions are described using a phenomenological force field whose careful parameterization will be reported in a following paper. The foremost quantity we calculate is the adsorption isotherm, i.e. the surface excess concentration as a function of the benzene bulk mole fraction at T = 283 K, which is in quite reasonable agreement with the experiment. Along with the isotherm we compare the surface induced ordering of the two components in terms of order parameter profiles.     

Interaction of dipalmitoylphosphatidylcholine and dimyristoylphosphatidylcholine-d54 mixtures with glycophorin. A fourier transform infrared investigation

Glycophorin from the human erythrocyte membrane has been isolated in pure form and reconstituted into large unilamellar vesicles comprised of binary mixtures of 1,2-dipalmitoyl-3-sn-phosphatidylcholine (DPPC) and chain perdeuterated 1,2-dimyristoyl-3-sn-phosphatidylcholine (DMPC-d54). The effect of temperature and protein on lipid structure and mixing was monitored by using Fourier transform infrared spectroscopy; deuteration of one of the components of the mixture permits observation of the protein interaction with each lipid species. The melting curves were analyzed by assuming that each lipid chain can exist in one of two physical states (i.e., gel or liquid crystalline), characterized by a temperature-dependent Lorentzian distribution for the line shape of the C-H or C-D stretching vibrations. The fraction of each lipid component melted at temperatures within the two-phase region of the phase diagram was calculated and approximate phase diagrams were constructed. Addition of protein lowers the liquidus line of the phase diagram while leaving the solidus line essentially unchanged. No lipid phase separation is observed. The effect of protein is more pronounced on the DPPC component than on the DMPC-d54. The former is significantly more disordered and/or fluidized at all lipid mole fractions in the ternary system than in the binary phospholipid mixture.     

Interaction of water vapour with twenty different poly-L-amino acids and their excess hydration in presence of sodium chloride

Using the isopiestic vapour pressure technique, the magnitudes of excess binding of water and NaCl per mole of twenty different poly-L-amino acid residues, respectively in the presence of different bulk molefractions (X2) of NaCl have been evaluated from the mathematical expressions for the Gibbs surface excesses. At certain high ranges of NaCl concentration, the plot of -Gamma1 (2) versus X1/X2 becomes linear, so that moles of water and NaCl, respectively bound per mole of amino acid residue can be evaluated. -Gamma(2)1 is the excess moles of H20 per mole of amino acid residue and X1 and X2 stand for mole fractions of the water and NaCl, respectively in the sample system. Also, using the integrated form of the Gibbs absorption equation, the values of standard free energy change (deltaG(0)) for the excess adsorption of NaCl per kg of poly-L-amino acids have been evaluated. These values are all positive as a result of positive excess hydration of polyamino acids. The standard free energy of excess hydration deltaG(0)hy (equal to -deltaG(0)) is negative due to spontaneous excess hydration of polyamino acid in the presence of a salt.     

A microscopic interaction model of maximum solubility of cholesterol in lipid bilayers

We recently reported the equilibrium maximum solubility of cholesterol in a lipid bilayer, chi*chol, to be 0.66 in four different phosphatidylcholines, and 0.51 in a phosphatidylethanolamine (Huang, J.,J.T. Buboltz, and G. W. Feigenson. 1999. Biochim. Biophys. Acta. in press). Here we present a model of cholesterol-phospholipid mixing that explains these observed values of chi*chol. Monte Carlo simulations show that pairwise-additivity of nearest-neighbor interactions is inadequate to describe all the chi*chol values. Instead, if cholesterol multibody interactions are assigned highly unfavorable energy, then jumps occur in cholesterol chemical potential that lead to its precipitation from the bilayer. Cholesterol precipitation is most likely to occur near three discrete values of cholesterol mole fraction, 0.50, 0.57, and 0.67, which correspond to cholesterol/phospholipid mole ratios of 1/1, 4/3, and 2/1, respectively. At these solubility limits, where cholesterol chemical potential jumps, the cholesterol-phospholipid bilayer mixture forms highly regular lipid distributions in order to minimize cholesterol-cholesterol contacts. This treatment shows that dramatic structural and thermodynamic changes can occur at particular cholesterol mole fractions without any stoichiometric complex formation. The physical origin of the unfavorable cholesterol multibody interaction is explained by an "umbrella model": in a bilayer, nonpolar cholesterol relies on polar phospholipid headgroup coverage to avoid the unfavorable free energy of cholesterol contact with water. Thus, at high cholesterol mole fraction, this unfavorable free energy, not any favorable cholesterol-phospholipid interaction, dominates the mixing behavior. This physical origin also explains the "cholesterol condensing effect" and the increase in acyl chain order parameter in cholesterol-phospholipid mixtures.     

Gel-state metastability and nature of the azeotropic points in mixtures of saturated phosphatidylcholines and fatty acids

The temperature-composition phase diagrams of dipalmitoylphosphatidylcholine (DPPC)/palmitic acid and distearoylphosphatidylcholine (DSPC)/stearic acid mixtures in excess water were recorded using high-sensitivity differential scanning calorimetry. New, slowly reversible phase transitions were found at 38° C in DPPC/palmitic acid mixtures at 0.4–0.9 mole fractions of palmitic acid and at 46° C in the DSCP/stearic acid binary. These transitions reveal gel-state metastability of the mixtures which is caused most probably by co-crystallization of the two lipids as it cannot be observed in the pure components. Both mixtures display azeotropic behavior at 2 fatty acids per 1 phospholipid. The physical reasons for such behavior have been analyzed theoretically in the framework of the Bragg-Williams and the UNIversal QUAsiChemical (UNIQUAC) approximations. This analysis shows that the azeotropic points in the phase diagrams are due to a combination of compound formation in the solid state and close to random mixing in the liquid state of the mixtures. UNIQUAC provides better fits to the experimental phase diagrams since it accounts also for the dimer-monomer character of the phospholipid/fatty acid mixtures. At fatty acid mole fractions greater than 0.65–0.7 the excess fatty acids phase separate from the compound phase. The stability of the compound phase domains at low fatty acid concentrations in relation to their possible physiological role has been discussed.     

Excess free energies of interaction of chlorophyll a with monogalactosyldiacylglycerol and phytol a mixed monolayer study

The surface pressure isotherms of chlorophyll a, monogalactosyldiacylglycerol and phytol at the air-water interface were studied on a Langmuir trough at 20.0±0.5°C. The subphase was a phosphate buffer, 10^?3 M at pH 8.0. The extrapolated limiting areas per molecule are 115, 82 and 38 Ų/molecule, respectively. The isotherms of eight mixtures of chlorophyll a with monogalactosyldiacylglycerol and eight mixtures of chlorophyll a with phytol, covering in both cases the whole range of molar fractions have also been measured. The results for the mixed monolayers were analysed in terms of the additivity rule. They show that a small negative deviation with respect to ideality is observed upon mixing chlorophyll a with monogalactosyldiacylglycerol. However, chlorophyll a forms an ideal two-dimensional solution when mixed with phytol. The excess free energies of mixing of chlorophyll a with monogalactosyldiacylglycerol as a function of concentration were calculated from the surface pressure isotherms at 10, 15, 20 and 25 mN·m^?1. The values are negative, reflecting the interaction prevailing between these components in the monolayers. For the four surface pressures studied, the excess free energies are symmetrical with respect to the mode fraction. The values for an equimolar mixture range from ?300 to ?540 J·mol^?1 at 10 and 25 mN·m^?1, respectively. A comparison between the thermodynamics of mixing of chlorophyll a with monogalactosyldiacylglycerol and phytol suggests that the polar head of monogalactosyldiacylglycerol together with the polar groups of chlorophyll a are probably involved in the interaction. However, this does not completely rule out the possibility that structural effects due to a different packing of chlorophyll a with monogalactosyldiacylglycerol and phytol may also be involved. Furthermore it is shown that the small interactions between these constituents are not inconsistent with the specific coupling existing between the apoprotein of the chlorophyll a-protein complexes and chlorophyll a.     

Effects of hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

Solid-liquid phase behavior of binary fatty acid mixtures. 2. Mixtures of oleic acid with lauric acid, myristic acid, and palmitic acid

Solid-liquid phase behavior was investigated for binary fatty acid mixtures composed of oleic acid (OA; cis-9-octadecenoic acid) and saturated fatty acids, lauric acid (LA; dodecanoic acid), myristic acid (MA; tetradecanoic acid), and palmitic acid (PA; hexadecanoic acid), by means of differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FT-IR). When the mixture was heated immediately after the solidification from the melt, the heat effect due to the gamma-to-alpha transformation of OA varied depending on the composition of the mixture. However, the mixture subjected to an annealing at the temperature slightly below the melting temperature provided the transformation at constant temperature which corresponds to the gamma-to-alpha transformation temperature of pure OA. This suggests that a solid phase formed by cooling of the melt of the mixture is not in an equilibrium state, but it relaxes to a stable solid during the annealing process. The T-X phase diagrams of these mixtures constructed from the DSC measurements demonstrate that the two fatty acid species are completely immiscible in a solid phase regardless of the type of polymorphs of OA, alpha- or gamma-form. According to a thermodynamic analysis of liquidus line basing on the regular solution model for the melt, the non-ideality of mixing tends to increase with the decrease in the acyl chain length of the saturated fatty acid, although the mixing is rather close to ideal.     

Solid-liquid phase behavior of binary fatty acid mixtures. 1. Oleic acid/stearic acid and oleic acid/behenic acid mixtures

Solid-liquid phase behavior of binary fatty acid mixtures was investigated by means of differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FT-IR) for the mixture composed of oleic acid (OA) and stearic acid (SA) and that composed of OA and behenic acid (BA). The DSC results provided a monotectic type T-X phase diagram for these mixtures, from which it was suggested that the two fatty acid species are completely immiscible in a solid phase regardless of the two polymorphs of OA, i.e., alpha-form or gamma-form. The solid phase immiscibility was confirmed by the FT-IR observation that the spectra obtained for the mixtures correspond to the superposition of the two spectra for respective components. Thermodynamic analysis of liquidus line demonstrated that OA and SA form an ideal mixture in a liquid phase, whereas the mixing of OA and BA in a liquid phase is slightly non-ideal.