A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model

A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure.     

Redetermination of the pressure dependence of the lipid bilayer phase transition.

The effect of pressure on the phase transition temperature for the dipalmitoyllecithin bilayer was redetermined by following the volume change accompanying the transition. These measurements were carried out isothermally with the transition from the ordered to the disordered phase induced by decreasing the pressure. This contrasts with our previous measurements which were carried out at constant pressure and increasing temperature. The transition at every temperature was sharp and confirmed our previous observation that the volume change associated with the transition (0.033 mL g-1) is invariant with pressure. However, our present measurements, in contrast to our previous results, indicate that dP m/dTm at all pressures is in agreement with the 1 atm value of delta H/Tm delta V within experimental error where Tm and Pm are the temperature and pressure of the phase transition, respectively. These results, which are now in agreement with all other known pressure data, indicate that the entropy change associated with the transition is invariant with pressure.     

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

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

Chain-length dependence of lipid bilayer properties near the liquid crystal to gel phase transition.

The temperature dependence of the mean orientational order parameter in the vicinity of the liquid crystal to gel phase transition is obtained from the first moment M1 of deuterium nuclear magnetic resonance spectra for bilayers of chain perdeuterated phosphatidylcholines with acyl chains of 12, 14, 16, and 18 carbons. The data clearly show an increasing temperature dependence of the orientational order parameter in the vicinity of the transition, with the effect becoming more pronounced with decreasing chain length. Assuming a linear relationship between the mean orientational order parameter and the extension of the acyl chain, estimates of the change in area of the membrane at the transition are shown to be consistent with those obtained from other measurements. It is shown that the transition may be modeled in terms of a Landau expansion of the free energy involving a small number of phenomenological parameters. From this it is shown that the behavior of these systems in the temperature range of interest is, in large part, controlled by the close proximity of a spinodal to the transition temperature.     

Interaction of surfactants with vesicle membrane of dipalmitoylphosphatidylcholine. Effect on gel-to-liquid-crystalline phase transition of lipid bilayer

The gel-to-liquid-crystalline phase transition of dipalmitoylphosphatidylcholine (DPPC) vesicle membrane was observed in the presence of various types of surfactants; sodium alkylsulfates, alkyltrimethylammonium bromides, alkanoyl-N-methylglucamides, and hexaethyleneglycol mono n-dodecyl ether. The phase transition was monitored by a change in scattered light intensity of the lipid suspension. For all the surfactants examined, the phase transition temperature was depressed linearly with the surfactant concentration in the measured concentration range, from which the partition coefficient, K, of the surfactant between bulk solution and lipid membrane was estimated. Except alkyltrimethylammonium bromides, log K and log CMC showed a linear relationship, which indicates that the driving force to transfer the surfactant from bulk solution to lipid membrane is a hydrophobic interaction. The addition of surfactants increased the transition width. The extent of widening the transition width was in the order of sodium alkylsulfate greater than alkyltrimethylammonium bromides greater than hexaethyleneglycol mono n-dodecyl ether; in the case of alkanoyl-N-methylglucamides, the transition width was not affected by the addition. These effects on the transition width was interpreted qualitatively in terms of the cooperativity of the transition.     

Application of the optical waveguide lightmode spectroscopy to monitor lipid bilayer phase transition

An instrument for optical waveguide lightmode spectroscopy (OWLS) was designed and developed for measurements at different and controlled temperatures in a range of 15 degrees C around room temperature. The instrument allows to scan the waveguide modes at different wavelengths on the same optical chip using different lasers. This instrument was used to monitor DMPC lipid bilayer main phase transition around the critical temperature. The main problem in these experiments is that the OWLS measurements do not give enough information about an optically anisotropic system like a lipid bilayer. Experimental OWLS data at two different wavelengths can however approximately solve the problem. The temperature dependence of the thickness and the refractive indices (ordinary and extraordinary) for the lipid bilayer around the phase transition is presented. (A theoretical derivation of the extraordinary refractive index is given in.)     

Permeability of bilayer lipid membranes in phase transition. The significance of intermolecular phosphate-phosphate hydrogen bonding

The effect of pH on the phase transition temperature of 1,2-dipalmitoyl-sn-glycero-3-phosphate (DPPA) and 1,2-dipalmitoyl-sn-glycero-3-thionphosphate (thion-DPPA) has been investigated. The phase transition was detected using the jump like increase effect in the conductance of the planar bilayer membrane. It is shown that the steepness of pH-dependence of the phase transition temperature differs for these two kinds of lipids in the pH range of 3.5-8. This result is explained in terms of decreased intermolecular hydrogen bonding between the head groups of thion-DPPA. Calculations taking into account the ability of DPPA molecules to intermolecular phosphate-phosphate hydrogen bonding were made. The results of calculations are in good agreement with the experimental data obtained in this study.     

A model for self-sustained potential oscillation of lipid bilayer membranes induced by the gel-liquid crystal phase transitions.

To clarify the mechanism of self-sustained oscillation of the electric potential between the two solutions divided by a lipid bilayer membrane, a microscopic model of the membrane system is presented. It is assumed, on the basis of the observed results (Yoshikawa, K., T. Omachi, T. Ishii, Y. Kuroda, and K. liyama. 1985. Biochem. Biophys. Res. Commun. 133:740-744; Ishii, T., Y. Kuroda, T. Omochi, and K. Yoshikawa. 1986. Langmuir. 2:319-321; Toko, K., N. Nagashima, S. liyama, K. Yamafuji, and T. Kunitake. Chem. Lett. 1986:1375-1378), that the gel-liquid crystal phase transition of the membrane drives the potential oscillation. It is studied, by using the model, how and under what condition the repetitive phase transition may occur and induce the potential oscillation. The transitions are driven by the repetitive adsorption and desorption of proton by the membrane surface, actions that are induced the periodic reversal of the direction of protonic current. The essential conditions for the periodic reversal are (a) at least one kind of cations such as Na+ or K+ are included in the system except for proton, and the variation of their permeability across the membrane due to the phase transition is noticeably larger than that of proton permeability; and (b) the phase transition has a hysteresis. When these conditions are fulfilled, the self-sustained potential oscillation may be brought about by adjusting temperature, pH, and the cation concentration in the solutions on both sides of the membrane. Application of electric current across the membrane also induces or modifies the potential oscillation. Periodic, quasiperiodic, and chaotic oscillations appear especially, depending on the value of frequency of the applied alternating current.     

Electrical capacitance of lipid bilayer membranes of hydrogenated egg lecithin at the temperature phase transition

Electrical capacitance of the planar bilayer lipid membrane (BLM) formed from hydrogenated egg lecithin (HEL) has been studied during many passages through the phase transition temperature. In contrast to the BLM from individual synthetic phospholipids, membranes from HEL did not demonstrate any capacitance change at the phase transition temperature maximum, as measured by differential scanning calorimeter at 52 degrees C. Instead, two temperatures have been discerned by capacitance records: thickening at 42-43 degrees C and thinning at 57-59 degrees C. The first temperature region is close to the transition temperature of dipalmitoyllecithin, whereas the second is close to that of distearoyllecithin, two main components of the HEL. It was suggested that capacitance measurements were able to reveal a phase separation in the BLM from HEL which was not detected by differential scanning calorimetry. The phase transition of the BLM from the liquid crystal state to the gel state is followed by thickening of the bilayer structure, partly due to a gauche- trans transition of lipid molecules but mainly due to redistribution of the solvent n-decane.     

A statistical mechanical analysis of the effect of long-chain alcohols and high pressure upon the phase transition temperature of lipid bilayer membranes.

Long-chain n-alcohols decrease the main phase-transition temperature of lipid vesicle membranes at low concentrations but increase it at high concentrations. The nonlinear phenomenon is unrelated to the interdigitation and is analyzed by assuming that alcohols form solid solutions with solid as well as liquid phases. The biphasic response originates from the balance of the free energy difference of alcohols in the liquid and solid membranes (delta gA) and the alcohol-lipid interaction free energy difference (delta u) between the two phases. When delta gA less than 0 and delta u greater than 0, or delta gA less than delta u less than 0, the transition temperature decreases monotonously according to the increase in the alcohol concentration. When delta gA greater than 0 and delta u less than 0, or delta gA greater than delta u greater than 0, it increases monotonously. Biphasic response occurs with a minimum temperature when delta u greater than delta gA greater than 0, and with a maximum temperature when delta u less than delta gA less than 0. When the alcohol carbon-chain length becomes closer to the lipid carbon-chain length, delta u is equalized by delta gA, and the temperature minimum of the main transition is shifted to extremely low alcohol concentrations. Hence, long-chain alcohols predominantly elevate the main transition temperature and lose their anesthetic potency. High pressure decreased both delta gA and delta u. Presumably, high pressure improves the packing efficiency of liquid membranes and decreases the difference between the solid and liquid membrane properties.     

A kinetic lattice model of the chain-melting phase transition in lipid membrane: its experimental calibration and physiological implications

A kinetic lattice model of chain-melting phase transition has been developed. Its time scale has been calibrated with the acoustic relaxation spectroscopic data. The model presents a tool for the analysis and predictions of kinetic features of those physiological processes in biological membranes whose mechanism is based on the phase transition in the lipid component. It has been shown that the phase-transitional mechanism can provide a high rate of synaptic exocytosis known for the fastest synapses in the central nervous system. It was also demonstrated that this mechanism can serve as an essential factor of synaptic plasticity.     

Exponential distribution of interimpulse current intervals in lipid bilayer membrane at phase transition temperature

The statistical analysis of current fluctuations in unmodified bilayer lipid membranes at the phase transition temperature was made. An exponential distribution of current fluctuations was revealed.     

Conductivity of bilayer lipid membranes in phase transition: the role of intramolecular phosphate-phosphate hydrogen bonds

pH effect on phase transition measured by jump of conductance in the BLM formed from DPPA and thio-DPPA was studied. The difference of pH dependence for these two lipids was shown. The corresponding calculation discovered significance of intermolecular phosphate-phosphate hydrogen bonds in induced conductance of BLM.     

A new method for membrane reconstitution: Fusion of protein-containing vesicles with planar bilayer membranes below lipid phase transition temperature

A new method of membrane reconstitution was developed by fusion of channel protein containing vesicles with planar bilayer membranes. The fusion process only occurred below and near the phase transition temperature of the lipid used. We obtained the following results: 1. Our system is solvent-free and vesicles do not come into contact with the air/water interface. This obviates a possible denaturation of hydrophobic proteins. 2. Channel forming proteins and protein complexes, respectively, are active in a frozen lipid matrix. 3. We detected an unknown channel in cilia fragments. 4. Purified acetylcholine receptors form fluctuating channels in a membrane consisting of a pure synthetic lecithin (two component system).     

A new method for membrane reconstitution: fusion of protein-containing vesicles with planar bilayer membranes below lipid phase transition temperature

A new method of membrane reconstitution was developed by fusion of channel protein containing vesicles with planar bilayer membranes. The fusion process only occurred below and near the phase transition temperature of the lipid used. We obtained the following results: 1. Our system is solvent-free and vesicles do not come into contact with the air/water interface. This obviates a possible denaturation of hydrophobic proteins. 2. Channel forming proteins and protein complexes, respectively, are active in a frozen lipid matrix. 3. We detected an unknown channel in cilia fragments. 4. Purified acetylcholine receptors form fluctuating channels in a membrane consisting of a pure synthetic lecithin (two component system).     

A mathematical model of tumor growth. III. comparison with experiment

In this paper a model of nonuniform inhibitor production is used to discuss some experimental results obtained by Folkman and Hochberg for multicellular spheroids (of V-79 Chinese hamster lung tissue). Built into the mathematical model is a parameter b which is a measure of the degree of nonuniformity of the inhibitor production rate. The “inverse problem” is solved by finding the value of b necessary to account for results with which the uniform model is incompatible [6]. The resulting value of b enables a good estimate to be made for the observed width of peripheral mitotic zones in the V-79 spheroids, and the resulting stability parameters lie in appropriate ranges for the model to be a significant improvement over uniform models. Further improvements are discussed, including a heuristic model for estimating the destabilizing effect of vascularization on tissue growth.