Lateral Compressibility Research Articles

On the image-charge model for the hydration force

The image-charge model for the repulsive hydration force in multilamellar systems of zwitterionic molecules (e.g. phospholipid bilayers) proposed by Jonsson and Wennerstrom (J. Chem. Soc., Faraday Trans. 2, 1983, 79, 19) is analysed in some detail. Some over-restrictive assumptions in their model are removed and the hydration force is calculated in a greater variety of cases. In general, the force follows a power law. The leading term for large lamellar spacing is a repulsive, zwitterionic self-image interaction. The total force for reasonably small spacings depends crucially on the zwitterionic correlation within each bilayer and may be attractive as well as repulsive. The results are very dependent on the model and change dramatically when the location of the dielectric discontinuities between water and hydrocarbon relative to the polar headgroups is varied, unless the zwitterions lie flat parallel to the interface. If the lateral compressibility is (assumed) negligible and the zwitterions are perpendicular to the lamellar plane, the force law is exponential for a very particular kind of correlation function; this was the main case considered explicitly by Jonsson and Wennerstrom. The different force laws are compared with experimental values of the forces.

Computer simulation of the main gel–fluid phase transition of lipid bilayers

Monte Carlo techniques have been applied to a study of two related quasi-two-dimensional microscopic interaction models which describe the phase behavior of phospholipid bilayers. The two models are Ising-like lattice models in which (a) the acyl chains of the phospholipids interact via anisotropic van der Waals forces and (b) the rotational isomerism of the chains is accounted for by two and ten selected conformational states, respectively. Monte Carlo experiments are performed on both models so as to determine whether the static thermodynamic properties of lipid bilayers are most accurately represented by a simple two state gel–fluid concept or whether a more complicated melting process involving intermediate states takes place. To this purpose, the temperature dependence of several static thermodynamic properties has been calculated for both models. This includes the chain cross-sectional area, the internal and free energies, the coherence length, the lateral compressibility, and the specific heat. Particular care has been devoted to the transition region, since no analytical results are available in this region for either model. The comparison between the Monte Carlo results for the two models demonstrates that, whereas the two-state model has a first-order transition with jumplike behavior in the transition region the ten-state model exhibits a first-order transition associated with a closed hysteresis loop. Next, the Monte Carlo results for cross-sectional areas per lipid chain, coherence lengths and lateral compressibilities are discussed in the context of experimental results for dipalmitoyl phosphatidylcholine (DPPC). A detailed comparison is made with the results of molecular field calculations throughout the paper. Finally, a Monte Carlo analysis of bilayers composed of both DPPC and cholesterol shows that a two-state model does not adequately describe the thermodynamic behavior of lipid–cholesterol mixtures implying that intermediate states have to be introduced to account for the experimental data.

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.

Elastic response of bilayers with intrinsic proteins

Intrinsic membrane proteins affect the ordering of neighbouring lipid chains. We have used a model of protein-lipid interactions in bilayers proposed by Owicki et al. (Owicki, J.C., Springgate, M.W. and McConnell, H.M. (1978) Proc. Natl. Acad. Sci. U.S.A. 75, 1616–1619) to show that near the lipid phase transition this effect may significantly increase the magnitude of a membrane's lateral compressibility (or correspondingly, decrease the magnitude of the membrane's elastic moduli).

Critical effects from lipid-protein interaction in membranes. I. Theoretical description

The ordered-fluid phase transition in lipid membranes is described within the framework of the Landau theory, a general theory for phase transitions. The long-range order of lipids is characterized by the orientational order of the hydrocarbon chains implying the ordered-fluid transition to be of first order. Approaching the transition from either side, thermodynamic fluctuations and response functions are shown to increase, e.g. the specific heat, the lateral compressibility, the permeability, and the lateral diffusion coefficient. A protein molecule incorporated in the membrane is represented as a boundary condition on the lipid order at the protein surface. In the surrounding lipid the perturbation falls off exponentially with the coherence length. Assuming the protein molecules to be distributed homogeneously in the membrane plane and the boundary condition to be temperature independent, the protein-induced shift of the transition temperature and the latent heat is calculated. The latent heat decreases linearly with the protein concentration until it vanishes at a critical point. The critical protein concentration is determined by the ratios of the coherence length to lipid and protein radii in the membrane plane. At the critical point the lipid specific heat, lateral compressibility, permeability, and lateral diffusion coefficient become maximal.

Critical effects from lipid-protein interaction in membranes. II. Interpretation of experimental results

The effects arising from lipid-protein and lipid-cholesterol interaction are discussed within the framework of a general theoretical description presented in the preceding paper. Available experimental results are interpreted, and new experiments are proposed. In the fluid lipid phase proteins and cholesterol increase the lipid orientational order in their neighborhood, in the ordered phase they decrease it. This leads to a decrease of the latent heat at the ordered-fluid transition, which vanishes at a critical concentration of protein or cholesterol. Theoretical predictions for the critical concentrations agree with results from calorimetry. The approach to the critical point is accompanied by an increase of thermal fluctuations of the lipid order and an increase of the lipid response on small perturbations. Thus proteins and cholesterol increase the lipid specific heat, lateral compressibility, permeability, and lateral diffusion on both sides of the phase transition. Notions such as decrease of cooperativity or fluidity due to protein or cholesterol are reviewed in this context.

Lipid phase separation mediates binding of porcine pancreatic phospholipase A 2 to its substrate

Multilamellar liposomes made of equimolar mixtures of dimyristoyl and distearoylphosphatidylcholine were hydrolysed by porcine pancreatic phospholipase A 2. Ph-stat titration, equilibrium gel filtration and differential scanning calorimetry were used to study respectively the enzymic hydrolysis, the enzyme binding and the lipid phase repartition. We demonstrated that the optimal enzyme activity observed in the region where liquid crystalline and gel lipid phases coexist, is due to a drastic increase of the enzyme binding to its substrate. It is suggested that the border region separating the lipid phases could be a privileged site for enzyme insertion. Increase of lateral compressibility due to coexistence of solid and fluid lipid phases will promote the penetration of the hydrophobic interface recognition site (IRS) of phospholipase A 2 into the lipid matrix whereas the active site, distinct from the IRS will attack its substrate independently of the lipid physical state.

Pressure-composition phase diagrams of cholesterol/lecithin, cholesterol/phosphatidic acid, and lecithin/phosphatidic acid mixed monolayers: A Langmuir film balance study

A highly sensitive Langmuir film balance was built which is free of leakages and which combines very good temperature control, high purity, and quick and easy operation. The isotherms of a pure lipid (dihexadecyl phosphatidylcholine) in the region below and above the critical temperature were studied. Although critical exponents could not be determined more evidence is provided that this is a tricritical point. The monolayer phase diagrams (i) of mixtures of cholesterol with dipalmitoyl phosphatidylcholine (DPPC) and dimyristoyl phosphatidic acid (DMPA), respectively, and (ii) of the DPPC/DMPA alloy were established in the whole accessible region of the lateral pressure π, i.e., between π = 0 and the film breakdown pressures. The pressure-composition phase diagrams were established by analyzing (i) the variation of the bulk lateral compressibility, κ, as a function of both the lateral density ϱ and the composition, (ii) the molecular area, A, as a function of composition, and (iii) by estimating solubilities on the basis of Raoult's law. Breaks in the A-versus-composition plots and discontinuities and (or) breaks in the κ-versus-ϱ plots indicated the location of phase boundaries. The phase diagram of the DPPC/cholesterol mixture decomposes into three regions: (1) a coexistence region of nearly pure crystalline DPPC and a DPPC/cholesterol mixture, (2) a coexistence region of the latter mixture and nearly pure cholesterol, and (3) the mixture of fluid DPPC and cholesterol which seems to be homogeneous. No indication of a special stoichiometric cholesterol/DPPC complex was obtained. At 25°C a phase line runs from 50 mole% cholesterol at π → 0 to 20% at the highest obtainable pressure. At high pressures the 20% phase boundary is nearly vertical, indicating the special role played by this composition for bilayers. Our results compare well with recent calorimetric mixed-bilayer studies. This agreement leads to the conclusion that the mixed-lipid monolayer exhibits long-time stability above zero pressure. The phase diagram of the DMPA/cholesterol system has qualitatively nearly the same form as that of the mixture with DPPC although the position of the phase boundaries is substantially different. The mixture of the single negatively charged DMPA (at pH 5.5 on pure water) with DPPC showed a distinct minimum of the liquidus line in the π-composition diagram at 50 mole% DMPA, demonstrating congruently melting behavior. Strong evidence for a stoichiometric 1/1 DMPA/DPPC complex in the crystalline state is provided. The 1/1 mixture shows an extremely sharp main phase transition with a considerably higher compressibility in the coexistence region as that observed even for pure DMPA. A distinct break in the solid-state region of the isotherm strongly suggests a second-order phase transition which could be an order-disorder transition. A different phase diagram was obtained for bilayer vesicles of the DPPC/DMPA mixture. Only a “cigar-like” diagram with complete miscibility in the solid and the fluid states was observed with the TEMPO spin-label technique.

The effect of cholesterol on measured interaction and compressibility of dipalmitoylphosphatidylcholine bilayers.

We have examined the phase diagram of dipalmitoylphosphatidylcholine (DPPC)--cholesterol-water mixtures at low cholesterol content, and report phase separation between 3 and 10 mol% cholesterol. The two lamellar phases at equilibrium in this region appear to be pure DPPC and 11 mol% cholesterol in DPPC. For these two lamellar phases, which are made up of alternating layers of water and bimolecular lipid leaflets, we have measured the forces of interaction between leaflets and the lateral pressure and compressibility of the leaflets. Both bilayers experience a strong repulsive force when forced together only a few ångströms (1 A = 0.1 nm) closer than their maximum separation in excess water. However, the presence of 11 mol% cholesterol causes the bilayers to move apart of 35-A separation from the 19-A characteristic of pure DPPC in excess water. This swelling may result from a decrease in van der Waals attraction between bilayers or from an increase in bilayer repulsion. Differences in bilayer interaction can be a cause for phase separation. More importantly these differences can cause changes in the composition of regions of membranes approaching contact. At 11 mol%, cholesterol substantially increases the lateral compressibility of DPPC bilayers leading to higher lateral density fluctuations and potentially higher bilayer permeability.

The correlation length and lateral compressibility of phospholipid bilayers in the presence of thermodynamic density fluctuations

Pink’s ten state statistical model for the gel–fluid (main) phase transitions of phospholipid bilayers is used in conjunction with linear response theory to obtain expressions for the coherence length, ξ and the lateral compressibility χL for wet lipid bilayers in the presence of thermodynamic density fluctuations near the temperature Tf of the main phase transition. The advantage of this method is that the parameters of Pink’s model are known for several lipid systems from previous fitting to experimental data. ξ and χL can therefore be calculated numerically and the relative importance of the static and fluctuation contributions to χL can be examined. One conclusion of the article is that the coherence length and Tf is short and therefore that the contribution of thermodynamic density fluctuations to χL is about 13%. This implies that the free energy barrier EB experienced by an ion as it penetrates the bilayer has a dominant contribution from the static lateral compressibility, provided that the interaction between the ion and the polar heads of the lipid molecules is a δ-force. However, it is further shown that the static and the density fluctuation effects contribute almost equally to EB at Tf when the range ξo of interaction between the ion and the polar heads is greater than half a molecule diameter. This remains true in the limit ξo→∞ as the coherence length ξ is quite short at any temperature.

Xe monolayer adsorption on Ag(111): Statistical mechanics

Interactions contributing to the lateral energy of a xenon monolayer are evaluated. Thermodynamic properties of the monolayer are derived from a statistical mechanical treatment of a realistic model of the interactions. At low temperatures the quasiharmonic theory of lattice dynamics is used; at intermediate temperatures the cell model approximation is used. The thermal expansion of the unconstrained two-dimensional solid, the lateral compressibility, and lateral energy contributions to the isosteric heat are evaluated; the results agree well with recent experimental data. Two-dimensional second virial coefficients are also evaluated.

Properties of mixed monolayers of lecithin and spin probe: I. Study of the interactions at the air—water interface

The perturbations induced in a lipid layer by the presence of a spin probe molecule (4-palmitamido-2,2,6,6-tetramethylpiperidine-l-oxyl, TAP) have been investigated in a model membrane. Mixed monolayers of probe and dipalmitoyl- dl-α-phosphatidylcholine (DPPC) were formed at the air-water interface and studied using classic surface techniques. In mixed films, surface pressure measurements showed that the spin probe induces a modification of the monolayer lateral compressibility giving rise to a more expanded structure. Two other methods, i.e., surface viscosity and enzymic hydrolysis, offered the possibility of detecting the propagation of the probe perturbation by observing modifications of the DPPC properties. The surface viscosity approach is based on a very specific property of the probe: The monolayer, even in a closepacked state, shows no detectable surface viscosity. In these conditions surface viscosity measurements carried out with mixed monolayers will depend only on the second component of the system, i.e., the lecithin. Any deviation from the predicted viscosity value indicates a change in the DPPC packing. Viscosity results indicate that the probe induces a more packed organization of the DPPC molecules. The changes in the enzymic hydrolysis kinetics of the mixed monolayers confirm these results. The phospholipases activity is strongly dependent on the lipid packing. Indeed, the probe molecule cannot be hydrolyzed and the inhibition observed must be interpreted in terms of a specific modification in the lipid organization induced by the probe.

Properties of bilayer membranes in the phase transition or phase separation region

The increase in passive permeability of bilayer membranes near the phase transition temperature is usually explained as caused by either the increase in the amount of ‘boundary lipid’ present in the membrane, or by the increase in lateral compressibility of the membrane. Since both the amount of ‘boundary lipid’ and the lateral compressibility show a similar anomaly near the transition temperature, it is difficult to distinguish experimentally between the two proposed mechanisms. We have examined some details of both of the proposed pictures. The fluid-solid boundary energy, neglected in previous work, has been computed as a function of the domain size. For a single component uncharged lipid bilayer, the results rule out the existence of even loosely defined solid domains in a fluid phase, or vice versa. Thermodynamic fluctuations, which are responsible for anomalous behaviour near the phase transition temperature, are not intense enough to approximate the formation of a domain of the opposite phase. Turning next to lateral compressibility of bilayer membranes we have considered two-component mixtures in the phase separation region. We present the first calculation of lateral compressibility for such systems. The behaviour shows interesting anomalies, which should correlate with existing and future data on transport across membranes.

Phospholipase activity of bovine milk lipoprotein lipase on phospholipid vesicles; Influence of apolipoproteins C-II and C-III

The effect of human plasma apolipoproteins C-II and C-III on the hydrolytic activity of lipoprotein lipase from bovine milk was determined using dimyristoyl phosphatidylcholine (DMPC) vesicles as substrate. In the absence of apoC-II or C-III, lipoprotein lipase has limited phospholipase activity. When the vesicles were preincubated with apoC-II and then phospholipase activity determined, there was a time dependent release of lysolecithin; activity was dependent upon both apoC-II and lipoprotein lipase concentrations. The addition of apoC-III to DMPC did not stimulate phospholipase activity. We conclude that apoC-II has an activator effect on the phospholipase activity of lipoprotein lipase and that the mechanism is beyond that of simply altering the lateral compressibility of the lipid.

Effects of lateral compression on a non-registered monolayer

A thermodynamic description is developed for the lateral compression observed in a non-registered monolayer as the pressure or temperature of coexisting three-dimensional gas is varied. The isothermal lateral compressibility of the monolayer is expressed in terms of structural data obtained in low energy electron diffraction studies. The limit-of-compression is determined by the onset of a second adsorbed layer. Detailed calculations of the limit-of-compression at zero temperature are performed for a Lennard-Jones pair potential model and for a model of xenon adsorbed on silver. The results show that the lateral spacing of the adsorbed monolayer at the onset of the second layer is very close to the nearest neighbor spacing of the bulk adsorbate, in agreement with observations on several non-registered systems. The calculations also predict a difference in the lateral lattice constant for the coexisting monolayer and bilayer; this has not been observed.

Lateral compressibility of lipid mono- and bilayers. Theory of membrane permeability

The passive sodium permeability of pure lipid vesicles and dispersions has a large peak at the bilayer phase transition temperature. We discuss this anomaly in terms of density fluctuations, which can open up cavities in the headgroup region into which small ions can enter, and which may be large if bilayer conditions at the melting point are similar to those near the critical point which seems to exist in monolayers. We present two arguments, one thermodynamic and one microscopic, which suggest that the permeability is proportional to the lateral compressibility. We then calculate the lateral compressibility for two previously published theoretical models and compare the results with experiment.

An Energy Analysis of the Mechanics of Weft-knitted Fabrics by Means of Optimal-control Theory: Relaxed-fabric Dimensions and Tensile Properties of the Plain-knitted Structure — Reply

The energy analysis of the plain-knitted structure reported in Part I of this work is further developed by studying the relaxed-fabric dimensions and the fabric tensile properties for extension in the two principal directions of the fabric structure. The relaxed-fabric dimensions are evaluated in terms of the parameters k a, k w and the thickness for fabrics of different tightness of construction and for yarns of different lateral compressibility. The following parameters are also evaluated: inter-yarn distances and inter-yarn forces in the regions of loop-interlocking and length- and width-jamming, the fabric-curling couples, the energies of yarn-bending and lateral yarn compression, and the total energy. Wherever possible, the values of these parameters are compared with experimental results reported in the literature and also with the results of previously reported theoretical models of the plain-knitted structure. The variation of the previously mentioned parameters is studied when a fabric tension is...

Thermodynamic fluctuations in phospholipid bilayers

A simplified statistical mechanical model of the solid–fluid melting transition of wet lipid bilayers is developed which allows for calculation of thermodynamic fluctuation effects. The model is used to estimate the lowering of the free energy barrier for transbilayer ion permeability due to enhanced lateral compressibility near the melting point. The calculation is used to fit permeability data for dipalmitoyl phosphatidyl choline vesicles and the fit provides evidence that the bilayer is quite close to a critical temperature at which the melting transition would go from first to second order.

Mechanical Response of a Tubular Braided Cable with an Elastic Core

A model is developed for the linear clastic response of a diamond tubular braid containing a flexil le elastic core. The analysis assumes small displacements, and special assumptions are made regarding strand crossover geometry and strand lateral compressibility. Key parameters influencing the mechanical response are the braid helix angle, the crimp angle at strand crossovers, and the modulus and Poisson's ratio of the core. Special attention is given to the case where the core is flexible but essentially incompressible. The braid strength and stiffness decrease as either the braid helivangle or crimp angle are increased. Furthermore the "Chinese finger" effect of the braid on the core significantly reduces the brand strength and modulus for larger braid helix angles. Limited experimental data is presented which supports the theoretical conclusions.

Polymorphism of phospholipid monolayers

2014 Monolayers of synthetic lecithins as well as phosphatidic acid at different stages of ionization were studied with the film balance technique at pressures above the lateral vapour pressure. Pressure (03C0) versus area (a) curves (isotherms) and, by application of a special technique, area (a) versus temperature (T) curves (isobars) were recorded. From these data, plots of the lateral compressibility, ~, as a function of lateral lipid density (a-1) and of the thermal expansion coefficient, 03B1, as a function of temperature (T) were obtained. The well known transition (at T = TM) between the expanded (fluid) and the condensed (crystalline) states of the films, called the main transition, is characterized by a non-horizontal deflection of the isotherms (and isobars) in the coexistence region. A pronounced hysteresis shows that it is a first order transition. Two additional phase transitions, one at T > TM (fluid region) and one at T TM (crystalline region), were revealed by breaks in the slopes of the isotherms and the isobars. Discontinuities in the compressibilities and in the expansion coefficients show that these transitions are of second order. A flow experiment showed : that the fluid ~ fluid transition is also characterized by a pronounced discontinuity in viscosity. In fatty acid monolayers the transition (at T TM) between two crystalline states is of weak first order ( 2014 10 J./Mole). LE JOURNAL DE PHYSIQUE TOME 39, MARS 1978,