INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Bilayer couple concept

The uptake of drugs or other solutes into biological or model membranes may increase the area requirement of the outer monolayer, whereas the inner monolayer tends to maintain its area requirement if the solute does not translocate into it. Sheetz and Singer (1974) have compared the fact that asymmetric area expansion tends to curve a bilayer with a bimetallic couple (bilayer couple hypothesis). However, changes in the local curvature of plasma membranes or lipid vesicles are constrained by the fact that these areas are closed and changes of the enclosed volume (by water exchange with the outside) are opposed by osmotic effects. Thus, consequences of asymmetric uptake of solutes into membranes are 1) the creation of mechanic stress, which 2) reduces the affinity for further incorporation, and 3) drives shape changes. At a certain limit, the energy stored in the stress promotes the 4) translocation of molecules to the inner monolayer.

New techniques

The aim of the current study is to introduce new experimental approaches based on isothermal titration calorimetry that serve to answer the following questions. What is the driving force for asymmetry-driven membrane translocation of originally impermeable substances to the inner monolayer? How large is the energy of the bending stress and which are the enthalpic versus entropic contributions to it? Does the partition coefficient for asymmetric uptake differ substantially from that for balanced incorporation? How can the translocation threshold of a solute be measured without specific labeling, and at which apparent area asymmetry does it occur? Does the translocation of the solute permeabilize the membrane to other aqueous solutes as well? The issues of membrane deformation, permeation, and permeabilization are of major relevance for the understanding of physiological effects and applications as outlined in the following.

Deformations

The area balance or imbalance between the two monolayers is one of the key properties of biological membranes. There is good evidence that it is actively regulated by transmembrane pumping or directed synthesis of, e.g., lipids to govern deformations initiating both endo and exocytosis and other physiologically required shape changes of cells (Rauch and Farge, 2000; Farge et al., 1999; Mui et al., 1995; Farge, 1994; Sackmann et al., 1986). Asymmetric incorporation of solutes interferes with these processes. Treatment of erythrocytes with impermeable amphiphiles such as dodecyl maltoside drives echinocytosis and exovesiculation, whereas preferential expansion of the inner monolayer causes stomatocytosis and endovesiculation (Bobrowska-Hagerstrand et al., 1999; Schwarz et al., 1999; Hagerstrand and Isomaa, 1992). Most reports on the elastic properties and deformations of membranes are based on the visualization of cells or giant liposomes and the micropipette aspiration technique (Olbrich et al., 2000; Rawicz et al., 2000; Evans and Needham, 1987). The methods applied here yield no direct information about deformations but the measurement of the energy, enthalpy, and entropy of asymmetric incorporation provides clues on the balance between dilation and deformation of the membrane.

Permeation

There are different pathways for the permeation of drugs into cells. Hydrophobic molecules partition into the core of the membrane and can be released to the cytoplasm from there. Hydrophilic compounds are typically taken up via endocytosis (cf. above). Others are transported via specific carrier proteins. Molecular "cargoes," which are covalently attached to certain, often lysine- or arginine-rich transporter peptides such as tat-derived peptides, penetratins, or transportan, are internalized into eukaryotic cells by means of a so-far unknown mechanism (Lindgren et al., 2000). This study aims to contribute to a more detailed understanding of asymmetry-driven flip-flop of originally impermeable molecules, which might be another pathway of unspecific membrane permeation of amphiphiles. It must be noted that the flip-flop of solutes across membranes is not easily measured. Kragh-Hansen et al. (1998) have used radiolabeled detergents for detecting whether or not certain detergents flip-flop out of multilamellar lipid vesicles. The choice of alkyl maltosides as model systems for our study is based on their result that dodecyl maltoside does not translocate across lipid bilayers within hours.

Permeabilization

The stress in the asymmetrically expanded bilayer may also lead to membrane permeabilization, i.e., a local destruction of the membrane leading to an exchange of all (not too large) aqueous solutes between the outside and inside of the cell or vesicle. This has been discussed for charged detergents such as cholates (Schubert et al., 1983, 1986). Growing resistance of bacteria against classic antibiotics has led to large research efforts toward the understanding of antibiotic peptides. These accumulate in the outer monolayer of, e.g., bacterial membranes, and kill the target cell upon translocation to the inner monolayer. The details of the latter phenomenon are an issue tackled by quite a number of, partially competing, models (for recent studies cf. Wieprecht et al., 1999; Vogt et al., 2000; Uematsu and Matsuzaki, 2000; Shai, 1999; Huang, 2000; Bechinger, 1999). The relevance of asymmetric membrane expansion for this translocation is still unclear and the methods presented here are potentially suitable to approach this problem.

Fusion

Area asymmetry effects have also been discussed to play a role upon fusion of viruses with target cells mediated by insertion of amphiphilic fusion peptides into the membrane by Longo et al. (1998). They raise the question whether the stability limit for symmetric vesicle inflation (~5 area-percent) applies also to mechanical failure of vesicles upon asymmetric expansion by peptides. The present study shows that such a comparison is not straightforward.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Materials

The lipid, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) was purchased from Avanti Polar Lipids, Alabaster, AL. The surfactants n-dodecyl--D-maltopyranoside (C₁₂-maltoside), n-tridecyl--D-maltopyranoside (C₁₃-maltoside) and n-tetradecyl--D-maltopyranoside (C₁₄-maltoside) were bought from Anatrace Inc., Maumee, OH in Anagrade purity (>99% HPLC). Prasoedymium nitrate was from Riedel del Haen. All substances were used without further purification.

Vesicle preparation

The lipid was dried from the storage solution, weighed, and dispersed in buffer (TRIS 10 mM + NaCl 100 mM, pH 7.4) by vortexing. After five freeze-thaw cycles, large unilamellar vesicles were prepared by 19 passages (back and forth) through two stacked Nuclepore polycarbonate membranes of 100 nm pore size in a 1 ml mini-extruder (MacDonald et al., 1991). The lipid concentration was confirmed by spot checks using a phosphate assay. The effective unilamellarity was checked by NMR (cf. below).

Isothermal titration calorimetry

The measurements were performed using a VP isothermal titration calorimeter produced by MicroCal Inc., Northampton, MA (Chellani, 1999). All fit procedures were performed with MicroCal Origin.

Partitioning experiment (uptake)

(1)

(2)

(3)

(4)

(5)

(6)

Release experiment

(7)

(8)

Solubilization experiment

NMR measurement of the accessible lipid fraction

A Bruker DRX (9.4 Tesla) wide-bore system with 10 mm broadband observe was used to monitor the ³¹P signal of vesicle suspensions as used in the ITC experiments. Praseodymium nitrate was added from an iso-osmotic stock solution to a final concentration of 5 mM to shift the signal of the lipids on the outer monolayer by ~20 Hz downfield, but leave that of the inner monolayer unchanged (De Kruijff et al., 1976; Frohlich et al., 2001). The FID was acquired after a 30° pulse. Waiting times of 3 s (T1  0.7 s) were used to ensure complete relaxation. The field was deuterium-locked (2% D₂O added to sample) and no proton decoupling was performed to avoid an effect of the nuclear Overhauser enhancement on the outside-to-inside intensity ratio.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Uptake and release

Fig. 1 shows the results of uptake and release experiments performed with different alkyl maltosides at 10°C. The uptake of the detergents into the membrane is studied by a titration of vesicles into a detergent solution. It yields endothermic heats of injection (triangles in Fig. 1) that decrease gradually when the remaining amount of free detergent becomes less and less. The data sets allow fitting the partition coefficient, K, the molar heat of detergent (D) transfer from water (w) into the bilayer (b), H, and the small heat of dilution, Q_dil, according to Eq. 5 (cf. solid lines). The fits were performed assuming that only the outer monolayer, i.e., about half of the total lipid, was accessible to the detergents ( = 0.5) and the results are listed in Table 1. If all lipid was accessible to the detergent ( = 1), K would be half the value in Table 1.

View larger version (17K): [in this window] [in a new window]   FIGURE 1   Results of ITC uptake () and release () experiments with POPC vesicles and dodecyl (left panel), tridecyl (middle panel), and teradecyl maltoside (right panel) at 10°C. The measured heats per mole of lipid injected, Q, are plotted versus the lipid concentration, C, in the cell. The solid lines represent fits of the uptake data according to Eq. 3 using  = 1 or  = 0.5 (the latter are listed in Table 1). Then, the desired results of the release protocol were simulated according to Eq. 5 and plotted as solid (assuming  = 1) and dashed ( = 0.5) lines. Free fits to the release data (dash-dot lines) yielded the parameters listed in Table 1.

Release experiments are based on injections of vesicles, preloaded homogeneously with detergent, into buffer. The fit function Eq. 8 with Eqs. 2 and 3 includes the same adjustable parameters as the one for the uptake, so it is possible to predict traces for the release experiment based on the parameters determined upon uptake. These model predictions are plotted as solid (assuming  = 1) and dashed ( = 0.5) lines in Fig. 1. Experiments with permeable detergents have, indeed, revealed a very good agreement of the release data with such a model prediction (Heerklotz et al., 1999; Heerklotz and Seelig, 2000b). Comparing the experimental results for the alkyl maltosides with the model curves, it must be stated that the data are, as expected, closer to the prediction for impermeable membranes. However, there is still a significant deviation. The dash-dot lines correspond to independent fits of the release data (assuming  = 0.5) and the corresponding parameters are listed in Table 1. Generally, it turns out that K measured upon uptake is smaller and H is more endothermic than measured upon release. The release experiment with C₁₄-maltoside gives rise to very small heat values that do not allow a separate fit with reasonable precision. However, qualitative comparison with the dashed curve suggests the same tendencies. The results are given in Table 1, including the free energies of transfer:

(9)

with

Solubilization protocol

Fig. 2 shows the calorimetric traces and consequent heats of micelle-to-bilayer transfer, H, of an ITC solubilization experiment titrating 10 mM POPC vesicles with a micellar dispersion of 50 mM C₁₃-maltoside. The abscissa is the mean detergent-to-lipid ratio in the membrane, R_b. Fig. 2 resembles the typical behavior of this protocol with an initial range of endothermic heat followed by a sudden jump to exothermic values at the onset of membrane solubilization to micelles (Heerklotz et al., 1995; Heerklotz and Seelig, 2000b). The integrated heat values in the lamellar range (Fig. 2, R_b < 0.8) exhibit a local minimum at R_b^min  0.2. Inspection of the raw calorimeter reading (cf. Fig. 2, top) reveals that kinetics of surfactant uptake change right at the minimum. Injections before the minimum lead to a fast uptake compared to the instrumental resolution of 15 s. At R_b^min (cf. arrows in Fig. 2), a second effect with a lifetime of the order of 10 min appears. Subsequent injections exhibit kinetics with an endothermic-exothermic-endothermic sequence. This order persists at higher concentration, but the overall process speeds up again.

View larger version (19K): [in this window] [in a new window]   FIGURE 2   Results of an ITC solubilization experiment titrating POPC vesicles (10 mM) with a micellar dispersion of tridecyl maltoside (50 mM). The upper panel shows a detail of the raw data of the compensation heat power versus time. Each injection gives rise to a peak, the area of which is plotted in the lower panel after normalization with the injected mole number. The abscissa of the lower panel is the total surfactant to lipid mole ratio in the sample, R  Rb. The composition at the local heat minimum (arrows) is denoted Rbmin and that at the sudden drop of the heats is referred to as Rbsat.

The equivalent experiment was performed with C₁₂- and C₁₄-maltoside, and the observed heat values are shown as solid lines in Fig. 3 (identical in top and bottom panels). The positions of the local minima and the onset of solubilization are given in Table 1.

View larger version (23K): [in this window] [in a new window]   FIGURE 3   Overview of results of ITC solubilization experiments with dodecyl (left column), tridecyl (middle column), and tetradecyl maltoside (right column) as introduced in Fig. 2. Micellar dispersions of alkyl maltosides were titrated into suspensions of POPC vesicles (solid lines) or into POPC vesicles pre-loaded homogeneously with the respective alkyl maltoside Rb = 0.1 for dodecyl and Rb = 0.08 for tridecyl and tetradecyl maltoside) (dashed lines). The top row shows the normalized heat of titration versus the mean (pre-loaded + injected) surfactant content in the sample. The bottom row shows details of the same data re-plotted versus the injected surfactant (ignoring the pre-load). Note that the local minima merge if plotted versus the asymmetrically incorporated surfactant (bottom row), whereas the drop from positive (endothermic) to negative values indicating the onset of solubilization is represented by the total Rb (top row).

Another experiment was performed using lipid vesicles that were produced (i.e., extruded) in alkyl maltoside solutions as used for the release protocol. The results were plotted versus the total (titrated plus pre-loaded) R_b (cf. dashed lines in Fig. 3, top) and versus the contribution to R_b arising exclusively from the titrated surfactant (bottom panel). Note that the onset of solubilization of both pre-loaded and non-pre-loaded vesicles occurs at the same total R_b. In contrast, the local minimum of the heat of titration occurs at the same amount of surfactant titrated into the cell.

NMR experiments

The top trace in Fig. 4 shows the ³¹P-spectrum of POPC vesicles prepared as described in Materials and Methods. The line is broadened in large vesicles used here (full-width at half-height 250 Hz at 60°C) compared to water-soluble phosphate (6 Hz). Addition of praseodymium nitrate to a concentration of 5 mM does not change the integral intensity (apart from the dilution effect). However, the signal of the lipid that is accessible from the outside is shifted downfield by 20 ppm. The signal of lipid localized in the inner monolayer of the vesicles is not shifted. Note that oligolamellar vesicles would expose only one outer monolayer to Pr³⁺, whereas the signal from all other lipid would remain unshifted.

View larger version (9K): [in this window] [in a new window]   FIGURE 4   31P-NMR spectra of POPC vesicles prepared as described before (top trace) and after (bottom trace) addition of 5 mM praseodymium nitrate. The bottom spectrum is split into a line representing the inner monolayer (not shifted) and one representing the outer monolayer (shifted). The areas below both lines agree with each other, implying  = 0.5. The same was found in the presence of dodecyl maltoside.

The integrals under the two well-separated peaks can be directly related to the number of accessible versus inaccessible lipid molecules, yielding an accessible fraction of  = 0.48 ± 0.02 in the present example. The same result is obtained at 25°C, but the substantially broader lines (700 Hz in the absence of Pr³⁺) lead to some overlap of the outside and inside signal, which requires a deconvolution to determine . Repeated vesicle preparations, including those in the presence of 0.8 mM dodecyl maltoside, lead to consistent results. Hence, we may state that deviations from unilamellarity play no substantial role in this study, and  = 50 ± 5% of the lipid is exposed to the bulk buffer.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Apparent versus real area changes

The techniques introduced here relate the asymmetric incorporation of molecules into vesicles to changes in thermodynamic properties. The perturbation of the system will be quantified in terms of the apparent relative area change per lipid, A_app/A₀:

(10)

where the change in the detergent-per-lipid mole ratio, R_b, is weighted by the intrinsic lateral area of the detergent, A_D, and normalized with respect to the relaxed area, A₀. The latter will be given per lipid molecule so that it includes the intrinsic lateral area of the lipid, A_L, and the fractional area of the detergent per lipid prior to the perturbation, R_bA_D. The areas are assumed as A_L  65 Å², (Lantzsch et al., 1994) and A_D  54 Å² measured for dodecyl maltoside on the film balance (X. Li-Blatter, personal communication).

It should be emphasized that A_app/A₀ is, in its essence, a measure of the concentration weighted with respect to the intrinsic area. The system will react on asymmetric uptake to the outer monolayer by 1) realizing an area change by increasing bilayer curvature (shape changes, budding) or stretching the inner monolayer; and 2) suppressing monolayer area changes by a strain compressing the area per molecule. Larger vesicles undergo shape changes more easily, whereas smaller ones establish stronger strains. Small asymmetries are essentially covered by smoothing undulations, whereas asymmetries of >~8 area-percent induce marked lateral stretching/compression (high-tension regime) (Farge et al., 1990; Evans and Rawicz, 1990; Farge, 1994; Evans and Needham, 1987). Real area changes are quantified in terms of A/A₀. The strain of monolayer compression can also be modeled in terms of a A/A₀, where A is just the intrinsic area of the incorporated solute. These effects cannot be monitored by calorimetry. However, A_app/A₀ constitutes an interface to relate calorimetric data to information from structural methods and theory. A detailed discussion of the relationship between energetics and structure must be beyond the scope of this paper. A first, crude approximation will be given below.

Comparison of uptake and release data reveals energetics of asymmetry stress

A comprehensive picture of the partitioning behavior is obtained by a parallel application of the classic partitioning protocol (uptake) and the "release" protocol. A very good agreement between the results of both protocols has been reported for surfactants that undergo a fast flip-flop between the outer and inner monolayer relative to the ITC time scale of some minutes ( = 1, Heerklotz et al., 1999; Heerklotz and Seelig, 2000b). The large discrepancy between the data and the solid curve in Fig. 1 rules out such fast membrane permeation for the investigated alkyl maltosides. This finding is in accord with the results of Kragh-Hansen et al. (1998). Hence, alkyl maltosides are exclusively taken up into or released from the outer monolayer, respectively.

The remaining discrepancy between the release data and the curve simulated for  = 0.5 and the parameters measured upon uptake implies that either 1) K and/or H differ between uptake and release or, 2)   0.5. To exclude artefacts from multilamellar vesicles (  0.5), which cannot be a priori ruled out in particular for the samples extruded in the presence of surfactant, we have measured the accessible lipid fraction by NMR, yielding  = 0.5 ± 0.05.

Table 1 collects the result of individual fits of Eqs. 6 or 8, respectively, to all uptake and release data assuming  = 0.5. In all three cases, the release protocol yields larger partition coefficients and less endothermic transfer enthalpies than the uptake protocol. Such a discrepancy should not occur in the case of equilibrium partitioning. However, asymmetric uptake creates asymmetry stress, the enthalpy of which adds to the enthalpy of (equilibrium) transfer, so that we may write for the effective enthalpy of uptake, H:

(11)

The effective enthalpy upon release is H (release):

(12)

Note that the equilibrium transfer is reversed (sign changes with direction) but again, stress is created when detergent is extracted asymmetrically out of an originally relaxed membrane. The universal fit equation (8) generally uses H for both uptake and release, i.e., Eq. 12 is reversed:

(13)

Equations 11 and 13 imply that the difference between the enthalpies obtained by the different protocols is a measure for the sum of the two stress enthalpies:

(14)

Analogously, one obtains for the free energy:

(15)

To which asymmetry, i.e., to which membrane composition do these statements refer? The membrane composition varies, naturally, in the course of the titration which will, in turn, vary the stress. Then, K and H cannot be strictly constant (as approximated in the evaluation procedure). Model calculations imply that the fit parameters represent in particular the conditions present upon the first injections, which give rise to the largest heat. In our case, that means that the data approximately reflect the situations with the largest asymmetries. We can, thus, tentatively assign the uptake data to membranes with a detergent-per-lipid ratio R  0.25 ± 0.05 in the outer monolayer, and R  0 in the inner (A_app/A₀  20%); and the release data to R  0.01 and R  0.08 (A_app/A₀  5%). Because H_stress(release) is supposed to be much smaller than H_stress(uptake) (cf. the next section), we may approximate H_stress H_stress(uptake) + H_stress(release) and assign this value approximately to A_app/A₀ slightly above 20% (cf. Table 1). The same applies to G.

Free energies of membrane stretching upon uptake versus release experiments, theoretical estimate

The elastic free energy contributions of membrane compression/expansion per unit area are described by the relation (Helfrich, 1973):

(16)

For comparison with ITC data, Eq. 16 must be re-normalized from energy per unit area to energy per mole of detergent added. This is achieved by multiplication with the factor A_LN_A/R_b:

(17)

where N_A is Avogadro's constant. The apparent bilayer stretching modulus in the high-tension regime, which includes contributions from both real area expansion and suppression of undulations, amounts to k_s  208 dyn/cm for POPC (Rawicz et al., 2000). Although the monolayer modulus may differ from half the bilayer value, we assume k_s  100 dyn/cm = 0.1 J/m² as a rough estimate for a POPC monolayer in the high-tension regime, which should, at least, apply to the uptake experiments. For the release experiments, which may lead to low-tension systems (Farge, 1994), the use of this value will yield an upper limit of the elastic energy. The modulus for a small compression of a bilayer (e.g., 221 dyn/cm for SOPC, Koenig et al., 1997) is similar to that for expansion.

Let us, for a first approximation, treat the bilayer as a flat surface (thus ignoring shape changes) so that both monolayers are constrained to share the same area. Then, the apparent area change must be accommodated by compression/expansion of the two monolayers, |A_app| = |A^out| + |Aⁱⁿ|. The square in Eq. 16 and the similarity of compression and expansion moduli imply that it is energetically cheaper to share the stress between both monolayers than to accommodate all A_app exclusively in the monolayer that changes its detergent content.

For the outer monolayer, we assume a compression by A^out = A_app/2 upon uptake of R detergent molecules per lipid. The corresponding elastic energy is obtained on the basis of Eqs. 17 and 10 as:

(18)

The other half of the apparent area asymmetry is balanced by an increase of the total bilayer area, which requires stretching of the inner monolayer: Aⁱⁿ = A_app/2. Altogether, we obtain:

(19)

Equation 19 suggests an elastic energy of stretching, G  1.4 kJ/mol for the uptake of R R  0.25 into an originally pure lipid bilayer (R = 0), a case which is approximately represented by the uptake experiments in this study. Analogously, one obtains 0.4 kJ/mol for the release (R  0.08, R  0.01, R  0.07) if the same apparent k_s applies to this small perturbation. If effects on undulations, etc. give rise to a low-tension regime also upon asymmetric stretching, G upon release will be even smaller.

The sum of the theoretical estimates, G(uptake) + G(release)  1.8 kJ/mol is indeed somewhat larger than the experimental values of ~G  1.5 and 0.6 kJ/mol for the different compounds (cf. Table 1), but the significance of the difference is questionable.

Entropic versus enthalpic effects

Little is known about the ethalpic versus entropic contributions to the elastic free energy described by the Helfrich model. We stated above that the asymmetry stress (high-tension regime) is driven by some +3 to +6 kJ/mol of enthalpy and accompanied by an entropic contribution of some 2 to 4 kJ/mol. The interpretation of this finding is not straightforward because asymmetric stress goes along with unknown contributions from local expansion and compression.

Symmetric membrane stretching driven by osmotic inflation of vesicles is endothermic (i.e., opposed by enthalpy) and compression is exothermic (i.e., opposed by entropy) as indicated by direct calorimetric measurements (Nebel et al., 1997). The asymmetric stress (outside compression versus inside stretching, or vice versa) studied here is observed to be opposed by enthalpy.

What are the molecular effects governing this behavior? The positive enthalpy might result from the fact that stretching perturbs the packing of the chains. This effect is endothermic but essentially compensated by entropy gains (Heerklotz and Epand, 2001) and could account for the principle behavior observed here (H > 0, TS < 0).

A variety of effects may reduce the entropy gain, thus leading to the dominance of enthalpy. 1) Expansion will increase the water-accessible apolar surface area, ASA_ap, of the membrane. A net increase of ASA_ap by 10 Å² per detergent costs entropy of TS_D  1 kJ/mol, whereas the accompanying enthalpy gain is small at 10°C (Heerklotz and Epand, 2001). 2) Upon membrane compression, the above effect may be overcompensated by the entropy loss upon gradual dehydration of the headgroups (Binder et al., 1999). 3) The restriction or suppression of undulations would also cost entropy.

The asymmetry-controlled permeability threshold

The ITC solubilization protocol (cf. Figs. 2 and 3) yields the molar heat of transfer of a surfactant from micelles to mixed membranes, H, because the experimental conditions ensure almost complete membrane binding of the detergent (cf. Materials and Methods). Such data have been published so far only for detergents that re-distribute quickly across the membrane (cf. Heerklotz and Seelig, 2000b, for a review). Typically, a continuous decrease of H versus R_b was observed that could be modeled according to regular solution theory, and the membrane perturbation induced by the detergent was the steeper the stronger. For the alkyl maltosides, which do not easily translocate to the inner monolayer, we observe a different pattern exhibiting a local minimum of H at R_b^min  0.2 (cf. Table 1 for details). Based on the models describing composition-dependent enthalpies of detergents in bilayers, it is unlikely that the enthalpy increases again when a certain local detergent concentration is reached. Instead, it must be suspected that addition of detergent (i.e., increase in R_b) leads to a decrease in the local detergent content R which, in turn, increases the enthalpy as usual. This seems a paradox at the first glance but does actually happen at a permeability threshold, when currently added molecules facilitate the translocation of previously added ones from the outer to the inner monolayer.

Let us, for the sake of the argument, imagine 10 injections which increase R_b of a detergent symmetrically in both outer and inner monolayer to 1 and H linearly (just for simplicity) from 4 to 3 kJ/mol. This case is illustrated by open bars in the background of Fig. 5. What is supposed to happen for a system with the same composition-dependent enthalpy but asymmetric insertion? It exhibits a local detergent content in the outer monolayer, R, which is twice R_b given in the abscissa. Hence, H would reach 3 kJ/mol already after five injections and, if the linearity holds, 2 kJ/mol after 10 (black bars in Fig. 5). The cumulative heat in the second case (black bars) is by 5 kJ/mol smaller, implying that 5 kJ/mol are "stored" in the asymmetric distribution of the surfactant. Now let us assume that a permeability threshold is reached during the 11th injection, which leads all of a sudden to a complete equilibration of the surfactant between the two monolayers. As a consequence, the stored 5 kJ/mol would be released at once and the system would turn to the scenario for symmetric incorporation for subsequent injections, as illustrated. Although sudden complete permeabilization is the extreme case, which is not quite realistic, we may state that a permeability threshold gives rise to a peak and an upward step in the heat of titration.

View larger version (22K): [in this window] [in a new window]   FIGURE 5   Schematic illustration of the consequences of a permeability threshold for the results of an ITC solubilization experiment. The hollow bars in the background refer to the case of a permeable membrane. The black bars describe the subsequent data for the case that the membrane is impermeable to the surfactant for the first 10 injections, but is completely permeabilized during the 11th injection (cf. text for explanation).

The experimental data show a local minimum followed by slightly increasing heats over a number of injections. This implies that the local minimum reflects not the total equilibration, but only the onset of a gradual equilibration process. Obviously, only surfactants superseding a certain threshold asymmetry can actually permeate the bilayer, and this threshold is gradually reduced during further injections. Again, we should note that, in terms of kinetics, the onset of permeation in the ITC experiment reflects the situation that permeation gets fast enough to occur within some tens of minutes.

The interpretation of the local minimum of the heat of titration as the threshold for the onset of membrane permeation is fairly compatible with the appearance of a second, slower effect in the raw data (cf. Fig. 2, top) mentioned above. Accordingly, the fast process can be assigned to outside incorporation and the slow one to the translocation to the inner monolayer.

Tuning the asymmetry

To study the asymmetry of surfactant incorporation as a function of the mean composition R_b, let us compare systems with the same R_b but different asymmetries (Fig. 3, top) and vice versa (bottom). For that purpose, we have repeated the titrations of surfactant micelles into lipid vesicles (Fig. 3, solid lines) with vesicles pre-equilibrated with R = R = 0.08 of the respective surfactant (dashed lines). The top panel shows the resulting heats of titration versus R_b. If the surfactant can equilibrate between both monolayers, it makes no difference whether a surfactant molecule was added before or after vesicle preparation. Then, R_b suffices to determine the state of the system and the two enthalpy functions should merge. Such a behavior is, in the frame of experimental resolution, observed above R_b  0.5. Notably, this is the typical concentration range where highly curved surfactant-rich structures can form and stabilize membrane leaks by covering the hydrophobic edges (Ueno, 1989; Edwards and Almgren, 1991; Kragh-Hansen et al., 1998; Lasch, 1995). At concentrations R_b < 0.4, however, the dashed traces are up-shifted in R_b compared to the solid ones. This implies that systems sharing the same R_b differ in the asymmetry of surfactant incorporation which, in turn, changes their enthalpy.

The bottom panel shows the same enthalpy data, but now plotted versus R_b of the surfactant added from the injection syringe, ignoring that the samples represented by dashed lines possess an additional 0.08 surfactants per lipid in both monolayers from pre-loading. This abscissa is proportional to A_app/A₀ as long as all titrated surfactant remains exclusively in the outer monolayer. It must be emphasized that the local minima of H merge in this plot, indicating that they are controlled by A_app/A₀ rather than by the total R_b. Beyond the minimum, the dashed traces become increasingly down-shifted in R_b. This has to be expected in the case of a surfactant translocation to the inner monolayer, which reduces the asymmetry. We summarize that Fig. 3 provides additional evidence for the idea that the local minimum of H is asymmetry-controlled and reflects the permeability threshold beyond which a gradual redistribution of surfactant between the outer and inner monolayer occurs.

The local enthalpy minimum R = 0.17 observed for dodecyl maltoside appears to coincide with the onset of calcein efflux measured by de la Maza and Parra (1997, 10% dequenching after 40 min at R_b = 0.14, 20% dequenching at R_b = 0.28). A comparison of the behavior of membrane permeation by the surfactant (ITC) and permeabilization to aqueous solutes (calcein) should shed light on the problem whether the translocation of the surfactant to the inner monolayer occurs via a stimulated flip of single molecules across intact membranes or via transient bursts. The latter effect is supposed to play a role for the activity of antimicrobial peptides. However, more detailed studies are required for a conclusive interpretation.

As explained above, we may assign R_b^min = 0.17 (i.e., R = 0.34) to the permeability threshold for dodecyl maltoside and somewhat larger for the longer-chain analogs (cf. Table 1). The corresponding apparent area asymmetry amounts to A_app/A₀  30%. It must be emphasized that Farge (1994) reports that "the compression constraint progressively relaxes" after addition of 30% of lysophosphatidylcholine (A_app/A₀  30%). In their case, permeabilization is discussed to go along with membrane solubilization to coexisting micelles. In our case, permeabilization starts, notably, at the same apparent area asymmetry, although micellization requires substantially higher detergent content, as discussed in the next section. It is an advantage of the new protocol introduced here that both phenomena can be well distinguished. The limiting free energy value for membrane permeabilization estimated according to Eq. 19 with R = R  0.4 and R = 0 is ~2 kJ/mol detergent or 0.4 kJ/mol lipid.

Note that symmetric stretching of bilayers upon vesicle inflation leads to mechanical failure of the vesicles already at A/A₀  5 area-percent (Olbrich et al., 2000). As argued above, symmetric and asymmetric stretching are quite different phenomena.

Vesicle solubilization

The onset of solubilization or lysis of the membrane by the appearance of coexisting mixed micelles is very precisely detected by the ITC solubilization experiment (Figs. 2 and 3) as a sudden drop of the titration heat, often from endothermic to exothermic values (Heerklotz et al., 1995; Heerklotz and Seelig, 2000b). Although the effect is small, it can be considered significant that the limiting surfactant content in bilayers increases with the chain length (cf. Table 1). The value for C₁₂-maltoside is quite consistent with the light-scattering maximum at R_b = 0.89 published by de la Maza and Parra (1997). The chain-length dependence can be explained by the fact that packing problems caused by the chain length mismatch between the lipid and the surfactant destabilize the membrane and, thus, contribute to the driving force for micellization. Similar effects can, for example, be observed comparing the lytic content of C₁₀EO₇ (R = 0.61) and C₁₂EO₇