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Thermodynamics of Lipid Membrane Solubilization by Sodium Dodecyl Sulfate

Sandro Keller ^*, Heiko Heerklotz , Nadin Jahnke ^* and Alfred Blume 

^* Leibniz Institute of Molecular Pharmacology FMP, Berlin, Germany; Department of Biophysical Chemistry, Biocenter of the University of Basel, Basel, Switzerland; and Institute of Physical Chemistry, Martin Luther University Halle-Wittenberg, Halle, Germany

Correspondence: Address reprint requests to Sandro Keller, Leibniz Institute of Molecular Pharmacology FMP, Robert-Rössle-Strasse 10, 13125 Berlin, Germany. Tel.: 49-30-94793-368; Fax: 49-30-94793-159; E-mail: mail{at}sandrokeller.com.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
We provide a comprehensive thermodynamic description of lipid membrane dissolution by a charged detergent. To this end, we have studied the interactions between the anionic detergent sodium dodecyl sulfate (SDS) and the zwitterionic phospholipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) in dilute aqueous solution (10 mM phosphate buffer, 154 mM NaCl, pH 7.4). Thermodynamic parameters of vesicle solubilization and reconstitution, membrane partitioning, and micelle formation were assessed by right-angle light scattering and isothermal titration calorimetry. Membrane translocation and dissolution proceed very slowly at 25°C but are considerably accelerated at 65°C. At this temperature, a simple SDS/POPC phase diagram (comprising vesicular, coexistence, and micellar ranges) and a complete set of partition coefficients and transfer enthalpies were obtained. Electrostatic repulsion effects at the membrane surface were implemented by combining Gouy-Chapman theory with a Langmuir adsorption isotherm to account for Na⁺ binding to membrane-incorporated DS^–. This approach offered a quantitative understanding of solubilization and reconstitution processes, which were interpreted in terms of partition equilibria between and ideal mixing in all phases. More than any other property, the transbilayer flip-flop rate under given experimental conditions hence appears to dictate a detergent's suitability for thermodynamically controlled lipid membrane solubilization and reconstitution.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Detergents are valuable tools for the permeabilization and solubilization of biological and model membranes (1) and for the purification and reconstitution of lipidic and proteinaceous membrane constituents (2). Solubilization and reconstitution of lipid vesicles are characterized by the appearance and disappearance of distinct surfactant aggregates (3–7), which, to a first approximation, can be regarded as pseudophases (8). In the initial stage of solubilization, a large excess of lipid ensures micelle disintegration and partitioning of detergent monomers between the aqueous phase and bilayers. Upon saturation of the mixed membranes with detergent, the appearance of first mixed micelles marks the beginning of the coexistence range. Further addition of detergent then shifts the equilibrium from bilayers to micelles without affecting the compositions of the two surfactant aggregates. Solubilization is completed when the last vesicles vanish, so that only micelles are left in the final range. Vesicle reconstitution proceeds in the opposite direction, that is, from mixed micelles to micelle/bilayer phase coexistence to mixed bilayer structures.

For systems comprising egg-yolk phosphatidylcholine and the nonionic detergent octylglucoside, a full set of transfer enthalpies between aqueous, micellar, and vesicular phases has been derived (9). If the critical micellar concentration (CMC) is low and the total surfactant concentration high enough, the fraction of monomeric detergent in solution becomes negligible (8). Then, both transfer enthalpies and partition coefficients are available, as is the case for mixtures composed of the nonionic detergent octa(ethylene oxide) dodecyl ether (C₁₂EO₈) and the zwitterionic lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) (10–12). For many practical purposes, however, detergents with CMC values in the millimolar rather than micromolar concentration range are preferable because they can be rapidly and conveniently removed by dialysis, chromatography, or other methods (2).

Unfortunately, quantification of membrane solubilization by charged surfactants, which normally possess high CMC values, has thus far been limited to the determination of the critical detergent/lipid ratios at the phase boundaries (13–19). A more thorough thermodynamic analysis is not straightforward but, nonetheless, appears desirable for a number of reasons. First, theoretical considerations predict dramatic discrepancies between ideally and nonideally mixing surfactant systems when it comes to isolating so-called detergent-resistant membrane fractions (20). It therefore seems crucial to differentiate between purely electrostatic effects and those potentially arising from nonideal mixing. Second, it cannot be taken for granted that data obtained at low detergent/lipid ratios (19,21) may be extrapolated to higher detergent contents necessary for membrane solubilization. For instance, counterion binding is expected to modulate electrostatic effects at the membrane surface but, unlike ion adsorption in micellar systems (22), has not been investigated in great detail. Third, largely diverging surfactant flip-flop rates have been inferred to be responsible for different solubilization pathways, which, in turn, can give rise to selective or preferential interactions with certain lipids or membrane proteins (1,23).

Sodium dodecyl sulfate (SDS) is one of the most frequently used anionic detergents and has been studied extensively with respect to micellization (19,24,25), partitioning into monolayers (26) and bilayers ((19,21), M. Apel-Paz, G. F. Doncel, and T. K. Vanderlick, unpublished), membrane permeabilization (28), transmembrane movement ((21,23,29), M. Apel-Paz, G. F. Doncel, and T. K. Vanderlick, unpublished), and interactions with membrane proteins (1,23). Over a wide temperature range, binding of SDS to POPC membranes at low detergent/lipid ratios can be described by a surface partition equilibrium subject to electrostatic repulsion effects (19,21). At ambient temperature, SDS exhibits only weak membrane permeabilization (28) and very slow flip-flop ((19,21,23,29), M. Apel-Paz, G. F. Doncel, and T. K. Vanderlick, unpublished). These two concomitant phenomena have been blamed (M. Apel-Paz, G. F. Doncel, and T. K. Vanderlick, unpublished) for the poor microbicidal potency of SDS as compared with nonionic surfactants that both permeabilize and permeate lipid membranes under the same conditions (30). Moreover, the slow kinetics of transbilayer movement seems to obstruct a straightforward evaluation of solubilization and reconstitution experiments performed at room temperature (19,23). Indeed, raising the temperature beyond 50°C greatly accelerates SDS permeation (19,21), thereby enabling the construction of detergent/lipid phase diagrams (17,19). Despite this obvious correlation between SDS flip-flop and membrane dissolution, calorimetric experiments at elevated temperature (17) have unveiled a solubilization behavior that looks much more complex than that observed for C₁₂EO₈ (10–12) and many other nonionic bilayer-permeant detergents. Therefore, it has remained unclear whether the rate of membrane translocation is the only discriminating feature or whether there exist other fundamental peculiarities in the mode of action of ionic surfactants.

Here, we present a comprehensive thermodynamic characterization of SDS/POPC mixtures in dilute aqueous solution (10 mM phosphate buffer, 154 mM NaCl, pH 7.4). This system offers the great advantage that variation of temperature alone can be exploited to tune membrane permeability without leaving the liquid-crystalline phase range (21). Right-angle light scattering was employed to compare solubilization and reconstitution of large unilamellar vesicles (LUVs) under conditions leading to either half-sided binding (25°C) or fast transbilayer equilibration (65°C). Applying isothermal titration calorimetry (ITC), we found that membrane binding and solubilization at 65°C can be understood quantitatively on the basis of a simple partitioning model assuming ideal mixing in all (i.e., aqueous, micellar, and vesicular) phases. Discrepancies between ionic and nonionic detergents stemming from electrostatic effects can be fully accounted for by Gouy-Chapman theory if counterion binding is included adequately. Thus, the ability to undergo flip-flop on experimental timescales turns out to be the single most important prerequisite of a detergent for the solubilization and reconstitution of lipid membranes in thermodynamically rather than kinetically controlled processes.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Materials
SDS was purchased from Sigma-Aldrich (Steinheim, Germany) and POPC from Avanti Polar Lipids (Alabaster, AL). All other chemicals were obtained from Merck (Darmstadt, Germany). All experiments were done in 10 mM phosphate buffer (154 mM NaCl, pH 7.4).

Vesicle preparation
POPC dissolved in chloroform at 20 mg/mL was dried in a rotary evaporator and subsequently under high vacuum overnight. The dry lipid films were suspended in buffer by vortex mixing for 5 min, yielding large multilamellar vesicles. LUVs were prepared by 35 extrusion steps through two stacked polycarbonate filters with a pore diameter of 100 nm using a LiposoFast extruder (Avestin, Ottawa, Canada). The vesicle size was narrowly distributed at around 100 nm, as checked by dynamic light scattering on an N4 Plus particle sizer (Beckman Coulter, Fullerton, CA) equipped with a 10-mW helium/neon laser with a wavelength of 632.8 nm at a scattering angle of 90°.

Right-angle light scattering
Light scattering intensities were taken at a wavelength of 632.8 nm and an angle of 90° in 1 cm x 1 cm polystyrene cuvettes (Sarstedt, Nümbrecht, Germany) on the N4 Plus instrument described in the preceding section. In solubilization assays, 10-, 20-, or 50-µL aliquots of a 25 or 50 mM SDS solution were titrated to 2.5 mL of a 0.1–2.5 mM POPC LUV suspension. In reconstitution experiments, 10-µL aliquots of a 10, 20, or 40 mM lipid vesicle suspension were injected into 1.25 mL of a 0–10 mM SDS solution. Intensity values were read 3 min after addition of detergent or lipid and stirring of the sample, which was sufficient to attain equilibrium at 65°C. By contrast, prohibitively long incubation times would have been required at 25°C, as the light scattering intensities did not remain constant even 24 h after injection (data not shown).

Isothermal titration calorimetry
High-sensitivity microcalorimetry (31) was performed on a VP-ITC (MicroCal, Northampton, MA) after vacuum degassing of the samples. For solubilization, 3- or 5-µL aliquots of 25, 50, or 100 mM SDS were injected to 0.1–5.0 mM POPC LUVs. For reconstitution, 3-µL aliquots of 20 or 40 mM lipid were titrated to 1.0–10 mM SDS. Before partitioning studies, POPC LUV suspensions were mixed with SDS solutions to yield final concentrations of 1.0 mM and 0.25–2.5 mM, respectively. After incubation for 1 h at 65°C, 10-µL aliquots of this mixture were injected into the calorimeter cell containing SDS at various concentrations.

The time spacings between the injections were chosen long enough to allow for complete reequilibration. Baseline subtraction and peak integration were accomplished using Origin 5.0 as described by the manufacturer (MicroCal Software, Northampton, MA). All reaction heats were normalized with respect to the molar amount of detergent or lipid injected. The first injection was always excluded from evaluation because it usually suffers from sample loss during the mounting of the syringe and the equilibration preceding the actual titration. Repetition of some representative experiments demonstrated high reproducibility.

Curve fitting
Nonlinear least-squares fitting was performed in an Excel (Microsoft, Redmond, WA) spreadsheet using the Solver (32) add-in (Frontline Systems, Incline Village, NV).

	THEORY

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Phase diagram
In solubilization experiments, the detergent (D) concentration, c_D, is increased by titration, whereas the lipid (L) concentration, c_L, slightly decreases as a consequence of dilution. In reconstitution experiments, c_L is increased by titration, while c_D slightly decreases. Breakpoints in light scattering assays (4–6) and inflection points in ITC measurements (8–12) yield two characteristic (c_D, c_L) pairs. In many cases, a simple phase diagram in dilute aqueous solution can then be obtained by plotting the critical c_D values versus the corresponding c_L values. The saturating (sat) detergent/lipid mole ratio,

(1)

provides the maximum detergent concentration, that can be incorporated into lipid bilayers (b) at a given lipid concentration, c_L = before the first mixed micelles appear. and the corresponding detergent concentration in the aqueous (aq) phase, are obtained as, respectively, the slope and the ordinate intercept of a linear regression analysis according to

(2)

Likewise, the solubilizing (sol) detergent/lipid mol ratio,

(3)

specifies the minimum detergent concentration, that is necessary to transfer all lipid, into micelles (m). Again, and define a straight line according to

(4)

Systematic deviations from the properties of ideal phases, such as intermicellar interactions or entropy changes associated with dispersing micelles, may account for (33), an effect that is particularly pronounced for bile salts (13,14). Within the frame of the phase separation model (8), however, the transition between the two surfactant aggregates is ascribed to a coexistence of bilayers and micelles having fixed compositions of and respectively. If this were to be strictly the case, the aqueous detergent concentration, would also need to remain constant throughout the transition range. Then, the two phase boundaries should intersect the ordinate at the same point, denoted by For SDS/POPC mixtures at 65°C, this is fulfilled to a good approximation (see Results). Note that < CMC because the former refers to free detergent in equilibrium with lipid-saturated micelles, whereas the latter gives the aqueous detergent concentration in equilibrium with pure detergent micelles.

Partition coefficients
From the slopes of the regression lines in the phase diagram, the SDS mol fractions in coexisting bilayers and micelles are calculated as, respectively,

(5)

The mol fraction partition coefficients of SDS and POPC between detergent-saturated bilayers and lipid-saturated micelles then read, respectively,

(6)

With being the molar concentration of water (W) and the SDS mol fraction in the bulk aqueous phase, the SDS partition coefficients between the latter and detergent-saturated bilayers or lipid-saturated micelles are, respectively,

(7)

It should be noted that partition coefficients as defined by Eq. 7 need not necessarily be constant but depend, in general, on the compositions of the phases and, in particular, on electrostatic repulsion or attraction effects at vesicular and micellar surfaces (see next section). values at arbitrary c_D and c_L values are afforded by an ITC protocol introduced by Zhang and Rowe (34). This approach is more laborious than the more frequently used uptake experiment (10,13,14,19,21,35) but, in exchange, enables a model-free quantification of partition equilibria as a function of membrane composition. To this end, detergent/lipid mixtures at given and values are injected from the syringe (s) into the calorimeter cell containing only detergent at various concentrations, c_D. The c_D value for which the reaction heat, Q_L+D, equals the heat of vesicle dilution must also correspond to the free detergent concentration in the syringe, Writing the equilibrium concentrations of SDS in the syringe as and the partition coefficient between the bulk aqueous phase and lipid bilayers takes the form

(8)

Electrostatic effects
Membrane binding of SDS at detergent concentrations much below the critical saturating value is adequately described by a partition equilibrium between the interfacial (i) aqueous phase having a detergent mol fraction of and bilayers characterized by (19,21). The intrinsic mol fraction partition coefficient, as defined by

(9)

is constant if mixing in both phases is ideal. is related to the detergent mol fraction in the bulk aqueous phase, by a Boltzmann term,

(10)

where z_D = –1 is the charge number of DS^–, e the elementary charge, ^i/aq the electrostatic potential at the membrane surface with respect to the bulk aqueous phase, k the Boltzmann constant, and T the absolute temperature. Thus, partitioning between the bulk solution and the bilayer phase obeys

(11)

^i/aq is conveniently obtained from Gouy–Chapman theory (36–38), which relates it to the membrane surface charge density, , according to

(12)

with R being the universal gas constant, ₀ the permittivity of free space, and _r the dielectric constant of the medium, which, for an aqueous solution at 65°C, amounts to _r = 66 (39). The summation in Eq. 12 goes over the bulk aqueous concentrations, of all ionic species (I), including the detergent, the buffer (here, 10 mM phosphate) and its counterions (16 mM Na⁺), and the additional salt (154 mM NaCl). As above, for SDS; the other bulk concentrations may be approximated by the corresponding total concentrations, The Henderson-Hasselbach equation provides the fraction of protonated buffer as 1/(1 + 10^{pH – p_Ka}), where pK_a refers to the buffering group. pK_a = 7.2 is the second pK_a value of phosphate, implying that 3.9 mM of the buffer carries a charge of –e, while the remaining 6.1 mM has a charge of –2e.

Neglecting counterion binding, a second, independent expression (40) for follows from its definition as

(13)

where A_L = 0.68 nm² (41) and A_D = 0.30 nm² (19) denote the molecular surface area requirements of POPC and SDS, respectively. is the detergent/lipid mol ratio in the bilayer. Hence, ^i/aq is given implicitly by the equality of Eqs. 12 and 13 and can be calculated by standard iteration methods. Using Eqs. 11–13, we have recently derived (21) an intrinsic mole fraction partition coefficient of from ITC uptake and release experiments performed under the same conditions as those used here.

Counterion binding
The most obvious shortcoming of the approach outlined in the preceding section is the complete neglect of counterion binding. As in a micelle (22), the high surface charge density conferred upon a membrane by incorporation of DS^– is partially neutralized by the binding of Na⁺ ions that are enriched near the bilayer surface. In analogy to the case of negatively charged lipids (40), the fraction of membrane-bound DS^– neutralized by Na⁺, , can be envisaged to follow a Langmuir binding isotherm,

(14)

where is the binding constant of Na⁺ to membrane-incorporated DS^–. The interfacial Na⁺ concentration, is related to the corresponding bulk value, by

(15)

Multiplication of Eq. 13 by (1 – ) yields

(16)

Using Eq. 15, ^i/aq can now be calculated from the equality of Eqs. 12 and 16 rather than Eqs. 12 and 13. As no data on the affinity of Na⁺ to membrane-bound DS^– seem to be available, has to be included as a fitting parameter to find the best agreement between the experimental values obtained from Eq. 8 and their theoretical counterparts calculated from Eq. 11.

Interpretation of ITC solubilization and reconstitution experiments
In this section, we lay out the rationale underlying the quantitative interpretation of ITC solubilization and reconstitution experiments; the equations used for simulations are derived in detail in the following section.

Solubilization
In the bilayer range of ITC solubilization experiments, several elementary processes take place sequentially or simultaneously upon injection of SDS micelles to POPC LUVs. Throughout this range, all micelles disintegrate; however, whereas detergents with CMC values in the micromolar range are virtually completely taken up into the membrane at sufficiently high c_L values (8,10), partitioning into the aqueous phase cannot be neglected in solubilization studies using SDS. This series of events is equivalent to complete demicellization followed by partial transfer from the aqueous solution into the bilayer phase The second process has two consequences. On one hand, a negative surface charge is imparted upon the membrane, which repels free DS^– ions. On the other hand, the bilayer phase becomes more abundant as compared with the aqueous phase, so that the equilibrium is shifted to membrane incorporation. At low detergent contents, the first effect dominates and gives rise to a drastic increase in and even a change in sign of the reaction heat, As the membrane becomes enriched in DS^–, addition of further detergent entails only a modest enhancement of the surface charge density, and the two effects basically cancel each other out, such that levels off.

In the coexistence region, both SDS and POPC are shifted from detergent-saturated bilayers to lipid-saturated micelles. In addition, some of the free detergent from the syringe partitions into micelles upon injection because the aqueous detergent concentration in the syringe (CMC) is higher than that in the cell These events correspond to detergent transfer from bilayers to water followed by micellization and concomitant lipid transfer from vesicles to micelles The extent to which these processes occur depends on the compositions of the phases involved, which are given by and for membranes, micelles, and aqueous solution, respectively. As these values remain constant throughout the phase coexistence range, so does (10).

In the micellar range, finally, part of the pure detergent micelles from the syringe disintegrate upon injection to maintain the SDS partition equilibrium between the aqueous phase and mixed micelles As the micellar detergent mol fraction and the aqueous SDS concentration in the sample cell approach unity and the CMC, respectively, smoothly decreases in magnitude. This is not the case for detergents with much lower CMC values, for which nonzero reaction heats beyond completion of solubilization can be explained only by nonideal mixing in the micellar phase or a second-order micellar transition (10).

Reconstitution
In the micellar region of reconstitution experiments, all of the injected lipid is transferred to micelles The ensuing decrease in the micellar detergent mole fraction entails redistribution of SDS from the aqueous phase into micelles This effect is most pronounced at the beginning of the experiment, and decreases in magnitude with consecutive injections. Here, the coexistence range corresponds to the transfer of detergent and lipid from micelles to vesicles. Again, constant compositions of all phases lead to constant values. In the bilayer range, the titration eventually reduces to an uptake experiment (19,21), where injection of lipid vesicles causes detergent binding from the aqueous solution approaches zero as less and less free detergent is available in the calorimeter cell.

Simulation of ITC solubilization and reconstitution experiments
Bilayer range
The normalized heats measured upon injection of SDS or POPC to a bilayer vesicle suspension, and respectively, are given by an equation recently derived (21) for evaluating uptake experiments,

(17)

where V stands for the volume of the calorimeter cell, V for the injection volume, and Q_D,dil (Q_L,dil) for the heat of dilution normalized with respect to the molar amount of detergent (lipid) injected, n_D (n_L). and denote the equilibrium concentrations of membrane-bound SDS in the cell before and after injection, respectively. Ideal mixing in both phases yields (10,21)

(18)

A corresponding equation holds for in turn, can be calculated from (21) with the aid of Eq. 11 using Eqs. 12 and 16.

Micellar range
In analogy to Eq. 17, the heats upon detergent or lipid titration to a micellar solution, and respectively, are

(19)

where all parameters have definitions analogous to those introduced above. The additional term in Eq. 19 as compared with Eq. 17 accounts for the concentration of micellar SDS in the syringe, (see Eq. 3 in (21)). The latter is – CMC for solubilization but for reconstitution, where the syringe contains lipid vesicles rather than detergent micelles. Assuming ideal mixing also in the micellar phase gives

(20)

A corresponding equation holds for Owing to the highly curved, rough, and dynamic surfaces of micelles, the intrinsic partition coefficient of SDS between the interfacial aqueous and the micellar phases, cannot be derived from electrostatic theory as easily as In the present case, however, the value of the apparent partition coefficient, is virtually constant (see Results and Supplementary Material) and thus can be directly inserted into Eq. 20.

Coexistence range
In the coexistence range, we need to consider the partitioning of SDS between the aqueous phase, bilayers, and micelles as well as the transfer of lipid between the two surfactant aggregates. In analogy to Eqs. 17 and 19, the heats upon detergent or lipid injection, and respectively, read

(21)

Now, the equilibrium concentrations and are readily obtained from the definitions of and according to Eqs. 1 and 3, respectively, from two equations of mass balance, and and from This yields

(22)

Corresponding equations hold for and whereas is again given by – CMC for solubilization or by for reconstitution.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Light scattering
Solubilization of 100-nm-diameter POPC LUVs by SDS in aqueous solution (10 mM phosphate buffer, 154 mM NaCl, pH 7.4) was monitored by right-angle light scattering (19). Fig. 1 depicts the relative scattering intensities, I, of 0.1–2.5 mM lipid suspensions as a function of c_D at 25°C (A) and 65°C (B). The I values taken 3 min after addition of detergent revealed a striking difference between these two temperatures. Although SDS titration at 25°C led to a continuous decrease in I, the curves depicted in Fig. 1 A are rather featureless. By contrast, three ranges could be distinguished at 65°C, as shown in Fig. 1 B: I varied only little with c_D up to a first breakpoint (arrow), then decreased rapidly and nearly linearly, and finally almost vanished at a second breakpoint (arrow). Importantly, kinetic experiments (data not shown) revealed that I values taken at 65°C represented equilibrium situations, whereas an incubation time of 3 min after each detergent injection was too short to allow the mixture to attain equilibrium at 25°C. At the latter temperature, in fact, I continued to decrease for more than 24 h after the first injection (data not shown).

View larger version (12K): [in this window] [in a new window]   FIGURE 1  Solubilization as monitored by right-angle light scattering at 25°C (A, open symbols) and 65°C (B, solid symbols). Scattering intensity at a wavelength of 632.8 nm, I, versus SDS concentration, cD. Initial POPC LUV concentrations in the cuvette were 0.1 mM (squares), 0.2 mM (circles), 0.3 mM (up-triangles), 0.5 mM (down-triangles), 1.0 mM (diamonds), 1.5 mM (left triangles), 2.0 mM (right triangles), and 2.5 mM (pentagons, breakpoints indicated by arrows). I was registered 3 min after addition of SDS, which was sufficient to attain equilibrium at 65°C but not at 25°C.

View larger version (14K): [in this window] [in a new window]   FIGURE 2  Reconstitution as monitored by right-angle light scattering at 25°C (open symbols, near the ordinate) and 65°C (solid symbols). Scattering intensity at a wavelength of 632.8 nm, I, versus POPC concentration, cL. Initial SDS concentrations in the cuvette were 0 (squares), 1.0 mM (circles), 1.5 mM (up-triangles), 2.0 mM (down-triangles), 2.5 mM (diamonds), 5.0 mM (left triangles), 7.5 mM (right triangles), and 10 mM (pentagons, breakpoint indicated by arrow). I was registered 3 min after addition of POPC, which was sufficient to attain equilibrium at 65°C but not at 25°C.

View larger version (10K): [in this window] [in a new window]   FIGURE 3  ITC solubilization experiment at 65°C. Three-microliter aliquots of 50 mM SDS were titrated to 1.0 mM POPC LUVs. Only 60 out of 100 injections are shown. (A) Differential heating power, p, versus time, t. (B) Normalized heats of reaction, QD, versus SDS concentration in the cell, cD. Experimental data (circles) and simulation (solid line) according to Eqs. 17–22. b, b + m, and m denote the ranges where, in addition to the aqueous phase, only bilayers, bilayers and micelles in coexistence, and only micelles are present, respectively.

View larger version (11K): [in this window] [in a new window]   FIGURE 4  ITC reconstitution experiment at 65°C. Three-microliter aliquots of 20 mM POPC LUVs were titrated to 3.0 mM SDS. Only 60 out of 100 injections are shown. (A) Differential heating power, p, versus time, t. (B) Normalized heats of reaction, QL, versus POPC concentration in the cell, cL. Experimental data (circles) and simulation (solid line) according to Eqs. 17–22. The values m, b + m, and b denote the ranges where, in addition to the aqueous phase, only micelles, bilayers and micelles in coexistence, and only bilayers are present, respectively.

Phase diagram and partition coefficients
A simple phase diagram of dilute aqueous SDS/POPC systems at 65°C was obtained by plotting the critical c_D values versus the corresponding c_L values, as shown in Fig. 5. Linear regression according to Eq. 2 yields = 1.5 and = 0.9 mM, implying that POPC LUVs can incorporate up to 1.5 SDS molecules per lipid before solubilization commences at a free detergent concentration of 0.9 mM. Analogously, Eq. 4 gives = 2.7 and = 1.4 mM, suggesting that a micelle must contain at least 2.7 SDS molecules per POPC. Linear regression analysis under the constraint is virtually as good as that illustrated in Fig. 5, yielding = 1.1 mM, whereas and are hardly affected (data not shown). According to Eq. 5, the SDS mole fractions in coexisting bilayers and micelles amount to and respectively. The mol fraction partition coefficients of SDS and POPC between detergent-saturated bilayers and lipid-saturated micelles are given by Eq. 6 as, respectively, and Equation 7 finally provides the partition coefficients of SDS between the bulk aqueous phase and bilayers or micelles as and respectively.

View larger version (9K): [in this window] [in a new window]   FIGURE 5  Phase diagram of dilute aqueous SDS/POPC mixtures. Data were taken from solubilization (circles) and reconstitution (triangles) experiments conducted with light scattering (open symbols) and titration calorimetry (solid symbols). Linear regression analyses for the onset (solid line) and the completion (dashed line) of solubilization correspond to Eqs. 2 and 4, respectively, and separate the bilayer (b) and the micellar (m) areas from the transition range (b + m). Note that the aqueous phase is always present. cL and cD are the concentrations of POPC and SDS, respectively.

View larger version (7K): [in this window] [in a new window]   FIGURE 6  ITC partitioning experiment at 65°C. 10-µL aliquots of a mixture consisting of 1.5 mM SDS and 1.0 mM POPC LUVs were injected to SDS at different concentrations. (A) Differential heating power, p, of the respective third peak of five independent titrations into the calorimeter cell containing SDS at the concentrations indicated in the panel. (B) Normalized heats of reaction, QL+D, versus SDS concentration in the cell, cD. Experimental data (circles) and linear regression analysis (solid line).

In Fig. 7, more values thus determined for the partitioning of SDS into 1.0 mM POPC LUVs are plotted versus (circles). An increase in led to a steep drop in because of electrostatic repulsion of DS^– ions from the membrane surface. According to Eq. 2 and the phase diagram in Fig. 5, the sample at the highest SDS concentration investigated consisted of detergent-saturated vesicles. For this case, we determined an apparent partition coefficient of which equals the value determined from Eq. 7 for bilayers in the coexistence range (see preceding section). Table 1 provides an overview of all partition coefficients, molar transfer enthalpies, and other thermodynamic parameters derived from these.

View larger version (8K): [in this window] [in a new window]   FIGURE 7  Partition coefficient of SDS between the bulk aqueous phase and POPC bilayers, as a function of the total detergent concentration in the syringe, The concentration of POPC LUVs was Experimental data as given by Eq. 8 (circles) and theoretical predictions according to Eq. 11 and calculated either without considering counterion binding by using Eqs. 12 and 13 (dashed line) or upon including Na+ adsorption to DS– by using Eqs. 12 and 16 (solid line).

Simulation of ITC solubilization and reconstitution experiments
The simulations (solid lines) depicted in Figs. 3 B and 4 B are based on Eqs. 17–22. In the bilayer ranges, the and values were calculated from Eqs. 17 and 18 using (21). was again obtained from (21) with the aid of Eqs. 11, 12, and 16, thus taking into account counterion binding. For the solubilization experiment, we inserted which equals the total heat of micelle disintegration and dilution determined from the initial injections in demicellization experiments (see Supplementary Material). For the reconstitution assay, was taken as the negligible heat of vesicle dilution observed toward the end of uptake experiments (21).

In the micellar ranges, the and values were calculated from Eqs. 19 and 20 on the basis of as provided by demicellization experiments (see Supplementary Material). Because the apparent partition coefficient between the bulk aqueous and the micellar phases, only slightly decreases from 3.7 x 10⁴ to 3.4 x 10⁴ when going from lipid-saturated to pure detergent micelles (see Table 1), we used a constant value of For the solubilization assay, demicellization (see Supplementary Material) also yielded For the reconstitution experiment, the constant heat contribution was assumed to amount to Neglecting the small heat of vesicle dilution this value must correspond to the molar transfer enthalpy of POPC from bilayers into micelles, so that Note that this was the only quantity not determined independently and, during the entire simulation of calorimetric solubilization and reconstitution titrations, therefore constituted the only adjustable parameter.

In the coexistence ranges, the and values were derived from Eqs. 21 and 22, again using enthalpy changes of and and were derived from the phase diagram shown in Fig. 5. As above, applied to the solubilization assay, whereas was used for simulation of the reconstitution experiment.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Phase diagram and partition coefficients
The anionic surfactant SDS undergoes rapid transbilayer flip-flop at 65°C (19,21) but not at 25°C ((19,21,23,29), M. Apel-Paz, G. F. Doncel, and T. K. Vanderlick, unpublished). As becomes obvious from inspection of Figs. 1 and 2, this has tremendous consequences for the solubilization of lipid membranes by SDS. At room temperature, the slow kinetics of vesicle dissolution largely precludes a thorough evaluation comparable to that described for nonionic detergents (4–6,8–12) because the detergent/lipid systems cannot reach their equilibrium states on experimental timescales. This calls for a cautious use of SDS and other nonpermeant detergents in biochemical procedures normally performed at low temperatures, such as dissolution of biological membrane samples, extraction of membrane constituents, and crystallization of membrane proteins. As seen in Fig. 5, however, a clearcut phase diagram of dilute aqueous SDS/POPC mixtures is obtained at 65°C, implying that the rate of detergent flip-flop is a crucial determinant of lipid bilayer solubilization and reconstitution.

A solubilizing SDS/POPC ratio of is in reasonable agreement with reported by Tan et al. (19) for similar conditions (56°C, 10 mM Tris, 100 mM NaCl, pH 7.4). A saturating ratio of is also in line with the slope of versus c_L obtained by these authors from light scattering and ITC experiments at low c_L values, whereas a much shallower slope of is implied by light scattering and NMR studies at considerably higher c_L values (see Fig. 3 C in (19)). The low susceptibility of POPC membranes to SDS at 65°C in terms of high and values can be explained by the small size of the sulfate headgroup as well as the high degree of acyl-chain disorder and the moderate extent of headgroup hydration expected at such a high temperature. For a homologous series of oligo(ethylene oxide) dodecyl ether (C₁₂EO_n) detergents and POPC (11), the saturating detergent/lipid mol ratio at 25°C has been found to augment from for n = 8 to for n = 5. For C₁₂EO₈, in turn, this ratio increases from at 10°C to at 75°C. An SDS partition coefficient between bilayers and micelles of is also comparable to the corresponding values of nonionic detergents with small headgroups, as a decrease from for C₁₂EO₈ to for C₁₂EO₅ is observed at 25°C (11).

SDS solubilization of LUVs made up of the saturated lipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) at 60°C is characterized by and in pure water but by and in the presence of 100 mM NaCl (17). A similar broadening of the coexistence range upon raising the ionic strength has been unveiled for bile salts (13,14). The remaining discrepancies between DMPC and POPC are due to systematic differences between saturated and unsaturated phospholipids. While the SDS and POPC partition coefficients amount to and respectively, the corresponding values for SDS and DMPC in 100 mM NaCl at 60°C are and respectively (17). This indicates that the saturated lipid DMPC can more readily be transferred into the micellar state. This phenomenon has also been observed for bile salts and has been explained by the greater affinity of saturated, short-chain phospholipids to positively curved surfaces (13,14).

Electrostatics and counterion binding
SDS partition coefficients between the bulk aqueous phase and bilayers or micelles of, respectively, and are 1–2 orders of magnitude below the corresponding values reported for the above-mentioned C₁₂EO_n series (11) because DS^– ions, unlike nonionic detergents, are subject to electrostatic repulsion from the negatively charged vesicular and micellar surfaces (19). However, correcting for electrostatic effects yields a much higher value of (21) for membrane adsorption of SDS from the interfacial aqueous phase. As for many nonionic surfactants, partitioning of SDS into POPC bilayers then follows a linear correlation between the detergent's hydrocarbon chain length and the standard molar Gibbs free energy of membrane binding, (19).

As becomes apparent from Fig. 7, implementing Na⁺ binding to membrane-incorporated DS^– (solid line) allows for a much better reproduction of the experimental data (circles) at high c_D values than does the simpler approach neglecting counterion adsorption (dashed line). At detergent contents in the membrane of as used in our previous study (21), counterion binding amounts to < 3% and can thus be neglected. In fact, replacing Eq. 13 by Eq. 16 does not affect the evaluation of uptake and release experiments performed at (data not shown, see (21)). In conclusion, a combination of a surface partition equilibrium with simple electrostatic theory is well suited for characterizing the interactions of SDS with POPC membranes even at very high detergent contents, provided that counterion binding is taken into account appropriately.

ITC solubilization and reconstitution experiments
The reasons for the lack of quantitative information about the solubilization of lipid membranes by charged detergents are threefold. First, the concentration of free detergent monomers usually cannot be neglected, such that, besides bilayers and micelles, an additional phase has to be taken into account. Second, partition equilibria are established between surfactant aggregates (vesicles, micelles) and the aqueous phase adjacent to their surfaces rather than the bulk solution. In comparison with the bulk detergent concentration, the interfacial concentrations can be lowered by several orders of magnitude as a consequence of electrostatic repulsion. Third, this is further complicated by the binding of counterions to the headgroups of membrane-incorporated detergent ions.

As demonstrated in this work, a wealth of data gathered from the SDS/POPC phase diagram (Fig. 5) as well as from partitioning (Fig. 7), demicellization (see Supplementary Material), and a combination of uptake and release (21) studies makes possible a quantitative treatment of ITC solubilization (Fig. 3) and reconstitution (Fig. 4) experiments. Clearly, the general hallmarks of the Q_D and Q_L values shown in Figs. 3 B and 4 B, respectively, are reproduced by a simple quantitative treatment assuming ideal mixing in all phases. The deviations at low c_D values in the bilayer range of the solubilization experiment in Fig. 3 B were more pronounced at higher c_L values but disappeared at c_L 0.5 mM (data not shown), thus pointing to an endothermic process involving intervesicle contacts. As for nonionic detergents (10–12), systematic discrepancies such as those in the micellar range of the reconstitution experiment in Fig. 4 B might be accounted for by considering nonideal mixing or second-order transitions. However, in view of the approximations already inherent in the present model, any refinement necessitating additional free parameters seems of doubtful validity. Furthermore, the small size of the SDS headgroup and the low degree of hydration of both detergent and lipid headgroups at elevated temperature point to small, or even negligible, nonideality parameters (11). Finally, the fact that and of SDS/POPC systems at 65°C can be identified with the breakpoints (arrows) in the light scattering studies shown in Figs. 1 and 2 argues against a noticeable population of large intermediate structures, such as wormlike micelles (10,42). The latter have been observed for many nonionic detergents and may severely obscure interpretation of light scattering data in terms of <