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Additive Action of Two or More Solutes on Lipid Membranes Andreas Beck,† Alekos D. Tsamaloukas,‡ Petar Jurcevic,† and Heiko Heerklotz*,‡ Department of Biophysical Chemistry, Biozentrum of the UniVersity of Basel, CH-4056 Basel, Switzerland, and Leslie Dan Faculty of Pharmacy, UniVersity of Toronto, 144 College Street, Toronto, Ontario M5S 3M2, Canada ReceiVed March 4, 2008. ReVised Manuscript ReceiVed May 16, 2008 A wide variety of biological processes, pharmaceutical applications, and technical procedures is based on the combined action of two or more soluble compounds to perturb, permeabilize, or lyse biological membranes. Here we present a general model describing the additive action of solutes on the properties of membranes or micelles. The onset and completion of membrane solubilization induced by two surfactants (lauryl maltoside, with nonyl maltoside, octyl glucoside, or CHAPS, respectively) are very well described by our model on the basis of their individual partition coefficients, cmc’s, and critical mole ratios Resat and Resol as detected by isothermal titration calorimetry. This suggests that the thermodynamic phase transition is governed by a single parameter (e.g., spontaneous curvature) in spite of the complexity of structural changes. Such surfactant mixtures show unique features such as nonlinear solubilization boundaries and concentration-dependent effective partition coefficients. Other phenomena such as membrane leakage are predicted to obey additive action if the solutes act via the same mechanism (e.g., toroidal pore formation) but deviate from the model in the case of independent, synergistic, or antagonistic action.
1. Introduction Membrane changes induced by amphiphilic solutes are involved in a wide variety of biological processes and technical procedures. Host defense compounds from bacteria, animals, and plants such as amphiphilic peptides1 and saponins2 as well as surfactants in antimicrobial or spermicidal drugs or cosmetics3 permeabilize the membranes of target cells. Fatty acids, lysolipids, and other amphiphiles may interfere with membrane processes that depend on membrane spontaneous curvature, such as fusion and fission events4–6 or the activation of proteins.7,8 Penetration enhancers are aimed at facilitating the transport of pharmacologically active compounds across barriers.9 Many of these phenomena comprise contributions from different compounds that bind to the membrane from the aqueous phase. The applications of surfactants to isolate, purify, and study membrane proteins may also involve mixtures of surfactants and other amphiphiles, either used for improving the purification process10,11 or occurring transiently upon exchanging the original surfactant * To whom correspondence should be addressed. E-mail: heiko.heerklotz@ utoronto.ca. † Biozentrum of the University of Basel. ‡ University of Toronto. (1) Bechinger, B.; Lohner, K. Biochim. Biophys. ActasBiomembranes 2006, 1758(9), 1529–1539. (2) Francis, G.; Kerem, Z.; Makkar, H. P. S.; Becker, K. Br. J. Nutr. 2002, 88(6), 587–605. (3) Apel-Paz, M.; Doncel, G. F.; Vanderlick, T. K. Langmuir 2005, 21(22), 9843–9849. (4) McIntosh, T. J.; Kulkarni, K. G.; Simon, S. A. Biophys. J. 1999, 76(4), 2090–8. (5) Kozlovsky, Y.; Chernomordik, L. V.; Kozlov, M. M. Biophys. J. 2002, 83(5), 2634–2651. (6) Vogel, S. S.; Leikina, E. A.; Chernomordik, L. V. J. Biol. Chem. 1993, 268(34), 25764–8. (7) Davies, S. M.; Epand, R. M.; Kraayenhof, R.; Cornell, R. B. Biochemistry 2001, 40(35), 10522–31. (8) Epand, R. M.; Lester, D. S. Trends Pharmacol. Sci. 1990, 11(8), 317–20. (9) Williams, A. C.; Barry, B. W. AdV. Drug DeliVery ReV. 2004, 56(5), 603– 618. (10) Grisshammer, R.; White, J. F.; Trinh, L. B.; Shiloach, J. J. Struct. Funct. Genomics 2005, 6(2-3), 159–63. (11) Yeliseev, A. A.; Wong, K. K.; Soubias, O.; Gawrisch, K. Protein Sci. 2005, 14(10), 2638–53.
for another surfactant,12 amphipol,13 or lipopeptide surfactant14 for improving protein stability or suitability for a certain experimental technique. Our model applies to additive, solute-induced effects that occur at a specific solute-to-lipid mole ratio in the membrane, Re, regardless of the aqueous concentration of the solute. Potential examples are a characteristic membrane leakage,15–18 a specific degree of membrane disordering and curvature strain as recognized by a spectroscopic signal19,20 or in terms of a certain excess enthalpy,21,22 or membrane saturation by a surfactant, inducing the onset of membrane lysis or solubilization to micelles.23–25 Analogously, the model applies to micelles and predicts, for example, the minimum surfactant content in micelles denoted by the mole ratio Rsol e (corresponds to Re at the completion of membrane solubilization) or the lipid-induced sphere-to-rod transition. By assigning an effective lipid concentration to a cell suspension,26 the model could also become applicable to the threshold solute concentration for inducing fast lipid flip-flop in erythrocytes,26 hemolysis, or minimum inhibitory concentrations of drugs and biomolecules on cells. (12) Krepkiy, D.; Gawrisch, K.; Yeliseev, A. Protein Pept. Lett. 2007, 14(10), 1031–1037. (13) Diab, C.; Winnik, F. M.; Tribet, C. Langmuir 2007, 23(6), 3025–3035. (14) McGregor, C. L.; Chen, L.; Pomroy, N. C.; Hwang, P.; Go, S.; Chakrabartty, A.; Prive, G. G. Nat. Biotechnol. 2003, 21(2), 171–176. (15) De la Maza, A.; Parra, J. L. Biochem. J. 1994, 303(Pt 3), 907–14. (16) de la Maza, A.; Parra, J. L. Biochim. Biophys. Acta 1996, 1300(2), 125– 34. (17) De La Maza, A.; Parra, J. L.; Sanchez Leal, J. Langmuir 1992, 8(10), 2422–2426. (18) Heerklotz, H.; Seelig, J. Eur. Biophys. J. 2007, 36, 305–314. (19) Heerklotz, H.; Binder, H.; Lantzsch, G.; Klose, G. Biochim. Biophys. Acta 1994, 1196(2), 114–22. (20) Paternostre, M.; Meyer, O.; Grabielle-Madelmont, C.; Lesieur, S.; Ghanam, M.; Ollivon, M. Biophys. J. 1995, 69(6), 2476–88. (21) Epand, R. M.; Epand, R. F. Biophys. J. 1994, 66(5), 1450–6. (22) Heerklotz, H. H.; Binder, H.; Schmiedel, H. J. Phys. Chem. B 1998, 102(27), 5363–5368. (23) Heerklotz, H.; Szadkowska, H.; Anderson, T.; Seelig, J. J. Mol. Biol. 2003, 329(4), 793–9. (24) Lichtenberg, D. Biochim. Biophys. Acta 1985, 821(3), 470–8. (25) Lichtenberg, D.; Opatowski, E.; Kozlov, M. M. Biochim. Biophys. Acta 2000, 1508(1-2), 1–19. (26) Pantaler, E.; Kamp, D.; Haest, C. W. Biochim. Biophys. Acta 2000, 1509(1-2), 397–408.
10.1021/la800682q CCC: $40.75 2008 American Chemical Society Published on Web 07/22/2008
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The anesthetic action of combined narcotics has been known to be additive for more than a century.27 This case is even simpler than the one explained here because the active membrane contents, Rei, of virtually all small anesthetics are identical so that the partition coefficients alone govern their activity (Meyer-Overton rule). This implies (although it has been argued otherwise) that membrane partitioning plays a key role in anesthesia, regardless of whether it involves subsequent drug-protein interactions (see also ref 28). All these phenomena are well understood where binary solute-lipid mixtures are concerned or if multicomponent mixtures can be approximately described as pseudobinary ones. However, little is known about possible peculiarities of systems of two or more solutes interacting with a lipid membrane. We establish a general model for additive, solute-induced effects in systems comprising more than one solute. The solutes chosen here are surfactants that are widely used for membrane protein solubilization; lauryl maltoside (LM) and CHAPS are actually used in specifically designed and optimized mixtures for the isolation of native G protein coupled receptors (GPCRs).10,11 To validate our model, we performed solubilization and reconstitution experiments using ITC29–31 and considered spectroscopic, light scattering, electron microscopy, and other data from the literature.
2. Theory 2.1. Lipid-Surfactant Systems. All phenomena addressed here have in common that they depend on the content of a solute, S1 (concentration C1), in solute-lipid mixed aggregates (often, but not exclusively, membranes) but not on that of “ineffective” solute monomers in aqueous solution (concentration Caq 1 ). We, thus, define an “effective S1-to-lipid mole ratio”, Re1, as24
Re1 )
C1 - Caq 1 CL
(1)
(2)
This equation is generally valid but particularly useful if a set of samples is considered in which all members share the same Re-dependent phenomenon, implying that all exhibit the same Re as discussed in the Introduction. Let us, without restriction of generality, consider the Re value at the onset of membrane lysis (solubilization), which is commonly denoted Rsat e (for “saturation”). Identifying total concentrations, Csat 1 , that yield the same signal at different lipid concentrations, CL, renders Re aq,sat ) Rsat constants, and the e and the equilibrium value of C1 sat function C1 (CL) becomes linear: sat aq,sat Csat 1 (CL) ) Re1 CL + C1
K1 ≡
C1 - Caq 1 ) aq Caq C C 1 L 1 Re1
(3)
aq,sat with Rsat the intercept with the ordinate. e1 being the slope and C1 The relationship between Caq 1 and Re1 is given in terms of the
partition coefficient. Here it is suggested to distinguish between membranes and micelles. Membranes are often best described (27) Overton, C. E. Studien ueber die Narkose; Verlag Gustav Fischer: Jena, Germany, 1901. (28) Heimburg, T.; Jackson, A. D. Proc. Natl. Acad. Sci. U.S.A. 2005, 102(28), 9790–5. (29) Heerklotz, H. J. Phys.: Condens. Matter 2004, 16, R441–467. (30) Heerklotz, H.; Lantzsch, G.; Binder, H.; Klose, G.; Blume, A. Chem. Phys. Lett. 1995, 235, 517–520. (31) Heerklotz, H.; Seelig, J. Biochim. Biophys. Acta 2000, 1508(1-2), 69– 85.
(4)
Analogously to the saturation boundary and other membrane phenomena, the model applies also to effects in mixed micelles. For micelles, it is however superior to use a partition coefficient, Km 1 , based on the mole fraction of surfactant S1 in the micelle, Xe1, because this is also defined for pure surfactant micelles where Xe ) 1 but Re f ∞. With the general conversion rule for mole fractions to mole ratios, X ) R/(R + 1), we obtain (this equation applies to systems of only micelles and monomers)
Km 1 ≡
Xe1 Caq 1
)
Re1 (1 + Re1)Caq 1
≈
1 cmc1
(5)
The latter approximation is an equality if all components mix ideally within the micelle so that Km 1 is constant for mixed and aq pure surfactant (Xm 1 ) 1, C1 ) cmc1) micelles. 2.2. Additive Action Model of Multiple Solutes. The additive action of anesthetics has been proven by the fact that all combinations of concentrations of anesthetics 1 and 2, C1 and C2, that cause the same characteristic degree of anesthesia lie on a straight line when C1 is plotted versus C2.33,34 Denoting the intercepts with ordinate and abscissa (i.e., the active concentrations act of the individual compounds) Cact 1 and C2 , the equation for the straight line can be written as
C1 Cact 1
CL denotes the lipid concentration (all lipid is assumed to be localized in aggregates). Solving for the total concentration, C1, yields
C1 ) Re1CL + Caq 1
by a constant mole ratio partition coefficient, K1,31,32 defined in a system of only mixed membranes and aqueous solution as
+
C2 Cact 2
)1
(6)
That means the fractional degrees of anesthetic action of the two compounds are additive, so that for instance a mixture of two narcotics, both at half the active dose, should be active. If the effect of two surfactants, S1 and S2, to solubilize a membrane (the onset of solubilization is denoted “sat” for saturation) is just the sum of the effects of the individual surfactants, we may analogously write for a mixture of S1 and S2 that causes saturation
C2 + )1 Csat Csat 1 2 C1
(7)
Denoting the mole fraction of surfactant that is S1 with ξ1
ξ1 )
C1 C1 + C2
(8)
and analogously for ξ2 (so that ξ1 + ξ2 ) 1 if only these two surfactants are present) and dividing both sides of eq 7 by C1 + C2 yield
ξ1 ξ2 1 ) sat + sat sat [C1 + C2] C1 C2
(9)
The brackets with superscript “sat” indicate that this equation was derived for the case that the combined, additive action of C1 and C2 causes saturation. For more than two surfactants, we may write (32) Seelig, J.; Ganz, P. Biochemistry 1991, 30(38), 9354–9359. (33) Fang, Z.; Ionescu, P.; Chortkoff, B. S.; Kandel, L.; Sonner, J.; Laster, M. J.; Eger Ii, E. I. Anesth. Analg. 1997, 84(5), 1042–1048. (34) Kamaya, H.; Ueda, I.; Eyring, H. Proc. Natl. Acad. Sci. U.S.A. 1976, 73(6), 1868–1871.
AdditiVe Action of Solutes on Lipid Membranes
1
[∑ C ]
sat
)
Langmuir, Vol. 24, No. 16, 2008 8835
ξ
∑ Csati
(10)
i
i
Note that [∑Ci]sat < ∑Cisat because the left side refers to a mixture where all concentrations in the brackets together induce saturation, whereas the values of Cisat on the right side refer to concentrations of the individual surfactants, Si, alone that are sufficient for saturation. Equation 9 is not limited to lipid-containing systems as illustrated by the fact that the well-known formula for the cmc of mixed micelles derived by Lange35,36 and discussed also by Clint37,38
1 ) cmc
4. Results
ξ
∑ cmci i
(11)
turns out to describe a specific case of the additive action model representing the onset of micelle formation. 2.3. Specific Equations for Systems Containing Two Surfactants. Insertion of eq 2 into eq 9 and solving for [C1 + C2]sat yield
[C1 + C2]sat )
sat Rsat e1 (K1CL + 1)Re2 (K2CL + 1) sat ξ1K1Rsat e2 (K2CL + 1) + ξ2K2Re1 (K1CL + 1) (12)
Note that eq 12 simplifies to the linear form, eq 2, if the second surfactant is eliminated (ξ1 f 1, ξ2 f 0). The expression for micelles is obtained analogously to the derivation of eq 12 but using cmci according to eq 5 instead of Ki for membranes according to eq 4. Again, we use the superscript “sol” (referring to the completion of solubilization, i.e., the minimum surfactant content in mixed micelles), but the equation serves for modeling all characteristic values of Re in micelles:
(
Rsol e1 CL + [C1 + C2]sol )
(
ξ1Rsol e2 CL +
cmc1 1 + Rsol e1 cmc2
1 + Rsol e2
)
) (
concentration (usually 1, 5, or 10 mM). The syringe was loaded with 0.3 mL of a micellar solution of LM, NM, OG, or CHAPS alone or with a binary mixture of LM with one of the other surfactants (typically around 80 mM total). For the reconstitution assay, the cell was loaded with a micellar surfactant solution (2, 3.5, or 7 mM) and titrated with lipid vesicles (typically 30-60 mM). All solutions were degassed before filling. The temperature of the ITC cell was kept constant by a power compensation feedback at 25 °C. To resolve low- and high-concentration effects with one or a few runs, the volume of injected aliquots was gradually increased from 2.9 to 26.5 µL during a titration. After each injection, the heat power of reaction was recorded for 40 min to ensure re-equilibration of the system.
Rsol e2 CL +
(
+ ξ2Rsol e1
cmc2
)
1 + Rsol e2 cmc1 CL + 1 + Rsol e1 (13)
)
3. Experimental Section 3.1. Materials. n-Dodecyl β-D-maltopyranoside (abbreviated lauryl maltoside, LM), n-nonyl β-D-maltopyranoside (NM), and CHAPS were obtained from Anatrace (Maumee, OH), whereas n-octyl β-D-glucopyranoside (OG) was obtained from Fluka (Buchs, CH). All surfactants were more than 99% pure and used without further purification. The lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) was purchased from Avanti Polar Lipids (Alabaster, AL). The dry lipid was suspended in 100 mM NaCl, 10 mM Tris buffer at pH 7.4 by gentle vortexing. Large unilamellar vesicles (LUVs) were prepared by five freeze/thaw cycles followed by extrusion through a Nucleopore polycarbonate filter (pore size 100 nm) at 20 °C in a Lipex extruder (Northern Lipids, Vancouver, Canada). 3.2. ITC. ITC experiments were performed on VP ITC and OMEGA calorimeters from MicroCal (Northampton, MA). The solubilization and reconstitution experiments done in this study are described elsewhere.29–31,39 Briefly, for the solubilization assay, the cell (∼1.4 mL) was filled with a vesicle solution of a given POPC (35) Lange, H. Kolloid Z. Z. Polym. 1953, 131(2), 96–103. (36) Lange, H.; Beck, K. H. Kolloid Z. Z. Polym. 1973, 251(6), 424–431. (37) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71(6), 1327–1334. (38) Clint, J. H. Surfactant Aggregation; Blackie & Son: Glasgow, Scotland, 1992.
4.1. Experimental Detection of Phase Boundaries in Binary and Ternary Systems. Figure 1A shows a typical ITC solubilization experiment as obtained upon titration of a micellar LM-CHAPS mixture (1:1 (mol/mol), C1 + C2 ) 70 mM) into a 5 mM POPC vesicle suspension. Each injection causes a peak of the compensation heat power, which is positive to compensate for an endothermic response of the system to an injection or negative (relative to the technically adjusted baseline) to compensate for exothermic effects. The peaks were integrated and normalized with respect to the mole number of surfactant injected to yield the heats, Q, shown as the violet curve in Figure 1B. The abscissa is the surfactant concentration reached in the cell after a given injection. The titration curves for the ternary system show the typical behavior described already for binary lipid-surfactant systems.30,39–41 Let us consider the violet curve for the LM-CHAPS mixture as an example. In the beginning of the titration, injected micelles disintegrate, and most of the surfactant is incorporated into the membranes: this transfer is endothermic. At C1 + C2 ) [C1 + C2]sat ) 2.3 mM, the titration reaches the saturation phase boundary to the lamellar-micellar coexistence range and solubilization starts to proceed. The corresponding normalized heats of titration are exothermic and largely constant. At [C1 + C2]sol ) 5.0 mM, solubilization is completed and the heat of titration changes its sign again. At this stage of the titration, the injections have displaced some of the preloaded lipid so that CL ) 4.6 mM. The system enters the exclusively micellar range, and a broad, endothermic transition from (lipid-rich) rodlike micelles to spherical micelles is seen.39 The violet arrow in Figure 1C illustrates the variation of the composition of the sample during this experiment in the phase diagram as established below. The local minimum of the LM solubilization curve within the exclusively lamellar range (∼1 mM; see Figure 1B) was reported before and explained in terms of the onset of membrane permeation by the surfactant;42 similar phenomena were also described for other amphiphiles.43,44 It should be noted that ITC not only detects the boundaries, saturation and solubilization, with unmatched precision but also provides information on the enthalpies and entropies of transfer of the surfactants and lipid between micelles and bilayers, as well as excess enthalpies of nonideal mixing within the membrane. Such information was discussed for single-surfactant systems with different complexities (e.g., with monomers being negligible or not) in a number of publications.39,45,46 We have not pursued such a detailed (39) Heerklotz, H.; Lantzsch, G.; Binder, H.; Klose, G.; Blume, A. J. Phys. Chem. 1996, 100(16), 6764–6774. (40) Wenk, M. R.; Seelig, J. J. Phys. Chem. B 1997, 101(26), 5224–5231. (41) Heerklotz, H.; Epand, R. M. Biophys. J. 2001, 80(1), 271–9. (42) Heerklotz, H. Biophys. J. 2001, 81(1), 184–95. (43) Hildebrand, A.; Neubert, R.; Garidel, P.; Blume, A. Langmuir 2002, 18(7), 2836–2847. (44) Binder, H.; Lindblom, G. Biophys. J. 2003, 85(2), 982–95.
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Figure 1. ITC solubilization experiment. (A) Compensation heat power as a function of time in the course of a titration of gradually increasing volumes (2.9-26.5 µL) of a micellar LM-CHAPS dispersion (1:1 (mol/ mol), 70 mM total) into a POPC vesicle suspension (5 mM). Each injection causes a peak that is integrated from the baseline (red dotted line) and normalized to yield the violet, solid up triangles in (B). Additionally, (B) shows experimental data obtained with either LM (blue pentagons) or CHAPS (red, down triangles). (C) represents the contribution of this experiment (violet triangles) to constructing the phase diagram in Figure 3 (left panels); the boundaries (gray lines) are established later in Figure 3 but shown here already to guide the eye. The concentrations during the titration are marked by a violet arrow.
interpretation here to avoid distracting the reader from the purpose of the study. Figure 2 shows an example of a reconstitution experiment titrating lipid vesicles into a mixed micellar dispersion of 3.5 mM CHAPS-LM (1:1, mol/mol). The arrow marking the changes in the sample composition in the course of the titration (Figure 2B) illustrates that this titration crosses the phase boundaries in the opposite order. (45) Heerklotz, H. H.; Binder, H.; Schmiedel, H. J. Phys. Chem. B 1998, 102(27), 5363–5368. (46) Keller, S.; Heerklotz, H.; Jahnke, N.; Blume, A. Biophys. J. 2006, 90(12), 4509–21. (47) Heerklotz, H.; Seelig, J. Biophys. J. 2000, 78(5), 2435–40. (48) de la Maza, A.; Parra, J. L. Biophys. J. 1997, 72(4), 1668–75.
Beck et al.
Figure 2. Result of an ITC reconstitution experiment titrating a micellar suspension of CHAPS and LM, 1:1 (mol/mol), total 3.5 mM, with POPC vesicles (60 mM) at 25 °C. Panel A shows the normalized heats of titration versus the lipid concentration in the cell and indicates the break points accompanying the crossing of the solubilization and saturation boundaries. Panel B shows the coordinates of these saturation and solubilization points in the phase diagram and illustrates the compositions reached during the titration by a violet arrow; the phase boundaries (gray lines) are established in Figure 3 and shown here to guide the eye only.
Figure 2A displays the integrated and normalized heats of this experiment. At the beginning of the titration, the injected lipid vesicles are completely solubilized and the lipid is taken up into the micelles. At a certain lipid content, the micelles convert from a spherical to a rodlike structure, which accounts for the exothermic heats measured. This transition has a midpoint at CL ) 0.5 mM and is completed at CL ) 1.1 mM. At Csol L ) 2.8 mM, the system crosses the phase boundary to the micelle-bilayer coexistence range where the surfactant and previously solubilized lipid are reconstituted into membranes. The boundary corresponding to the completion of reconstitution centered at Csat L ) 5.9 mM is somewhat broadened, probably due (49) Anatrace Catalogue; Anatrace, Inc.: Maumee, OH, 2004. (50) Viriyaroj, A.; Kashiwagi, H.; Ueno, M. Chem. Pharm. Bull. 2005, 53(9), 1140–1146. (51) Schurholz, T. Biophys. Chem. 1996, 58(1-2), 87–96. (52) Stark, R. E.; Leff, P. D.; Milheim, S. G.; Kropf, A. J. Phys. Chem. 1984, 88(24), 6063–6067. (53) Walter, A.; Kuehl, G.; Barnes, K.; VanderWaerdt, G. Biochim. Biophys. Acta 2000, 1508(1-2), 20–33. (54) Ueno, M. Biochemistry 1989, 28(13), 5631–4. (55) Opatowski, E.; Kozlov, M. M.; Lichtenberg, D. Biophys. J. 1997, 73(3), 1448–1457. (56) Keller, M.; Kerth, A.; Blume, A. Biochim. Biophys. Acta 1997, 1326(2), 178–92.
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Figure 3. Comparison of experimental data (symbols) and model curves (lines) of phase boundaries as a function of the lipid concentration, CL. Binary surfactant-lipid systems are denoted by open symbols and thin solid lines, ternary surfactant-surfactant-lipid systems by solid symbols and bold lines. The three columns correspond to LM-CHAPS (left), LM-OG (middle), and LM-NM (right), and the two rows show the complete solubilization (SOL; top) and saturation (SAT; bottom) boundaries, thus separating the two boundaries of each phase diagram (see Figures 1C and 2B) into two panels for the sake of clarity. Mixtures of 1:1 (mol/mol) ratio are denoted by solid triangles (LM-CHAPS), squares (LM-OG), and pentagons (LM-NM); solid stars refer to a 3:1 (mol/mol) mixture of NM-LM. The lines are obtained according to eqs 12 (bottom row) and 13 (top row) with the parameters listed in Table 1. Right-pointing triangles correspond to reconstitution assays (LM-CHAPS, 1:1); all other data arise from solubilization assays. Table 1. Fit Parameters Corresponding to the Model Curves in Figure 3a K (mM-1) LM NM CHAPS OG
Resat
6 ( 2 (5, 8-19 ) 0.1 0.06 (0.07 at Rb ≈ 0.1,50 0.6,47,b 0.4-0.551) 0.08 (0.08-0.120,53–56) 47
48
Resol
cmc (mM)
0.7 ( 0.3 (0.9, 0.73-0.88 ) 0.48 0.11 (0.1/0.21,50,b 0.77-1.551)
1.44 ( 0.04 1.45 0.5 (0.550)
0.23 ( 0.01 (0.1749) 9.1 (649) 4.4 (8,49 3/1152,b)
1.28 (1.4-1.7,53 1.3,20 1.655,56)
2.2 (2.4-3.1,53 3.8,20 3.155,56)
25 (1849)
48
42
a
The data for LM varied within the given range in global fits of the different mixtures. Literature data are shown in parentheses for a rough comparison (source data may differ in lipid species, temperature within 20-28 °C, salt/buffer, etc.). b A detailed discussion of the values for CHAPS in section 5.4 explains at least part of the apparent discrepancies observed here.
to the occurrence of intermediate structures of surfactant-saturated membranes, such as perforated bilayer sheets. Subsequent injections induce nothing but a redistribution of the surfactant over more vesicles and some additional uptake of surfactant monomers into membranes. The coordinates of the break points, CLsol and CLsat, of this experiment (Figure 2B) and many other solubilization and reconstitution experiments are compiled in the left panels of Figure 3. In contrast to a common phase diagram (e.g., Figures 1C and 2B), the solubilization and saturation boundaries are shown in different plot windows (top and bottom, respectively) for the sake of clarity. The points obtained by solubilization (up triangles) as well as reconstitution assays (right-pointing triangles, reminiscent of the arrow in Figure 2B) lie on smooth saturation and solubilization lines (the lines shown correspond to the model; see the next section). The agreement of the phase boundaries observed upon crossing them in different directions establishes
that equilibrium is reached during the ITC experiments. The phase boundaries of the LM-CHAPS mixture lie between those of the pure LM and CHAPS micelles, respectively (see the blue and red curves in Figure 1B). Symbols in the middle and right panels of Figure 3 show experimental results for the position of the phase boundaries of LM, OG, and NM and mixtures of LM (as one component, S1) with solute S2, being either OG or NM, interacting with POPC at different concentrations, CL. 4.2. Validating the Model. Figure 3 compares experimental data (symbols) with simulated or fitted curves based on our model, as obtained according to the following strategies. Strategy 1 is to fit the individual boundaries of the pure systems and use the corresponding fit parameters for predicting the behavior of the mixture. Let us consider the bottom left panel of Figure 3, which shows the onset of solubilization (saturation boundary) for LM, CHAPS, and a 1:1 (mol/mol) mixture of the two. A linear regression to the LM data (blue open pentagons,
8838 Langmuir, Vol. 24, No. 16, 2008
choosing LM ) S1) yields a slope of Rsat e1 ) 0.67 and an intercept -1 of Rsat e1 /K1 ) 0.18 mM corresponding to K1 ) 4 mM . For CHAPS -1. These four (S2), we obtain Rsat ) 0.10 and K ) 0.06 mM e2 2 parameters are the only unknowns in eq 12 so that we can directly calculate the predicted boundary for a 1:1 mixture (ξ1 ) ξ2 ) 0.5) as illustrated by the bold, violet solid line shown in the figure. Since in this approach, the curve for the mixed system is not fitted but fully predicted from independent parameters, each individual data point measured by a solubilization or reconstitution assay for the mixture (solid violet triangles) provides an independent test for the model. The agreement is excellent. This strategy illustrates that all information needed to predict the behavior of the mixture is contained already in the data of the individual surfactants. It suffers, however, from the drawback that the measurements for mixtures are not considered to improve the precision of the fit parameters. Strategy 2 resolves this problem by fitting the four parameters of our model, eqs 12 and 13, globally to all data points within each panel of Figure 3 (bold solid curves). We have, in the following, pursued this strategy since it provides the most precise values of the parameters; the fit curves for the saturation boundaries of LM-CHAPS are virtually identical with those obtained by strategy 1. In all six panels, we obtained a consistent global fit in terms of parameters (see Table 1) that are in line with literature data (only for the solution boundary of LM-CHAPS, we constrained the cmc of LM to 0.24 mM; a free (but not substantially better) global fit would have yielded 0.5 mM). The fact that all curves can be fitted with only four parameters per panel provides strong evidence for the applicability of the model (see the next section). The parameters corresponding to the fit lines in Figure 3 are summarized in Table 1. The fit parameters agree well with most comparable literature data as indicated in parentheses in Table 1. Some at least apparent ambiguities exist for CHAPS in the literature; a more detailed discussion in section 5.4 suggests that the apparent discrepancies in the data can at least largely be explained in terms of the very complex behavior of CHAPS.
5. Discussion 5.1. Additive Action. There are at least two principal applications of the new model: (i) to test whether two or more solutes act additively, independently, or show a mutual enhancement or attenuation of their effects on a certain membrane or micelle property and (ii) to describe and predict the behavior of systems that were shown or can be assumed to obey additive action. For the systems studied here, the phase boundaries of the membrane-to-micelle transition induced by two surfactants could be well described in terms of additive action. This might be surprising considering the variety of structural states and phenomena that may be involved in membrane solubilization, such as vesicles, perforated vesicles, bilayer sheets and discs, interconnected and free threadlike micelles, and so on.57–59 However, a “phase” is a well-defined, thermodynamic term (it has to obey, for example, the Gibbs phase rule), and not all different structures behave approximately as separate phases; only those with different principal topologies are likely to do so. For membrane solubilization all the types of local interfacial topologies are grouped into either the lamellar or the micellelike (with high local interfacial curvature) pseudophase, but it (57) Almgren, M. Biochim. Biophys. Acta 2000, 1508(1-2), 146–63. (58) Kragh-Hansen, U.; le Maire, M.; Moller, J. V. Biophys. J. 1998, 75(6), 2932–46. (59) Walter, A.; Vinson, P. K.; Kaplun, A.; Talmon, Y. Biophys. J. 1991, 60(6), 1315–1325.
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is not straightforward to assign structures to phases. For example, the extensive formation of surfactant-lined perforations or edges of a lamella may already be part of the phase transition (molecules are converted from a lamellar to a locally curved interface), althoughnoindividualmicellesareformedyet.60 Alamella-micelle phase transition in a binary system can be recognized by a constant aqueous concentration (i.e., a virtually perpendicular increase of the binding isotherm),19,50,58 constant local compositions of the phases, linear changes of most aggregate properties with Re, and an essentially constant heat of titration in ITC solubilization and reconstitution experiments. True phase boundaries cause sudden changes of the titration heats (found experimentally to a better or worse approximation). Hence, calorimetry fails to provide explicit information on aggregate structure, but it is superior to other techniques for the detection of phase boundaries. Our result is in accord with the hypothesis that phase behavior is essentially governed by a single physical parameter, such as the effective spontaneous curvature61,62 or effective packing parameter.63 This is what accounts for additive action: Both surfactants act by the same mechanism, by increasing the spontaneous curvature. We have tested the model for surfactants spanning a broad range in Rsat e and K, including a steroid-type one (CHAPS) which might act somehow differently from the head-and-tail surfactants and one with a very large Rsat e (OG) where detergent-detergent contacts in the membrane become abundant and challenge the constancy of K (even when based on mole ratios). The fact that the model fits all these systems quite well may be taken as a hint that it is quite robust and should apply to a good approximation to the saturation and solubilization boundaries of most nonionic surfactants and at varying temperature, in spite of some nonideal mixing. Critical might be combinations of extremely weak surfactants such as C12EO5 and OG or maybe ionic surfactants at low salt. The model should also fail for membranes demixing into coexisting domains. Strong deviations from additive action are to be expected for membrane phenomena that can arise from different, independent mechanisms. This may apply, for example, to solute-induced membrane leakage, an effect that is of high biomedical and technical interest. Leakage can, for example, be caused by (i) the formation of a toroidal pore with the curved edge stabilized by the solute (for surfactants, analogously to Figure 9A of ref 58), (ii) the asymmetric expansion of the bilayer by solutes inserting exclusively into the outer leaflet (bilayer couple mechanism,18,42), or (iii) the formation of channel-like oligomers (including “barrel staves”) of the solute.64,65 One may speculate that two solutes acting by the same mechanism (particularly (i) or (ii)) act additively and obey, approximately, the model derived here. Two compounds acting by different mechanisms (or that act as oligomers (iii) but do not co-oligomerize to channels) will show partially independent (nonadditive) action, and the threshold concentration of the mixture will be higher than predicted by the model. Further to independent action, a solute reducing the membrane stiffness or enhancing flip-flop between the leaflets can also tend to inhibit the leakage induced by another one acting according to the bilayer-couple effect. A mutual attenuation or (60) Kadi, M.; Hansson, P.; Almgren, M. J. Phys. Chem. B 2004, 108(22), 7344–7351. (61) Andelman, D.; Kozlov, M. M.; Helfrich, W. Europhys. Lett. 1994, 25(3), 231–236. (62) Helfrich, W. Z. Naturforsch., C: J. Biosci. 1973, 28(11-1), 693–703. (63) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. (64) Matsuzaki, K.; Murase, O.; Fujii, N.; Miyajima, K. Biochemistry 1996, 35(35), 11361–8. (65) Pokorny, A.; Almeida, P. F. F. Biochemistry 2004, 43(27), 8846–8857.
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at low CL (where significant parts of both surfactants are dissolved in water) toward the lower Ki at higher CL, where the surfactant with the higher Ki is almost completely membrane-bound. Generalizing the usual definition for Rsat e to include all surfactants
Rsat e )
Figure 4. Illustration of the implications of the additive action model. Whereas Resat (top panel) and K (bottom panel) for a single surfactant (blue for S1 and red for S2) are constants, effective values for mixtures (violet for a 1:1, mol/mol, mixture of S1 and S2, other ratios in the bottom panel as labeled) are dependent on the lipid concentration. The phase boundaries are nonlinear (see Figures 1C, 2B, and 3), and their slope, d[C1 + C2]sat/dCL, as represented by the dotted curve in the top panel is no longer identical with the effective Re. The curves shown here are calculated on the basis of the parameters for LM (blue, S1) and CHAPS (red, S2), but extrapolated, for the sake of the argument, to concentrations where the model could not be tested.
enhancement of the activities of two solutes can also arise from one changing the membrane-water partition coefficient of the other. Summarizing, the additive action model provides an approach to test whether different solutes act by the same or different mechanisms. The model can be useful for detecting and understanding enhancing or inhibitory effects of compounds on antimicrobial, hemolytic, or other membrane-related effects of biomolecules or drugs. 5.2. Unique Properties of Surfactant Mixtures. The data and model obtained here reveal the fundamentally different properties of surfactant mixtures in membrane solubilization compared to those of single-surfactant systems. Figure 3 illustrates the special features of surfactant mixtures as predicted by our model. The phase boundaries (Figures 1C, 2B, and 3) become nonlinear at low concentrations, where KiCL is not .1 for both surfactants Si. The apparent partition coefficient (Figure 4, bottom)
Kapp )
∑ (Ci - Ciaq) CL ∑ Ciaq
(14)
becomes strongly dependent on the lipid concentration, ranging from a weighted average of the individual partition coefficients
[∑ (C - C )] i
CL
aq sat i
(15)
yields an effective Rsat e that is no longer a constant but depends on the lipid concentration (see the violet line in Figure 4, top). It is no longer true (as for single-surfactant systems) that Rsat e is just the slope of the phase boundary (dotted line in Figure 4, top). This is realized to a good approximation only for very high CL, where virtually all surfactant, S1 and S2, is membranebound. De la Maza and Parra studied equimolar mixtures of Triton and SDS16 and found values of Rsat e ) 0.87 and Re(50% dequenching) ) 0.19, which are just average values between those for Triton15 and SDS17 alone and which are virtually constant at CL ) 1-5 mM as indicated by linear relationships between [C1 + C2]* and CL. This is in line with our model but represents the special case that the (apparent) partition coefficients of both surfactants are virtually identical (∼4 mM-1, converted to the definition used here). As illustrated by Figure 3, this is not true for mixtures of solutes with substantially different partition coefficients. In the latter case, plots of C1 + C2 (characteristic dequenching) versus CL might become nonlinear (in a certain range of CL). One should be aware of these phenomena when more than one surfactant is present in the process of isolation, purification, and study of a membrane protein. Commercial surfactant brands (such as Triton, Lubrol, and Tween) as well as surfactant-like compounds from biological sources are often mixtures of structurally somewhat diverse compounds. Although they can often be described analogously to pure compounds at least within a given concentration range, the model illustrates that and how such systems might show, for example, variable apparent partition coefficients at particularly low or high effective lipid concentration. 5.3. Alternative Models. We should note that there are other models describing lipid-surfactant systems which could, at least in principle, be extended to account for the case of two or more solutes acting additively on a membrane. Andelman et al.61 have described solubilization in terms of the spontaneous curvature of the membrane constituents and elastic properties of the membrane. Another multicomponent model based on chemical potentials of transfer among water, membranes, and micelles was applied to systems of two lipids and one surfactant to study surfactant-induced changes in membrane domains and surfactant resistance.66 However, an advantage of the model established here is its general applicability to all effects of additive action that are connected to a certain membrane/aggregate composition, regardless of the specific structural or functional phenomenon of interest and the kind of solute considered. It is much simpler to handle; it yields a simple analytical formula rather than requiring extensive numerical optimization. Finally, the input parameters, the threshold Re, and the partition coefficient, K, for each solute are often known or are easy to measure with a variety of techniques.As soon as this is warranted by experimental data deviating from the additive action model, it can be extended to consider synergistic or antagonistic effects between the solutes. (66) Keller, S.; Tsamaloukas, A.; Heerklotz, H. J. Am. Chem. Soc. 2005, 127(32), 11469–11476.
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5.4. Complex Behavior of CHAPS. The fact that the published data on CHAPS seem inconsistent with each other (Table 1) could essentially be explained by an unusually complex phase and partitioning behavior. The partitioning isotherm into egg yolk phosphatidylcholine published by Ueno and coworkers50 is essentially linear up to Re ≈ 0.09 and Caq 1 ≈ 1.5 mM, corresponding to K ) 0.06 mM-1. There, a sudden increase of the aggregate-bound concentration, Xe, at virtually constant Caq 1 and a steep increase of turbidity indicate the onset of a pseudophase transition; electron micrographs show a coexistence of perforated vesicles and small particles described as very small vesicles, SUV*. These findings are in precise agreement with K and Rsat e obtained here. The isotherm then levels off to a moderate slope until a second, even more pronounced sudden increase (transition) starts at Xe ≈ 0.17 (Re ≈ 0.2) and Caq 1 ≈ 2.0 mM, corresponding to a much larger K of ∼0.1 mM-1. The authors refer to this transition as the onset of solubilization since they found the typical wormlike micelles above this surfactant content. Our thermodynamic data imply a continuous lamellar-to-micellar phase transition that starts already at Rsat e ) 0.1 and comprises both sequential structural transitions revealed by other methods (see also section 5.1 on the relationship between thermodynamic boundaries and structural changes). Another complication for CHAPS compared to most other surfactants seems to be the relevance of premicellar aggregates. Stark et al.52 report a cmc of 11 mM but dimers to appear already at 3-4 mM. The “extrapolated cmc of pure CHAPS” as obtained by our model, 4.4 mM (Table 1), and the very low value of the sat aqueous concentration at the onset of solubilization, Caq, ) 1 sat Re /K ) 1.7 mM (typically, this value is only slightly below the cmc), imply that the aqueous CHAPS is at least partially dimerized upon solubilization. Since the dimerization screens much of the hydrophobic surface of the molecule, dimerization must reduce the effective membrane/water partition coefficient greatly compared to that of the partitioning of true monomers at lower concentration. Indeed, some (but not all) partition measurements
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well below saturation have yielded much higher partition coefficients.
6. Conclusions (1) We have introduced an “additive action model” for multiple solutes partitioning into membranes and affecting membrane properties. “Additive action” of two solutes suggests that they act via the same mechanism and show no mutual effects on their membrane partitioning. The phase boundaries corresponding to the onset and completion of membrane solubilization by several surfactant mixtures were found to agree with the prediction of the model. (2) The model also describes the additive action of solutes on other membrane (or micelle) properties, such as leakage, changes in geometry, order/dynamics, and curvature strain, or micellar transitions. It will thus be useful for identifying different mechanisms of, e.g., leakage, and for detecting and understanding synergistic or antagonistic effects of solutes on membrane changes induced by biomolecules and drugs. (3) In contrast to a pseudobinary lipid-surfactant system, ternary surfactant-surfactant-lipid systems exhibit nonlinear phase boundaries, variable compositions of membranes and micelles in the coexistence range, and apparent values of the partition coefficient and the critical membrane compositions, sol Rsat e and Re , that vary as a function of the lipid concentration. This must be taken into account when one works with surfactant mixtures or in complex systems. Acknowledgment. We thank Gil Prive´, University of Toronto, Joachim Seelig, Biozentrum Basel, Sandro Keller, FMP Berlin, and Thomas Heimburg, University of Copenhagen, for important comments on the manuscript. H.H. acknowledges financial support from the Swiss National Science Foundation (SNF; Grant 3100-067216) and the Natural Sciences and Engineering Research Council of Canada (NSERC). LA800682Q
