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Membranes of Palmitoyloleoylphosphatidylcholine and C12E4sA Lattice Model Simulation Gotthard Klose Institut fu¨ r Experimentelle Physik I, BIM, Fakulta¨ t fu¨ r Physik und Geowissenschaften, Universita¨ t Leipzig, Linne´ strasse 5, D-04103 Leipzig, Germany
Yehudi K. Levine* Section for Computational Biophysics, Debye Institute, Buys Ballot Laboratory, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands Received April 2, 1999. In Final Form: September 7, 1999
The structure of the lamellar phase of the ternary system of palmitoyloleoylphosphatidylcholine (POPC)/ tetra(ethylene oxide) monododecyl ether (C12E4) has been characterized in detail by a X-ray and neutron scattering and by 2H NMR spectroscopy. The addition of small amounts of surfactant to the POPC bilayers causes the bilayer to become more rigid, while the addition of large amounts of surfactants induces a fluidization of the structure. Here, we report a Monte Carlo study of the underlying mechanisms yielding these changes in the orientational order of POPC/C12E4 bilayers. The study employs a lattice Monte Carlo dynamics algorithm that rests on the assumption that the conformational dynamics of chain molecules can be described as the superposition of local structural rearrangements involving short-chain segments. This approach is particularly useful for following structural and conformational changes on time scales longer than those associated with the gauche/trans isomerization of hydrocarbon chains. The simulations reproduce the principal features of the order parameter profiles of the surfactant molecules found in pure bilayers and bilayers of POPC/C12E4 mixtures and provide a physical framework for understanding the experimental observations.
Introduction Lipid/nonionic surfactant mixtures are used in membrane biochemistry as a tool for membrane solubilization,1,2 disruption of bilayers, protein extraction,3,4 and reconstitution.5 However, they form convenient model systems for studying fundamental properties such as the interrelation of hydration,6 structural,7,8 and dynamic properties9 in complex systems. The structure of the lamellar phase of the ternary system of palmitoyl-oleoyl-phosphatidylcholine (POPC)/tetra(ethylene oxide) mono dodecyl ether (C12E4) has been characterized in detail by X-ray and neutron scattering6,7 and by 2H NMR spectroscopy.10 It appears that the addition of small amounts of surfactant to the POPC bilayers causes the bilayer to become more rigid, while the addition of large amounts of surfactants induces a fluidization of the structure. In particular, it was found that the C-D bond order parameter profiles along the palmitoyl chains of * Corresponding author. E-mail:
[email protected]. Fax: +31 30 2532363. (1) Heerklotz, H.; Binder, H.; Lantzsch, G.; Klose, G. J. Phys. Chem. B 1997, 101, 639. (2) Moller, J. V.; Le Mair, M.; Andersen J. P. In Progress in ProteinLipid Interactions; Elsevier: Amsterdam, 1986; Vol. 1. (3) Levy, D.; Gulik, A.; Seigneuret, M.; Rigaud, J. L. Biochemistry 1990, 29, 9480. (4) Paternostre, M. T.;Roux, M.; Rigaud, J. L. Biochemistry 1988, 27, 2668. (5) Kra¨mer, R. Biochim. Biophys. Acta 1994, 1185, 1. (6) Ko¨nig, B.; Dietrich, U.; Klose, G. Langmuir 1997, 13, 525. (7) Klose, G.; Islamov, A.; Ko¨nig, B.; Cherezov, V. Langmuir 1996, 12, 409. (8) Struppe, J.; Noack, F.; Klose, G. Z. Naturforsch. 1997, 52a, 681. (9) Baekmark, T. R.; Pedersen, S.; Jørgensen, K.; Mouritsen, O. G. Biophys. J. 1997, 73, 1479. (10) Klose, G.; Ma¨dler, B.; Scha¨fer, H.; Schneider, K.-P. J. Phys. Chem. 1999, 103, 3022.
the POPC molecules in bilayers of pure lipid and 5:1 lipid/ surfactant mixtures are almost the same. However, lower order parameters were found in bilayers of 1:1 mixtures. In marked contrast, the order parameters of the C-D bonds of the surfactant alkyl chains were found to be higher in the mixtures than in the pure surfactant bilayers. Interestingly, the order parameters of the tetra(ethylene oxide) groups were lower in the mixtures than in the pure surfactant bilayers. To gain further insight into the underlying mechanisms yielding these changes in the orientational order of POPC/ C12E4 bilayers, we have undertaken a Monte Carlo study of the systems. To this end we employed a lattice Monte Carlo dynamics algorithm.11,12 We have previously shown that this simulation method reproduces the principal structural features of lipid bilayers13 above the phase transition of the chains as well as the rotational behavior of elongated probe molecules anchored to the aqueous interface.14,15 The method rests on the assumption that the conformational dynamics of chain molecules can be described as the superposition of local structural rearrangements involving short-chain segments. This approach is particularly useful for following structural and conformational changes on time scales longer than those associated with the gauche/trans isomerization of hydrocarbon chains. The method thus complements molecular dynamics studies. The simulations presented below reproduce the principal features of the order parameter (11) Rey, A.; Kolinski, A.; Skolnick, J.; Levine, Y. K. J. Chem. Phys. 1992, 97, 1240. (12) Levine, Y. K. Mol. Phys. 1993, 78, 619. (13) Sijs, van der D. A.; Levine, Y. K. J. Chem. Phys. 1994, 100, 6783. (14) Heide, van der U. A.; Levine, Y. K. Mol. Phys. 1994, 83, 1251. (15) Eviatar, H.; Heide, van der U. A.; Levine, Y. K. J. Chem. Phys. 1995, 102, 3135.
10.1021/la990384a CCC: $19.00 © 2000 American Chemical Society Published on Web 11/11/1999
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Table 1. Square Well Potentials for the Torsion about a C-C Bond in the Model Chains torsional angle (deg)
energy (K) sp3-sp3
155° e | φ | e 180° 90° e | φ | e 155° 30° e | φ | e 90° 0° e | φ | e 30°
1815.0 280.0 700.0 0.0 sp3-sp2
155° e | φ | e 180° 90° e | φ | e 155° 30° e | φ | e 90° 0° e | φ | e 30°
366.0 660.0 0.0 415.0
profiles of the surfactant molecules found in pure bilayers and bilayers of POPC/C12E4 mixtures10 and provide a physical framework for understanding the experimental observations. Simulation Model A. Geometric Representation on a Lattice. The Knight’s Gambit lattice technique for simulating the dynamic behavior of hydrocarbon chains of lipids in monolayer and monolayer structures has been discussed and validated in detail previously10-14 and only the salient points will be summarized here. Essentially the method makes use of a representation of hydrocarbon chains, on a cubic lattice. The model hydrocarbon chain consists of N atoms representing the methylene groups that are connected by N - 1 bonds of length x5. The bonds are obtained by a cyclic permutation of the 24 vectors of the type {(2, (1, 0}. As the C-C bond length is 0.154 nm, one lattice unit is equivalent to a distance of 0.069 nm. The vectors are chosen from this basis set under the condition that the distance R13 between atoms n and n + 2 lies in the interval x10 e R13 e x18. This representation leads to multiple dihedral conformational states about each bond. Therefore, the continuous torsional potential U(φ),11 where φ is the angle of rotation about the sp3sp3 bond in a polymethylene chain, is replaced by symmetric square wells corresponding to the trans (-30° e φ e 30°) and the two gauche states g+ (90° e φ e 155°) and g- (-155° e φ e -90°).12 The widths of the barriers between the wells were chosen so that each of the effective trans and gauche wells contain the same number of dihedral states. The depths of the wells are adjusted so as to reproduce the values of 〈cos φ〉 obtained from the continuous potential over the temperature range 200-800 K. The potential parameters are given in Table 1. The representation of a cis double-bond segment on the lattice is chosen so as to reproduce its rigid planar configuration. Fortyeight distinct triplet vector combinations taken from the basis set are found to satisfy this condition. The square-well description of the continuous torsional potential for the rotation about the sp3-sp2 bond11 is chosen in the way described for the sp3-sp3 bonds12 and the parameters shown in Table 1. The excluded volume effects are implemented by assigning an impenetrable spherical envelope of radius 2.1 lattice units (0.145 nm) to each of the chain atoms. Intrachain effects are simulated by rejecting any chain conformations exhibiting an overlap of spheres representing atoms separated by more than three bonds in the chain. The interchain excluded volume effects are implemented by occupying all the lattice sites within the sphere representing the atom. B. Conformational Transitions. The conformational dynamics of the model hydrocarbon chain are assumed to arise from a superposition of local structural arrangements involving the transfer of a pair of adjacent atoms, -Cn-Cn+1-, together with their impenetrable envelopes to different lattice sites. This essentially involves making random interchanges between triplets of basis vectors whose end-to-end distance is the same as that between the stationary atoms Cn-1 and Cn+2. This algorithm needs to be modified for the motions of a rigid and planar cis unsaturated segment of the oleoyl chains -C8-C9d C10-C11-. Now, the atoms C8-C11 can only be displaced to different lattice sites by invoking concerted moves. This is achieved by executing asymmetric, concerted four-atom moves
involving all the atoms in segments of the type -C7-C8-C9d C10- or -C9dC10-C11-C12-. Each random elemental move attempted by the atoms is accepted only if the final lattice positions of the excluded volume envelopes of the atoms are unoccupied. C. Construction of a Model POPC Bilayer. The bilayer used in the simulations reported below was constructed of 1152 model chains contained in a Monte Carlo box having a square cross-section in the xy plane, with periodic boundary conditions. Water molecules were not included. The first atom (headgroup) of each of the model lipid chains was held near interfaces at z ) (1/2Tbil, where Tbil is the bilayer thickness. Typically, we used Tbil ≈ 4.2 nm for the model lipid bilayers, but the results were found to be fairly insensitive to the choice of the thickness. The headgroups were subjected to an asymmetric potential of the form U(z) ) 0 for |z| > 1/2Tbil and U(z) ) 1/2kz(z - 1/2Tbil)2 for |z| < 1/2Tbil. Moreover, the effective methylene and terminal methyl groups were subjected to a repulsive harmonic potential on crossing the interface into the aqueous phase, U(z) ) 1/2kz(z - 1/2Tbil)2 for |z| > 1/2Tbil. In this study we took kz ) 1.0kBT. Note that only hard-sphere interatomic interactions were taken into account so that the total energy of a model chain is simply the sum of the torsional energy U(φ) and the anchoring energy U(z). D. Construction of a Model Surfactant Bilayer. The surfactant bilayer was built in the spirit of the coarse-grained models widely used to predict the phase diagram of surfactant systems.16-21 However, water molecules are not treated explicitly and that hydration effects enter the model through the effective potentials acting on the headgroups in the simulation. The main difference between the surfactant and POPC bilayers is that in the surfactant systems the tetra(ethyl oxide) (TEO) headgroups protruded into the effective aqueous phase, while the methyl chains formed the bilayer interior. The interface is defined by the junction between the TEO headgroup of the surfactant molecule and its methyl chain in the middle of the molecule. The lattice representation of the TEO headgroups of the surfactant molecules C12E4, atoms 1-13 in Figure 1, was taken to the same as for a polymethylene chain described above. The headgroup atoms, with the exception of atom 1, were subjected to an asymmetric potential of the form U(z) ) 0 for |z| > 1/2Tbil and U(z) ) 1/2kTEO(z - 1/2Tbil)2 for |z| < 1/2Tbil so that they protruded into the aqueous phase. The same potential, but of strength kOH, was applied to the OH group, atom 1, Figure 1. The methylene groups of the surfactant molecules were subjected to the repulsive harmonic potential on crossing the interface into the aqueous phase, U(z) ) 1/2kz(z - 1/2Tbil)2 for |z| > 1/2Tbil. Note that the constant kz is common to the lipid and surfactant methylene groups. In the simulations (see below) atoms 14 and 15 of the surfactant chain, Figure 1, were localized at the aqueous interface separating the hydrophilic and hydrophobic parts of the surfactant molecules. The thickness of the interior of the bilayer containing the methyl groups was taken to be Tbil ≈ 3.0 nm. The mixed POPC/C12E4 bilayers were constructed with the first atom of each of the lipid chains anchored to the interfaces, while the regions between atoms 14 and 15 of the surfactant chains were localized through their amphiphilic character only. E. Monte Carlo Algorithm. The Monte Carlo algorithm for a system containing M model chains each consisting of N atoms was executed in the following way. Given a particular structural configuration of the bilayer, Ωj, M × N local conformational moves are attempted at random with each atom in the system having an equal chance of being picked. These moves generate a new configuration of the monolayer, Ωj+1. This new configuration was (16) Larson, R. G. Macromolecules 1994, 27, 4198. (17) Rector, D. R.; Swol, van F.; Henderson, J. R. Mol. Phys. 1994, 82, 1009. (18) Palmer, B. J.; Liu, J. Langmuir 1997, 12, 7746. (19) Mackie, A. D.; Panagiotopoulos, A. Z.; Szleifer, I. Langmuir 1997, 13, 5022. (20) Goetz, R.; Lipowsky, R. J. Chem. Phys. 1998, 108, 7397. (21) Gottberg, von F. K.; Smith, K. A.; Hatton, T. A. J. Chem. Phys. 1998, 108, 2232.
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Figure 1. Schematic structure of a tetra(ethylene oxide) surfactant molecule. accepted with a probability P given by the symmetric scheme
P ) exp(-Enew/kBT)/{exp(-Eold/kBT) + exp(-Enew/kBT)} We note that the effects of temperature enter the simulation only through this acceptance test. The cycle is now repeated using Ωj+1 as the starting configuration. We have typically generated a trajectory consisting of 240 000 bilayer configurations at a temperature of 300 K, though only every 20th configuration was used in evaluating the order parameters of the effective C-D bonds (see below). A typical simulation run required 6 h of CPU time on a Dec Alpha 500 au personal workstation. F. Calculation of the NMR Order Parameter SCD along the Model Chains. The order parameter SCD ) 1/2〈3 cos2 β 1〉 for the C-D bond of a given methylene group was evaluated along the trajectories from the known orientations of the bond vectors.12 For saturated chains, the angle β between the effective C-D vector and the normal to the bilayer plane, the lattice z axis, was calculated assuming a tetrahedral orientation of the C-D vectors relative to the plane defined by the bond vectors.12 On the other hand, the C-D vector of a carbon atom of the unsaturated cis segment was taken to lie in the plane defined by the bond vectors. We note that the order parameters SCD are negative because they exhibit a preferential orientation in the xy plane that is parallel to the bilayer plane.
Results and Discussion A. Parametrization of the Potentials Used for Modeling the Headgroups of Surfactant Chains. The first step in simulating bilayers of C12E4 surfactant molecules is the parametrization of the effective potentials acting on the TEO headgroups in the bilayer structure. This is necessary in view of the fact that water molecules are not treated explicitly in the simulations so that hydration effects enter the model through the effective potentials used. An additional uncertainty is the length of the headgroups. It is not immediately transparent whether their vicinity to oxygen atom 12 affects the physicochemical properties of the methylene groups 13 and 14. The alkyl chains of the surfactants are confined between two planes, the aqueous interfaces, by subjecting them to the asymmetric potential discussed above, with strength kz. In a similar way a hydrophilic character was endowed on the TEO headgroups of the surfactant molecules by subjecting them to a repulsive harmonic potential of strength kTEO on crossing the interface toward the bilayer interior. Similarly, the terminal OH group (atom 1, Figure 1) of the TEO headgroups was subjected to a potential of constant kOH on leaving the aqueous phase. Finally, free rotation was allowed about the O-C bonds of the TEO headgroups. It is important to note that the order parameters SCD of the C-D bonds of the methylene atoms in the surfactant chain are determined by the strengths of the potentials, as well as by the restriction on the conformational freedom of the chains imposed by the packing of the molecules into a bilayer structure. We now stress that the tetra(ethylene oxide)/alkyl junction in the surfactant chain forms a bottleneck for conformational motions as a result of the sudden transition in the effective potentials acting on the constituent atoms. Consequently, the vertical motion of the headgroup atoms
Figure 2. The experimental (continuous line) and simulated (dashed line) order parameter profiles for a bilayer of tetraethyleneoxide surfactant molecules. The simulations correspond to an area per molecule of 0.85 nm2 with kOH ) 0.5kT and kTEO ) 0. Note the reduction in the order parameters of the TEO groups, atoms 1-11 in Figure 1, on using kOH ) kTEO ) 0.5kT (dotted line). The lines are given as a guide to the eye.
is severely restricted by the fact that the alkyl methylene groups are penalized for crossing the aqueous interface into the headgroup region of the bilayer. Moreover, this imparts a strong coupling in the conformational freedom of the TEO headgroups and alkyl segments of the surfactant molecules. This coupling turns out to play an important role in determining the conformational behavior of surfactant molecules in bilayer systems. To estimate the magnitudes of kOH and kTEO, we carried out simulations of a bilayer of pure tetra(ethylene oxide) surfactants as a function of the area per molecule of the model chains. Simulations were run for different values of the potential parameters for areas per molecule in the range 0.28 e a e 1.10 nm2. The order parameters of all the C-D bonds of the surfactant chains were found to decrease continuously on increasing the area per molecule in this range for all values of the constants kOH and kTEO. However, to reproduce the shape of the profile at the ethylene oxide/alkyl junction, it was necessary to consider the first two methylene groups of the alkyl chain (atoms 13 and 14) to be part of the TEO headgroup. At an area per molecule of 0.28 nm2, the order parameters for atoms 12-15 were found to be high, SCD ≈ -0.3, but they decreased to SCD ≈ -0.08 at 1.10 nm2. Interestingly, the variation of the order parameters with the area per molecule closely tracked the trend found in simulations of bilayers of soaps and lipids. The experimental order parameter profile for surfactant bilayers was well-reproduced in the simulations (Figure 2) at an area per molecule of ) 0.85 nm2, with kOH ) 0.5kT and kTEO ≈ 0. This means that the model headgroup atoms 2-14 incur no energy penalty in crossing the aqueous interface of the bilayer. Nevertheless, the value of kOH needs to be relatively large to reproduce the correct form of the order parameter profile. The effect on the order parameter profile on assigning the same potential to all the headgroup atoms, kTEO ) kOH ) 0.5kT is also shown in Figure 2. The discrepancies between the simulated and experimental10,22 order parameter profiles (Figure 2) reflect the simplified description of the aqueous interface of the (22) Ward, A. J. I.; Ku, H.; Phillippi, M. A.; Marie, C. Mol. Cryst., Liq. Cryst. 1988, 154, 55.
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Figure 3. The height distribution of atoms of model tetra(ethylene oxide) surfactants relative to the center of a surfactant bilayer. The simulations correspond to an area per molecule of 0.85 nm2.
Figure 4. The experimental, ×, and simulated, 9, order parameter profiles of a palmitoyl chain in a bilayer of POPC. The simulations were carried out at an area per molecule of 0.72 nm2. The line is given as a guide to the eye.
bilayer used in our model. Moreover, the area per molecule needed to reproduce the order parameter profile is larger than the experimental value of 0.45 nm2.6,7,11 It is interesting to note that a similar value of the area per molecule is needed to reproduce such low values of the order parameters in bilayers of soaps and lipids. This latter observation can be taken to indicate that the conformational behavior of bilayers of tetra(ethylene oxide) surfactants is different from that in bilayers of soaps and lipids. One possible reason for the difference could well be the nature of the bilayer interface. This interface is quite well-defined for lipid bilayers, but could be far more diffuse in the surfactant ones. Consequently, the surfactant chains will only be loosely localized and more disordered than lipid chains at the same area per molecule. We have, unfortunately, been unable to reproduce this in the simulations, possibly because of the small size of the system used. Despite the discrepancies between the experimental and simulated area per molecule in the surfactant bilayers, we found that the simulations yielded linear dimensions consistent with experimental findings.6,7 The simulations yield not only the order parameters of the C-D bonds of the model surfactants but also the distribution of the positions of the atoms relative to the aqueous interface. This latter distribution is obtained in the simulations as the z coordinates of the atoms because the bilayer plane is taken as the lattice xy plane. Figure 3 shows the distribution of atoms 1, 4, 7, 10, 13, and 15 (Figure 1) in the bilayer at an area per molecule of 0.85 nm2, measured relative to the bilayer interfaces. It can be seen that the distribution of atom 1 (the OH group) is quite broad, but the distributions narrow considerably for atoms nearer the tetra(ethylene oxide)/ alkyl junction. The distribution of the centers of the TEO groups is in good agreement with the experimentally observed thickness (3.25 nm) of the bilayer structure and the position of the atoms found in neutron-scattering experiments.6,7 B. Conformation of the TEO Headgroups in Model Tetra(ethylene oxide) Surfactant Bilayers. In all the simulations reported below, we had fixed the parameters as follows: (1) The headgroup consists of the first 14 atoms, (2) kOH ) 0.5kT, (3) kTEO ) 0kT, and (4) a ) 0.85 nm2. The conformations of the TEO headgroups of the model surfactant chains is most conveniently characterized in terms of their moments of inertia calculated in the lattice frame. These are monitored throughout the simulation run using the atomic coordinates. On average at a ) 0.85 nm2 the headgroups undertake an ellipsoidal shape: Ixx ) Iyy ≈ 0.094 nm2 and Izz ≈ 0.119 nm2. Here, we have taken each methylene group and oxygen atom to have a
mass of 1. When the area per molecules are decreased, the ellipsoids are found to extend outward along the normal to the bilayer plane (the lattice z axis). At a ) 0.28 nm2, the moments of inertia were found to be Ixx ) Iyy ≈ 0.087 nm2 and Izz ≈ 0.136 nm2. This behavior is indeed expected as a result of the closer packing of the headgroups in the aqueous plane, which reduces their conformational freedom. C. NMR Order Parameter Profile of Lipid Chains in Bilayers of Model POPC molecules. To gain insight into the effects of the tetra(ethylene oxide) surfactant molecules on lipid bilayers, we had first characterized the order parameter profiles of bilayers of model palmitoyloleoylphosphatidylcholine (POPC) molecules. The POPC molecule was modeled as a dimer of palmitoyl and oleoyl chains joined to a point outside the bilayer, in the space corresponding to the aqueous phase. This point represented the PC group of the lipid molecules and was assigned zero volume. The first atom of each chain, corresponding to the carboxylic group, was restricted to remain within a distance of 5 nm from the virtual headgroup. During the simulations the virtual headgroup was allowed to undergo three-dimensional translational motions in the aqueous phase. However, these motions were penalized by a factor of 100 relative to the internal conformational moves of the alkyl chain to mimic its larger mass and interaction with the water layer. As a first step, simulations were run as a function of the area of the model lipid molecule to fit the experimental order parameter profile of the palmitoyl chain of POPC.10,23,24 The profile was reproduced (Figure 4) at a ) 0.72 nm2. This value for a was then taken as the reference area in all further simulations. The corresponding profile for the oleoyl chain is shown in Figure 6. This profile exhibits a minimum at the 10 position and is in excellent agreement with experimental profiles for unsaturated chains.25,26 We have also simulated the order parameter profiles of both the C16:0 and C18:1 chains for a ) 0.742 and 0.785 nm2. In these latter bilayer configurations the model lipid molecules have the average area per molecule calculated for lipid/surfactant ratios of 5:1 and 1:1. The increase in the area, and consequently the looser packing of the molecules in the bilayer structure, causes the order parameters of the alkyl chain to decrease. D. NMR Order Parameter Profiles of Model Lipid Chains in Bilayers of Surfactant/Lipid Mixtures. To (23) Seelig, J. Quart. Rev. Biophys. 1977, 10, 353. (24) Davis, J. H. Biochim. Biophys. Acta 1983, 737, 117. (25) Seelig, J.; Waespe-Sˇ arcˇevic, K. Biochemistry 1978, 17, 3310. (26) Rance, M.; Jeffrey, K. R.; Tulloch, A. P.; Butler, K. W.; Smith, I. C. P. Biochim. Biophys. Acta 1980, 600, 245.
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Figure 5. The order parameter profiles of model palmitoyl chains in pure POPC and POPC/C12E4 bilayer systems. O, a pure POPC bilayer at an area per molecule of 0.72 nm2; 0; a 5:1 POPC/surfactant bilayer at an area per molecule of 0.742 nm2; ), a 1:1 POPC/surfactant bilayer at an area per molecule of 0.785 nm2; ×, a pure POPC bilayer at an area per molecule of 0.742; +, a pure POPC bilayer at an area per molecule of 0.785 nm2. The lines are given as a guide to the eye.
Figure 6. The order parameter profiles of model oleoyl chains in pure POPC and POPC/C12E4 bilayer systems. O, a pure POPC bilayer at an area per molecule of 0.72 nm2; 0, a 5:1 POPC/ surfactant bilayer at an area per molecule of 0.742 nm2; ), a 1:1 POPC/surfactant bilayer at an area per molecule of 0.785 nm2; ×, a pure POPC bilayer at an area per molecule of 0.742; +, a pure POPC bilayer at an area per molecule of 0.785 nm2. The lines are given as a guide to the eye.
simulate the order parameter profiles of lipid molecules in bilayers containing surfactant molecules, we have assumed for the sake of simplicity that the system can be considered as an ideal mixture. The model lipid molecules were each assigned an area of 0.72 nm2, with the surfactant molecules each undertaking an area of 0.85 nm2, as found above for the pure systems. The average area per molecule in the bilayer was 0.742 nm2 for the 5:1 mixture and 0.785 nm2 for the 1:1 mixture. We have found that a reduction in the area of either one or both components of the mixture simply resulted in higher order parameter profiles reflecting the tighter packing of the molecules within the bilayer structure. The order parameter profiles obtained from the simulations of a 5:1 POPC/surfactant and 1:1 POPC/surfactant mixtures are shown in Figures 5 and 6 for the palmitoyl and oleoyl chains, respectively. Also shown are the profiles obtained for the chains in pure model POPC bilayers having the same area per molecule. Importantly, the simulations show a differential effect of the surfactants on the two chains of the model POPC molecule. It can be seen from Figure 5 that the order parameter profile of the palmitoyl chain in the 5:1 mixture is somewhat lower than that for the pure POPC bilayer. Nevertheless, it is significantly higher in the mixtures than in the pure lipid bilayers at the same value of a. This finding is in excellent agreement with the experimental observations of Klose et al.10 that low surfactant concen-
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Figure 7. The order parameter profiles of model stearoyl chains in pure PSPC and PSPC/C12E4 bilayer systems. O, a pure PSPC bilayer at an area per molecule of 0.72 nm2; 0, a 5:1 PSPC/ surfactant bilayer at an area per molecule of 0.742 nm2; ), a 1:1 PSPC/surfactant bilayer at an area per molecule of 0.785 nm2; ×, a pure PSPC bilayer at an area per molecule of 0.742; +, a pure PSPC bilayer at an area per molecule of 0.785 nm2. The lines are given as a guide to the eye.
trations do not affect the order parameters of the palmitoyl chains to a significant extent. The addition of surfactant molecules to the POPC bilayer lowers the order parameter profiles of the tails of oleoyl chains (atoms 10-17 between the cis double bond and terminal methyl group) at all concentrations (Figure 6). The simulations show that the order parameter profiles of these chain segments in the mixtures are essentially the same as that found in the pure POPC bilayers at the same area per molecule. Moreover, at low surfactant concentration the order parameters of the atoms in the chain segments between the cis double bond and the headgroup were not significantly affected. The question now arises as to whether the differential effect of the surfactant molecules on the ordering of the C16:0 and C18:1 chains can indeed be ascribed to the presence of a cis double-bond segment in the oleoyl chain. As discussed above, the rigid structure of the unsaturated segment implies that the four carbon atoms C-CdC-C must move in concert.12 Moreover, we have shown in previous simulations of unsaturated chains that the presence of the rigid segment in the middle of the chain effectively decouples the conformational changes of the two alkyl segments attached to it.11 We had therefore carried out simulations of the order parameter profiles of a mixture of the model surfactants with model palmitoylstearoylPC (PSPC) molecules, in which both alkyl chains are saturated but of unequal length. Identical area per molecules were used for the simulations of the POPC mixtures. The effect of the surfactant on the order parameter profile of the stearoyl (C18:0) chain parallels that observed for the palmitoyl (C16: 0) chains in both the model POPC and PSPC bilayers (Figures 7 and 8). This finding indicates strongly that the presence of the cis segment in the oleoyl chain is responsible for the experimentally observed behavior of the order parameters of the palmitoyl chains in the POPC/ surfactant mixtures. E. NMR Order Parameter Profiles of Surfactant Chains in Bilayers of Surfactant/Lipid Mixtures. The order parameter profiles of the model surfactants incorporated in POPC bilayers are shown in Figure 9 for the 5:1 and 1:1 mixtures. We note here that, in the model systems simulated here, the aqueous phase only contains the headgroups of the surfactant molecules. It can be seen that the order parameters of the C-D bonds of the alkyl chains and headgroup segments near the tetra(ethylene oxide)/alkyl junction in the mixtures are higher than those in the pure surfactant bilayers as observed experimen-
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Figure 8. The order parameter profiles of model palmitoyl chains in pure PSPC and PSPC/C12E4 bilayer systems. O, a pure PSPC bilayer at an area per molecule of 0.72 nm2; 0, a 5:1 PSPC/surfactant bilayer at an area per molecule of 0.742 nm2; ), a 1:1 PSPC/surfactant bilayer at an area per molecule of 0.785 nm2; ×, a pure PSPC bilayer at an area per molecule of 0.742; +, a pure PSPC bilayer at an area per molecule of 0.785 nm2. The lines are given as a guide to the eye.
Figure 9. The order parameter profile of model tetra(ethylene oxide) surfactant molecules in pure surfactant bilayers and in bilayers of mixtures with POPC. O, pure C12E4 bilayer at an area per molecule of 0.85 nm2; ), a 5:1 bilayer POPC/surfactant bilayer at an area per molecule of 0.742 nm2; 0, a 1:1 POPC/ surfactant bilayer at an area per molecule of 0.785 nm2.
tally.10 This trend can be simply rationalized in terms of the low area per molecule occupied by the surfactant in the lipid bilayer. Moreover, in our model, the increase in
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the order parameters of the headgroup segments is a direct consequence of the coupling of the conformational motions of the alkyl segments and the headgroups at their junction. Interestingly, the order parameter profiles of the headgroup segments close to the OH terminal (atom 1 in Figure 1) exhibit a concave shape in the mixtures rather than the slightly convex profile yielded by the simulations of the pure bilayer in accord with experimental observations.10 The curvature is more pronounced in the 5:1 than in the 1:1 mixture. This behavior appears to be governed by the space available for motion in the aqueous phase. In the 5:1 mixture the surfactant headgroups are widely separated and can undertake loose structures. Thus, the average moments of inertia, Ixx ) Iyy ≈ 1.06 nm2 and Izz ≈ 1.16 nm2, indicate that the headgroups essentially undertake an expanded spherical structure. As before, the normal to the bilayer plane is taken as the z axis. However, in the 1:1 mixtures, the headgroups are more tightly packed and undertake a cylindrical structure with Ixx ) Iyy ≈ 0.29 nm2 and Izz ≈ 0.34 nm2. Simulations of other mixtures of surfactant molecules in model lipid bilayers indicate that the concave order parameter profile is a signature of an expanded headgroup structure. Conclusions We have used here a lattice Monte Carlo dynamics model to simulate the order parameter profiles of surfactant and lipid molecules in phospholipid/surfactant mixtures. The approach used reproduces the principal features of the profiles and provides a physical framework for understanding the experimental observations. Although neither the water phase nor the lipid headgroups are treated explicitly, the model accounts semiquantitatively for the conformational behavior of the surfactant headgroups in bilayers of phospholipid/surfactant mixtures. Acknowledgment. This work was supported by grants from the Deutsche Forschungsgemeinschaft in the framework of SFB 294 and from the Bundesministerium fu¨r Bildung, Wissenschaft, Forschung und Technologie (BMBF, DUBLEI). LA990384A
