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* Laboratory of Physics and Helsinki Institute of Physics, Helsinki University of Technology, FIN-02015 HUT, Finland; Institute of Macromolecular Compounds, Russian Academy of Sciences, St. Petersburg, 199004 Russia; and Biophysics and Statistical Mechanics Group, Laboratory of Computational Engineering, Helsinki University of Technology, FIN-02015 HUT, Finland
Correspondence: Address reprint requests to Dr. Andrey A. Gurtovenko, Laboratory of Physics, Helsinki University of Technology, PO Box 1100, FIN-02015 HUT, Finland. Tel.: 358-9-4515803; E-mail: agu{at}fyslab.hut.fi.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONSYSTEMRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONSYSTEMRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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; Langer, 1998; Mönkkönen and Urtti, 1998). The majority of the delivery vectors proposed are of viral nature. The viral vectors have been demonstrated to be very efficient but their use is restricted by accompanied toxicity (Anderson, 1998). This has stimulated a search for nonviral delivery systems, which should be characterized by greater safety and ease of manufacturing (Langer, 1998). Numerous examples of nonviral delivery vectors include cationic liposomes, cationic polymers (such as polyamidoamine dendrimers, polyethylenimine, and spermine), and block copolymers (Astafieva et al., 1996; Fischer et al., 1999; Gao and Huang, 1996; Kukowska-Latallo et al., 1996; Mönkkönen and Urtti, 1998; Pitard et al., 1997; Smedt et al., 2000).
In the light of the above, it is surprising how little attention has been devoted to computational studies of membranes containing cationic lipids. Bandyopadhyay et al. (1999) performed an atomistic molecular dynamics (MD) study of a mixture of dimyristoylphosphatidylcholine (DMPC) and dimyristoyltrimethylammonium propane (DMTAP) in the presence of a short DNA fragment. Apart from the very elegant piece of work above, there are, to the best of our knowledge, no published atomistic computational studies of systems containing cationic lipids—this is very much in contrast to the great number of computational studies of various neutral and anionic phospholipid bilayer systems (Feller, 2000; Saiz et al., 2002; Saiz and Klein, 2002; Tieleman et al., 1997; Tobias, 2001). Another related example is the recent molecular dynamics study of Böckmann et al. (2003), who showed the importance of monovalent ions on the properties and organization of lipid membranes—ions are always present in cationic lipid systems. The above examples demonstrate that detailed molecular dynamics studies can provide valuable insight into the atomistic organization of systems containing cationic lipids and yield useful information for experimentalists about the underlying mechanisms on the atomic and molecular levels.
In this work, our objective is to gain insight into the structural and electrostatic properties of cationic lipid bilayers through atomic classical molecular dynamics simulations. We concentrate on a bilayer mixture composed of two kinds of lipids: neutral (zwitterionic) DMPC and cationic DMTAP (see Fig. 1 for their chemical structures). Since DMTAP is positively charged under physiological conditions, we have neutralized its positive charges by chloride counterions. From the computational point of view, this choice for a model system is motivated by the fact that DMPC and DMTAP have the same nonpolar hydrocarbon chains and differ only by their headgroups. On the practical side, DMPC/DMTAP binary lipid mixtures have been widely studied in the presence of DNA by various experimental techniques (Artzner et al., 1998; Pohle et al., 2000; Zantl et al., 1999a,b), and also by computational methods (Bandyopadhyay et al., 1999).
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Force field parameters for the lipids were taken from the recent united atom force field (Berger et al., 1997). This force field has been previously validated (Lindahl and Edholm, 2000; Tieleman and Berendsen, 1996) and is essentially based on the GROMOS force field for lipid headgroups, the Ryckaert-Bellemans potential (Ryckaert and Bellemans, 1975, 1978) for hydrocarbon chains, and the OPLS parameters (Jorgensen and Tirado-Rives, 1988) for the Lennard-Jones interactions between united CHn groups of acyl chains reparameterized for long hydrocarbon chains to reproduce experimentally observed values of volume per lipid (Nagle and Wiener, 1988). The parameters for this force field are available online at http://moose.bio.ucalgary.ca/Downloads/files/lipid.itp. Water was modeled using the SPC water model (Berendsen et al., 1981). The unit positive charge carried by each DMTAP molecule is compensated by the introduction of the corresponding number of explicit Cl– counterions. Although being aware of the effects of different models for chloride (Patra and Karttunen, 2004), we decided to use the default set of chloride parameters supplied within the GROMACS force field (Berendsen et al., 1995; Lindahl et al., 2001).
Following the original parameterization (Berger et al., 1997), the Lennard-Jones interactions were cut off at 1 nm without shift or switch function. Since long-range electrostatic interactions are essential in this study, and since truncation of these interactions has been shown to lead to artifacts in simulations of phospholipid bilayers (Anézo et al., 2003; Patra et al., 2003; Tobias, 2001, and references therein), we employ the particle-mesh Ewald method (Darden et al., 1993). The long-range contribution to the electrostatics is updated every 10th time step.
The simulations were performed in the NPT ensemble. The temperature was kept constant using a Berendsen thermostat (Berendsen et al., 1984) with a coupling time constant of 0.1 ps. Lipid molecules and water (including counterions) were separately coupled to a heat bath. Pressure was controlled by a Berendsen barostat (Berendsen et al., 1984) with a coupling time constant of 1.0 ps. Pressure coupling was applied semiisotropically: The extension of the simulation box in the z direction (i.e., in the direction of the bilayer normal) and the cross-sectional area of the box in the x-y plane were allowed to vary independently of each other. Periodic boundary conditions were applied in all three dimensions.
We considered 11 DMPC/DMTAP mixtures ranging from pure DMPC to pure DMTAP. The molar fractions of the cationic DMTAP, 
TAP, were taken to be 0.0, 0.06, 0.16, 0.25, 0.31, 0.39, 0.50, 0.63, 0.75, 0.89, and 1.0.
The hydration level used was essentially constant for all mixtures, ranging from 28.5 (pure DMPC bilayer) to 27.5 (pure DMTAP bilayer) water molecules per lipid. For comparison, Mashl et al. (2001) found recently that each headgroup in a pure dioleoylphosphatidylcholine bilayer can accommodate 
12 water molecules. Thus, we are confident that our DMPC bilayer is fully hydrated. As far as lipid bilayer mixtures are concerned, we excluded possible artifacts due to hydration (caused, e.g., by the binding of water molecules by Cl ions) by additional simulations with excess water: For DMTAP concentrations of 0.06, 0.50, and 0.75, we increased the number of water molecules by 50%. During multi-nanosecond simulations (20 ns) we did not observe noticeable deviations in the structural properties discussed in this work (such as, e.g., the area per molecule).
The main transition temperature of a pure DMPC bilayer is Tm = 24°C (Cevc and Marsh, 1987). For DMPC/DMTAP binary mixtures, it has been found (Zantl et al., 1999b) that the main transition temperature changes nonmonotonically with the mole fraction of DMTAP, demonstrating a maximum of 37°C at TAP 
0.45. All our simulations were done at a temperature of 50°C, such that the bilayers are in the liquid-crystalline phase.
All bond lengths of the lipid molecules were constrained to their equilibrium values using the LINCS algorithm (Hess et al., 1997) whereas the SETTLE algorithm (Miyamoto and Kollman, 1992) was used for water molecules. The time step in all simulations was set to 2 fs. All simulations were performed using the GROMACS package (Berendsen et al., 1995; Lindahl et al., 2001). The combined simulated time of all simulations amounts to 250 ns. Each simulation was run in parallel over four processors on an IBM eServer Cluster 1600 system. In total, the simulations took 20,000 h of CPU time.
Simulation setup
Mixtures of DMPC and DMTAP were prepared and equilibrated in several steps as follows:
as our initial configuration. The structure is available electronically at http://www.softsimu.org/downloads.shtml. ). To neutralize the unit charges in DMTAP headgroups, randomly chosen water molecules were replaced by chloride ions while ensuring a minimum separation of 0.5 nm between ions. To retain symmetry between the two leaflets, each of them contains the same number of cationic DMTAP. After equilibration, for each DMPC/DMTAP mixture, we performed a production run of 10 ns in the NPT ensemble to collect the data for analysis. Final structures of all DMPC/DMTAP mixtures are available online at http://www.softsimu.org/downloads.shtml.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONSYSTEMRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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A
, is one of the most fundamental characteristics of lipid bilayers (Nagle and Tristram-Nagle, 2000). Although being one of the rather few structural quantities that can be measured accurately from model membranes via experiments, it also plays a major role in a number of quantities, including the ordering of acyl chains and the dynamics of lipids in a bilayer. Further, from a computational point of view, it is highly useful as a means of monitoring the equilibration process.
Due to the lack of experimental data for the average area per lipid in binary DMPC/DMTAP bilayer mixtures, or in a pure DMTAP bilayer (apart from the low-temperature phase (Lewis et al., 2001)), reproduction of the experimental data available for pure DMPC membranes is essential to validate our approach. To this end, let us first consider the temporal behavior of the area per lipid, A(t), presented in Fig. 2. It shows that the obtained average area per lipid for a pure DMPC system has a value of A = 0.656 ± 0.008 nm2. As for experimental data on the area per lipid, it is well known that the results can vary significantly (up to 20%) depending on the method used (Nagle and Tristram-Nagle, 2000). In particular, for the DMPC bilayer at 50°C, values of 0.629 nm2 (Nagle et al., 1996), 0.654 nm2 (Petrache et al., 2000), and 0.703 nm2 (Costigan et al., 2000) have been reported. Therefore, our findings for a pure DMPC bilayer are in good agreement with the experimentally observed values, thereby validating our model in this respect. As for the pure DMTAP bilayer, Lewis et al. (2001) have been able to extract the area per lipid in the low-temperature phase, finding A = 0.40 nm2 at 25°C. Studies of A above the main transition temperature are lacking, however.
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TAP, with a pronounced minimum roughly at TAP = 0.5 (see Fig. 3). This behavior is not trivial, as modest amounts of the cationic DMTAP lead to a compression of the bilayer, whereas high concentrations lead to a major expansion of the membrane. More specifically we find that for 0<TAP
0.8, the average area per lipid is smaller than the corresponding counterpart for any of the pure lipid systems. Such a behavior cannot be explained by steric interaction alone but most likely is rather of electrostatic origin.
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considered DMPC/DMTAP monolayers using Langmuir-type film balance and found that, for pressures corresponding to the liquid-crystalline phase, the headgroup area decreased monotonically for small TAP, then had a minimum at about the equimolar ratio (TAP 
0.5), and increased for larger DMTAP mole fractions. This is in accord with our observations.
Another related work concerns Langmuir balance studies of mixed monolayers of zwitterionic palmitoyloleoylphosphatidylcholine (POPC) and cationic 2,3-dimethoxy-1,4-bis(N-hexadecyl-N;N-dimethyl-ammonium)butane dibromide (SS-1) (Säily et al., 2001). Although SS-1 is dicationic, one can qualitatively compare this system to our DMPC/DMTAP mixture. For the POPC/SS-1 system, Säily et al. (2001) found that the average area per lipid has a nonmonotonic behavior with a minimum at SS-1 0.38. They also found that this effect depends on the charge of the headgroup, and it disappeared when POPC (having a zwitterionic headgroup) was replaced by neutral dioleylglycerol.
Our results in Fig. 3 suggest local extrema in A when TAP is between 0.16 and 0.5 (in addition to global minimum at TAP = 0.5). In addition to the above-mentioned POPC and SS-1 study (Säily et al., 2001), similar and even more dramatic effects have been observed for mixtures of POPC and sphingosine (Säily et al., 2003). The existence of critical concentrations in lipid membranes has also been theoretically postulated by Somerharju et al. (Somerharju et al., 1999; Virtanen et al., 1998). In this case, the local extrema for DMPC/DMTAP mixtures are within error bars, and therefore may be interpreted as fluctuations of A. To study such features in more detail, one needs to decrease the fluctuations in the average area per lipid by, e.g., increasing the system size (Lindahl and Edholm, 2000). This, however, is beyond the scope of this study.
Nevertheless, we decided to approach this issue from a different perspective. To determine the average area per lipid separately for the two different components, we used the Voronoi tessellation technique in two dimensions (Patra et al., 2003). In Voronoi tessellation, we first calculated the center of mass (CM) positions for the lipids and projected them onto the x-y plane. A point in the plane is then considered to belong to a particular Voronoi cell, if it is closer to the projected CM of the lipid molecule associated with that cell than to any other CM position. As there is no unique definition for the area per molecule in a multi-component system, it is clear that the Voronoi results should be considered as suggestive rather than quantitative, providing insight mainly of the trends.
Fig. 4 demonstrates that the areas occupied by DMPC and DMTAP are distinctly different. For small TAP, the area per DMPC is considerably larger than that of DMTAP. For larger DMTAP mole fractions above TAP = 0.5, the situation is the opposite. This behavior is related to electrostatic effects and the ordering of acyl chains, and will be discussed in more detail in the next section. Here we only note that the fluctuations in A (see Fig. 3) at 0.1 TAP 0.5 arise from fluctuations in the area occupied by DMTAP. Whether this is a true result due to, e.g., clustering of lipids in this region remains to be resolved.
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is the angle between a CD bond and the bilayer normal, the order parameter is defined as
 | (1) |
; Hofsäss et al., 2003). In practice, we calculated SCD following the standard approach described elsewhere (Patra et al., 2003).
Fig. 5 shows |SCD| averaged over the two similar atoms in the sn-1 and sn-2 chains, for both DMPC (top) and DMTAP (bottom) at different DMTAP concentrations. For the pure DMPC bilayer, we find |SCD| 0.18 close to the glycerol group of the molecule, in good agreement with recent experiments (Petrache et al., 2000) and molecular dynamics simulation studies (Róg and Pasenkiewicz-Gierula, 2001; Smondyrev and Berkowitz, 2001).
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). For a pure DMTAP bilayer, the plateau value of SCD is considerably smaller, being 0.147 ± 0.011. Therefore, chains in a pure DMTAP bilayer are on average more disordered than in a DMPC system, in agreement with our findings for A.
Orientation of phosphatidylcholine headgroups
Since the chemical structures of the acyl chains of DMPC and DMTAP are identical, it is obvious that the differences between their behavior are due to their headgroups. Since the headgroup of DMPC is zwitterionic (cf. Fig. 1), it possesses a dipole moment along the P-N vector. The electrostatic potential across a monolayer thus depends sensitively on the distribution of the angle 
between the P-N vector and the interfacial normal 
(where has been chosen to point away from the bilayer center along the z coordinate).
Fig. 7 shows the probability distribution function P() for the angle in question. For a pure DMPC bilayer, we find the distribution to be wide, thus allowing the P-N vector to fluctuate substantially, pointing at times in the direction of the membrane normal as well as into the bilayer interior. The average angle found in this case is (80 ± 1)° (see Fig. 8), i.e., the PC heads are on average almost parallel to the membrane surface. This is in agreement with experimental observations (Hauser et al., 1981; Scherer and Seelig, 1989) as well as with recent computer simulations (Gabdoulline et al., 1996; Pasenkiewicz-Gierula et al., 1999; Smondyrev and Berkowitz, 1999).
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TAP is increased, the profile of the distribution becomes considerably narrower and its maximum shifts to smaller angles. This trend continues up to the high-concentration limit TAP 0.75, beyond which the distribution is essentially similar with the case found for TAP = 0.75.
Results for the average angle between the P-N vector and the membrane normal shown in Fig. 8 are consistent with this picture. On average, upon increasing TAP, PC headgroups become more and more vertically oriented. Also this has been observed in several experiments (Scherer and Seelig, 1989; Säily et al., 2003, 2001; Zantl et al., 1999b). Moreover, our findings are in fairly good agreement with an atomistic MD study of a complex composed of DNA and a mixture of DMPC and DMTAP (Bandyopadhyay et al., 1999), in which the average angle between the P-N dipole vector and the bilayer normal was found to be (50 ± 8)° at an almost equimolar mixture of DMPC and DMTAP. In this case without DNA, we found = (42 ± 2)° at TAP = 0.5.
Perhaps surprisingly, the correlation between the average area per lipid (Fig. 3) and the reorientation of the P-N dipole is not complete. As Fig. 8 shows, the reorientation extends by and large linearly up to TAP = 0.75, whereas the membrane compression completes at TAP 0.5. This contradicts the conclusions of Säily et al. (2001), who studied POPC/SS-1 cationic lipid mixtures using the Langmuir balance technique and suggested that the maximal average angle between the P-N dipole vector and membrane surface is achieved at the cationic lipid concentration that corresponds to the point where the membrane compression ends.
A closer inspection of Figs. 3 and 8 shows that the observed reduction of the average area per molecule is likely related to the reorientation of PC dipoles, and this in turn is related to the role of electrostatic interactions between DMPC and DMTAP headgroups. To bridge the two issues, we propose the following schematic scenario. At small TAP where the DMTAP molecules are far apart and their mutual interaction is rather weak, we essentially suggest that the role of DMTAP is to reorient the headgroups of those DMPC molecules that are beside a DMTAP molecule. This favors more dense packing at small TAP, leading to a reduction in A, and consequently to a minimum in the area per molecule at intermediate concentrations because for large TAP the repulsive electrostatic interactions between TAP headgroups enforce A to be expanded.
To validate this scenario, we complemented our results in Fig. 7 by calculating the probability distribution function P() for those DMPC molecules that are nearest neighbors to DMTAP. As a criterion that a DMPC and a DMTAP form a pair, we monitored the distance between PC phosphorus and TAP nitrogen. For that, we first calculated the radial distribution functions (RDFs) between pairs of PPC and NTAP and determined the distance rnn at which the RDF had its first minimum after the main peak (see also "Radial distribution functions and coordination numbers" below). The distance obtained in this fashion (rnn 0.665 nm) (and found not to depend on TAP) was applied to identify the DMPCs residing next to a DMTAP. As shown in Fig. 8, the reorientation of the P-N vector of these DMPCs is considerably stronger at small DMTAP concentrations as compared to that averaged over all DMPC lipids.
The above results imply that at small TAP, the effect of DMTAP on the reorientation is mainly local, i.e., the alternating PC and TAP headgroups pack more tightly than in a pure DMPC system. This idea is supported by the results for the radial distribution functions discussed in "Radial distribution functions and coordination numbers". Beyond the small TAP regime, for intermediate concentrations 0.3 TAP 0.5, further increase in the concentration of DMTAP continues to increase the number of units composed of PC and TAP heads, thus favoring a reduction in A. However, as repulsive electrostatic interactions between DMTAP molecules also become more and more important, the two effects compensate each other and A is found to be approximately constant. Finally, for large TAP, the repulsive electrostatic interactions between TAP groups dictate the case discussed here and lead to an enhancement of the average area per molecule.
Though this picture does not account for the explicit influence of counterions, it grasps the essence of the process. The effect of counterions is discussed separately in "Radial distribution functions and coordination numbers".
Density profiles of lipid headgroups and chloride ions
To quantify the locations of charge groups and counterions, we computed the density profiles across the bilayer, separated into the different constituents of the system. The positions of all atoms in the system were determined with respect to the instantaneous center of mass position of the bilayer, exploiting mirror symmetry such that atoms with z < 0 were folded to z > 0 (the bilayer center being at z = 0).
Fig. 9 shows the scaled number densities 
N(z) for a few selected cases. Additionally, we note that the essential information is given by the positions of the density maxima depicted in Fig. 10.
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TAP, the density maxima of the nitrogen and phosphorus atoms in the DMPC heads almost coincide (see Fig. 9). The density profile of nitrogen in DMPC is nevertheless broader and extends further out of the bilayer plane. For larger TAP, the density profiles of phosphorus and nitrogen are distinctly separated, and nitrogen in particular extends rather deeply into the water phase. The TAP group represented by the nitrogen atom, however, is found to be deep in the bilayer. It seems obvious that these two issues are related, i.e., the density profiles of nitrogens in PC and TAP groups are well separated due to the electrostatic repulsion that essentially leads to the reorientation of PC headgroups. These results are hence consistent with those in the prior section and reflect the dependence of DMPC headgroup orientation on TAP. Interestingly, although being attracted by the DMTAP headgroups, the chloride anions cannot penetrate the outer boundary of the bilayer formed by the DMPC choline groups. This is in a sense to be expected since the DMPC headgroup is longer than the TAP group and thus extends further outward from the bilayer. There is thus a significant amount of shielding of the chloride ions in the presence of DMPC. Only for an almost pure DMTAP bilayer the chloride ions are located in the vicinity of the TAP headgroups.
Charge density, electrostatic potential, and orientation of water
The charge distribution shown in Fig. 11 was calculated in the same fashion as the density profiles. The results are clearly reminiscent of the density profiles in Fig. 9 and demonstrate the competition between charged PC and TAP groups, Cl anions, and water. The role of the TAP group is prominent.
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; Gabdoulline et al., 1996; Smondyrev and Berkowitz, 1999). Experimental data for phospholipid membranes ranges from –0.2 V to –0.6 V (Clarke, 2001; Flewelling and Hubbel, 1986; Gawrisch et al., 1992; Hladky and Haydon, 1973; Pickard and Benz, 1978).
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TAP, chloride ions or DMPC phosphate groups. Most of the electrostatic potential across the bilayer thus is not due to the DMTAP itself but rather due to the reorientation of the DMPC headgroups. A clear indication of this is that the potential build-up saturates at TAP 0.75, i.e., at the same value at which the distribution of headgroup orientation saturates (see Fig. 8). The total potential of the bilayer increases with increasing DMTAP concentration, with a difference of 0.6 V between pure DMPC and pure DMTAP. This increase agrees well with the experimental data on cationic POPC/SS-1 monolayers (Säily et al., 2001), and the authors offer the same explanation for their observations.
Many of the conclusions drawn from the charge density already follow from the number densities presented in the prior section, since for charged particles number density and charge density are trivially related. Water, however, has an additional internal degree of freedom, and a quick discussion of the orientation of the water molecules seems appropriate. As seen from Fig. 13, the average direction of the water dipoles in the membrane-water interface region is inverted for TAP = 0.5 TAP = 1.0. This is closely related with the familiar "hump" close to the interface, which is due to a subtle imbalance between the orientation of the water molecules and lipid headgroups (Chiu et al., 1995). At higher DMTAP concentrations, this "hump" disappears. A related issue concerns the pure DMTAP bilayer, in which case the density profile of water penetrates rather deep into the membrane (see Fig. 9), extending up to the interface region between the polar TAP group and the hydrophobic core. This is in accord with the interpretation of Fourier transform infrared spectroscopic measurements by Lewis et al. (2001).
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The RDFs between the center of mass positions indicated that the leading (main) peak for DMPC-DMPC and DMTAP-DMTAP pairs was rather broad and at 1.0 nm (data not shown). For DMPC-DMTAP pairs, however, the main peak of the RDF was much closer, at 0.7 nm. This supports the conclusion made in "Orientation of phosphatidylcholine headgroups", i.e., DMPC and DMTAP form units that allow more dense packing than in a pure DMPC bilayer.
The NPC-NPC and NTAP-NTAP pairs were found to be rather far apart, the position of their main peak being at 0.83 nm, whereas the NPC-NTAP pair was slightly closer (0.8 nm). The positions of the main peaks did not depend on TAP. As for the RDFs of the phosphorus atoms in the PC headgroups, its main peak with respect to NPC and NTAP was found to be at a much closer distance, at 0.465 nm for NPC and 0.485 nm for NTAP. Again, the positions of these peaks did not depend on the DMTAP concentration.
We also calculated the coordination numbers for the phosphorus and nitrogen atoms at different DMTAP concentrations. These are shown in Fig. 14 (top). It turns out that in the range from TAP = 0 to 0.75, the PC nitrogens are to an increasing extent being replaced by NTAP in the vicinity of P. This has twofold consequences: First, the electrostatic attraction between N+ (TAP) and P– (PC) enhances the compression of the bilayer for 0.0 < TAP 0.5 (see Fig. 3). Second, the decreasing coordination number for P-NPC with TAP supports the view that the DMPC nitrogens are pushed toward water, thereby PC headgroups are reoriented to a more vertical alignment with respect to the membrane plane (Fig. 8).
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0.475 nm, and do not depend on TAP (data not shown). In Fig. 14 (bottom), we plot the coordination numbers of chlorides in the vicinity of both types of nitrogens as a function of DMTAP concentration. The figure confirms that Cl ions are preferentially bound to PC nitrogens rather than to NTAP. This holds up to a DMTAP mole fraction of 0.75. The explanation for this is straightforward: as TAP increases, the PC headgroups become more and more vertically oriented with respect to the bilayer plane. This, in turn, makes PC nitrogens more easily accessible for the Cl ions. In contrast, small TAP heads are located much deeper in the membrane surface region than the PC heads and therefore are able to attract fewer chlorides regardless of the fact that TAP heads carry a net positive charge. Interestingly, when the reorientation of PC heads is accomplished (at TAP 0.75), the coordination number for NPC-Cl pairs seems to saturate (see Fig. 14, bottom). |
SUMMARY AND CONCLUSIONS |
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being the only exception, to the authors' knowledge, in this regard.
As a first step toward a detailed understanding of cationic membrane-DNA complexes on an atomic level, we have employed extensive molecular dynamics simulations of lipid bilayer mixtures composed of cationic DMTAP and neutral (zwitterionic) DMPC. Such binary DMPC/DMTAP mixtures have been studied widely through experiments, and have been shown to form stable complexes with DNA (Artzner et al., 1998; Pohle et al., 2000; Zantl et al., 1999a,b). In this work, we have focused on the influence of the composition of the cationic bilayer on its structural and electrostatic properties. For this purpose, we studied numerous DMPC/DMTAP mixtures in the liquid-crystalline phase by varying the mole fraction of DMTAP, TAP, from the pure DMPC to the pure DMTAP bilayer.
We have found that the properties of the DMPC/DMTAP bilayer mixture are largely dominated by the electrostatic properties of the headgroup region around the membrane-water interface. Most notably, our results indicate that there is a strong interplay between the PC and TAP groups together with the Cl counterions that concentrate in the vicinity of the bilayer-water interface.
The interplay between the PC and TAP groups leads to a number of intriguing observations. The key factor here is the reorientation of PC groups due to an introduction of DMTAP in the bilayer. The reorientation of the PC headgroups arises from electrostatic interactions that lead phosphate and choline groups to rearrange their positions with respect to the cationic TAP. This effect is enhanced as TAP is increased, and extends up to large molar fractions of approximately TAP = 0.75. Beyond this limit, a further increase of DMTAP concentration has no additional effect on the orientation of PC headgroups. Interestingly, at small TAP the effect of the reorientation is of local nature, i.e., the P-N dipoles of DMPCs beside DMTAP molecules reorient considerably.
At small molar fractions of DMTAP, the reorientation of PC dipoles leads to considerable compression of the bilayer, as alternating PC and TAP groups are able to pack more tightly than in a pure DMPC bilayer. The minimum of the area per lipid at TAP 0.5 is 12% smaller than in the pure DMPC bilayer. A further increase of TAP leads to major expansion of the bilayer. This is essentially due to an increasing number of neighboring TAP groups whose cationic nature leads to repulsive electrostatic interactions that do not favor close packing. As expected, the ordering of acyl chains closely follows the change in the area per lipid. When these results are summarized, the view of the average area per lipid coupled to the reorientation of the headgroups can be summarized schematically as in Fig. 15.
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1.4 x 10–7 cm2/s, leading to a diffusion length of 1.15 nm during a simulation of 22 ns. This is 1.5 times the diameter of a single lipid in the plane of the membrane, thus indicating that the lipid molecules in this study do mix rather well. In more general terms, dynamic properties of cationic lipid bilayers are of great importance on their own. However, such properties are beyond the scope of this work and will be discussed elsewhere.
In view of future studies of DNA-membrane systems, it is important to pay attention to the influence of DMTAP on the electrostatic properties of the membrane, including the increase in the electrostatic potential across the bilayer and the ordering of water in the vicinity of the membrane-water interface. Another often ignored aspect of electrostatics is that the ionic buffer liquids may affect membranes significantly (Böckmann et al., 2003).
Perhaps the most significant observation in this study is the spatial rearrangement of PC and TAP headgroups, which is expected to play a significant role in the condensation of DNA onto the membrane surface. The cationic TAP and choline groups then play a key role as the anionic phosphate groups of DNA come into contact with the membrane. Although this study clarifies some of the underlying questions related to binary mixtures of cationic and neutral (zwitterionic) lipid membranes, further atomic-level studies are essential to resolve other important issues related to DNA-membrane systems, such as the influence of salt and its screening effects, and the stability and interface properties under those conditions. Work in this direction is under way.
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ACKNOWLEDGEMENTS |
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This work has been supported by the Academy of Finland Grant Nos. 202598 (A.G.), 54113 (M.K.), and 80246 (I.V.); the Academy of Finland through its Center of Excellence Program (A.G. and I.V.); and by the European Union through the Marie Curie fellowship HPMF-CT-2002-01794 (M.P.).
Submitted on December 16, 2003; accepted for publication February 11, 2004.
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0.31) are shown on the top, and the high concentration regime (
0.63) is illustrated at the bottom. For clarity's sake, the results at intermediate concentrations are not shown here.
) Results averaged over only those DMPC molecules that are beside DMTAP. See text for details.
onto the interfacial normal 
. Here, z = 0 corresponds to the center of the bilayer, and the bilayer normal 
