Why is the sn-2 Chain of Monounsaturated ... - ACS Publications

J. Phys. Chem. B 2009, 113, 8347–8356

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Why is the sn-2 Chain of Monounsaturated Glycerophospholipids Usually Unsaturated whereas the sn-1 Chain Is Saturated? Studies of 1-Stearoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (SOPC) and 1-Oleoyl-2-stearoyl-sn-glycero-3-phosphatidylcholine (OSPC) Membranes with and without Cholesterol Hector Martinez-Seara,† Tomasz Ro´g,‡ Mikko Karttunen,§ Ilpo Vattulainen,‡,|,⊥ and Ramon Reigada*,† Department of Physical Chemistry, Barcelona UniVersity, c/ Marti i Franques 1, Pta 4, 08028 Barcelona, Spain, Department of Physics, Tampere UniVersity of Technology, Tampere, Finland, Department of Applied Mathematics, The UniVersity of Western Ontario, London (ON), Canada, Department of Applied Physics and Helsinki Institute of Physics, Helsinki UniVersity of Technology, Helsinki, Finland, and MEMPHYS-Center for Biomembrane Physics, UniVersity of Southern Denmark, DK-5230 Odense, Denmark ReceiVed: March 10, 2009; ReVised Manuscript ReceiVed: May 14, 2009

Despite the large number of possible glycerol-based phospholipids, biological membranes contain only a small number of them. For example, double bonds in acyl chains are preferably located in the sn-2 chain. The question that emerges is: Why? We have addressed this question through atomistic simulations by considering pure one-component bilayers comprising monounsaturated glycerophospholipids [1-stearoyl-2oleoyl-sn-glycero-3-phosphatidylcholine (SOPC) and 1-oleoyl-2-stearoyl-sn-glycero-3-phosphatidylcholine (OSPC)] and membranes of these lipids mixed with cholesterol. By considering the cases in which an individual double bond is in either the sn-1 or the sn-2 chain, we elucidated how membrane properties depend on this intrinsic feature. We found small but systematic differences in all structural and dynamic membrane properties that we considered. It turns out that the differences are driven by two factors: the mismatch in the acyl chain lengths and the interaction of the double bond in the acyl chains with the cholesterol off-plane methyl groups. The results highlight the fact that unsaturated sn-2 chains lead to more disordered membranes than systems with unsaturated sn-1 chains. The differences between the two isomers are enhanced when cholesterol is present as a result of the interaction of the off-plane cholesterol methyl groups with the double-bond carbon segments in the lipid acyl chains. 1. Introduction Although the compositions of biological membranes are highly complex, certain patterns do exist. Glycerol-based lipids such as phosphatidylcholines (PCs) or phosphatidylethanolamines (PEs) are highly heterogeneous because of variations in their acyl chains, which can differ, for example, in length and the number and position(s) of double bond(s). Additional heterogeneity arises through the nonequivalence of the two chains of a PC molecule (the sn-1 chain attached at carbon/ position 3 and the sn-2 tail attached at carbon/position 2 of the glycerol moiety; see Figure 1). Taking into account all of these possibilities together with possible variations in the headgroup region, one can imagine thousands of possible glycerol-based phospholipids. Biological systems, however, are selective. For example, in erythrocyte membranes, only about 100 phospholipid species have been identified.1 Meanwhile, contrary to PCs or PEs, cholesterol (Chol) is a single molecular species, and it can be found in eukaryotic cell membranes in relatively high quantities, highlighting its biological relevance, especially in * Address correspondence to R. Reigada. E-mail: [email protected]. † Barcelona University. ‡ Tampere University of Technology. § The University of Western Ontario. | Helsinki University of Technology. ⊥ University of Southern Denmark.

eukaryotic plasma membranes. Its molar concentration can be as high as 50-70 mol %,2,3 although it is typically around 20%.4,5 Lipids with two different acyl chains can have positional isomers, that is, either chain has two possible locations, sn-1 or sn-2. For all glycerol-based lipids present in cells, the sn-1 chain is most commonly the saturated one, and the sn-2 chain is monoor polyunsaturated, that is, double bonds are preferably located in the sn-2 chain. This preference has been observed in both eukaryotic6-8 and prokaryotic9,10 membranes. Measurements for mycoplasma show an 8:1 preference for the double bond(s) to be located in the sn-2 position for lipids containing 18:1 chains.10 This preference appears to be very systematic, but its is unknown. To our knowledge, only relatively few articles have addressed this issue.11-16 Calorimetric studies have shown that the main transition temperature, Tm, depends slightly on the particular chain in which the double bond is located; if it is in the sn-1 chain, Tm is about 2-4 K higher for a lipid with two 18-carbon chains as compared to the double bond being in the sn-2 chain.11,12,14,15 In addition, calorimetry and other methods have shown that a mixture of cholesterol with positional isomers indicates cholesterol interactions with PC in the gel phase to be influenced by the position of the unsaturated chain.12,13,17 Also, biological data concerning positional isomers of saturated and unsaturated chains are rather limited. It was shown that, in hepatoma cells, there is a loss of positional specificity associated

10.1021/jp902131b CCC: $40.75  2009 American Chemical Society Published on Web 05/26/2009

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J. Phys. Chem. B, Vol. 113, No. 24, 2009

Martinez-Seara et al.

Figure 1. (a) Molecular structure of DSPC with numbering of atoms and torsion angles (T). The unsaturated bonds in the other studied species are marked: SOPC (db2), OSPC (db3), and DOPC (db2 and db3). (b) Numbering of atoms for cholesterol. In both panels, the chemical symbol for carbon atoms, C, is omitted.

with elevated concentrations of cholesterol.18 Similarly, in mycoplasmas with high levels of cholesterol, large amount of lipids with sn-1 unsaturated and sn-2 saturated chains have been observed.10,19 Data concerning the regulation of membrane composition are nearly nonexistent, although the topic has been receiving an increasing amount of attention (see, e.g., ref 20). In our previous studies, we investigated how the presence and position of a double bond along an acyl chain21-24 influences membrane properties and how the membrane interacts with cholesterol.4,25-27 The latter issue is highly relevant from the point of view of raft formation. We found that, when the double bond was placed in the middle of an acyl chain, the studied bilayers were in their most disordered states.21 This position corresponds to the situation most commonly encountered in natural membranes.6,28 When cholesterol is present, differential interactions of cholesterol with double bond in different positions are observed. Out-of-plane methyl groups (C19 and C18; see Figure 1b) have been shown to be relevant for the interactions of cholesterol with a lipid acyl chain having a double bond: the closer the contacts between the cholesterol methyl groups and the double bond, the more disordered the system was found to be.4,29 This interaction is strongest when the double bond is located in the middle of an acyl chain, thus amplifying the disorder previously reported in this situation.4,25 In this article, we employ atomistic simulations to consider positional sn-1/sn-2 isomers in a pure bilayer and in a binary mixture with cholesterol. The glycerophospholipids used in this work are monounsaturated, having only a single double bond in either the sn-1 or the sn-2 chain. We found that differences between isomers are small but persistent and that they increase in binary mixtures with cholesterol. The molecular mechanism of these differences seems to be related to the mismatch in chain length along the bilayer and is enhanced in the cholesterolcontaining membranes by the interaction of the double bond in the PC acyl chain with the C18 cholesterol methyl group. Our main finding is that membranes composed by positional isomers have unequal physical properties. The nature of these differences is rather small but clearly detectable.

2. Methods Atomic-scale molecular dynamics (MD) simulations of four different membrane systems have been carried out. The first two (pure) bilayers were composed of a total of 128 PC molecules, and the remaining two (mixed) systems contained 32 cholesterol molecules in addition to the 128 PCs. All of the bilayers were hydrated with 3800 water molecules. Two different monounsaturated PC lipids that are positional isomers were used in this study: 1-stearoyl-2-oleoyl-sn-glycero-3phosphatidylcholine (SOPC: 18:0;18:1) and 1-oleoyl-2-stearoylsn-glycero-3-phosphatidylcholine (OSPC: 18:1;18:0). The structures are shown in Figure 1a. As reference systems, we used fully saturated 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC: 18:0;18:0) and diunsaturated 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC: 18:1;18:1) bilayers and their binary mixtures with 20 mol % cholesterol from our previous studies.4,25 The initial structures of SOPC and OSPC bilayers were obtained from the final configurations of our previous simulations of DOPC (100 ns)21 and DOPC-Chol (150 ns).4 The force-field parameters are provided at our web site at www.softsimu.org. The simulations were performed using the GROMACS software package.30,31 We used the standard united-atom forcefield parameters,32 which have been extensively tested and verified. The partial charges were taken from the underlying model description.33 For the double bond, we used the description by Bachar et al.,34 which explicitly describes the skew states of bonds next to the double bond. (For a detailed discussion on this issue, see ref 25.) For cholesterol (see Figure 1b), we used a description based on that of Holtje et al.35,36 The simple point charge (SPC) model37 was used for water. The single-component systems were simulated for 100 ns, and the binary mixtures were run for 150 ns. In both cases, the first 20 ns was considered as an equilibration period and hence discarded from analysis; equilibration was determined by monitoring temperature, potential energy, and area per lipid. Temperature and pressure were controlled by using the weak coupling method38 with relaxation times set to 0.6 and 1.0 ps,

SOPC and OSPC Membranes with and without Cholesterol

J. Phys. Chem. B, Vol. 113, No. 24, 2009 8349

TABLE 1: Membrane Propertiesa,b,c 15

Tm for LR/Lβ transition (K) APC (Å2) double-bond efficiency (Å2) P-P distance (Å ( 0.1 Å) 〈-SCD〉 ((0.003; no double bond) sn-1 sn-2 z-axis tilt (deg) sn-1 sn-2 cholesterol ring cholesterol tail PN 〈dbilayer center〉 (Å) ( 0.1 Å sn-1 (C318) sn-2 (C218) chain mismatch 〈dC18〉 (Å ( 0.1 Å)c sn-1 (C39-C310) sn-2 (C29-C210)

DSPC

OSPC

SOPC

DOPC

328.80 66.95 ( 0.31/56.39 ( 0.19 NA/NA 40.2/46.4

281.90 70.21 ( 0.19/61.88 ( 0.31 3.27/5.49 38.5/42.9

279.90 70.67 ( 0.34/62.63 ( 0.17 3.73/6.24 38.3/42.5

232.90 73.08 ( 0.21/66.25 ( 0.24 3.06/4.93 37.1/40.4

0.151/0.261 0.154/0.262

0.114/0.177 0.140/0.217

0.136/0.208 0.113/0.172

0.106/0.150 0.106/0.152

34.25/21.74 33.46/21.06 19.63 28.70 100.24/98.90

37.36/28.53 34.73/25.34 24.29 34.93 100.81/99.30

35.76/26.72 37.08/28.64 25.91 37.17 100.80/99.51

37.75/31.56 36.59/30.65 26.52 37.89 101.50/100.49

2.17/2.06 2.57/2.62 0.40/0.56

2.72/2.75 2.16/2.16 -0.56/-0.59

1.72/1.72 3.04/3.11 1.32/1.39

2.24/2.33 2.52/2.66 0.28/0.33

0.07 -0.70

0.36 -0.37

0.70 -0.02

-0.06 -0.65

a Light-face letters are used for the values for pure systems, whereas bold letters are used for the systems containing 20 mol % cholesterol. db stands for double bond. NA stands for not available. b Errors are explicitly given in the table. c Underlined: db chain.

respectively. The temperatures of the solute and solvent were controlled independently, and pressure coupling was applied separately in the bilayer plane (xy) and the perpendicular direction (z). The simulations were carried out in the NpT (constant particle number, pressure, and temperature) ensemble at p ) 1 atm and T ) 338 K. The selected temperature is above the main phase transition of DSPC (Tm ) 328 K), the highest among the studied lipid species. The SETTLE algorithm39 was used to preserve the bond lengths in water molecules, whereas the lipid bond lengths were constrained using the LINCS algorithm.40 A single 1.0-nm cutoff distance was used for the Lennard-Jones interactions. Long-range electrostatic interactions were handled using the particle-mesh Ewald method41 with a real-space cutoff of 1.0 nm, B-spline interpolation (of order 6), and a direct sum tolerance of 10-5. Periodic boundary conditions with the usual minimum image convention were applied in all three directions, and the time step was set to 2 fs. This simulation protocol has been successfully applied in a number of previous MD studies; see, for example, refs 4, 21, 25, 29, and 36. 3. Results and Discussion To provide a complete picture of the behavior of membranes containing the two studied positional isomers, we calculated a number of physical properties covering a major fraction of the relevant ones, regarding both structure and dynamics. In all of the presented results, error bars were estimated using the block analysis method42 and are given as twice the standard error. 3.1. Structural Properties. Area per Molecule. We calculated the average area per PC molecule, APC, in the singlecomponent systems by dividing the total average area of the membrane, A, by the number of PC molecules in a single leaflet. Although this property is straightforward to define in the case of a single-component bilayer, it becomes nontrivial when more than one lipid species are present, as there is no unique way to decompose the cross-sectional area between the components.43-46 For the mixed membranes, we followed the procedure of Hofsa¨ss et al.45 that defines the area per PC as

APC )

( )(

NcholVchol 2A 1NPC VNwVw

)

where V is the volume of the simulation box, NPC is the number of PC molecules, Nw is the number of water molecules, Vw is the volume occupied by a water molecule, Nchol is the number of cholesterols, and Vchol is the volume of a cholesterol molecule. This equation expresses the point that the cross-sectional area of a lipid divided by its volume equals the area of a membrane leaflet divided by its volume. Then, APC can be computed provided that Vw and Vchol are known. The value for Vw was obtained from an independent simulation of a slab of 7161 water molecules under identical simulation conditions, and the volume occupied by a cholesterol molecule was taken to be 541 Å3.43-45 SOPC bilayers have larger APC values than their OSPC counterparts (see the results listed in Table 1). The difference between SOPC and OSPC is small but statistically significant for both single-component (0.46 Å2) and cholesterol-containing (0.75 Å2) systems. We can conclude that the lipid with the double bond in its sn-2 chain (SOPC) induces more disorder. The differential behavior is enhanced by the addition of cholesterol (see Table 1). Comparison to experimentally measured areas per molecule is limited to pure SOPC bilayers. Experiments47 give APC ) 66 Å2 at 303 K for fully hydrated SOPC bilayers. In our simulations, we obtained a larger value (70.67 Å2) but at a temperature that is 35 K higher. A typical increase of 1 Å2 per 5-7 K48 leads to good agreement with our simulated value for APC. Moreover, our model has already been validated in previous works for the areas per molecule in DSPC and DOPC bilayers.4,25 Important to notice is the agreement between calorimetric experiments and the observed differences in area per molecule. Table 1 provides the main transition temperatures, Tm, for the single-component systems studied here. They are inversely correlated with the areas per molecule, as has also been observed for many phosphatidylcholines.25 The nature of such a correlation is not unequivocal, but has been shown to be accurate enough to compare lipids with small structural differences.25 For monounsaturated species, a difference of 2-4 K was found between SOPC and OSPC.11,14,15,49 In this case, the difference is associated with a small difference in the area per molecule, 0.46 Å2, and captures the predicted correlation between Tm and area per lipid. In the systems containing cholesterol, the comparison is not as straightforward. Calorimetric profiles show

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minor differences in shape between SOPC and OSPC with 17-23 mol % cholesterol,12 as well as differences in area observed in our systems with 20 mol % cholesterol. At this point, a simple evaluation of the efficiency of the double bond in inducing disorder seems adequate and can be accomplished as follows: Consider the increase in the area per lipid with respect to the saturated lipid (DSPC) for the pure and cholesterol-containing systems independently and divide the result by the number of double bonds (see Table 1). This analysis shows that placing the double bond in the sn-2 chain increases the disordering effect considerably. It is also important to notice that the addition of a second double bond (DOPC), giving a lipid with two monounsaturated chains, does not double its effect. Instead, a drop in the ratio for the area increase per double bond is found. This feature is enhanced in the presence of cholesterol. Bilayer Thickness. Another important structural parameter is the bilayer thickness. This property is related to ordering, membrane permeability,50 and the activity of transmembrane proteins.51,52 There is no unique definition for membrane thickness, but because we are mainly interested in comparing the two studied monounsaturated lipid systems, we chose the simplest measure, namely, the average distance between the phosphorus atoms in the opposite leaflets (P-P distance). This choice allowed us to validate our model in previous works for DSPC and DOPC by comparing the obtained results with the available experimental values.4,25 The observed differences between SOPC and OSPC, although statistically different, are small: 0.2 Å for the pure systems and 0.4 Å for the mixed systems (see Table 1). Despite the smallness, the observed trend is consistent with area per molecule. Acyl Chain Mismatch. Previous studies of the asymmetry between the two lipid acyl chain lengths concluded that phospholipid chain-length mismatch can induce disorder; see, for example, refs 53 and 54. Such mismatch can be understood as the difference in depth reached by the two chains of a given molecule, so it can be rationalized by computing the distance between the terminal methyl groups at each tail of the lipid. To do so, we calculated the mass density profiles in the direction perpendicular to the bilayer plane for the end methyl groups (C318 for the sn-1 chain and C218 for the sn-2 chain; see Figure 1a) of each leaflet. We considered the barycenter (center of gravity) positions of mass density profiles, computed separately for each of the terminal methyl groups in each leaflet. For a given terminal methyl group (C318 or C218), the distance between the two barycenters corresponds to twice the distance from the terminal methyl group to the bilayer center (see data for 〈dbilayer center〉 given in Table 1). Subtracting this distance for C318 (which, in principle, is less deeply inserted) from the value for C218, we obtained the mismatch between the chains (see chainmismatch data in Table 1). Positive values correspond to a situation where C318 (the sn-1 chain) penetrates more deeply into membrane center than C218 (the sn-2 chain). For symmetric lipids (i.e., lipids with the same numbers of double bonds and chain lengths), such as the DSPC, DSPC-Chol, DOPC, and DOPC-Chol membranes, the chain mismatch is positive. This means that the sn-1 end methyl group is inserted more deeply than the sn-2 one, as a result of a more deeply inserted ester linkage with the glycerol in the sn-1 chain compared to the sn-2 chain (see Figure 1a). A similar positive but much larger chain mismatch is found in SOPC and SOPC-Chol membranes, indicating that the saturated sn-1 chain of SOPC extends deep into the membrane like a semirigid rod

Martinez-Seara et al. whereas the unsaturated sn-2 chain adopts a more disordered conformation. In the case of the OSPC and OSPC-Chol systems, the situation is the opposite. One finds a negative value for chain mismatch: the ester linkage of the unsaturated sn-1 chain is deeper in the membrane than the ester linkage of the saturated sn-2 chain, the sn-1 chain adopts a more disordered conformation because of the double bond, and this latter effect dominates. The absolute value of the mismatch is a relevant quantity in terms of disordering. The larger the value, the more disorder is induced by the mismatch effect explained above. Symmetric lipids (DSPC, DOPC) are a good reference for small mismatch effects (0.28-0.56 Å; see Table 1). We observed similar values for OSPC (0.56 and 0.59 Å), but values that were at least twice as large for SOPC (1.32 and 1.39 Å). This justifies why the SOPC moiety (having a greater chain-length mismatch) displays a larger area per molecule than OSPC (having a smaller mismatch effect). In membranes with cholesterol, a systematic increase within the range 0.04-0.16 Å in absolute value was observed. No major changes are expected from such small increments between pure and mixed bilayers. Interaction between Double Bond and Off-Plane Cholesterol Methyl Group. So far, we have justified the differences in area per molecule observed between SOPC and OSPC bilayers. However, we have not explained the mechanism that causes these differences to increase when cholesterol is added. In a previous article,4 it was shown that the proximity of the double bond to the off-plane methyl group of cholesterol, C18 (see Figure 1b), induces disorder in the system. To elucidate the role of this feature in our mixed bilayers, we tracked the relative position in the z direction (normal to the bilayer plane) of both groups in the system. Following a procedure similar to that described in the former section, we computed the distance in the z axis between the center of mass of the double bond and the C18 group in cholesterol. The relative z positions of the center of mass of the lipid chain segments C39-C310 and C29-C210 with respect to C18 of cholesterol, 〈dC18〉, are given in Table 1. It is observed that segments corresponding to the double bond interact with C18 and promote disorder in the membrane. We can clearly see that, in the case of SOPC, the z positions are almost the same (-0.02 Å), whereas the vertical positions in the case of OSPC are considerably different (0.36 Å). This explains why the SOPC membrane is more disordered upon addition of cholesterol than OSPC or, from another perspective, why the ability of cholesterol to order the surrounding lipids is lower for SOPC than for OSPC. In brief, cholesterol promotes ordering through the sn-1 chain, cholesterol promotes disordering through the sn-2 chain, and a monounsaturated acyl chain is preferred for sn-2 over sn-1. Deuterium Order Parameter. To quantify the ordering of chains, we computed the deuterium order parameter,55 SCD, profiles along the chains. SCD is defined as

1 SCD ) 〈3 cos2 θ - 1〉 2 where θ is the angle between the carbon-deuterium (CD) bond and the bilayer normal and the angular brackets denote averaging over time and over all CD bonds in a given carbon position. Because we employed a united-atom model, the deuterium positions were constructed from the neighboring carbons, assuming ideal geometries separately for single and double



Figure 2. SCD order parameter profile for both chains, sn-1 (solid) and sn-2 (dashed), in the pure systems (SOPC in blue, OSPC in red) and in mixtures including 20 mol % cholesterol (SOPC in black, OSPC in green) at 338 K. The error bars are smaller than (0.005.

Figure 3. Form factors, |F(q)|, as a function of the wavenumber q for the simulated pure SOPC (black), pure OSPC (red), SOPC-cholesterol (blue), and OSPC-cholesterol (green) bilayers at 338 K.

bonds. -SCD profiles along the chains are plotted in Figure 2 for pure OSPC and SOPC bilayers and their cholesterol mixtures. Analysis of the -SCD profiles reveals that the saturated chains in OSPC and SOPC lipids display different behaviors. For the saturated chains (sn-1 in SOPC and sn-2 in OSPC), we found essentially identical order close to glycerol, whereas for carbons 7-18, there was considerably less order in SOPC. For the unsaturated chains (sn-2 in SOPC and sn-1 in OSPC), SOPC is less ordered close to the glycerol group than OSPC (carbons 1-7), but it is slightly more ordered in the membrane center beyond the double-bond position (carbons 12-18). To clarify which acyl chains are globally more ordered, we computed the average of -SCD (see Table 1). Averages for DOPC and DSPC membranes are also given as references. We can conclude that both saturated and unsaturated chains display a higher ordering in OSPC systems than in SOPC bilayers, although the differences are small. Both chains contribute to the higher ordering of OSPC systems, but most of this effect is due to the saturated acyl chain. In mixed bilayers with cholesterol, the conclusions are precisely the same, the only difference being that cholesterol increases the differences between SOPC and OSPC. Molecular Tilt. The average tilt angles with respect to the z axis for the sn-1 and sn-2 chains, cholesterol ring, and cholesterol tail are given in Table 1. The measurements and definitions of the axes were identical to those in our previous work.4,27 The data support the suggestion that the saturated chain shows differential behavior between positional isomers. That is, whereas the tilt of an unsaturated chain remains nearly unaltered between isomers (differences of about 0.28° for pure bilayers and 0.11° for mixed systems), the differences are larger for saturated chains (1.03° and 1.38° for pure and mixed membranes, respectively). Interestingly, positional isomers change the tilt of cholesterol quite significantlysa difference of 1.62° between OSPC and SOPC was observed (see Table 1). The tilt of cholesterol has recently been recognized to be a relevant measure of a sterol’s ability to condense a bilayer, and differences in sterol tilt explain why the differential behavior between positional isomers is amplified by cholesterol.27,56,57 Here, we indeed found that the cholesterol tilt is smaller in OSPC, in agreement with the higher average order of lipid acyl chains and the smaller area per lipid compared to the SOPC system. Form Factors. Considering the difficulties in rigorously comparing computer simulation data with experiments, we introduce the scattering form factor, F(q). The benefit of using

the form factor is that it can be computed from simulations and then compared with experimental “model-free” measurements; the form factor is essentially primary data measured from experiments. First, the relative electron density profile Fr(z) is computed by subtracting the electron density of bulk water from that of the simulated system, where z is the direction perpendicular to the bilayer. Here, we found 315.3 e-/nm3 for the single-component systems and 318.2 e-/nm3 for cholesterolcontaining ones. The scattering form factors were then calculated using the expression58

|F(q)| )

√[ ∫

L/2

-L/2

] [∫ 2

Fr(z) cos(qz) dz +

L/2

-L/2

]

Fr(z) sin(qz) dz

2

where L is the length of the simulation cell in the z direction and q is the wavenumber. The form factors are plotted in Figure 3 for the simulated pure and cholesterol-containing systems for both SOPC and OSPC membranes. Currently, no experimental data are available for such systems, but the obtained results could be validated in future experiments. However, form-factor curves for simulated DOPC bilayers were successfully compared to experimental data in our previous study.4 The positions of the minima of F(q) are correlated with the area per molecule: minima at smaller wave numbers q imply a smaller area per molecule.48 Interactions at the Interface. To complete our analysis of structural properties, we considered interactions at the water/ membrane interface. We considered the same three types of interactions as used in our previous studies:59 hydrogen (H) bonds (when the distance between a donor and an acceptor was less than 0.325 nm and the angle between a donor-H bond vector and a donor-acceptor vector was less than 35°), water bridges (water molecules simultaneously H-bonded with two lipid molecules), and charge pairs (interactions between positively charged choline groups and negatively charged oxygen atoms of other lipids within 0.4 nm). We focused solely on cholesterol-PC interactions. Their average values per cholesterol are given in Table 2. It is observed that the interaction pattern is almost the same in all bilayers, namely, cholesterol is H-bonded mainly to the carbonyl group of sn-2 chain. The observed small quantitative differences originate from the changes in the surface area, which is in agreement with our previous studies.60 We did not observe qualitative differences in the case of PC-PC interactions (data not shown), which is consistent with our previous simulations.4

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TABLE 2: Interactions at the Membrane/Water Interfacea,b sterol-PC H-bonds total O22/O21 O32/O31 sterol-PC water bridges sterol-PC charge pairs

DSPC

OSPC

SOPC

DOPC

0.80 0.33/0.15 0.09/0.06 0.31 1.02

0.80 0.36/0.13 0.08/0.06 0.32 1.02

0.79 0.41/0.13 0.08/0.06 0.29 1.12

0.79 0.33/0.13 0.08/006 0.32 0.99

a All systems contain 20 mol % cholesterol. than 0.02.

b

Errors are smaller

3.2. Dynamical Properties. Lipid and Cholesterol Rotational Motion. The rotational motions of the different lipid species can be studied by computing time-dependent autocorrelation functions (ACFs). ACFs are defined as the first associated Legendre function of an intramolecular vector, f, of the analyzed molecule, C(τ) ) 〈f(t) f(t + τ)〉, where the brackets represent an average over time and molecules. Physically, ACFs measure how fast a molecule, or part of a molecule, rearranges its orientation as a response to changes in its surroundings. We examined four different rotational modes: the headgroup, the two acyl chains, and the cholesterol plane. For the phospholipid headgroup, we studied the vector connecting the phosphorus and nitrogen atoms in the headgroup (see Figure 1a), hereafter referred to as the PN vector. This choice corresponds to the headgroup mode only and does not account for the complex intramolecular motion of the flexible PC chains. Figure 4a shows the ACFs for the PN vector in SOPC and OSPC membranes with and without cholesterol. Data for the reference systems (i.e., DSPC and DOPC) are also provided. The relaxation times are observed to follow the same order with and without cholesterol: the saturated DSPC system has the longest relaxation time, but systems containing OSPC and SOPC display very similar temporal correlation decays. Finally, the diunsaturated DOPC system shows faster relaxation times. These results follow the same trends as found for the area per molecule. In all cases, the presence of cholesterol dramatically slows the vector motion. Importantly, the ACF curves decay but reach a nonzero plateau value as τ f ∞; as a consequence, the studied vector does not rotate freely in all directions. Although PN vector rotation in the xy plane is basically unrestricted, the motion in the z direction is restricted by its tilt angle, Ω; that is, the vector wobbles in a vertical cone with the average angle Ω. Values of Ω for different systems are close to 100°, and it is easy to prove that C(τf∞) ) 〈cos2(Ω)〉. No qualitative differences were found for Ω between the studied lipid species (see Table 1). Similar behavior for the PN vector was also found for the glycerol vector, corresponding to the vectors joining atoms C1 and C3 (see Figure 1a). The relaxation times were about twice as large as those for the PN vector, and the vector itself is much less tilted [C(τf∞) ≈ 0.3; data not shown]. To study chain rotation, we focused on the vectors connecting carbon group pairs C32-C318 and C22-C218 for sn-1 and sn-2 chains, respectively. The correlation curves are shown in Figure 4b,c. Values for Ω for the acyl chains are directly related to the tilt angle provided in Table 1. Inspection of the correlation curves allows some clear conclusions to be made. First, acyl chain vector rotation is restricted to a smaller tilt angle Ω as compared to that seen with PN vectors. In addition, the relaxation time is much shorter than for the PN vector. Second, the area per molecule is an important factor: the larger the area, the faster the decay. Third, a double bond enhances rotational motion (see OSPC and SOPC in Figure 4b,c) and typically

Figure 4. Autocorrelation functions, C(t), of the (a) PN vector; (b) C2 f C18 vector of the two lipid chains in the pure systems; (c) C2 f C18 vector of the two lipid chains in the cholesterol mixtures; and (d) C6 f C11 cholesterol vector for the moieties DSPC (solid), OSPC (dotted), SOPC (dashed), and DOPC (dot-dashed). In panel a, pure systems are represented by thin lines, and binary systems are represented by thick ones. In panels b and c, thin lines correspond to sn-1 chains, and thick ones correspond to sn-2.

increases the tilt angle. Fourth, for a given symmetric lipid (e.g, DSPC, DOPC), the sn-1 chain rotation loses its correlation slightly faster than the sn-2 chain rotation. This is a consequence of the fact that sn-1 chains are inserted more deeply into the bilayer. For the monounsaturated PCs studied in this work, the combination of the previous effects results in a large difference between the behaviors of the two chains in OSPC, whereas the decays for the two chains in SOPC are only moderately different (consequences of the presence of the double bond are compensated by the sn-2 effect in SOPC). When mixed with cholesterol, the previous features are typically enhanced, and as general trends, rotational motion is slowed, and the values of Ω are reduced as a result of the increase in chain ordering and the reduction in area per molecule. Finally, to study the rotational modes of cholesterol molecules, we chose the vector between the cholesterol atom groups C6 and C11 (Figure 4d). This choice accounts for the rotation



of the rigid ring system of the sterol molecule. For this mode, the ACF curves show the same correlation with the area per molecule as was observed for the PN rotation: cholesterol motion is slower when mixed with DSPC than when mixed with DOPC. The motions of cholesterol in SOPC and OSPC are intermediate between those of DOPC and DSPC and practically indistinguishable. Chain Dynamics. To characterize chain dynamics, we computed the autocorrelation functions, C2(τ), corresponding to the second associated Legendre function

1 C2(τ) ) 〈3[f(t) f(t + τ)]2 - 1〉 2 for each CH vector f. Because we used a united-atom simulation approach, the CH vectors were first reconstructed assuming a perfect geometry according to the carbon hybridization (sp3 for the saturated segments and sp2 for the unsaturated ones). This choice allows for a straightforward comparison with NMR experiments.60-62 Our first analysis consisted of the computation of the fastest decay modes, quantified by the decay half-times, t1/2. As a general result, the values of t1/2 for most of the carbon groups are on the order of picoseconds (t1/2 ≈ 10 ps). When approaching the carbon group directly attached to the headgroup, the fastest modes become slower, resulting in half-times of t1/2 ≈ 80-100 ps. A more detailed analysis covering all possible time scales is usually performed by fitting the correlation curves to particular functions and extracting the different relaxation times from those curves. In general, correlation functions reveal stretched exponential decays that can be fitted by a sum of exponentials, each with a different decay time scale.61 Here, we choose the three exponentials

C2(τ) ) k + Ae-τ/a + Be-τ/b + Ce-τ/c In principle, each exponential corresponds to a distinct mode. For example, a fast mode might correspond to a reorientation due to local trans-gauche isomerization, whereas a slow one might correspond to rigid-body-like rotation of the whole molecule. Other modes such as translation could be present, but for the time scales in this work, their impact is limited. We also tried to fit four exponentials to decay curves. In many cases, however, we obtained negative values for amplitudes, which would be physically unreasonable. There were only a few cases where a good fitting was obtained for four exponentials, but then the amplitude coefficient of one of the exponentials was close to zero, which implied a nearly nonexistent mode. However, when three exponentials were used, reasonable amplitude values were obtained for all exponentials. Of significance, the obtained decay times were found to be comparable to typical experimental NMR relaxation times,63 and because NMR relaxation measurements are lacking for the PCs studied in this work, our focus was on comparing simulated systems with each other. Therefore, the choice of three exponentials is technically acceptable for our comparison purposes. After performing the fitting, we computed an average relaxation time, hereafter referred to as the average time constant (ATC), by weighting the characteristic relaxation times of each exponential decay type by their amplitudes [ATC ) (Aa + Bb + Cc)/(A + B + C)]. This property is inversely proportional to the rotational velocity of the studied carbon segment. We have plotted the obtained values for the chains of the monounsaturated

Figure 5. Average time constant for the CH vectors in the sn-1 (solid) and sn-2 (dashed) acyl chains of SOPC (black) and OSPC (red): (a) pure systems, (b) bilayers with cholesterol.

lipids in pure systems in Figure 5a and for bilayers with cholesterol in Figure 5b. Qualitatively, the curves display decays in a roughly exponential fashion along the carbon segments approaching the bilayer center. The slowest rotations (up to ∼1 ns) were found for the carbons close to the membrane/water interface, whereas the inner carbon groups in the bilayer center were found to rotate much faster (10-20 ps). The latter is a signature of the disordered nature of the hydrophobic region. Moreover, in systems with cholesterol, one finds larger correlation times as a signature of area reduction and increase of chain ordering. Although our focus was on comparing the two monounsaturated lipids with each other, it is noteworthy that the experimental values of NMR experiments for DPPC63 show good agreement with the general behavior and the order of magnitude of the computed correlation times. Similar agreement was found with effective characteristic times computed from autocorrelation functions in simulations of polyunsaturated PCs.24 Looking at the curves in Figure 5a (pure systems), one can see that the effect of a double bond consists of an enhancement of rotation of the neighboring methyl groups along the same chain (carbon numbers 8, 11, 12, and 13). The carbons involved in the double bond (9 and 10), however, are slower than their neighbors but have relaxation times similar to those of the same carbon numbers in the saturated chain. On the other hand, in cholesterol-containing systems, the effect is different, as can be seen from Figure 5b. In that case, the methyl groups neighboring double-bond carbons do not show enhancement in their rotational motion, and carbons involved in the double bond are significantly slowed. For example, carbon 10 in the sn-2 chain of SOPC has ATC ) 91.98 ps, whereas the corresponding carbon in the sn-1 chain has ATC ) 34 ps. This effect is more pronounced in the case of the unsaturated SOPC acyl chain than in the case of corresponding OSPC chain: carbon 10 in the sn-1 chain of OSPC has ATC ) 71.0 ps, whereas carbon 10 in sn-2 has ATC ) 34.0 ps. Therefore, cholesterol increases the rigidity of the double-bond region. It is interesting that this effect is stronger when the double bond is in the sn-2 chain (SOPC)

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Figure 6. Temporal evolution of the mean-squared displacements in the xy plane for the PC lipids in the pure bilayers (solid lines) and in the mixed systems (dashed lines).

TABLE 3: Lateral Diffusion Coefficients (µm2/s) for the Lipids in the Pure and Mixed Systemsa,b pure bilayer mixed bilayer

DSPC

OSPC

SOPC

DOPC

11.7 3.21

17.2 7.95

18.7 7.08

18.8 11.1

a Computed from the slopes in the 20-30-ns period of the MSD plots in Figure 6. b Errors associated with diffusivities are (14% in the pure systems and (10% in the mixed bilayers.

than when it is placed in the sn-1 chain (OSPC), so that, even though the area per molecule for SOPC-Chol bilayers is larger than that for OSPC-Chol mixtures, the atoms involved in the double bond rotate much more slowly in SOPC-Chol bilayers than in OSPC-Chol systems. It seems plausible that the origin of the greater area per molecule for SOPC lies in the increased rigidity of the double-bond region, which interacts weakly with the cholesterol ring. Lateral Diffusion. Finally, we examined the lateral diffusion of lipids in the bilayer plane by measuring the diffusion coefficient

Di ) lim tf∞

[ 4t1 〈r(t) 〉 ] 2

i,t

where 〈r(t)2〉 is the mean-square displacement (MSD) of the center of mass of a lipid in the xy plane averaged over all molecules of type i in the membrane. Because each monolayer in the membrane can drift during the simulation, the motion of the center of mass of individual leaflets is eliminated from the computation of the lipid MSD. The mean-square displacements are presented in Figure 6. A linear regime can be identified at long times for both pure and mixed systems. Slopes in the 20-30-ns period were computed to determine the lateral diffusion coefficients provided in Table 3. System-specific comparisons with experimental values are not possible because there do not appear to be any data for any of the studied lipids under the same conditions; in particular, no diffusion coefficients have been reported for OSPC and SOPC at any temperature. For DOPC, diffusion coefficients were measured by Filippov et al.64 at T ) 303 K (D ) 10 µm2/s) and T ) 333 K (D ) 26 µm2/s) using the pulsed-field gradient NMR technique. In comparison, we found D ) 18.8 µm2/s for pure DOPC at 338 K. An additional simulation of DOPC at 303 K for 140 ns yielded D ) 6.8 µm2/s. Both of our measured values are in a good agreement with the available experimental data, although larger systems and longer times would be appropriate for better comparisons. Considering diffusion to

express Arrhenius-type behavior, we estimated the activation energy for pure DOPC bilayers to be 25 kJ/mol. From their experiments, Filippov et al.64 estimated the barrier to be 27 kJ/ mol. On the basis of our experience, the reported error estimates for lateral diffusion coefficients determined from atomistic simulations are commonly too optimistic. This is largely because of the practice of determining the diffusion coefficient from the early-time data in the MSD, where fluctuations are the smallest. However, as the above definition for D indicates, the diffusion coefficient is well-defined only in the long-time limit where the MSD is proportional to time to the power of 1. At short times, the exponent is less than 1, and only above some characteristic time scale that is about 20 ns in the fluid phase does one find the true diffusive behavior with an exponent of 1. In practice, this implies that one should find the regime where the MSD is proportional to t1, and because this occurs at longer times, the fluctuations in the MSD data are also quite pronounced, increasing the error bars for diffusion. Using our simulation data, we found the errors associated with lateral diffusion coefficients to be at least (10%. Recent studies by Bockmann et al. are consistent with this view.65 When rational error estimates are taken into account (Table 2), the diffusion coefficients of SOPC and OSPC are, in practice, identical. Nonetheless, what we can conclude reliably is the trend of diffusion rate for increasing disorder: as the systems evolve from saturated to increasingly unsaturated ones, the lateral diffusion increases accordingly. The same feature is found in mixed systems with cholesterol. An additional effect that modulates diffusion is interleaflet friction or viscosity, generally associated with interdigitation. The motion of the individual leaflets with respect to each other is a good measure for quantifying such friction. We computed the mean-square displacements of the center of mass position of each leaflet with respect to each other. Although the statistics is rather poor, one can draw some qualitative conclusions: OSPC displays the largest leaflet center-of-mass MSD (∼13 nm2 after 30 ns), larger than those of DOPC (∼8 nm2 after 30 ns) and SOPC (∼3 nm2 after 40 ns). As expected, SOPC displays the largest interdigitation because of the largest chain mismatch. It is surprising, however, that SOPC, despite having much greater interdigitation than OSPC, diffuses slightly faster and almost as fast as DOPC, which has a much larger area per molecule and weaker interdigitation. It is plausible, although not quantified, that the faster diffusion of SOPC is a result of the free volume available inside the bilayer.66,67 The order parameter plotted in Figure 2 shows that the unsaturated chain of SOPC is less ordered than that of OSPC, indicating that free volume might indeed play a role. It might also be the case that dynamical processes such as collective motion and fluctuations contribute to the observed behavior, as has been recently reported.68,69 Whether or not that is the case here is beyond the scope of the current study. Also, because of the limited statistics of the above results, we stress the importance of considering lateral dynamics more carefully in future studies where long-time scale simulations will be more feasible. As already mentioned above, when mixed with cholesterol, OSPC and SOPC display very similar diffusivities. Analysis of interleaflet friction displays similar extents of interdigitation for OSPC and SOPC when mixed with cholesterol. It is significant that the addition of cholesterol reduces the available free area in lipid membranes.70 Because SOPC and OSPC are isomers, and thus very similar, the reductions in free volume are likely also similar and could explain why the diffusion behaviors in

SOPC and OSPC Membranes with and without Cholesterol SOPC and OSPC membranes with added cholesterol are almost identical. The differences might arise from the small differences in packing of cholesterol with the saturated chains. 4. Concluding Remarks and Discussion We have described and discussed the results of atomistic simulations of two glycerol-based phospholipids, SOPC and OSPC, that differ in a seemingly minor manner: the only difference is the position of an individual double bond. In SOPC, the double bond is located in the sn-2 chain, as in many abundant lipid types,6-10 whereas in OSPC, it is instead in the sn-1 chain. Despite such a minor difference that one could consider marginal, nature prefers double bond(s) to be placed in the sn-2 chain for reasons that have remained largely unknown. Our simulations showed small but consistent differences between the properties of the membranes characterized by the two isomers, in agreement with the available experimental data. SOPC, which has the double bond in the sn-2 chain, is more disordered than OSPC, and the results for all of the physical quantities that we exploredsboth structural and dynamicalsare consistent with this picture. Further, in mixed systems with cholesterol, the differences between the SOPC and OSPC systems become even larger, suggesting that the location of the double bond in monounsaturated glycerol-based phospholipids does indeed make a difference. Although the differences between SOPC- and OSPC-based systems are small, differences of similar order of magnitude have been discussed and successfully interpreted in the literature. For example, the results for SCD profiles show that the differences between the SOPC-Chol and OSPC-Chol systems can be as large as 10% or even more. Differences of this size can readily be detected by NMR spectroscopy, which is a particularly sensitive technique. It has been successfully used in similar systems where the differences have been even smaller than those proposed here.71,72 As our simulation data show relatively small but consistent differences between SOPC- and OSPC-based membranes, there is reason to mention that these predictions can be tested by experiments, given that SOPC and especially also OSPC are available for experiments; they can be ordered, for instance, from Avanti Lipids. The origin of the differences in membrane properties between the two positional isomers is obviously of particular interest. Results of our simulations suggest that the acyl-chain-length mismatch is, in particular, the factor to take into account. We showed that the average positions along the z axis of the terminal sn-1 and sn-2 carbon atoms differ even in lipids with symmetric chains, but to a small extent. In DSPC and DOPC bilayers, we found chain mismatches of 0.40 and 0.28 Å, respectively. The chain mismatch changed substantially in lipids with different acyl chains: OSPC showed a chain mismatch of -0.56 Å, whereas for SOPC, this value was 1.32 Å. That is, we found a difference of almost 2 Å between two monounsaturated species that are identical except for the position of the double bond. For comparison, the carbon-carbon distance in hydrocarbon chains is about 1.5 Å. Experimental studies on monolayers built of highly asymmetric lipids such as 18:0-8:0 PC, and their comparison to symmetric ones such as 18:0-18:0 PC, have also shown that chain asymmetry is a strong disordering factor.53 One of the most interesting questions arising from this work is why the presence of cholesterol increases the observed differences between SOPC and OSPC bilayers. Our previous studies4 demonstrated that the effects of a double bond depend on its position in the acyl chain, particularly in cases where cholesterol is present. We showed4 that the ordering and

J. Phys. Chem. B, Vol. 113, No. 24, 2009 8355 condensing effects of cholesterol were the lowest when the double bond was located in the middle of a chain, close to the cholesterol off-plane methyl group, C18. Thus, interference of the double bond with methyl group C18 seems to be responsible for the decrease of cholesterol condensation and the ordering effect in the bilayer. Because, on average, the double bond in SOPC is placed closer to the cholesterol methyl group than that in OSPC, the more disordered nature of the SOPC bilayer compared to the OSPC bilayer is evident when cholesterol is present. The data suggest that lipid selectivity in nature is determined not only by the properties of the lipid itself, but also by its differential interaction with other membrane components, particularly cholesterol.4 Acknowledgment. This work was carried out under the HPCEUROPA Project (RII3-CT-2003-506079), with the support of the European CommunitysResearch Infrastructure Action under the FP6 “Structuring the European Research Area” Programme. Computational resources were provided by the Barcelona Supercomputing Center, The Finnish IT Centre for Science (CSC), and the SharcNet grid computing facility (www. sharcnet.ca). We thank the SIMBIOMA (ESF) network (H.M.S.), the Academy of Finland (T.R., I.V.), and the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. Partial financial support was provided by SEID through Project FIS200603525 and by DURSI through Project 2005-SGR000653. Note Added after ASAP Publication. This paper was published on the Web on May 26, 2009, with errors to Section Chain Dynamics. The corrected version was reposted on May 28, 2009. References and Notes (1) Uran, S.; Larsen, Å.; Jacobsen, P. B.; Skotland, T. J. Chromatogr. B: Biomed. Sci. Appl. 2001, 758, 265–275. (2) Sackmann, E. Biological membranes architecture and function. In Structure and Dynamics of Membranes; Lipowsky, R., Sackmann, E., Eds.; Elsevier: Amsterdam, 1995; pp 1-64. (3) Li, L. K.; So, L. A. J. Lipid Res. 1985, 26, 600–609. (4) Martinez-Seara, H.; Ro´g, T.; Pasenkiewicz-Gierula, M.; Vattulainen, I.; Karttunen, M.; Reigada, R. Biophys. J. 2008, 95, 3295–3305. (5) Ro´g, T.; Pasenkiewicz-Gierula, M.; Vattulainen, I.; Karttunen, M. Biochim. Biophys. Acta 2009, 1788, 97–121. (6) Ramstedt, B.; Slotte, J. P. FEBS Lett. 2002, 531, 33–37. (7) Berenholz, Y.; Thompson, T. E. Chem. Phys. Lipids 1999, 102, 29–34. (8) van Meer, G. EMBO J. 2005, 24, 3159–3165. (9) Isken, S.; de Bont, J. A. M. Extremophiles 1998, 2, 229–238. (10) Rottem, S.; Markowitz, O. FEBS Lett. 1979, 107, 379–382. (11) Davis, P. J.; Fleming, B. D.; Coolbear, K. P.; Keough, K. M. W. Biochemistry 1981, 20, 3633–3636. (12) Davis, P. J.; Keough, K. M. W. Biochemistry 1983, 22, 6334–6340. (13) Davis, P. J.; Keough, K. M. W. Biochim. Biophys. Acta, Biomembr. 1984, 778, 305–310. (14) Inoue, T.; Kitahashi, T.; Nibu, Y. Chem. Phys. Lipids 1999, 99, 103–109. (15) Ichimori, H.; Hata, T.; Matsuki, H.; Kaneshina, S. Chem. Phys. Lipids 1999, 100, 151–164. (16) Siminovitch, D. J.; Wong, P. T. T.; Berchtold, R.; Mantsch, H. H. Chem. Phys. Lipids 1988, 46, 79–87. (17) Huang, C.-H. Lipids 1977, 12, 348–356. (18) Dyatlovitskaya, E. V.; Yanchevskaya, G. V.; Bergelson, L. D. Chem. Phys. Lipids 1974, 12, 132–149. (19) Rottem, S.; Markowitz, O. Biochemistry 1979, 18, 2930–2935. (20) Zhang, Y.-M.; Rock, C. O. Nat. ReV. Microbiol. 2008, 6, 222– 233. (21) Martinez-Seara, H.; Ro´g, T.; Pasenkiewicz-Gierula, M.; Vattulainen, I.; Karttunen, M.; Reigada, R. J. Phys. Chem. B 2007, 111, 11162–11168. (22) Ro´g, T.; Murzyn, K.; Gurbiel, R.; Kitamura, K.; Kusumi, A.; Pasenkiewicz-Gierula, M. J. Lipid Res. 2004, 45, 326–336. (23) Niemela¨, P. S.; Hyvo¨nen, M. T.; Vattulainen, I. Biophys. J. 2006, 90, 851–863.

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